%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SCT061-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:38:10 AM UTC 2026
% Result : Unsatisfiable 177.64s 29.93s
% Output : CNFRefutation 177.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 614
% Syntax : Number of formulae : 5794 (3468 unt; 0 typ; 0 def)
% Number of atoms : 33027 (11578 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 133660 (7082 ~;10269 |; 0 &;116309 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 127 ( 124 usr; 15 con; 0-7 aty)
% Number of variables : 22907 ( 0 ^;22907 !; 0 ?;22907 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1,type,
c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XDomainE__1__1,type,
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thf(tp_c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XIdE__1__1,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XId__onE__1__1,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XImageE__1__1,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XImage__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XRangeE__1__1,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XRange__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1,type,
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thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_OIIA,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(tp_c_Arrow__Order__Mirabelle_OProf,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(tp_c_Arrow__Order__Mirabelle_Odictator,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(tp_c_Arrow__Order__Mirabelle_Omkbot,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_Omktop,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_Ounanimity,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_FuncSet_OPi,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(tp_c_FuncSet_Osko__FuncSet__XPi__I_H__1__1,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_FuncSet_Osko__FuncSet__XPi__I__1__1,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tp_c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(tp_c_List_Osko__Recdef__Xcuts__eq__1__1,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__Recdef__Xtfl__wf__induct__1__1,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_OSigma,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Ocut,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(tp_c_Relation_OField,type,
c_Relation_OField: $i > $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Relation_Oconverse,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_Osym,type,
c_Relation_Osym: $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tp_class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_t_b,type,
t_b: $i ).
thf(tp_tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tp_tc_Arrow__Order__Mirabelle_Oindi,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_F,type,
v_F: $i ).
thf(tp_v_P_H____,type,
v_P_H____: $i ).
thf(tp_v_P____,type,
v_P____: $i ).
thf(tp_v_a____,type,
v_a____: $i ).
thf(tp_v_b____,type,
v_b____: $i ).
thf(tp_v_c____,type,
v_c____: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__XIIA__def__1,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__XIIA__def__2,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__2: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__XIIA__def__3,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__3: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__XIIA__def__4,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__4: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__XIIA__def__5,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__5: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xdictator__def__1,type,
v_sko__Arrow__Order__Mirabelle__Xdictator__def__1: $i > $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1: $i > $i > $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3: $i > $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4: $i > $i ).
thf(tp_v_sko__Transitive__Closure__Xrtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xrtrancl__Xcases__1: $i > $i > $i > $i ).
thf(tp_v_sko__Transitive__Closure__Xtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).
thf(tp_v_sko__Wellfounded__Xacc__Xinduct__1,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(tp_v_sko__Wellfounded__Xacc__Xinducts__1,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(tp_v_sko__local__X1__1,type,
v_sko__local__X1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_v_sko__local__X2__1,type,
v_sko__local__X2__1: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_v_sko__local__X3__1,type,
v_sko__local__X3__1: $i > $i > $i > $i > $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(4,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(6,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(8,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(9,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(10,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(11,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(12,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(13,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(14,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(15,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(16,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(17,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(18,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(19,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(20,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(21,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cP_0) ).
thf(22,axiom,
v_a____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I3_J_0) ).
thf(23,axiom,
! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(24,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(25,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I5_J_0) ).
thf(26,axiom,
! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(27,axiom,
! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(28,axiom,
! [T_b: $i,T_a: $i,V_r: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(29,axiom,
v_b____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I2_J_0) ).
thf(30,axiom,
! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_0) ).
thf(31,axiom,
! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_1) ).
thf(32,axiom,
! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(33,axiom,
! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(34,axiom,
! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(35,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(36,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(37,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(38,axiom,
! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(39,axiom,
! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(40,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I4_J_0) ).
thf(41,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I1_J_0) ).
thf(42,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(43,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(44,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(45,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(46,axiom,
! [V_a: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(47,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(48,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(49,axiom,
! [V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(50,axiom,
! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(51,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_B: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(52,axiom,
! [V_b: $i,V_B: $i,V_a: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(53,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(54,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(55,axiom,
! [V_b: $i,V_r: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(56,axiom,
! [V_a: $i,V_r: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(57,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(58,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(59,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(60,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(61,axiom,
! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(62,axiom,
! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(63,axiom,
! [V_y: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(64,axiom,
! [V_a: $i,V_r: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(65,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(66,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(67,axiom,
! [V_F: $i,V_x: $i,V_i: $i] :
( ( ( hAPP @ V_F @ V_x )
= ( hAPP @ V_x @ V_i ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F @ V_i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_0) ).
thf(68,axiom,
! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_0) ).
thf(69,axiom,
! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_1) ).
thf(70,axiom,
! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_0) ).
thf(71,axiom,
! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i,V_b_H: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_1) ).
thf(72,axiom,
! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_2) ).
thf(73,axiom,
! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i,V_b_H: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_3) ).
thf(74,axiom,
! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ V_a @ V_b @ V_x ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_0) ).
thf(75,axiom,
! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_0) ).
thf(76,axiom,
! [V_a: $i,V_b: $i,V_F: $i,V_x: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_1) ).
thf(77,axiom,
! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_2) ).
thf(78,axiom,
! [V_a: $i,V_b: $i,V_F: $i,V_x: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_3) ).
thf(79,axiom,
! [V_b: $i,V_a: $i,V_P_H: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_0) ).
thf(80,axiom,
! [V_a: $i,V_b: $i,V_P: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_1) ).
thf(81,axiom,
! [V_b: $i,V_a: $i,V_P_H: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_2) ).
thf(82,axiom,
! [V_a: $i,V_b: $i,V_P: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_3) ).
thf(83,axiom,
! [V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(84,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(85,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(86,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(87,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(88,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(89,axiom,
! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(90,axiom,
! [V_x: $i,V_y: $i,V_L: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(91,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(92,axiom,
! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(93,axiom,
! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(94,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(95,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(96,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_f: $i,V_B: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(97,axiom,
! [V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(98,axiom,
! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(99,axiom,
! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(100,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(101,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_R: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(102,axiom,
! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(103,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
thf(104,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(105,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(106,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(107,axiom,
! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(108,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(109,axiom,
! [V_a: $i,V_b: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(110,axiom,
! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i,V_y: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(111,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_A: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(112,axiom,
! [V_f: $i,V_y: $i,V_z: $i,T_a: $i,V_r: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(113,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(114,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(115,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(116,axiom,
! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(117,axiom,
! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(118,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(119,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(120,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(121,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(122,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(123,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(124,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(125,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(126,axiom,
! [T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(127,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(128,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(129,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(130,axiom,
! [T_a: $i,V_r: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(131,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(132,axiom,
! [T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(133,axiom,
! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(134,axiom,
! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(135,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
thf(136,axiom,
! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(137,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(138,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(139,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(140,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(141,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(142,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(143,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(144,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(145,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(146,axiom,
! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(147,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(148,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(149,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(150,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(151,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(152,axiom,
! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(153,axiom,
! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(154,axiom,
! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(155,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_u_0) ).
thf(156,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(157,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(158,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(159,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(160,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(161,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(162,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(163,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(164,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(165,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(166,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(167,axiom,
! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(168,axiom,
! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(169,axiom,
! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(170,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(171,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(172,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(173,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(174,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) )
= ( c_Relation_OId__on @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(175,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(176,axiom,
! [T_a: $i,V_R: $i,V_f: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_b ) @ V_R ) @ V_f @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(177,axiom,
! [T_a: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) )
= ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(178,axiom,
! [T_b: $i,T_a: $i,V_r: $i,V_s: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_a ) @ V_s ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r ) @ T_a @ T_c @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(179,axiom,
! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(180,axiom,
! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(181,axiom,
! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(182,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(183,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(184,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(185,axiom,
! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(186,axiom,
! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(187,axiom,
! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(188,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(189,axiom,
! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(190,axiom,
! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(191,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(192,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(193,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(194,axiom,
! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(195,axiom,
! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(196,axiom,
! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(197,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(198,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(199,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(200,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(201,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(202,axiom,
! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(203,axiom,
! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(204,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(205,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(206,axiom,
! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(207,axiom,
! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(208,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(209,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(210,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(211,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(212,axiom,
! [V_y: $i,V_Q: $i,T_a: $i,V_R: $i,V_x: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(213,axiom,
! [V_y: $i,V_Q: $i,T_a: $i,V_r: $i,V_xa: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(214,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_1) ).
thf(215,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(216,axiom,
! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ c_Arrow__Order__Mirabelle_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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_1) ).
thf(217,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_4) ).
thf(218,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ c_Arrow__Order__Mirabelle_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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_5) ).
thf(219,axiom,
! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i,T_a: $i,V_r1: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(220,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(221,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(222,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( c_in @ V_x @ V_A @ T_a )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(223,axiom,
! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(224,axiom,
! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(225,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(226,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(227,axiom,
! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(228,axiom,
! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(229,axiom,
! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(230,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(231,axiom,
! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(232,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(233,axiom,
! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(234,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(235,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(236,axiom,
! [V_F: $i,V_i: $i] :
( ( ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ V_i ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_2) ).
thf(237,axiom,
! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i,V_r1: $i,T_c: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(238,axiom,
! [V_Q: $i,V_r: $i,T_a: $i,V_xa: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(239,axiom,
! [V_Q: $i,V_R: $i,T_a: $i,V_x: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(240,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(241,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(242,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(243,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(244,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(245,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(246,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(247,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(248,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(249,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(250,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(251,axiom,
! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(252,axiom,
! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(253,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(254,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(255,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(256,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(257,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(258,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(259,axiom,
! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(260,axiom,
! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(261,axiom,
! [V_a: $i,V_r: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(262,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(263,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(264,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(265,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(266,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_8) ).
thf(267,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_9) ).
thf(268,axiom,
! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_6) ).
thf(269,axiom,
! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_7) ).
thf(270,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(271,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(272,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(273,axiom,
! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(274,axiom,
! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(275,axiom,
! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(276,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(277,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(278,axiom,
! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(279,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
thf(280,axiom,
! [V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
thf(281,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_1) ).
thf(282,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
thf(283,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
thf(284,axiom,
! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(285,axiom,
! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(286,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_x: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(287,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(288,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
thf(289,axiom,
! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(290,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
thf(291,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
thf(292,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(293,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
thf(294,axiom,
! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(295,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(296,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
thf(297,axiom,
! [V_P: $i,V_Ra: $i,V_y: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
thf(298,axiom,
! [V_P: $i,V_xa: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
thf(299,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
thf(300,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
thf(301,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
thf(302,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
thf(303,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
thf(304,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
thf(305,axiom,
! [V_z: $i,V_y: $i,T_a: $i,V_r: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(306,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
thf(307,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
thf(308,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
thf(309,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
thf(310,axiom,
! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
thf(311,axiom,
! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
thf(312,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
thf(313,axiom,
! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
thf(314,axiom,
! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_2) ).
thf(315,axiom,
! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_3) ).
thf(316,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ V_r @ T_a ) @ V_r @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).
thf(317,axiom,
! [T_a: $i,V_r: $i,V_x: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
thf(318,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(319,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_r: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(320,axiom,
! [V_x: $i,T_a: $i,V_r: $i,V_y: $i,V_A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
thf(321,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(322,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(323,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(324,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(325,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(326,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(327,axiom,
! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
thf(328,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(329,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(330,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(331,axiom,
! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
thf(332,axiom,
! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(333,axiom,
! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(334,axiom,
! [V_p: $i,V_s: $i,T_a: $i,V_r: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(335,axiom,
! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(336,axiom,
! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(337,axiom,
! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(338,axiom,
! [V_y: $i,V_z: $i,V_x: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(339,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(340,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
thf(341,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
thf(342,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(343,axiom,
! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(344,axiom,
! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(345,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
thf(346,axiom,
! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
thf(347,axiom,
! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(348,axiom,
! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(349,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(350,axiom,
! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
thf(351,axiom,
! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(352,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(353,axiom,
! [V_r: $i,T_a: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_COMBK @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).
thf(354,axiom,
! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(355,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(356,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(357,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(358,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(359,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(361,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(362,axiom,
! [V_p: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(363,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(364,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(365,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(366,axiom,
! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(367,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(368,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(369,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(370,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(371,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(372,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(373,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(374,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(375,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(376,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(377,axiom,
! [V_r: $i,T_a: $i] :
( ( 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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def_0) ).
thf(378,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(379,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(380,axiom,
! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(381,axiom,
! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(382,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(383,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_R ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(384,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).
thf(385,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(386,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(387,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(388,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(389,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(390,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(391,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(392,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(393,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(394,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(395,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(396,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(397,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(398,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(399,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(400,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(401,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(402,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(403,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(404,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(405,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(406,axiom,
! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(407,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(408,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(409,axiom,
! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
thf(410,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(411,axiom,
! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(412,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(413,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(414,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(415,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(416,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(417,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(418,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(419,axiom,
! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
thf(420,axiom,
! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
thf(421,axiom,
! [V_x: $i,T_a: $i,V_r: $i,V_y: $i,V_A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
thf(422,axiom,
! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(423,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).
thf(424,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(425,axiom,
! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(426,axiom,
! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(427,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(428,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(429,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(430,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(431,axiom,
! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(432,axiom,
! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(433,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(434,axiom,
! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(435,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(436,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(437,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(438,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(439,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(440,axiom,
! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(441,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(442,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(443,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(444,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(445,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(446,axiom,
! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(447,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(448,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(449,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(450,axiom,
! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(451,axiom,
! [T_a: $i] :
( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__empty_0) ).
thf(452,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
thf(453,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(454,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
thf(455,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(456,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(457,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(458,axiom,
! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(459,axiom,
! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
thf(460,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(461,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(462,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(463,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(464,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(465,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def__raw_0) ).
thf(466,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(467,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(468,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(469,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(470,axiom,
! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(471,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(472,axiom,
! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(473,axiom,
! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(474,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__Un_0) ).
thf(475,axiom,
! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(476,axiom,
! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(477,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(478,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(479,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(480,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(481,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(482,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(483,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(484,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(485,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(486,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(487,axiom,
! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(488,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(489,axiom,
! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
thf(490,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(491,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__insert_0) ).
thf(492,axiom,
! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
thf(493,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(494,axiom,
! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(495,axiom,
! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(496,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(497,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(498,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(499,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(500,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(501,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(502,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(503,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(504,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(505,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(506,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(507,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(508,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(509,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(510,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(511,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(512,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(513,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(514,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(515,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(516,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(517,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(518,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(519,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(520,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(521,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(522,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(523,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(524,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(525,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(526,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(527,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(528,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(529,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(530,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(531,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(532,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(533,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(534,axiom,
! [V_P: $i,V_xb: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
thf(535,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).
thf(536,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).
thf(537,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(538,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(539,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(540,axiom,
! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(541,axiom,
! [V_A: $i,T_a: $i,V_R: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(542,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(543,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(544,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(545,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(546,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(547,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(548,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(549,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(550,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(551,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(552,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(553,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(554,axiom,
! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(555,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(556,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(557,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(558,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(559,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(560,axiom,
! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(561,axiom,
! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(562,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(563,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(564,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(565,axiom,
! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(566,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(567,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(568,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(569,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(570,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(571,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(572,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(573,axiom,
! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(574,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(575,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(576,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(577,axiom,
! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).
thf(578,axiom,
! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(579,axiom,
! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
thf(580,axiom,
! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
thf(581,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(582,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(583,axiom,
! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(584,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
thf(585,axiom,
! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(586,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(587,axiom,
! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(588,axiom,
! [V_A: $i,V_B: $i,T_b: $i,V_C: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(589,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(590,axiom,
! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(591,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(592,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(593,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(594,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(595,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(596,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(597,axiom,
! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(598,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(599,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(600,axiom,
! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(601,axiom,
! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(602,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(603,axiom,
! [V_P: $i,V_Rb: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
thf(604,axiom,
! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
thf(605,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(606,axiom,
! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(607,axiom,
! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(608,axiom,
! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(609,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(610,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(611,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(612,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[611]) ).
thf(613,negated_conjecture,
! [V_i: $i] :
( ( 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 ) @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(614,negated_conjecture,
! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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 ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(615,negated_conjecture,
v_b____ = v_a____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(616,plain,
$false = $false,
inference(unfold_def,[status(thm)],[612]) ).
thf(617,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(618,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(619,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(620,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(621,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(622,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(623,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(624,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(625,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(626,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(627,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(628,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(629,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(630,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(631,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(632,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(633,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(634,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(635,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(636,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(637,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(638,plain,
( ( v_a____ != v_c____ )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(639,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(640,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(641,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(642,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(643,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(644,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(645,plain,
( ( v_b____ != v_c____ )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(646,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(647,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(648,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(649,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(650,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(651,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(652,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(653,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(654,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(655,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(656,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(657,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(658,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(659,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(660,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(661,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(662,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(663,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(664,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(665,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(666,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(667,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_B: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(668,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(669,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(670,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(671,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(672,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(673,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(674,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(675,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(676,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(677,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(678,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(679,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(680,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(681,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(682,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(683,plain,
( ( ! [V_F: $i,V_x: $i,V_i: $i] :
( ( ( hAPP @ V_F @ V_x )
= ( hAPP @ V_x @ V_i ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F @ V_i ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(684,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(685,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(686,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(687,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i,V_b_H: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(688,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(689,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i,V_b_H: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(690,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ V_a @ V_b @ V_x ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(691,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(692,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(693,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(694,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(695,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(696,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(697,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(698,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(699,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(700,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(701,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(702,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(703,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(704,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(705,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(706,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(707,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(708,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(709,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(710,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(711,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(712,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_f: $i,V_B: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(713,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(714,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(715,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(716,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(717,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(718,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(719,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(720,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(721,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(722,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(723,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(724,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(725,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(726,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i,V_y: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(727,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_A: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(728,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i,V_r: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(729,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(730,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(731,plain,
( ( ! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(732,plain,
( ( ! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(733,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(734,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(735,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(736,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(737,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(738,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(739,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(740,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(741,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(742,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(743,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(744,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(745,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(746,plain,
( ( ! [T_a: $i,V_r: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(747,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(748,plain,
( ( ! [T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(749,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(750,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(751,plain,
( ( c_Arrow__Order__Mirabelle_OIIA @ v_F )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(752,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(753,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(754,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(755,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(756,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(757,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(758,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(759,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(760,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(761,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(762,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(763,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(764,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(765,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(766,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(767,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(768,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(769,plain,
( ( ! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(770,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(771,plain,
( ( c_Arrow__Order__Mirabelle_Ounanimity @ v_F )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(772,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(773,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(774,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(775,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(776,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(777,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(778,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(779,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(780,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(781,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(782,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(783,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(784,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(785,plain,
( ( ! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(786,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(787,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(788,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(789,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(790,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(791,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(792,plain,
( ( ! [T_a: $i,V_R: $i,V_f: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_b ) @ V_R ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(793,plain,
( ( ! [T_a: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(794,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_a ) @ V_s ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(795,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(796,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(797,plain,
( ( ! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(798,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(799,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(800,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(801,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(802,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(803,plain,
( ( ! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(804,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(805,plain,
( ( ! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(806,plain,
( ( ! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(807,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(808,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(809,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(810,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(811,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(812,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(813,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(814,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(815,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(816,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(817,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(818,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(819,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(820,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(821,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(822,plain,
( ( ! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(823,plain,
( ( ! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(824,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(825,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(826,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(827,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(828,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i,V_R: $i,V_x: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(829,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i,V_r: $i,V_xa: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(830,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(831,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(832,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(833,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(834,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(835,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i,T_a: $i,V_r1: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(836,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 ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(837,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(838,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( c_in @ V_x @ V_A @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(839,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(840,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(841,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(842,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(843,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(844,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(845,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(846,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(847,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(848,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(849,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(850,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(851,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(852,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ V_i ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(853,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i,V_r1: $i,T_c: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(854,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i,V_xa: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(855,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i,V_x: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(856,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(857,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(858,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(859,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(860,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(861,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(862,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(863,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(864,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(865,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(866,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(867,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(868,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(869,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(870,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(871,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(872,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(873,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(874,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(875,plain,
( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(876,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(877,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(878,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(879,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(880,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(881,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(882,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(883,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(884,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(885,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(886,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(887,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(888,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(889,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(890,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(891,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(892,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(893,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(894,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(895,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(896,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(897,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(898,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(899,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(900,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(901,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(902,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_x: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(903,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(904,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(905,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(906,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(907,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(908,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(909,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(910,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(911,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(912,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(913,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(914,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(915,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(916,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(917,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(918,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(919,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(920,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(921,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(922,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(923,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(924,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(925,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(926,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(927,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(928,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(929,plain,
( ( ! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(930,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(931,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(932,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ V_r @ T_a ) @ V_r @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(933,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(934,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(935,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_r: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(936,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i,V_A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(937,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(938,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(939,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(940,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(941,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(942,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(943,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(944,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(945,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(946,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(947,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(948,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(949,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(950,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i,V_r: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(951,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(952,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(953,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(954,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(955,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(956,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(957,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(958,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(959,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(960,plain,
( ( ! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(961,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(962,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(963,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(964,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(965,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(966,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(967,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(968,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(969,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_COMBK @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(970,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(971,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(972,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(973,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(974,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(975,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(976,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(977,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(978,plain,
( ( ! [V_p: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(979,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(980,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(981,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(982,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(983,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(984,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(985,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(986,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(987,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(988,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(989,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(990,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(991,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(992,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(993,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(994,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(995,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(996,plain,
( ( ! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(997,plain,
( ( ! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(998,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(999,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_R ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1000,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1001,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1004,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1005,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1006,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1008,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1009,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1010,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1011,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1012,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1013,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1021,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1023,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(1024,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1025,plain,
( ( ! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1026,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1027,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1028,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1029,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1030,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1031,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1032,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1033,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1034,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1035,plain,
( ( ! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1036,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1037,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i,V_A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1038,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1039,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1040,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1042,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1043,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1044,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1045,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1046,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1047,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1048,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(1049,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1050,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1051,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1052,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1053,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1054,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1055,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1056,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1057,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1058,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1059,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1060,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1061,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1062,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1063,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1064,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1065,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1066,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1067,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1068,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1069,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1070,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1072,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1073,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1074,plain,
( ( ! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1076,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1077,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1080,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1081,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1087,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1088,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1089,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1090,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1091,plain,
( ( ! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1092,plain,
( ( ! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1093,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1095,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1096,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1097,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1098,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1099,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1100,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1101,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1102,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1103,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1104,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1105,plain,
( ( ! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1106,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1107,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1108,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1109,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1110,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1111,plain,
( ( ! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1113,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1116,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1117,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1119,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1124,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1125,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1126,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1127,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1131,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1132,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1137,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1138,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1139,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1140,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1145,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1148,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1149,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1150,plain,
( ( ! [V_P: $i,V_xb: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1151,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1152,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1155,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1157,plain,
( ( ! [V_A: $i,T_a: $i,V_R: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1158,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1159,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1163,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1164,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1165,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1166,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1167,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1168,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1169,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1170,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1171,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1172,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1173,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1174,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1175,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1176,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1177,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1178,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1179,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(1180,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1181,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1182,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1183,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1184,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1185,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1186,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1187,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1188,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1189,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1190,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1191,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1192,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1195,plain,
( ( ! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1196,plain,
( ( ! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1197,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1198,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1199,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1200,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1201,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1202,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1203,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1204,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1205,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1206,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1207,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1208,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1209,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1210,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1212,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1213,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1214,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1215,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1216,plain,
( ( ! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1217,plain,
( ( ! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1218,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1219,plain,
( ( ! [V_P: $i,V_Rb: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1220,plain,
( ( ! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1221,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(1222,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1223,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1224,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1225,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1226,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1227,plain,
( ( ! [V_i: $i] :
( ( 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 ) @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1228,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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 ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1229,plain,
( ( v_b____ = v_a____ )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1230,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[616]) ).
thf(1231,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[617]) ).
thf(1232,plain,
( ( v_a____ != v_c____ )
= $true ),
inference(extcnf_combined,[status(esa)],[638]) ).
thf(1233,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[639]) ).
thf(1234,plain,
( ( ! [V_x: $i,V_S: $i] :
( ! [T_a: $i] : ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[640]) ).
thf(1235,plain,
( ( v_b____ != v_c____ )
= $true ),
inference(extcnf_combined,[status(esa)],[645]) ).
thf(1236,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
( ! [V_b_H: $i] :
( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[652]) ).
thf(1237,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[653]) ).
thf(1238,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ! [T_d: $i] :
( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ! [V_v: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[654]) ).
thf(1239,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ! [T_d: $i,T_e: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[655]) ).
thf(1240,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(extcnf_combined,[status(esa)],[657]) ).
thf(1241,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[662]) ).
thf(1242,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[663]) ).
thf(1243,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[664]) ).
thf(1244,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[665]) ).
thf(1245,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ! [V_A: $i] :
( ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[666]) ).
thf(1246,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [T_b: $i,V_B: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[667]) ).
thf(1247,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[668]) ).
thf(1248,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_b: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[669]) ).
thf(1249,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[670]) ).
thf(1250,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[671]) ).
thf(1251,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[672]) ).
thf(1252,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[673]) ).
thf(1253,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[674]) ).
thf(1254,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(1255,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[677]) ).
thf(1256,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[678]) ).
thf(1257,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[679]) ).
thf(1258,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[680]) ).
thf(1259,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[684]) ).
thf(1260,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[685]) ).
thf(1261,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[686]) ).
thf(1262,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b_H: $i,V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[687]) ).
thf(1263,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[688]) ).
thf(1264,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b_H: $i,V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[689]) ).
thf(1265,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[691]) ).
thf(1266,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_xa: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[692]) ).
thf(1267,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[693]) ).
thf(1268,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_xa: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[694]) ).
thf(1269,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[695]) ).
thf(1270,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[696]) ).
thf(1271,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[697]) ).
thf(1272,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[698]) ).
thf(1273,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[699]) ).
thf(1274,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[700]) ).
thf(1275,plain,
( ( ! [V_xa: $i,V_x: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[701]) ).
thf(1276,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(1277,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[707]) ).
thf(1278,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ! [V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[712]) ).
thf(1279,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(1280,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(1281,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(1282,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[718]) ).
thf(1283,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[721]) ).
thf(1284,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(1285,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ! [V_y: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(1286,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[727]) ).
thf(1287,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [T_b: $i] :
~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(1288,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(1289,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[730]) ).
thf(1290,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(1291,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[736]) ).
thf(1292,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[743]) ).
thf(1293,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[746]) ).
thf(1294,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[750]) ).
thf(1295,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(1296,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[757]) ).
thf(1297,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[775]) ).
thf(1298,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[776]) ).
thf(1299,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[781]) ).
thf(1300,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[782]) ).
thf(1301,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[795]) ).
thf(1302,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(1303,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[802]) ).
thf(1304,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[804]) ).
thf(1305,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[807]) ).
thf(1306,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[808]) ).
thf(1307,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[809]) ).
thf(1308,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[817]) ).
thf(1309,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[818]) ).
thf(1310,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[819]) ).
thf(1311,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[820]) ).
thf(1312,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[822]) ).
thf(1313,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[823]) ).
thf(1314,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[828]) ).
thf(1315,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[829]) ).
thf(1316,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ! [T_a: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ! [V_r1: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[835]) ).
thf(1317,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( V_A = V_B )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[838]) ).
thf(1318,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[842]) ).
thf(1319,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[849]) ).
thf(1320,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ V_i ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[852]) ).
thf(1321,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ! [V_r1: $i] :
( ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ! [T_c: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[853]) ).
thf(1322,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[854]) ).
thf(1323,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(1324,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[856]) ).
thf(1325,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[859]) ).
thf(1326,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[860]) ).
thf(1327,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[861]) ).
thf(1328,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[863]) ).
thf(1329,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[864]) ).
thf(1330,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[866]) ).
thf(1331,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[869]) ).
thf(1332,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[870]) ).
thf(1333,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[871]) ).
thf(1334,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[872]) ).
thf(1335,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[873]) ).
thf(1336,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[874]) ).
thf(1337,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[877]) ).
thf(1338,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[880]) ).
thf(1339,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ! [V_i: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[884]) ).
thf(1340,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ! [V_i: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[885]) ).
thf(1341,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[896]) ).
thf(1342,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[902]) ).
thf(1343,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[903]) ).
thf(1344,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[912]) ).
thf(1345,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[913]) ).
thf(1346,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[914]) ).
thf(1347,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[915]) ).
thf(1348,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[917]) ).
thf(1349,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[919]) ).
thf(1350,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[921]) ).
thf(1351,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[922]) ).
thf(1352,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[923]) ).
thf(1353,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[924]) ).
thf(1354,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[925]) ).
thf(1355,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ! [V_i: $i] : ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[930]) ).
thf(1356,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ V_r @ T_a ) @ V_r @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[932]) ).
thf(1357,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[933]) ).
thf(1358,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[934]) ).
thf(1359,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[935]) ).
thf(1360,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[936]) ).
thf(1361,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[947]) ).
thf(1362,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[950]) ).
thf(1363,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[953]) ).
thf(1364,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i] :
( ( V_y = V_z )
| ! [T_b: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[954]) ).
thf(1365,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[956]) ).
thf(1366,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[957]) ).
thf(1367,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[958]) ).
thf(1368,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[961]) ).
thf(1369,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ! [V_s: $i] :
( ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[972]) ).
thf(1370,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[973]) ).
thf(1371,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[974]) ).
thf(1372,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[975]) ).
thf(1373,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[976]) ).
thf(1374,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[977]) ).
thf(1375,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[978]) ).
thf(1376,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[979]) ).
thf(1377,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[980]) ).
thf(1378,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[983]) ).
thf(1379,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[984]) ).
thf(1380,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[985]) ).
thf(1381,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[986]) ).
thf(1382,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[987]) ).
thf(1383,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[988]) ).
thf(1384,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[989]) ).
thf(1385,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[990]) ).
thf(1386,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[991]) ).
thf(1387,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[992]) ).
thf(1388,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[995]) ).
thf(1389,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1002]) ).
thf(1390,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1003]) ).
thf(1391,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1007]) ).
thf(1392,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1008]) ).
thf(1393,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1014]) ).
thf(1394,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1015]) ).
thf(1395,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1016]) ).
thf(1396,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1017]) ).
thf(1397,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1018]) ).
thf(1398,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1019]) ).
thf(1399,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1020]) ).
thf(1400,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1026]) ).
thf(1401,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1031]) ).
thf(1402,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1032]) ).
thf(1403,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1033]) ).
thf(1404,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1034]) ).
thf(1405,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1037]) ).
thf(1406,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1043]) ).
thf(1407,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1044]) ).
thf(1408,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1045]) ).
thf(1409,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1046]) ).
thf(1410,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1049]) ).
thf(1411,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1053]) ).
thf(1412,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1054]) ).
thf(1413,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1055]) ).
thf(1414,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1056]) ).
thf(1415,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1059]) ).
thf(1416,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1060]) ).
thf(1417,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1062]) ).
thf(1418,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1064]) ).
thf(1419,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1065]) ).
thf(1420,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1068]) ).
thf(1421,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1070]) ).
thf(1422,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1071]) ).
thf(1423,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1072]) ).
thf(1424,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1078]) ).
thf(1425,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1079]) ).
thf(1426,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1082]) ).
thf(1427,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1083]) ).
thf(1428,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1084]) ).
thf(1429,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1085]) ).
thf(1430,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1086]) ).
thf(1431,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1087]) ).
thf(1432,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1088]) ).
thf(1433,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1089]) ).
thf(1434,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1093]) ).
thf(1435,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1094]) ).
thf(1436,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1095]) ).
thf(1437,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1096]) ).
thf(1438,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1099]) ).
thf(1439,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1101]) ).
thf(1440,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1104]) ).
thf(1441,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1106]) ).
thf(1442,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1110]) ).
thf(1443,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1112]) ).
thf(1444,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1114]) ).
thf(1445,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1115]) ).
thf(1446,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1117]) ).
thf(1447,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1118]) ).
thf(1448,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1119]) ).
thf(1449,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1120]) ).
thf(1450,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1121]) ).
thf(1451,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1122]) ).
thf(1452,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1123]) ).
thf(1453,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1128]) ).
thf(1454,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1129]) ).
thf(1455,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1130]) ).
thf(1456,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1133]) ).
thf(1457,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1134]) ).
thf(1458,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1135]) ).
thf(1459,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1136]) ).
thf(1460,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1138]) ).
thf(1461,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1141]) ).
thf(1462,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1142]) ).
thf(1463,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1143]) ).
thf(1464,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1144]) ).
thf(1465,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1145]) ).
thf(1466,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1146]) ).
thf(1467,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1147]) ).
thf(1468,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1148]) ).
thf(1469,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1149]) ).
thf(1470,plain,
( ( ! [V_P: $i,V_xb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1150]) ).
thf(1471,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1151]) ).
thf(1472,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1152]) ).
thf(1473,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1153]) ).
thf(1474,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1154]) ).
thf(1475,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1155]) ).
thf(1476,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_R: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1157]) ).
thf(1477,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1161]) ).
thf(1478,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1162]) ).
thf(1479,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1165]) ).
thf(1480,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1166]) ).
thf(1481,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1167]) ).
thf(1482,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1168]) ).
thf(1483,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1172]) ).
thf(1484,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1175]) ).
thf(1485,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1177]) ).
thf(1486,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1179]) ).
thf(1487,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1184]) ).
thf(1488,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1185]) ).
thf(1489,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1191]) ).
thf(1490,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1192]) ).
thf(1491,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1200]) ).
thf(1492,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1202]) ).
thf(1493,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1203]) ).
thf(1494,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [T_a: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1204]) ).
thf(1495,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1207]) ).
thf(1496,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1210]) ).
thf(1497,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1211]) ).
thf(1498,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1215]) ).
thf(1499,plain,
( ( ! [V_P: $i,V_Rb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1219]) ).
thf(1500,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1224]) ).
thf(1501,plain,
( ( v_b____ = v_a____ )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1502,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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 ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(1503,plain,
( ( ! [V_i: $i] :
( ( 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 ) @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1504,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(1505,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1506,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(1507,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1508,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1509,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1510,plain,
( ( ! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1511,plain,
( ( ! [V_P: $i,V_Rb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(1512,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1513,plain,
( ( ! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(1514,plain,
( ( ! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1515,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1498]) ).
thf(1516,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1517,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1518,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1519,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(1520,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(1521,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1522,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1523,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(1524,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1525,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1526,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [T_a: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(1527,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(1528,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(1529,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1530,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1491]) ).
thf(1531,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1532,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1533,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1534,plain,
( ( ! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1535,plain,
( ( ! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1537,plain,
( ( ! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1538,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(1539,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1489]) ).
thf(1540,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1541,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1542,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1543,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1544,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1545,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1488]) ).
thf(1546,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(1547,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1548,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1549,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1550,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1551,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(1552,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1553,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(1554,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1555,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1484]) ).
thf(1556,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1557,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1558,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(1559,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1560,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1561,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1562,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(1563,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(1564,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(1565,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(1566,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1567,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1568,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(1569,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(1570,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1571,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1572,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1573,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_R: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(1574,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1575,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(1576,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(1577,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(1578,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(1579,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(1580,plain,
( ( ! [V_P: $i,V_xb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(1581,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(1582,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(1583,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(1584,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(1585,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(1586,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(1587,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(1588,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(1589,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(1590,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1591,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1592,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(1593,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1594,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(1595,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(1596,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(1598,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1599,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1600,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(1601,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(1602,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(1603,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(1604,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1605,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1606,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1607,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(1608,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(1609,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(1610,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(1611,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(1612,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(1613,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(1614,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1615,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(1616,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(1617,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1618,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(1619,plain,
( ( ! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1620,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(1621,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1622,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1623,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1624,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(1625,plain,
( ( ! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1626,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(1627,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1628,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1629,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(1630,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1631,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(1632,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1633,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1634,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(1635,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(1636,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(1637,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(1638,plain,
( ( ! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1639,plain,
( ( ! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1640,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(1641,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(1642,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(1643,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(1644,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(1645,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1429]) ).
thf(1646,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(1647,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(1648,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(1649,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 ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1650,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1651,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(1652,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(1653,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1654,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1655,plain,
( ( ! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(1656,plain,
( ( ! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(1657,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(1658,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(1659,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(1660,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(1661,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(1662,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(1663,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1664,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1665,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(1666,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(1667,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1668,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(1669,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1670,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(1671,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(1672,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1673,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1674,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(1675,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(1676,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(1677,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(1678,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(1679,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1680,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1681,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(1682,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1683,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1684,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(1685,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(1686,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(1687,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(1688,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1689,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1690,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1691,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1692,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_s ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1693,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(1694,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1695,plain,
( ( ! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1696,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(1697,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(1698,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(1699,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(1700,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1701,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1702,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1703,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1704,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(1705,plain,
( ( ! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1706,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1707,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1708,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1709,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1710,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(1711,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(1712,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(1713,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(1714,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(1715,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(1716,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(1717,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1718,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1719,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1720,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1721,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1722,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(1723,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(1724,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1725,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1726,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1727,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(1728,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1389]) ).
thf(1729,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1730,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_Relation_OField @ V_s @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1731,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_R ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1732,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1733,plain,
( ( ! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1734,plain,
( ( ! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1735,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1388]) ).
thf(1736,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(1737,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1738,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(1739,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1386]) ).
thf(1740,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1385]) ).
thf(1741,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1384]) ).
thf(1742,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(1743,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(1744,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1381]) ).
thf(1745,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1380]) ).
thf(1746,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1379]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(1748,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1749,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1750,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1751,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(1752,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(1753,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(1754,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(1755,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(1756,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(1757,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1370]) ).
thf(1758,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ! [V_s: $i] :
( ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(1759,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1760,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1761,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ V_r @ T_a ) @ ( c_COMBK @ ( c_Relation_OField @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1762,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1763,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1764,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(1765,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1766,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(1767,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1768,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1769,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1368]) ).
thf(1770,plain,
( ( ! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(1771,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(1772,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(1773,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1366]) ).
thf(1774,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1365]) ).
thf(1775,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1776,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i] :
( ( V_y = V_z )
| ! [T_b: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(1777,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(1778,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1779,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(1780,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(1781,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1782,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1783,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1361]) ).
thf(1784,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1785,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1786,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1787,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1788,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(1789,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1790,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1791,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1792,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1793,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1794,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_r @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(1795,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1359]) ).
thf(1796,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1358]) ).
thf(1797,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1357]) ).
thf(1798,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Relation_OField @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ V_r @ T_a ) @ V_r @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1799,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1800,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ! [V_i: $i] : ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1355]) ).
thf(1801,plain,
( ( ! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1802,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(1803,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1804,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1805,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(1806,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1807,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1808,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1809,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1810,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1811,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1812,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1813,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(1814,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1815,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(1816,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1346]) ).
thf(1817,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(1818,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1819,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1820,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1821,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1822,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1823,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1824,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1825,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1826,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1827,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1828,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1342]) ).
thf(1829,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1830,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1831,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1832,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1833,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1834,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1341]) ).
thf(1835,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ ( hAPP @ V_B @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1836,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1837,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1838,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1839,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(1840,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1841,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1842,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1843,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1844,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1845,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ! [V_i: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1846,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ! [V_i: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1847,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1848,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ V_F ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ V_F ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(1849,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1850,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1851,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1852,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1853,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1854,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1855,plain,
( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1856,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1857,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(1858,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1859,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1860,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1861,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1331]) ).
thf(1862,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1863,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1864,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1330]) ).
thf(1865,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1866,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1329]) ).
thf(1867,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(1868,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1869,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1870,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1871,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(1872,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1873,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1874,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(1875,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(1876,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1877,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ! [V_r1: $i] :
( ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ! [T_c: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1878,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( ( hAPP @ V_F @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ V_i ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1879,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1880,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1881,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(1882,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1883,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1884,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1885,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1886,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1887,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1888,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1318]) ).
thf(1889,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1890,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1891,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1892,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( V_A = V_B )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1317]) ).
thf(1893,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1894,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 ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1895,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ! [T_a: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ! [V_r1: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1316]) ).
thf(1896,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1897,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1898,plain,
( ( ! [V_F: $i,V_i: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ V_F @ V_i )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ V_F @ V_i ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1899,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1900,plain,
( ( ! [V_F: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ V_F )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ V_F ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1901,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(1902,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(1903,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1904,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1905,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1906,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1907,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1908,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1909,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1910,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(1911,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(1912,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1913,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(1914,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1915,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1916,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1917,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1918,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1919,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1920,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1921,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1922,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1306]) ).
thf(1923,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1305]) ).
thf(1924,plain,
( ( ! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1925,plain,
( ( ! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1926,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(1927,plain,
( ( ! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1928,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1929,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1930,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1931,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1932,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1933,plain,
( ( ! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1934,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1935,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(1936,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_s: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_a ) @ V_s ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1937,plain,
( ( ! [T_a: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1938,plain,
( ( ! [T_a: $i,V_R: $i,V_f: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_b ) @ V_R ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1939,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1940,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1941,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1942,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1943,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
= ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1944,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1945,plain,
( ( ! [V_A: $i,T_a: $i,V_r: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1946,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1947,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1948,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1949,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1299]) ).
thf(1950,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1951,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1952,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1953,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1954,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(1955,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1297]) ).
thf(1956,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1957,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1958,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1959,plain,
( ( c_Arrow__Order__Mirabelle_Ounanimity @ v_F )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1960,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1961,plain,
( ( ! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1962,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1963,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1964,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1965,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1966,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1967,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1968,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1969,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1970,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1971,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1972,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1973,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(1974,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1975,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1976,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1977,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1978,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1979,plain,
( ( c_Arrow__Order__Mirabelle_OIIA @ v_F )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1980,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1981,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1982,plain,
( ( ! [T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1983,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1984,plain,
( ( ! [T_a: $i,V_r: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1985,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1986,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1987,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(1988,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1989,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1990,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1991,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1992,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1993,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1994,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(1995,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1996,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1997,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1998,plain,
( ( ! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1999,plain,
( ( ! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(2000,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(2001,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(2002,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [T_b: $i] :
~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(2003,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(2004,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ! [V_y: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1285]) ).
thf(2005,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(2006,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(2007,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(2008,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(2009,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(2010,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(2011,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(2012,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(2013,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(2014,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(2015,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(2016,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(2017,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(2018,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ! [V_B: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( c_in @ V_f @ ( c_FuncSet_OPi @ V_A @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(2019,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(2020,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(2021,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(2022,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(2023,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(2024,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(2025,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(2026,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(2027,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(2028,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(2029,plain,
( ( ! [V_xa: $i,V_x: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(2030,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(2031,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(2032,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(2033,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(2034,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(2035,plain,
( ( ! [V_b: $i,V_a: $i,V_P_H: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( 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 @ V_P_H @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( 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 @ ( v_sko__local__X3__1 @ V_P @ V_P_H @ V_a @ V_b ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(2036,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_xa: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(2037,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(2038,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_xa: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(2039,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_xa: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_xa @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ V_a @ V_b @ V_x @ V_xa ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_xa @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(2040,plain,
( ( ! [V_a: $i,V_b: $i,V_F: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_F @ V_x ) @ ( 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_x @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ V_a @ V_b @ V_x ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(2041,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b_H: $i,V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(2042,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(2043,plain,
( ( ! [V_a: $i,V_b: $i,V_P: $i,V_a_H: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b_H: $i,V_P_H: $i] :
( ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(2044,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X2__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(2045,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(2046,plain,
( ( ! [V_a_H: $i,V_b_H: $i,V_P_H: $i,V_a: $i] :
( ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P_H ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_b: $i,V_P: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ V_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ V_a_H @ V_b_H @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ V_P_H @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( 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 @ ( v_sko__local__X1__1 @ V_P @ V_P_H @ V_a @ V_a_H @ V_b @ V_b_H ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( 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_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 ) ) )
| ( V_b = V_a_H )
| ( V_a = V_b_H )
| ( V_a_H = V_b_H )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(2047,plain,
( ( ! [V_F: $i,V_x: $i,V_i: $i] :
( ( ( hAPP @ V_F @ V_x )
= ( hAPP @ V_x @ V_i ) )
| ~ ( c_in @ V_x @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ V_F @ V_i ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(2048,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(2049,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(2050,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(2051,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(2052,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(2053,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(2054,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(2055,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(2056,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(2057,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(2058,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(2059,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(2060,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(2061,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_b: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(2062,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(2063,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [T_b: $i,V_B: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(2064,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ! [V_A: $i] :
( ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(2065,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(2066,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1243]) ).
thf(2067,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(2068,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(2069,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(2070,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(2071,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(2072,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_a ) @ V_r ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(2073,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(2074,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 ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(2075,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ! [T_d: $i,T_e: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(2076,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ! [T_d: $i] :
( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ! [V_v: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(2077,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(2078,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
( ! [V_b_H: $i] :
( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(2079,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(2080,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(2081,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ V_r ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(2082,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(2083,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(2084,plain,
( ( ! [V_i: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ V_i ) @ ( 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____ @ V_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(2085,plain,
( ( v_b____ != v_c____ )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(2086,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r ) )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(2087,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(2088,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(2089,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 ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(2090,plain,
( ( ! [V_x: $i,V_S: $i] :
( ! [T_a: $i] : ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(2091,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(2092,plain,
( ( v_a____ != v_c____ )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(2093,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 ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(2094,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(2095,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(2096,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(2097,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(2098,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(2099,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(2100,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(2101,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(2102,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(2103,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(2104,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(2105,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(2106,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(2107,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(2108,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(2109,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(2110,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(2111,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(2112,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(2113,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(2114,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1230]) ).
thf(2115,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV1 ) @ ( 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 ) @ SV1 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2116,plain,
! [SV2: $i] :
( ( ( 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 ) @ SV2 ) @ ( 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____ @ SV2 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(2117,plain,
! [SV3: $i] :
( ( ! [SY2160: $i,SY2161: $i,SY2162: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SY2160 @ ( tc_fun @ SY2161 @ tc_bool ) ) @ SY2162 @ ( tc_fun @ SY2161 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2160 @ SY2162 @ ( tc_fun @ SY2161 @ tc_bool ) ) @ ( tc_fun @ SY2161 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(2118,plain,
! [SV4: $i] :
( ( ! [SY2163: $i,SY2164: $i,SY2165: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2163 @ SY2164 @ ( tc_fun @ SY2165 @ tc_bool ) ) @ ( tc_fun @ SY2165 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2163 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ SY2164 @ ( tc_fun @ SY2165 @ tc_bool ) ) @ ( tc_fun @ SY2165 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(2119,plain,
! [SV5: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i,SY2169: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SY2166 @ SY2167 @ SY2168 ) @ SY2169 @ ( tc_fun @ SY2168 @ tc_bool ) )
| ! [SY2170: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY2170 @ ( c_COMBK @ SY2169 @ ( tc_fun @ SY2168 @ tc_bool ) @ SY2167 ) @ SY2167 @ SY2168 ) @ ( tc_fun @ ( tc_prod @ SY2167 @ SY2168 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2120,plain,
! [SV6: $i] :
( ( ! [SY2171: $i,SY2172: $i] :
( ( c_Set_Oinsert @ SV6 @ ( c_Set_Oinsert @ SY2171 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2172 @ tc_bool ) ) @ SY2172 ) @ SY2172 )
= ( c_Set_Oinsert @ SY2171 @ ( c_Set_Oinsert @ SV6 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2172 @ tc_bool ) ) @ SY2172 ) @ SY2172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(2121,plain,
! [SV7: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_OId @ SV7 ) @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(2122,plain,
! [SV8: $i] :
( ( ! [SY2173: $i,SY2174: $i,SY2175: $i] :
( ( hAPP @ ( c_COMBK @ SV8 @ SY2173 @ SY2174 ) @ SY2175 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2123,plain,
! [SV9: $i] :
( ( ! [SY2176: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SY2176 ) @ tc_bool ) ) @ SV9 @ SY2176 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV9 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2124,plain,
! [SV10: $i] :
( ( ! [SY2177: $i] :
( ( hBOOL @ ( hAPP @ SV10 @ SY2177 ) )
| ! [SY2178: $i,SY2179: $i] :
( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SY2178 @ SY2179 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2178 @ SY2179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2125,plain,
! [SV11: $i] :
( ( ! [SY2180: $i,SY2181: $i,SY2182: $i,SY2183: $i] :
( ( c_Relation_OImage @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2180 @ SY2181 @ ( tc_fun @ SY2182 @ tc_bool ) ) @ SY2182 @ SY2183 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV11 @ SY2180 @ SY2182 @ SY2183 ) @ ( c_Relation_OImage @ SV11 @ SY2181 @ SY2182 @ SY2183 ) @ ( tc_fun @ SY2183 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2126,plain,
! [SV12: $i] :
( ( ! [SY2184: $i,SY2185: $i,SY2186: $i,SY2187: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV12 @ SY2184 @ ( tc_fun @ ( tc_prod @ SY2185 @ SY2186 ) @ tc_bool ) ) @ SY2187 @ SY2185 @ SY2186 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV12 @ SY2187 @ SY2185 @ SY2186 ) @ ( c_Relation_OImage @ SY2184 @ SY2187 @ SY2185 @ SY2186 ) @ ( tc_fun @ SY2186 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2127,plain,
! [SV13: $i] :
( ( ! [SY2188: $i,SY2189: $i,SY2190: $i,SY2191: $i,SY2192: $i,SY2193: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SY2188 @ SY2189 @ SY2190 @ SY2191 ) @ ( c_Relation_Orel__comp @ SY2192 @ SY2193 @ SY2189 @ SY2190 @ SY2191 ) @ ( tc_fun @ ( tc_prod @ SY2189 @ SY2191 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2188 @ SY2193 @ ( tc_fun @ ( tc_prod @ SY2190 @ SY2191 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SY2192 @ ( tc_fun @ ( tc_prod @ SY2189 @ SY2190 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(2128,plain,
! [SV14: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV14 )
| ! [SY2194: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2194 @ SY2194 @ SV14 )
= SY2194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2129,plain,
! [SV15: $i] :
( ( ! [SY2195: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV15 @ SV15 @ ( tc_fun @ SY2195 @ tc_bool ) )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(2130,plain,
! [SV16: $i] :
( ( ! [SY2196: $i,SY2197: $i] :
( ( c_lessequals @ SV16 @ ( c_Product__Type_OSigma @ SY2196 @ ( c_COMBK @ SY2196 @ ( tc_fun @ SY2197 @ tc_bool ) @ SY2197 ) @ SY2197 @ SY2197 ) @ ( tc_fun @ ( tc_prod @ SY2197 @ SY2197 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SY2196 @ SV16 @ SY2197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(2131,plain,
! [SV17: $i] :
( ( ! [SY2198: $i] : ( c_lessequals @ ( c_Relation_OId__on @ SV17 @ SY2198 ) @ ( c_Product__Type_OSigma @ SV17 @ ( c_COMBK @ SV17 @ ( tc_fun @ SY2198 @ tc_bool ) @ SY2198 ) @ SY2198 @ SY2198 ) @ ( tc_fun @ ( tc_prod @ SY2198 @ SY2198 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(2132,plain,
! [SV18: $i] :
( ( ! [SY2199: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV18 )
| ! [SY2200: $i,SY2201: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2199 @ SY2200 @ SV18 ) @ SY2201 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2199 @ SY2201 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2200 @ SY2201 @ SV18 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2133,plain,
! [SV19: $i] :
( ( ! [SY2202: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV19 )
| ! [SY2203: $i,SY2204: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2202 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2203 @ SY2204 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2202 @ SY2203 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2202 @ SY2204 @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2134,plain,
! [SV20: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2205 @ SY2206 @ ( tc_fun @ SY2207 @ tc_bool ) ) @ ( tc_fun @ SY2207 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY2205 @ ( tc_fun @ SY2207 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY2206 @ ( tc_fun @ SY2207 @ tc_bool ) ) @ ( tc_fun @ SY2207 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2135,plain,
! [SV21: $i] :
( ( ! [SY2208: $i,SY2209: $i,SY2210: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SY2208 @ ( tc_fun @ SY2209 @ tc_bool ) ) @ SY2210 @ ( tc_fun @ SY2209 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV21 @ SY2210 @ ( tc_fun @ SY2209 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2208 @ SY2210 @ ( tc_fun @ SY2209 @ tc_bool ) ) @ ( tc_fun @ SY2209 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2136,plain,
! [SV22: $i] :
( ( ! [SY2211: $i] :
( ( SV22 = SY2211 )
| ! [SY2212: $i] :
~ ( c_in @ SV22 @ ( c_Set_Oinsert @ SY2211 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2212 @ tc_bool ) ) @ SY2212 ) @ SY2212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2137,plain,
! [SV23: $i] :
( ( ! [SY2213: $i,SY2214: $i,SY2215: $i,SY2216: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV23 @ SY2213 @ ( tc_fun @ SY2214 @ tc_bool ) ) @ SY2215 @ SY2214 @ SY2216 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV23 @ SY2215 @ SY2214 @ SY2216 ) @ ( c_Product__Type_OSigma @ SY2213 @ SY2215 @ SY2214 @ SY2216 ) @ ( tc_fun @ ( tc_prod @ SY2214 @ SY2216 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2138,plain,
! [SV24: $i] :
( ( ! [SY2217: $i,SY2218: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SY2217 ) @ SY2218 @ ( tc_fun @ ( tc_prod @ SY2217 @ SY2217 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SY2217 ) @ SY2218 @ ( tc_fun @ ( tc_prod @ SY2217 @ SY2217 ) @ tc_bool ) ) @ SV24 @ SY2217 @ SY2217 @ SY2217 ) @ SY2218 @ ( tc_fun @ ( tc_prod @ SY2217 @ SY2217 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV24 @ SY2218 @ ( tc_fun @ ( tc_prod @ SY2217 @ SY2217 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(2139,plain,
! [SV25: $i] :
( ( ! [SY2219: $i,SY2220: $i,SY2221: $i] :
( ( c_lessequals @ SV25 @ SY2219 @ ( tc_fun @ SY2220 @ tc_bool ) )
| ! [SY2222: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SY2221 @ ( tc_fun @ SY2222 @ tc_bool ) @ SY2220 ) @ SY2220 @ SY2222 ) @ ( c_Product__Type_OSigma @ SY2219 @ ( c_COMBK @ SY2221 @ ( tc_fun @ SY2222 @ tc_bool ) @ SY2220 ) @ SY2220 @ SY2222 ) @ ( tc_fun @ ( tc_prod @ SY2220 @ SY2222 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2221 @ SY2222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2140,plain,
! [SV26: $i] :
( ( ! [SY2224: $i,SY2225: $i,SY2226: $i,SY2227: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SY2224 @ ( tc_fun @ SY2225 @ tc_bool ) @ SY2226 ) @ SY2226 @ SY2225 ) @ ( c_Product__Type_OSigma @ SY2227 @ ( c_COMBK @ SY2224 @ ( tc_fun @ SY2225 @ tc_bool ) @ SY2226 ) @ SY2226 @ SY2225 ) @ ( tc_fun @ ( tc_prod @ SY2226 @ SY2225 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV26 @ SY2227 @ ( tc_fun @ SY2226 @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2224 @ SY2225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(2141,plain,
! [SV27: $i] :
( ( ! [SY2229: $i,SY2230: $i] :
( ( c_lessequals @ SV27 @ SY2229 @ ( tc_fun @ SY2230 @ tc_bool ) )
| ! [SY2231: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY2231 @ SV27 @ SY2230 ) @ SY2229 @ ( tc_fun @ SY2230 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2142,plain,
! [SV28: $i] :
( ( ! [SY2232: $i,SY2233: $i,SY2234: $i] :
( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SY2232 @ SY2233 @ SY2234 ) @ ( tc_fun @ SY2234 @ tc_bool ) )
| ~ ( c_lessequals @ SV28 @ SY2233 @ ( tc_fun @ SY2234 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2143,plain,
! [SV29: $i] :
( ( ! [SY2235: $i] :
( ( hBOOL @ ( hAPP @ SV29 @ SY2235 ) )
| ! [SY2236: $i,SY2237: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SY2236 @ SY2237 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2236 @ SY2237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2144,plain,
! [SV30: $i] :
( ( ! [SY2238: $i,SY2239: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV30 @ SY2238 ) @ ( c_Transitive__Closure_Ortrancl @ SY2239 @ SY2238 ) @ ( tc_fun @ ( tc_prod @ SY2238 @ SY2238 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV30 @ SY2239 @ ( tc_fun @ ( tc_prod @ SY2238 @ SY2238 ) @ tc_bool ) ) @ SY2238 ) @ ( tc_fun @ ( tc_prod @ SY2238 @ SY2238 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(2145,plain,
! [SV31: $i] :
( ( ! [SY2240: $i,SY2241: $i,SY2242: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV31 @ SY2240 @ SY2241 ) @ SY2242 @ ( tc_fun @ SY2241 @ tc_bool ) )
= ( c_Set_Oinsert @ SV31 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2240 @ SY2242 @ ( tc_fun @ SY2241 @ tc_bool ) ) @ SY2241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2146,plain,
! [SV32: $i] :
( ( ! [SY2243: $i,SY2244: $i,SY2245: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Set_Oinsert @ SY2243 @ SY2244 @ SY2245 ) @ ( tc_fun @ SY2245 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2243 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SY2244 @ ( tc_fun @ SY2245 @ tc_bool ) ) @ SY2245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2147,plain,
! [SV33: $i] :
( ( ! [SY2246: $i,SY2247: $i,SY2248: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SY2246 ) @ tc_bool ) ) @ SY2247 @ SV33 @ SY2246 @ SY2248 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SY2248 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2148,plain,
! [SV34: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i] :
( ( c_Relation_Orel__comp @ SV34 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2249 @ SY2250 ) @ tc_bool ) ) @ SY2251 @ SY2249 @ SY2250 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2251 @ SY2250 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2149,plain,
! [SV35: $i] :
( ( ! [SY2252: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV35 @ tc_bool ) ) @ SY2252 @ ( tc_fun @ SV35 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2150,plain,
! [SV36: $i] :
( ( ! [SY2253: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV36 @ SV36 ) @ tc_bool ) ) @ SY2253 @ ( tc_fun @ ( tc_prod @ SV36 @ SV36 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2151,plain,
! [SV37: $i] :
( ( ~ ( class_Orderings_Obot @ SV37 )
| ! [SY2254: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV37 ) @ SY2254 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2152,plain,
! [SV38: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ( c_Set_Oinsert @ SV38 @ SY2255 @ SY2256 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2256 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2153,plain,
! [SV39: $i] :
( ( ! [SY2257: $i,SY2258: $i,SY2259: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV39 @ SY2257 @ SY2258 ) @ ( c_Set_Oinsert @ SV39 @ SY2259 @ SY2258 ) @ ( tc_fun @ SY2258 @ tc_bool ) )
= ( c_Set_Oinsert @ SV39 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2257 @ SY2259 @ ( tc_fun @ SY2258 @ tc_bool ) ) @ SY2258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2154,plain,
! [SV40: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ( c_Relation_OImage @ SV40 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2260 @ tc_bool ) ) @ SY2260 @ SY2261 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2261 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2155,plain,
! [SV41: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SY2262 @ ( tc_fun @ ( tc_prod @ SY2263 @ SY2263 ) @ tc_bool ) ) @ SY2263 )
| ~ ( c_Relation_Osym @ SY2262 @ SY2263 )
| ~ ( c_Relation_Osym @ SV41 @ SY2263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2156,plain,
! [SV42: $i] :
( ( ! [SY2264: $i,SY2265: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV42 @ SY2264 ) @ ( c_Transitive__Closure_Ortrancl @ SY2265 @ SY2264 ) @ ( tc_fun @ ( tc_prod @ SY2264 @ SY2264 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV42 @ SY2265 @ ( tc_fun @ ( tc_prod @ SY2264 @ SY2264 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2157,plain,
! [SV43: $i] :
( ( ! [SY2266: $i,SY2267: $i,SY2268: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV43 @ SY2266 @ ( tc_fun @ ( tc_prod @ SY2267 @ SY2268 ) @ tc_bool ) ) @ SY2267 @ SY2268 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV43 @ SY2267 @ SY2268 ) @ ( c_Relation_ODomain @ SY2266 @ SY2267 @ SY2268 ) @ ( tc_fun @ SY2267 @ tc_bool ) ) @ ( tc_fun @ SY2267 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2158,plain,
! [SV44: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV44 )
| ! [SY2269: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2269 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= ( c_Orderings_Obot__class_Obot @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2159,plain,
! [SV45: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV45 )
| ! [SY2270: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV45 ) @ SY2270 @ SV45 )
= ( c_Orderings_Obot__class_Obot @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2160,plain,
! [SV46: $i] :
( ( ! [SY2271: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV46 @ tc_bool ) ) @ SY2271 @ ( tc_fun @ SV46 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV46 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2161,plain,
! [SV47: $i] :
( ( ! [SY2272: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV47 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2272 @ tc_bool ) ) @ ( tc_fun @ SY2272 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2272 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2162,plain,
! [SV48: $i] :
( ( ! [SY2273: $i,SY2274: $i] : ( c_lessequals @ SV48 @ ( c_Set_Oinsert @ SY2273 @ SV48 @ SY2274 ) @ ( tc_fun @ SY2274 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2163,plain,
! [SV49: $i] :
( ( ! [SY2275: $i,SY2276: $i,SY2277: $i,SY2278: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV49 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2275 @ SY2276 @ ( tc_fun @ SY2277 @ tc_bool ) ) @ SY2277 @ SY2278 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV49 @ SY2275 @ SY2277 @ SY2278 ) @ ( c_Relation_OImage @ SV49 @ SY2276 @ SY2277 @ SY2278 ) @ ( tc_fun @ SY2278 @ tc_bool ) ) @ ( tc_fun @ SY2278 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2164,plain,
! [SV50: $i] :
( ( ! [SY2279: $i,SY2280: $i,SY2281: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SY2279 @ ( tc_fun @ SY2280 @ tc_bool ) ) @ SY2281 @ ( tc_fun @ SY2280 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2279 @ SY2281 @ ( tc_fun @ SY2280 @ tc_bool ) ) @ ( tc_fun @ SY2280 @ tc_bool ) ) )
| ( c_lessequals @ SY2281 @ SV50 @ ( tc_fun @ SY2280 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2165,plain,
! [SV51: $i] :
( ( ! [SY2282: $i,SY2283: $i,SY2284: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SY2282 @ ( tc_fun @ SY2283 @ tc_bool ) ) @ SY2284 @ ( tc_fun @ SY2283 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2282 @ SY2284 @ ( tc_fun @ SY2283 @ tc_bool ) ) @ ( tc_fun @ SY2283 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2284 @ SV51 @ ( tc_fun @ SY2283 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2166,plain,
! [SV52: $i] :
( ( ! [SY2285: $i,SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i,SY2290: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SY2285 @ SY2286 @ SY2287 @ SY2288 ) @ ( c_Product__Type_OSigma @ SY2289 @ ( c_COMBK @ SY2290 @ ( tc_fun @ SY2288 @ tc_bool ) @ SY2286 ) @ SY2286 @ SY2288 ) @ ( tc_fun @ ( tc_prod @ SY2286 @ SY2288 ) @ tc_bool ) )
| ! [SY2291: $i] :
( ~ ( c_lessequals @ SY2285 @ ( c_Product__Type_OSigma @ SY2291 @ ( c_COMBK @ SY2290 @ ( tc_fun @ SY2288 @ tc_bool ) @ SY2287 ) @ SY2287 @ SY2288 ) @ ( tc_fun @ ( tc_prod @ SY2287 @ SY2288 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SY2289 @ ( c_COMBK @ SY2291 @ ( tc_fun @ SY2287 @ tc_bool ) @ SY2286 ) @ SY2286 @ SY2287 ) @ ( tc_fun @ ( tc_prod @ SY2286 @ SY2287 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2167,plain,
! [SV53: $i] :
( ( ! [SY2292: $i,SY2293: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SY2292 @ ( tc_fun @ ( tc_prod @ SY2293 @ SY2293 ) @ tc_bool ) ) @ SY2293 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SY2292 @ SY2293 @ SY2293 @ SY2293 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SY2293 @ SY2293 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2292 @ SY2293 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SY2293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2168,plain,
! [SV54: $i] :
( ( ! [SY2294: $i] :
( ( hBOOL @ ( hAPP @ SV54 @ SY2294 ) )
| ! [SY2295: $i] :
( ( hBOOL @ ( hAPP @ SY2295 @ SY2294 ) )
| ! [SY2296: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2295 @ SV54 @ ( tc_fun @ SY2296 @ tc_bool ) ) @ SY2294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2169,plain,
! [SV55: $i] :
( ( ! [SY2297: $i,SY2298: $i,SY2299: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SY2297 @ ( tc_fun @ SY2298 @ tc_bool ) ) @ SY2299 ) )
| ~ ( hBOOL @ ( hAPP @ SY2297 @ SY2299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2170,plain,
! [SV56: $i] :
( ( ! [SY2300: $i,SY2301: $i,SY2302: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SY2300 @ ( tc_fun @ SY2301 @ tc_bool ) ) @ SY2302 ) )
| ~ ( hBOOL @ ( hAPP @ SV56 @ SY2302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2171,plain,
! [SV57: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SY2303 @ SY2303 ) @ ( c_Relation_ORange @ SY2304 @ SY2303 @ SY2303 ) @ ( tc_fun @ SY2303 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2303 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SY2304 @ SY2303 )
| ~ ( c_Wellfounded_Owf @ SV57 @ SY2303 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SY2304 @ ( tc_fun @ ( tc_prod @ SY2303 @ SY2303 ) @ tc_bool ) ) @ SY2303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2172,plain,
! [SV58: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i,SY2308: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SY2305 @ ( tc_fun @ SY2306 @ tc_bool ) ) @ ( c_COMBK @ SY2307 @ ( tc_fun @ SY2308 @ tc_bool ) @ SY2306 ) @ SY2306 @ SY2308 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV58 @ ( c_COMBK @ SY2307 @ ( tc_fun @ SY2308 @ tc_bool ) @ SY2306 ) @ SY2306 @ SY2308 ) @ ( c_Product__Type_OSigma @ SY2305 @ ( c_COMBK @ SY2307 @ ( tc_fun @ SY2308 @ tc_bool ) @ SY2306 ) @ SY2306 @ SY2308 ) @ ( tc_fun @ ( tc_prod @ SY2306 @ SY2308 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2173,plain,
! [SV59: $i] :
( ( ! [SY2309: $i,SY2310: $i,SY2311: $i,SY2312: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SY2309 @ SY2310 @ SY2311 @ SY2312 ) @ SY2310 @ SY2312 )
| ~ ( c_Relation_Osingle__valued @ SY2309 @ SY2311 @ SY2312 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SY2310 @ SY2311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2174,plain,
! [SV60: $i] :
( ( ! [SY2313: $i,SY2314: $i,SY2315: $i,SY2316: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SY2313 @ ( tc_fun @ SY2314 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2315 @ SY2316 @ ( tc_fun @ ( tc_prod @ SY2314 @ SY2314 ) @ tc_bool ) ) @ SY2314 )
| ~ ( c_Relation_Orefl__on @ SY2313 @ SY2316 @ SY2314 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SY2315 @ SY2314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2175,plain,
! [SV61: $i] :
( ( ! [SY2317: $i] :
( ~ ( class_Lattices_Olattice @ SV61 )
| ! [SY2318: $i,SY2319: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2317 @ SY2318 @ SV61 ) @ SY2319 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2317 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2318 @ SY2319 @ SV61 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2176,plain,
! [SV62: $i] :
( ( ! [SY2320: $i] :
( ~ ( class_Lattices_Olattice @ SV62 )
| ! [SY2321: $i,SY2322: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2320 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2321 @ SY2322 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2321 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2320 @ SY2322 @ SV62 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2177,plain,
! [SV63: $i] :
( ( ! [SY2323: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV63 )
| ! [SY2324: $i,SY2325: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2323 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2324 @ SY2325 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2324 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2323 @ SY2325 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2178,plain,
! [SV64: $i] :
( ( ! [SY2326: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV64 )
| ! [SY2327: $i,SY2328: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2326 @ SY2327 @ SV64 ) @ SY2328 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2326 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2327 @ SY2328 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2179,plain,
! [SV65: $i] :
( ( ! [SY2329: $i,SY2330: $i,SY2331: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ SY2329 @ ( tc_fun @ SY2330 @ tc_bool ) ) @ SY2331 @ ( tc_fun @ SY2330 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2329 @ SY2331 @ ( tc_fun @ SY2330 @ tc_bool ) ) @ ( tc_fun @ SY2330 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2180,plain,
! [SV66: $i] :
( ( ! [SY2332: $i,SY2333: $i,SY2334: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2332 @ SY2333 @ ( tc_fun @ SY2334 @ tc_bool ) ) @ ( tc_fun @ SY2334 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2332 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ SY2333 @ ( tc_fun @ SY2334 @ tc_bool ) ) @ ( tc_fun @ SY2334 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2181,plain,
! [SV67: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV67 )
| ! [SY2335: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2335 @ ( c_Orderings_Obot__class_Obot @ SV67 ) @ SV67 )
= SY2335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2182,plain,
! [SV68: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV68 )
| ! [SY2336: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV68 ) @ SY2336 @ SV68 )
= SY2336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2183,plain,
! [SV69: $i] :
( ( ! [SY2337: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV69 @ tc_bool ) ) @ SY2337 @ ( tc_fun @ SV69 @ tc_bool ) )
= SY2337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2184,plain,
! [SV70: $i] :
( ( ! [SY2338: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2338 @ tc_bool ) ) @ ( tc_fun @ SY2338 @ tc_bool ) )
= SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2185,plain,
! [SV71: $i] :
( ( ! [SY2339: $i,SY2340: $i,SY2341: $i,SY2342: $i,SY2343: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SY2339 @ SY2340 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY2341 @ SY2342 @ SY2343 ) @ ( tc_fun @ SY2343 @ tc_bool ) @ SY2340 ) @ SY2340 @ SY2343 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SY2341 @ SY2340 @ SY2343 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SY2339 @ ( c_COMBK @ ( c_Set_Oinsert @ SY2341 @ SY2342 @ SY2343 ) @ ( tc_fun @ SY2343 @ tc_bool ) @ SY2340 ) @ SY2340 @ SY2343 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SY2339 @ SY2340 ) @ ( c_COMBK @ SY2342 @ ( tc_fun @ SY2343 @ tc_bool ) @ SY2340 ) @ SY2340 @ SY2343 ) @ ( tc_fun @ ( tc_prod @ SY2340 @ SY2343 ) @ tc_bool ) ) @ ( tc_prod @ SY2340 @ SY2343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2186,plain,
! [SV72: $i] :
( ( ! [SY2344: $i] :
( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2344 @ tc_bool ) ) )
| ! [SY2345: $i] :
( ~ ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SY2345 @ SV72 @ SY2344 @ SY2344 ) @ ( tc_fun @ SY2344 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2345 @ SY2344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2187,plain,
! [SV73: $i] :
( ( ! [SY2346: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV73 @ tc_bool ) ) @ SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2188,plain,
! [SV74: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
( ~ ( c_in @ SV74 @ SY2347 @ SY2348 )
| ! [SY2349: $i] :
( ~ ( c_in @ SV74 @ SY2349 @ SY2348 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2349 @ SY2347 @ ( tc_fun @ SY2348 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2348 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2189,plain,
! [SV75: $i] :
( ( ! [SY2350: $i] :
( ~ ( class_Lattices_Olattice @ SV75 )
| ! [SY2351: $i,SY2352: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2350 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2351 @ SY2352 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2350 @ SY2351 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2350 @ SY2352 @ SV75 ) @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2190,plain,
! [SV76: $i] :
( ( ~ ( class_Lattices_Olattice @ SV76 )
| ! [SY2353: $i,SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2353 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2353 @ SY2354 @ SV76 ) @ SV76 )
= SY2353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2191,plain,
! [SV77: $i] :
( ( ! [SY2355: $i,SY2356: $i] :
( ( ( c_Relation_Orel__comp @ SV77 @ SY2355 @ SY2356 @ SY2356 @ SY2356 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2356 @ SY2356 ) @ tc_bool ) ) )
| ! [SY2357: $i] :
( ( ( c_Relation_Orel__comp @ SY2357 @ SY2355 @ SY2356 @ SY2356 @ SY2356 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2356 @ SY2356 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2357 @ SV77 @ ( tc_fun @ ( tc_prod @ SY2356 @ SY2356 ) @ tc_bool ) ) @ SY2355 @ SY2356 @ SY2356 @ SY2356 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2356 @ SY2356 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2192,plain,
! [SV78: $i] :
( ( ! [SY2358: $i,SY2359: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY2358 @ SY2359 @ SY2359 @ SY2359 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2359 @ SY2359 ) @ tc_bool ) ) )
| ! [SY2360: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY2360 @ SY2359 @ SY2359 @ SY2359 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2359 @ SY2359 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2360 @ SY2358 @ ( tc_fun @ ( tc_prod @ SY2359 @ SY2359 ) @ tc_bool ) ) @ SY2359 @ SY2359 @ SY2359 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2359 @ SY2359 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2193,plain,
! [SV79: $i] :
( ( ! [SY2361: $i] :
( ( hBOOL @ ( hAPP @ SV79 @ SY2361 ) )
| ! [SY2362: $i,SY2363: $i] :
( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SY2362 @ SY2363 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2362 @ SY2363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2194,plain,
! [SV80: $i] :
( ( ! [SY2364: $i] :
( ( SV80 = SY2364 )
| ! [SY2365: $i] :
( ~ ( c_lessequals @ SY2364 @ SV80 @ ( tc_fun @ SY2365 @ tc_bool ) )
| ~ ( c_lessequals @ SV80 @ SY2364 @ ( tc_fun @ SY2365 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2195,plain,
! [SV81: $i] :
( ( ! [SY2366: $i] :
( ( SV81 = SY2366 )
| ! [SY2367: $i] :
( ~ ( c_lessequals @ SY2366 @ SV81 @ ( tc_fun @ SY2367 @ tc_bool ) )
| ~ ( c_lessequals @ SV81 @ SY2366 @ ( tc_fun @ SY2367 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2196,plain,
! [SV82: $i] :
( ( ~ ( class_Orderings_Oorder @ SV82 )
| ! [SY2368: $i,SY2369: $i] :
( ( SY2368 = SY2369 )
| ~ ( c_lessequals @ SY2369 @ SY2368 @ SV82 )
| ~ ( c_lessequals @ SY2368 @ SY2369 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2197,plain,
! [SV83: $i] :
( ( ~ ( class_Orderings_Oorder @ SV83 )
| ! [SY2370: $i,SY2371: $i] :
( ( SY2370 = SY2371 )
| ~ ( c_lessequals @ SY2371 @ SY2370 @ SV83 )
| ~ ( c_lessequals @ SY2370 @ SY2371 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2198,plain,
! [SV84: $i] :
( ( ~ ( class_Orderings_Oorder @ SV84 )
| ! [SY2372: $i,SY2373: $i] :
( ( SY2372 = SY2373 )
| ~ ( c_lessequals @ SY2372 @ SY2373 @ SV84 )
| ~ ( c_lessequals @ SY2373 @ SY2372 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2199,plain,
! [SV85: $i] :
( ( ~ ( class_Lattices_Olattice @ SV85 )
| ! [SY2374: $i,SY2375: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2374 @ SY2375 @ SV85 ) @ SV85 )
= SY2374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2200,plain,
! [SV86: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV86 )
| ! [SY2376: $i,SY2377: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2376 @ SY2377 @ SV86 )
= SY2376 )
| ~ ( c_lessequals @ SY2377 @ SY2376 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2201,plain,
! [SV87: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV87 )
| ! [SY2378: $i,SY2379: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2378 @ SY2379 @ SV87 )
!= SY2379 )
| ( c_lessequals @ SY2378 @ SY2379 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2202,plain,
! [SV88: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ! [SY2380: $i,SY2381: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2380 @ SY2381 @ SV88 )
= SY2381 )
| ~ ( c_lessequals @ SY2380 @ SY2381 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2203,plain,
! [SV89: $i] :
( ( ! [SY2382: $i,SY2383: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV89 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) )
= SY2382 )
| ~ ( c_lessequals @ SV89 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2204,plain,
! [SV90: $i] :
( ( ! [SY2384: $i,SY2385: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV90 @ SY2384 @ ( tc_fun @ SY2385 @ tc_bool ) )
= SV90 )
| ~ ( c_lessequals @ SY2384 @ SV90 @ ( tc_fun @ SY2385 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2205,plain,
! [SV91: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV91 @ SY2386 @ ( tc_fun @ SY2387 @ tc_bool ) )
!= SY2386 )
| ( c_lessequals @ SV91 @ SY2386 @ ( tc_fun @ SY2387 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2206,plain,
! [SV92: $i] :
( ( ! [SY2388: $i,SY2389: $i,SY2390: $i,SY2391: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SY2388 @ ( tc_fun @ SY2389 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2390 @ SY2391 @ ( tc_fun @ ( tc_prod @ SY2389 @ SY2389 ) @ tc_bool ) ) @ SY2389 )
| ~ ( c_Relation_Orefl__on @ SY2388 @ SY2391 @ SY2389 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SY2390 @ SY2389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2207,plain,
! [SV93: $i] :
( ( ! [SY2392: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV93 )
| ! [SY2393: $i,SY2394: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2392 @ SY2393 @ SV93 ) @ SY2394 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2392 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2393 @ SY2394 @ SV93 ) @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2208,plain,
! [SV94: $i] :
( ( ! [SY2395: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV94 )
| ! [SY2396: $i,SY2397: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2395 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2396 @ SY2397 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2396 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2395 @ SY2397 @ SV94 ) @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2209,plain,
! [SV95: $i] :
( ( ! [SY2398: $i] :
( ~ ( class_Lattices_Olattice @ SV95 )
| ! [SY2399: $i,SY2400: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2398 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2399 @ SY2400 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2399 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2398 @ SY2400 @ SV95 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2210,plain,
! [SV96: $i] :
( ( ! [SY2401: $i] :
( ~ ( class_Lattices_Olattice @ SV96 )
| ! [SY2402: $i,SY2403: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2401 @ SY2402 @ SV96 ) @ SY2403 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2401 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2402 @ SY2403 @ SV96 ) @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2211,plain,
! [SV97: $i] :
( ( ! [SY2404: $i,SY2405: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV97 @ SY2404 @ ( tc_fun @ SY2405 @ tc_bool ) )
= SV97 )
| ~ ( c_lessequals @ SV97 @ SY2404 @ ( tc_fun @ SY2405 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2212,plain,
! [SV98: $i] :
( ( ! [SY2406: $i,SY2407: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SY2406 @ ( tc_fun @ SY2407 @ tc_bool ) )
= SY2406 )
| ~ ( c_lessequals @ SY2406 @ SV98 @ ( tc_fun @ SY2407 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2213,plain,
! [SV99: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV99 )
| ! [SY2408: $i,SY2409: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2408 @ SY2409 @ SV99 )
= SY2408 )
| ~ ( c_lessequals @ SY2408 @ SY2409 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2214,plain,
! [SV100: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV100 )
| ! [SY2410: $i,SY2411: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2410 @ SY2411 @ SV100 )
!= SY2410 )
| ( c_lessequals @ SY2410 @ SY2411 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2215,plain,
! [SV101: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV101 )
| ! [SY2412: $i,SY2413: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2412 @ SY2413 @ SV101 )
= SY2413 )
| ~ ( c_lessequals @ SY2413 @ SY2412 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2216,plain,
! [SV102: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SY2414 @ ( tc_fun @ SY2415 @ tc_bool ) ) @ SY2416 @ ( tc_fun @ SY2415 @ tc_bool ) )
| ~ ( c_lessequals @ SY2414 @ SY2416 @ ( tc_fun @ SY2415 @ tc_bool ) )
| ~ ( c_lessequals @ SV102 @ SY2416 @ ( tc_fun @ SY2415 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2217,plain,
! [SV103: $i] :
( ( ! [SY2417: $i,SY2418: $i] : ( c_lessequals @ SV103 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2417 @ SV103 @ ( tc_fun @ SY2418 @ tc_bool ) ) @ ( tc_fun @ SY2418 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2218,plain,
! [SV104: $i] :
( ( ! [SY2419: $i,SY2420: $i] : ( c_lessequals @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SY2419 @ ( tc_fun @ SY2420 @ tc_bool ) ) @ ( tc_fun @ SY2420 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2219,plain,
! [SV105: $i] :
( ( ! [SY2421: $i,SY2422: $i,SY2423: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SY2421 @ ( tc_fun @ SY2422 @ tc_bool ) ) @ SY2423 @ ( tc_fun @ SY2422 @ tc_bool ) )
| ~ ( c_lessequals @ SY2421 @ SY2423 @ ( tc_fun @ SY2422 @ tc_bool ) )
| ~ ( c_lessequals @ SV105 @ SY2423 @ ( tc_fun @ SY2422 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2220,plain,
! [SV106: $i] :
( ( ! [SY2424: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV106 )
| ! [SY2425: $i,SY2426: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2424 @ SY2425 @ SV106 ) @ SY2426 @ SV106 )
| ~ ( c_lessequals @ SY2425 @ SY2426 @ SV106 )
| ~ ( c_lessequals @ SY2424 @ SY2426 @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2221,plain,
! [SV107: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV107 )
| ! [SY2427: $i,SY2428: $i] : ( c_lessequals @ SY2427 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2427 @ SY2428 @ SV107 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2222,plain,
! [SV108: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV108 )
| ! [SY2429: $i,SY2430: $i] : ( c_lessequals @ SY2429 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2430 @ SY2429 @ SV108 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2223,plain,
! [SV109: $i] :
( ( ! [SY2431: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV109 )
| ! [SY2432: $i,SY2433: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2431 @ SY2432 @ SV109 ) @ SY2433 @ SV109 )
| ~ ( c_lessequals @ SY2432 @ SY2433 @ SV109 )
| ~ ( c_lessequals @ SY2431 @ SY2433 @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2224,plain,
! [SV110: $i] :
( ( ! [SY2434: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV110 )
| ! [SY2435: $i,SY2436: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2434 @ SY2435 @ SV110 ) @ SY2436 @ SV110 )
| ~ ( c_lessequals @ SY2435 @ SY2436 @ SV110 )
| ~ ( c_lessequals @ SY2434 @ SY2436 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2225,plain,
! [SV111: $i] :
( ( ~ ( class_Lattices_Olattice @ SV111 )
| ! [SY2437: $i,SY2438: $i] : ( c_lessequals @ SY2437 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2438 @ SY2437 @ SV111 ) @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2226,plain,
! [SV112: $i] :
( ( ~ ( class_Lattices_Olattice @ SV112 )
| ! [SY2439: $i,SY2440: $i] : ( c_lessequals @ SY2439 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2439 @ SY2440 @ SV112 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2227,plain,
! [SV113: $i] :
( ( ! [SY2441: $i,SY2442: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV113 @ SY2441 @ ( tc_fun @ SY2442 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2441 @ SV113 @ ( tc_fun @ SY2442 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2228,plain,
! [SV114: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV114 )
| ! [SY2443: $i,SY2444: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2443 @ SY2444 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2444 @ SY2443 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2229,plain,
! [SV115: $i] :
( ( ~ ( class_Lattices_Olattice @ SV115 )
| ! [SY2445: $i,SY2446: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2445 @ SY2446 @ SV115 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2446 @ SY2445 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2230,plain,
! [SV116: $i] :
( ( ! [SY2447: $i] :
( ( c_Wellfounded_Oacyclic @ SV116 @ SY2447 )
| ~ ( c_Wellfounded_Owf @ SV116 @ SY2447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2231,plain,
! [SV117: $i] :
( ( ! [SY2448: $i] :
( ~ ( class_Lattices_Olattice @ SV117 )
| ! [SY2449: $i,SY2450: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2448 @ SY2449 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2448 @ SY2450 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2448 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2449 @ SY2450 @ SV117 ) @ SV117 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2232,plain,
! [SV118: $i] :
( ( ! [SY2451: $i,SY2452: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SY2451 )
= ( c_Transitive__Closure_Ortrancl @ SY2452 @ SY2451 ) )
| ~ ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SY2452 @ SY2451 ) @ ( tc_fun @ ( tc_prod @ SY2451 @ SY2451 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2452 @ SV118 @ ( tc_fun @ ( tc_prod @ SY2451 @ SY2451 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2233,plain,
! [SV119: $i] :
( ( ! [SY2453: $i,SY2454: $i] :
( ( ( c_Set_Oinsert @ SV119 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2453 @ tc_bool ) ) @ SY2453 )
!= ( c_Set_Oinsert @ SY2454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2453 @ tc_bool ) ) @ SY2453 ) )
| ( SV119 = SY2454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2234,plain,
! [SV120: $i] :
( ( ! [SY2455: $i,SY2456: $i,SY2457: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV120 @ SY2455 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2455 @ SY2457 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2457 @ SV120 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( tc_fun @ SY2456 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SY2455 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2455 @ SY2457 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2457 @ SV120 @ ( tc_fun @ SY2456 @ tc_bool ) ) @ ( tc_fun @ SY2456 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2235,plain,
! [SV121: $i] :
( ( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV121 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV121 @ SV121 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2236,plain,
! [SV122: $i] :
( ( ! [SY2458: $i,SY2459: $i,SY2460: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SY2458 @ SY2459 @ SY2459 ) @ SY2460 @ ( tc_prod @ SY2459 @ SY2459 ) ) @ SY2459 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV122 @ ( c_Set_Oinsert @ SY2458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2459 @ tc_bool ) ) @ SY2459 ) @ SY2459 ) @ ( c_Relation_OField @ SY2460 @ SY2459 ) @ ( tc_fun @ SY2459 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2237,plain,
! [SV123: $i] :
( ( ! [SY2461: $i,SY2462: $i] :
( ( ( c_Set_Oinsert @ SV123 @ SY2461 @ SY2462 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2462 @ tc_bool ) ) )
| ( c_in @ SV123 @ SY2461 @ SY2462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2238,plain,
! [SV124: $i] :
( ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV124 @ SV124 ) @ tc_bool ) ) @ SV124 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2239,plain,
! [SV125: $i] :
( ( ! [SY2463: $i,SY2464: $i] :
( ( c_in @ SV125 @ SY2463 @ SY2464 )
| ! [SY2465: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SY2465 @ SY2464 ) @ SY2463 @ ( tc_fun @ SY2464 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2240,plain,
! [SV126: $i] :
( ( ! [SY2466: $i,SY2467: $i,SY2468: $i,SY2469: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SY2466 @ ( tc_fun @ SY2467 @ tc_bool ) ) @ SY2468 @ SY2467 @ SY2469 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV126 @ SY2468 @ SY2467 @ SY2469 ) @ ( c_Product__Type_OSigma @ SY2466 @ SY2468 @ SY2467 @ SY2469 ) @ ( tc_fun @ ( tc_prod @ SY2467 @ SY2469 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2241,plain,
! [SV127: $i] :
( ( ! [SY2470: $i,SY2471: $i,SY2472: $i] :
( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SY2470 @ SY2471 @ SY2472 ) @ ( tc_fun @ SY2472 @ tc_bool ) )
| ~ ( c_lessequals @ SV127 @ SY2471 @ ( tc_fun @ SY2472 @ tc_bool ) )
| ( c_in @ SY2470 @ SV127 @ SY2472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2242,plain,
! [SV128: $i] :
( ( ! [SY2473: $i,SY2474: $i] :
( ( c_lessequals @ SV128 @ SY2473 @ ( tc_fun @ SY2474 @ tc_bool ) )
| ! [SY2475: $i] :
( ( c_in @ SY2475 @ SV128 @ SY2474 )
| ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SY2475 @ SY2473 @ SY2474 ) @ ( tc_fun @ SY2474 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2243,plain,
! [SV129: $i] :
( ( ! [SY2476: $i,SY2477: $i,SY2478: $i] :
( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SY2476 @ SY2477 @ SY2478 ) @ ( tc_fun @ SY2478 @ tc_bool ) )
| ~ ( c_lessequals @ SV129 @ SY2477 @ ( tc_fun @ SY2478 @ tc_bool ) )
| ( c_in @ SY2476 @ SV129 @ SY2478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2244,plain,
! [SV130: $i] :
( ( ! [SY2479: $i,SY2480: $i] :
( ( c_lessequals @ SV130 @ SY2479 @ ( tc_fun @ SY2480 @ tc_bool ) )
| ! [SY2481: $i] :
( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SY2481 @ SY2479 @ SY2480 ) @ ( tc_fun @ SY2480 @ tc_bool ) )
| ( c_in @ SY2481 @ SV130 @ SY2480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2245,plain,
! [SV131: $i] :
( ( ! [SY2482: $i,SY2483: $i,SY2484: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ ( c_Set_Oinsert @ SY2482 @ SY2483 @ SY2484 ) @ ( tc_fun @ SY2484 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SY2483 @ ( tc_fun @ SY2484 @ tc_bool ) ) )
| ( c_in @ SY2482 @ SV131 @ SY2484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2246,plain,
! [SV132: $i] :
( ( ! [SY2485: $i,SY2486: $i,SY2487: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV132 @ SY2485 @ SY2486 ) @ SY2487 @ ( tc_fun @ SY2486 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2485 @ SY2487 @ ( tc_fun @ SY2486 @ tc_bool ) ) )
| ( c_in @ SV132 @ SY2487 @ SY2486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2247,plain,
! [SV133: $i] :
( ( ! [SY2488: $i,SY2489: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 @ SY2488 @ ( tc_fun @ SY2489 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2489 @ tc_bool ) ) )
| ( SY2488
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2489 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2248,plain,
! [SV134: $i] :
( ( ! [SY2490: $i,SY2491: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ SY2490 @ ( tc_fun @ SY2491 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2491 @ tc_bool ) ) )
| ( SV134
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2491 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2249,plain,
! [SV135: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV135 )
| ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2492 @ SY2493 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) )
| ( SY2492
= ( c_Orderings_Obot__class_Obot @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2250,plain,
! [SV136: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV136 )
| ! [SY2494: $i,SY2495: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2494 @ SY2495 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
| ( SY2495
= ( c_Orderings_Obot__class_Obot @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2251,plain,
! [SV137: $i] :
( ( ! [SY2496: $i,SY2497: $i,SY2498: $i,SY2499: $i,SY2500: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SY2496 @ ( tc_fun @ ( tc_prod @ SY2497 @ SY2498 ) @ tc_bool ) ) @ SY2499 @ SY2497 @ SY2498 @ SY2500 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SY2499 @ SY2497 @ SY2498 @ SY2500 ) @ ( c_Relation_Orel__comp @ SY2496 @ SY2499 @ SY2497 @ SY2498 @ SY2500 ) @ ( tc_fun @ ( tc_prod @ SY2497 @ SY2500 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2252,plain,
! [SV138: $i] :
( ( ! [SY2501: $i,SY2502: $i,SY2503: $i,SY2504: $i,SY2505: $i] :
( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2501 @ SY2502 @ ( tc_fun @ ( tc_prod @ SY2503 @ SY2504 ) @ tc_bool ) ) @ SY2505 @ SY2503 @ SY2504 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SY2501 @ SY2505 @ SY2503 @ SY2504 ) @ ( c_Relation_Orel__comp @ SV138 @ SY2502 @ SY2505 @ SY2503 @ SY2504 ) @ ( tc_fun @ ( tc_prod @ SY2505 @ SY2504 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2253,plain,
! [SV139: $i] :
( ( ! [SY2506: $i,SY2507: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV139 @ SY2506 @ ( tc_fun @ ( tc_prod @ SY2507 @ SY2507 ) @ tc_bool ) ) @ SY2507 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV139 @ SY2507 ) @ ( c_Relation_OField @ SY2506 @ SY2507 ) @ ( tc_fun @ SY2507 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2254,plain,
! [SV140: $i] :
( ( ! [SY2508: $i,SY2509: $i] :
( ( c_lessequals @ SV140 @ SY2508 @ ( tc_fun @ SY2509 @ tc_bool ) )
| ! [SY2510: $i] :
~ ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2510 @ SY2508 @ ( tc_fun @ SY2509 @ tc_bool ) ) @ ( tc_fun @ SY2509 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2255,plain,
! [SV141: $i] :
( ( ! [SY2511: $i,SY2512: $i] :
( ( c_lessequals @ SV141 @ SY2511 @ ( tc_fun @ SY2512 @ tc_bool ) )
| ! [SY2513: $i] :
~ ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2511 @ SY2513 @ ( tc_fun @ SY2512 @ tc_bool ) ) @ ( tc_fun @ SY2512 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2256,plain,
! [SV142: $i] :
( ( ! [SY2514: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV142 )
| ! [SY2515: $i] :
( ( c_lessequals @ SY2514 @ SY2515 @ SV142 )
| ! [SY2516: $i] :
~ ( c_lessequals @ SY2514 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2515 @ SY2516 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2257,plain,
! [SV143: $i] :
( ( ! [SY2517: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ! [SY2518: $i] :
( ( c_lessequals @ SY2517 @ SY2518 @ SV143 )
| ! [SY2519: $i] :
~ ( c_lessequals @ SY2517 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2519 @ SY2518 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2258,plain,
! [SV144: $i] :
( ( ! [SY2520: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ! [SY2521: $i,SY2522: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2520 @ SY2521 @ SV144 ) @ SY2522 @ SV144 )
| ~ ( c_lessequals @ SY2520 @ SY2522 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2259,plain,
! [SV145: $i] :
( ( ! [SY2523: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV145 )
| ! [SY2524: $i,SY2525: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2523 @ SY2524 @ SV145 ) @ SY2525 @ SV145 )
| ~ ( c_lessequals @ SY2524 @ SY2525 @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2260,plain,
! [SV146: $i] :
( ( ! [SY2526: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV146 )
| ! [SY2527: $i] :
( ( c_lessequals @ SY2526 @ SY2527 @ SV146 )
| ! [SY2528: $i] :
~ ( c_lessequals @ SY2526 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2527 @ SY2528 @ SV146 ) @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2261,plain,
! [SV147: $i] :
( ( ! [SY2529: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV147 )
| ! [SY2530: $i] :
( ( c_lessequals @ SY2529 @ SY2530 @ SV147 )
| ! [SY2531: $i] :
~ ( c_lessequals @ SY2529 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2531 @ SY2530 @ SV147 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2262,plain,
! [SV148: $i] :
( ( ! [SY2532: $i,SY2533: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV148 @ SY2532 @ ( tc_fun @ SY2533 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2532 @ SV148 @ ( tc_fun @ SY2533 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2263,plain,
! [SV149: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV149 )
| ! [SY2534: $i,SY2535: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2534 @ SY2535 @ SV149 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2535 @ SY2534 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2264,plain,
! [SV150: $i] :
( ( ~ ( class_Lattices_Olattice @ SV150 )
| ! [SY2536: $i,SY2537: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2536 @ SY2537 @ SV150 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2537 @ SY2536 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2265,plain,
! [SV151: $i] :
( ( ! [SY2538: $i,SY2539: $i,SY2540: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SY2538 @ ( tc_fun @ ( tc_prod @ SY2539 @ SY2540 ) @ tc_bool ) ) @ SY2539 @ SY2540 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV151 @ SY2539 @ SY2540 ) @ ( c_Relation_ODomain @ SY2538 @ SY2539 @ SY2540 ) @ ( tc_fun @ SY2539 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2266,plain,
! [SV152: $i] :
( ( ! [SY2541: $i,SY2542: $i] :
( ( c_Set_Oinsert @ SV152 @ SY2541 @ SY2542 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV152 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2542 @ tc_bool ) ) @ SY2542 ) @ SY2541 @ ( tc_fun @ SY2542 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2267,plain,
! [SV153: $i] :
( ( ! [SY2543: $i,SY2544: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV153 @ tc_bool ) ) @ SY2543 @ SV153 @ SY2544 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV153 @ SY2544 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2268,plain,
! [SV154: $i] :
( ( ! [SY2545: $i,SY2546: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV154 @ SY2545 ) @ ( c_Wellfounded_Oacc @ SY2546 @ SY2545 ) @ ( tc_fun @ SY2545 @ tc_bool ) )
| ~ ( c_lessequals @ SY2546 @ SV154 @ ( tc_fun @ ( tc_prod @ SY2545 @ SY2545 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2269,plain,
! [SV155: $i] :
( ( ! [SY2547: $i,SY2548: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SY2547 @ ( tc_fun @ SY2548 @ tc_bool ) ) @ ( tc_fun @ SY2548 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SY2547 @ ( tc_fun @ SY2548 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2270,plain,
! [SV156: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV156 )
| ! [SY2549: $i,SY2550: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) @ SV156 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2271,plain,
! [SV157: $i] :
( ( ~ ( class_Lattices_Olattice @ SV157 )
| ! [SY2551: $i,SY2552: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) @ SV157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2272,plain,
! [SV158: $i] :
( ( ! [SY2553: $i,SY2554: $i] :
( ( ( c_Relation_ODomain @ SV158 @ SY2553 @ SY2554 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2553 @ tc_bool ) ) )
| ( SV158
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2553 @ SY2554 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2273,plain,
! [SV159: $i] :
( ( ! [SY2555: $i,SY2556: $i,SY2557: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SY2555 @ ( tc_fun @ ( tc_prod @ SY2556 @ SY2557 ) @ tc_bool ) ) @ SY2556 @ SY2557 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV159 @ SY2556 @ SY2557 ) @ ( c_Relation_ORange @ SY2555 @ SY2556 @ SY2557 ) @ ( tc_fun @ SY2557 @ tc_bool ) ) @ ( tc_fun @ SY2557 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2274,plain,
! [SV160: $i] :
( ( ! [SY2558: $i] :
( ( hBOOL @ ( hAPP @ SV160 @ SY2558 ) )
| ! [SY2559: $i,SY2560: $i] :
( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SY2559 @ SY2560 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2559 @ SY2560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2275,plain,
! [SV161: $i] :
( ( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV161 @ SV161 ) @ tc_bool ) ) @ SV161 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV161 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2276,plain,
! [SV162: $i] :
( ( ! [SY2561: $i,SY2562: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV162 @ SY2561 ) @ ( c_Transitive__Closure_Ortrancl @ SY2562 @ SY2561 ) @ ( tc_fun @ ( tc_prod @ SY2561 @ SY2561 ) @ tc_bool ) ) @ SY2561 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV162 @ SY2562 @ ( tc_fun @ ( tc_prod @ SY2561 @ SY2561 ) @ tc_bool ) ) @ SY2561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2277,plain,
! [SV163: $i] :
( ( ! [SY2563: $i] :
( ( hBOOL @ ( hAPP @ SV163 @ SY2563 ) )
| ! [SY2564: $i,SY2565: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2564 @ SV163 @ ( tc_fun @ SY2565 @ tc_bool ) ) @ SY2563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2278,plain,
! [SV164: $i] :
( ( ! [SY2566: $i] :
( ( hBOOL @ ( hAPP @ SV164 @ SY2566 ) )
| ! [SY2567: $i,SY2568: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SY2567 @ ( tc_fun @ SY2568 @ tc_bool ) ) @ SY2566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2279,plain,
! [SV165: $i] :
( ( ! [SY2569: $i,SY2570: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SY2569 @ ( tc_fun @ ( tc_prod @ SY2570 @ SY2570 ) @ tc_bool ) ) @ SY2570 )
| ~ ( c_Relation_Osym @ SY2569 @ SY2570 )
| ~ ( c_Relation_Osym @ SV165 @ SY2570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2280,plain,
! [SV166: $i] :
( ( ! [SY2571: $i,SY2572: $i,SY2573: $i,SY2574: $i,SY2575: $i] :
( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SY2571 @ SY2572 @ SY2573 @ SY2574 @ SY2575 ) )
!= ( hAPP @ SY2571 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SY2571 @ SY2572 @ SY2573 @ SY2574 @ SY2575 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SY2572 @ SY2573 @ SY2574 @ SY2575 )
= ( c_Recdef_Ocut @ SY2571 @ SY2572 @ SY2573 @ SY2574 @ SY2575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2281,plain,
! [SV167: $i] :
( ( ! [SY2576: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ SV167 @ SY2576 ) @ SY2576 @ SY2576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2282,plain,
! [SV168: $i] :
( ( ! [SY2577: $i] :
( ( c_Wellfounded_Oacyclic @ SV168 @ SY2577 )
| ! [SY2578: $i,SY2579: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY2578 @ SY2579 @ SY2577 @ SY2577 ) @ SV168 @ ( tc_prod @ SY2577 @ SY2577 ) ) @ SY2577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2283,plain,
! [SV169: $i] :
( ( ! [SY2580: $i,SY2581: $i] :
( ~ ( class_HOL_Oord @ SV169 )
| ! [SY2582: $i] :
( ( c_lessequals @ ( hAPP @ SY2580 @ SY2581 ) @ ( hAPP @ SY2582 @ SY2581 ) @ SV169 )
| ! [SY2583: $i] :
~ ( c_lessequals @ SY2580 @ SY2582 @ ( tc_fun @ SY2583 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2284,plain,
! [SV170: $i] :
( ( ! [SY2584: $i,SY2585: $i,SY2586: $i] :
( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2584 @ SY2585 @ ( tc_fun @ SY2586 @ tc_bool ) ) @ SY2586 )
| ~ ( c_in @ SV170 @ SY2585 @ SY2586 )
| ~ ( c_in @ SV170 @ SY2584 @ SY2586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2285,plain,
! [SV171: $i] :
( ( ! [SY2587: $i,SY2588: $i,SY2589: $i] :
( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2587 @ SY2588 @ ( tc_fun @ SY2589 @ tc_bool ) ) @ SY2589 )
| ~ ( c_in @ SV171 @ SY2588 @ SY2589 )
| ~ ( c_in @ SV171 @ SY2587 @ SY2589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2286,plain,
! [SV172: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ( c_in @ SV172 @ SY2590 @ SY2591 )
| ! [SY2592: $i] :
( ~ ( c_in @ SV172 @ SY2592 @ SY2591 )
| ~ ( c_lessequals @ SY2592 @ SY2590 @ ( tc_fun @ SY2591 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2287,plain,
! [SV173: $i] :
( ( ! [SY2593: $i,SY2594: $i] :
( ( c_in @ SV173 @ SY2593 @ SY2594 )
| ! [SY2595: $i] :
( ~ ( c_lessequals @ SY2595 @ SY2593 @ ( tc_fun @ SY2594 @ tc_bool ) )
| ~ ( c_in @ SV173 @ SY2595 @ SY2594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2288,plain,
! [SV174: $i] :
( ( ! [SY2596: $i,SY2597: $i] :
( ( c_in @ SV174 @ SY2596 @ SY2597 )
| ! [SY2598: $i] :
( ~ ( c_in @ SV174 @ SY2598 @ SY2597 )
| ~ ( c_lessequals @ SY2598 @ SY2596 @ ( tc_fun @ SY2597 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2289,plain,
! [SV175: $i] :
( ( ! [SY2599: $i,SY2600: $i] :
( ( c_in @ SV175 @ SY2599 @ SY2600 )
| ! [SY2601: $i] :
( ~ ( c_in @ SV175 @ SY2601 @ SY2600 )
| ~ ( c_lessequals @ SY2601 @ SY2599 @ ( tc_fun @ SY2600 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2290,plain,
! [SV176: $i] :
( ( ! [SY2602: $i,SY2603: $i,SY2604: $i] :
( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2602 @ SY2603 @ ( tc_fun @ SY2604 @ tc_bool ) ) @ SY2604 )
| ~ ( c_in @ SV176 @ SY2602 @ SY2604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2291,plain,
! [SV177: $i] :
( ( ! [SY2605: $i,SY2606: $i,SY2607: $i] :
( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2605 @ SY2606 @ ( tc_fun @ SY2607 @ tc_bool ) ) @ SY2607 )
| ~ ( c_in @ SV177 @ SY2606 @ SY2607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2292,plain,
! [SV178: $i] :
( ( ! [SY2608: $i] :
~ ( c_in @ SV178 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2608 @ tc_bool ) ) @ SY2608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2293,plain,
! [SV179: $i] :
( ( ! [SY2609: $i] :
( ( hBOOL @ ( hAPP @ SV179 @ SY2609 ) )
| ! [T_a: $i] :
~ ( c_in @ SY2609 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2294,plain,
! [SV180: $i] :
( ( ! [SY2611: $i] :
~ ( c_in @ SV180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2611 @ tc_bool ) ) @ SY2611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2295,plain,
! [SV181: $i] :
( ( ! [SY2612: $i] :
~ ( c_in @ SV181 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2612 @ tc_bool ) ) @ SY2612 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2296,plain,
! [SV182: $i] :
( ( ! [SY2613: $i,SY2614: $i] :
( ( c_in @ SV182 @ SY2613 @ SY2614 )
| ! [SY2615: $i] :
( ( c_in @ SV182 @ SY2615 @ SY2614 )
| ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2615 @ SY2613 @ ( tc_fun @ SY2614 @ tc_bool ) ) @ SY2614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2297,plain,
! [SV183: $i] :
( ( ! [SY2616: $i,SY2617: $i] :
( ( c_in @ SV183 @ SY2616 @ SY2617 )
| ! [SY2618: $i] :
~ ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2618 @ SY2616 @ ( tc_fun @ SY2617 @ tc_bool ) ) @ SY2617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2298,plain,
! [SV184: $i] :
( ( ! [SY2619: $i,SY2620: $i] :
( ( c_in @ SV184 @ SY2619 @ SY2620 )
| ! [SY2621: $i] :
~ ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2619 @ SY2621 @ ( tc_fun @ SY2620 @ tc_bool ) ) @ SY2620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2299,plain,
! [SV185: $i] :
( ( ! [SY2622: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ SY2622 ) )
| ! [T_a: $i] :
~ ( c_in @ SY2622 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2300,plain,
! [SV186: $i] :
( ( ! [SY2624: $i,SY2625: $i,SY2626: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SY2624 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2625 @ SY2626 @ ( tc_fun @ ( tc_prod @ SV186 @ SY2624 ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SY2624 ) @ SY2625 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SY2624 ) @ SY2626 ) @ ( tc_fun @ ( tc_prod @ SY2624 @ SV186 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2301,plain,
! [SV187: $i] :
( ( ! [SY2627: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV187 @ SV187 ) @ SY2627 ) @ SV187 )
| ~ ( c_Wellfounded_Oacyclic @ SY2627 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2302,plain,
! [SV188: $i] :
( ( ! [SY2628: $i] :
( ( c_Wellfounded_Oacyclic @ SV188 @ SY2628 )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SY2628 @ SY2628 ) @ SV188 ) @ SY2628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2303,plain,
! [SV189: $i] :
( ( ! [SY2629: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ SV189 @ SV189 ) @ SY2629 ) @ SV189 )
= ( c_Relation_OField @ SY2629 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2304,plain,
! [SV190: $i] :
( ( ! [SY2630: $i,SY2631: $i,SY2632: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SY2630 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2631 @ SY2632 @ ( tc_fun @ ( tc_prod @ SV190 @ SY2630 ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SY2630 ) @ SY2631 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SY2630 ) @ SY2632 ) @ ( tc_fun @ ( tc_prod @ SY2630 @ SV190 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2305,plain,
! [SV191: $i] :
( ( ! [SY2633: $i,SY2634: $i,SY2635: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2633 @ tc_bool ) ) @ SY2633 ) @ SY2634 @ SY2633 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY2635 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2633 @ tc_bool ) ) @ SY2633 ) @ SY2634 @ SY2633 ) )
| ~ ( c_in @ ( c_Pair @ SV191 @ SY2635 @ SY2633 @ SY2633 ) @ SY2634 @ ( tc_prod @ SY2633 @ SY2633 ) )
| ! [SY2636: $i] :
( ~ ( c_in @ SY2635 @ SY2636 @ SY2633 )
| ~ ( c_in @ SV191 @ SY2636 @ SY2633 )
| ~ ( c_Equiv__Relations_Oequiv @ SY2636 @ SY2634 @ SY2633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2306,plain,
! [SV192: $i] :
( ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV192 @ SV192 ) @ tc_bool ) ) @ SV192 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2307,plain,
! [SV193: $i] :
( ( ! [SY2637: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV193 @ SY2637 ) @ tc_bool ) ) @ SV193 @ SY2637 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2637 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2308,plain,
! [SV194: $i] :
( ( ! [SY2638: $i,SY2639: $i,SY2640: $i,SY2641: $i] :
( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SY2638 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2639 @ tc_bool ) ) @ SY2639 ) @ SY2639 )
!= ( c_Set_Oinsert @ SY2640 @ ( c_Set_Oinsert @ SY2641 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2639 @ tc_bool ) ) @ SY2639 ) @ SY2639 ) )
| ( SV194 = SY2641 )
| ( SV194 = SY2640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2309,plain,
! [SV195: $i] :
( ( ! [SY2642: $i,SY2643: $i,SY2644: $i] :
( ! [SY2645: $i] :
( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SY2642 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2643 @ tc_bool ) ) @ SY2643 ) @ SY2643 )
!= ( c_Set_Oinsert @ SY2644 @ ( c_Set_Oinsert @ SY2645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2643 @ tc_bool ) ) @ SY2643 ) @ SY2643 ) )
| ( SY2642 = SY2644 )
| ( SV195 = SY2644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2310,plain,
! [SV196: $i] :
( ( ! [SY2646: $i,SY2647: $i,SY2648: $i,SY2649: $i] :
( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SY2646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2647 @ tc_bool ) ) @ SY2647 ) @ SY2647 )
!= ( c_Set_Oinsert @ SY2648 @ ( c_Set_Oinsert @ SY2649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2647 @ tc_bool ) ) @ SY2647 ) @ SY2647 ) )
| ( SV196 = SY2649 )
| ( SY2646 = SY2649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2311,plain,
! [SV197: $i] :
( ( ! [SY2650: $i,SY2651: $i,SY2652: $i,SY2653: $i] :
( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SY2650 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2651 @ tc_bool ) ) @ SY2651 ) @ SY2651 )
!= ( c_Set_Oinsert @ SY2652 @ ( c_Set_Oinsert @ SY2653 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2651 @ tc_bool ) ) @ SY2651 ) @ SY2651 ) )
| ( SY2650 = SY2652 )
| ( SY2650 = SY2653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2312,plain,
! [SV198: $i] :
( ( ! [SY2654: $i,SY2655: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV198 @ SY2654 ) @ ( c_Product__Type_OSigma @ SY2655 @ ( c_COMBK @ SY2655 @ ( tc_fun @ SY2654 @ tc_bool ) @ SY2654 ) @ SY2654 @ SY2654 ) @ ( tc_fun @ ( tc_prod @ SY2654 @ SY2654 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV198 @ ( c_Product__Type_OSigma @ SY2655 @ ( c_COMBK @ SY2655 @ ( tc_fun @ SY2654 @ tc_bool ) @ SY2654 ) @ SY2654 @ SY2654 ) @ ( tc_fun @ ( tc_prod @ SY2654 @ SY2654 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2313,plain,
! [SV199: $i] :
( ( ! [SY2656: $i,SY2657: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV199 @ SY2656 ) @ ( c_Transitive__Closure_Ortrancl @ SY2657 @ SY2656 ) @ ( tc_fun @ ( tc_prod @ SY2656 @ SY2656 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ ( c_Transitive__Closure_Ortrancl @ SY2657 @ SY2656 ) @ ( tc_fun @ ( tc_prod @ SY2656 @ SY2656 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2314,plain,
! [SV200: $i] :
( ( ! [SY2658: $i] :
( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2658 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2658 @ tc_bool ) ) @ ( tc_fun @ SY2658 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2315,plain,
! [SV201: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV201 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV201 @ tc_bool ) ) @ ( tc_fun @ SV201 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2316,plain,
! [SV202: $i] :
( ( ! [SY2659: $i,SY2660: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY2659 @ SY2660 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2317,plain,
! [SV203: $i] :
( ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV203 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV203 @ SV203 ) @ tc_bool ) ) @ SV203 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2318,plain,
! [SV204: $i] :
( ( ! [SY2661: $i,SY2662: $i,SY2663: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SY2661 @ SY2662 ) @ SY2663 @ ( tc_fun @ SY2662 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2661 @ SY2663 @ ( tc_fun @ SY2662 @ tc_bool ) ) @ SY2662 ) )
| ~ ( c_in @ SV204 @ SY2663 @ SY2662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2319,plain,
! [SV205: $i] :
( ( ! [SY2664: $i,SY2665: $i,SY2666: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SY2664 @ SY2665 @ SY2666 ) @ ( tc_fun @ SY2666 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2664 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SY2665 @ ( tc_fun @ SY2666 @ tc_bool ) ) @ SY2666 ) )
| ~ ( c_in @ SY2664 @ SV205 @ SY2666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2320,plain,
! [SV206: $i] :
( ( ! [SY2667: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV206 @ tc_bool ) ) @ SY2667 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2321,plain,
! [SV207: $i] :
( ( ! [SY2668: $i,SY2669: $i,SY2670: $i,SY2671: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SY2668 @ ( tc_fun @ SY2669 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2670 @ SY2671 @ ( tc_fun @ SY2669 @ tc_bool ) ) @ ( tc_fun @ SY2669 @ tc_bool ) )
| ~ ( c_lessequals @ SY2668 @ SY2671 @ ( tc_fun @ SY2669 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SY2670 @ ( tc_fun @ SY2669 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2322,plain,
! [SV208: $i] :
( ( ~ ( class_Lattices_Olattice @ SV208 )
| ! [SY2672: $i,SY2673: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2672 @ SY2673 @ SV208 ) @ SY2672 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2323,plain,
! [SV209: $i] :
( ( ~ ( class_Lattices_Olattice @ SV209 )
| ! [SY2674: $i,SY2675: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2674 @ SY2675 @ SV209 ) @ SY2675 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2324,plain,
! [SV210: $i] :
( ( ! [SY2676: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV210 )
| ! [SY2677: $i,SY2678: $i] :
( ( c_lessequals @ SY2676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2677 @ SY2678 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SY2676 @ SY2678 @ SV210 )
| ~ ( c_lessequals @ SY2676 @ SY2677 @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2325,plain,
! [SV211: $i] :
( ( ! [SY2679: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV211 )
| ! [SY2680: $i,SY2681: $i] :
( ( c_lessequals @ SY2679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2680 @ SY2681 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SY2679 @ SY2681 @ SV211 )
| ~ ( c_lessequals @ SY2679 @ SY2680 @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2326,plain,
! [SV212: $i] :
( ( ! [SY2682: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV212 )
| ! [SY2683: $i,SY2684: $i] :
( ( c_lessequals @ SY2682 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2683 @ SY2684 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SY2682 @ SY2684 @ SV212 )
| ~ ( c_lessequals @ SY2682 @ SY2683 @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2327,plain,
! [SV213: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV213 )
| ! [SY2685: $i,SY2686: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2685 @ SY2686 @ SV213 ) @ SY2686 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2328,plain,
! [SV214: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV214 )
| ! [SY2687: $i,SY2688: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2687 @ SY2688 @ SV214 ) @ SY2687 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2329,plain,
! [SV215: $i] :
( ( ! [SY2689: $i,SY2690: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 @ SY2689 @ ( tc_fun @ SY2690 @ tc_bool ) ) @ SV215 @ ( tc_fun @ SY2690 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2330,plain,
! [SV216: $i] :
( ( ! [SY2691: $i,SY2692: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV216 @ SY2691 @ ( tc_fun @ SY2692 @ tc_bool ) ) @ SY2691 @ ( tc_fun @ SY2692 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2331,plain,
! [SV217: $i] :
( ( ! [SY2693: $i,SY2694: $i,SY2695: $i] :
( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2693 @ SY2694 @ ( tc_fun @ SY2695 @ tc_bool ) ) @ ( tc_fun @ SY2695 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SY2694 @ ( tc_fun @ SY2695 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SY2693 @ ( tc_fun @ SY2695 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2332,plain,
! [SV218: $i] :
( ( ! [SY2696: $i,SY2697: $i,SY2698: $i] :
( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2696 @ SY2697 @ ( tc_fun @ SY2698 @ tc_bool ) ) @ ( tc_fun @ SY2698 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SY2697 @ ( tc_fun @ SY2698 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SY2696 @ ( tc_fun @ SY2698 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2333,plain,
! [SV219: $i] :
( ( ! [SY2699: $i,SY2700: $i,SY2701: $i,SY2702: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SY2699 @ ( tc_fun @ SY2700 @ tc_bool ) ) @ ( c_COMBK @ SY2701 @ ( tc_fun @ SY2702 @ tc_bool ) @ SY2700 ) @ SY2700 @ SY2702 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV219 @ ( c_COMBK @ SY2701 @ ( tc_fun @ SY2702 @ tc_bool ) @ SY2700 ) @ SY2700 @ SY2702 ) @ ( c_Product__Type_OSigma @ SY2699 @ ( c_COMBK @ SY2701 @ ( tc_fun @ SY2702 @ tc_bool ) @ SY2700 ) @ SY2700 @ SY2702 ) @ ( tc_fun @ ( tc_prod @ SY2700 @ SY2702 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2334,plain,
! [SV220: $i] :
( ( ! [SY2703: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV220 )
| ! [SY2704: $i,SY2705: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2703 @ SY2704 @ SV220 ) @ SY2705 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2703 @ SY2705 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2704 @ SY2705 @ SV220 ) @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2335,plain,
! [SV221: $i] :
( ( ! [SY2706: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV221 )
| ! [SY2707: $i,SY2708: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2707 @ SY2708 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2706 @ SY2707 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2706 @ SY2708 @ SV221 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2336,plain,
! [SV222: $i] :
( ( ! [SY2709: $i,SY2710: $i,SY2711: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2709 @ SY2710 @ ( tc_fun @ SY2711 @ tc_bool ) ) @ ( tc_fun @ SY2711 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SY2709 @ ( tc_fun @ SY2711 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SY2710 @ ( tc_fun @ SY2711 @ tc_bool ) ) @ ( tc_fun @ SY2711 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2337,plain,
! [SV223: $i] :
( ( ! [SY2712: $i,SY2713: $i,SY2714: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV223 @ SY2712 @ ( tc_fun @ SY2713 @ tc_bool ) ) @ SY2714 @ ( tc_fun @ SY2713 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV223 @ SY2714 @ ( tc_fun @ SY2713 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2712 @ SY2714 @ ( tc_fun @ SY2713 @ tc_bool ) ) @ ( tc_fun @ SY2713 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2338,plain,
! [SV224: $i] :
( ( ! [SY2715: $i,SY2716: $i,SY2717: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SY2715 @ SY2716 ) @ SY2717 @ ( tc_fun @ SY2716 @ tc_bool ) )
| ~ ( c_lessequals @ SY2715 @ SY2717 @ ( tc_fun @ SY2716 @ tc_bool ) )
| ~ ( c_in @ SV224 @ SY2717 @ SY2716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2339,plain,
! [SV225: $i] :
( ( ~ ( class_Lattices_Olattice @ SV225 )
| ! [SY2718: $i,SY2719: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) @ SV225 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2340,plain,
! [SV226: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV226 )
| ! [SY2720: $i,SY2721: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) @ SV226 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2341,plain,
! [SV227: $i] :
( ( ! [SY2722: $i,SY2723: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SY2722 @ ( tc_fun @ SY2723 @ tc_bool ) ) @ ( tc_fun @ SY2723 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SY2722 @ ( tc_fun @ SY2723 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2342,plain,
! [SV228: $i] :
( ( ! [SY2724: $i,SY2725: $i] :
( ( c_lessequals @ ( c_Relation_OField @ SV228 @ SY2724 ) @ ( c_Relation_OField @ SY2725 @ SY2724 ) @ ( tc_fun @ SY2724 @ tc_bool ) )
| ~ ( c_lessequals @ SV228 @ SY2725 @ ( tc_fun @ ( tc_prod @ SY2724 @ SY2724 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2343,plain,
! [SV229: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i,SY2729: $i] :
( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2726 @ SY2727 @ ( tc_fun @ SY2728 @ tc_bool ) ) @ SY2728 @ SY2729 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SY2726 @ SY2728 @ SY2729 ) @ ( c_Relation_OImage @ SV229 @ SY2727 @ SY2728 @ SY2729 ) @ ( tc_fun @ SY2729 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SY2728 @ SY2729 ) @ SV229 ) @ SY2729 @ SY2728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2344,plain,
! [SV230: $i] :
( ( ! [SY2730: $i,SY2731: $i,SY2732: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SY2730 @ ( tc_fun @ ( tc_prod @ SY2731 @ SY2732 ) @ tc_bool ) ) @ SY2731 @ SY2732 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV230 @ SY2731 @ SY2732 ) @ ( c_Relation_ORange @ SY2730 @ SY2731 @ SY2732 ) @ ( tc_fun @ SY2732 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2345,plain,
! [SV231: $i] :
( ( ! [SY2733: $i,SY2734: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV231 @ SY2733 @ ( tc_fun @ ( tc_prod @ SY2734 @ SY2734 ) @ tc_bool ) ) @ SY2734 )
| ~ ( c_Wellfounded_Owf @ SV231 @ SY2734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2346,plain,
! [SV232: $i] :
( ( ! [SY2735: $i,SY2736: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV232 @ SY2735 @ ( tc_fun @ ( tc_prod @ SY2736 @ SY2736 ) @ tc_bool ) ) @ SY2736 )
| ~ ( c_Wellfounded_Owf @ SY2735 @ SY2736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2347,plain,
! [SV233: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV233 )
| ! [SY2737: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2737 @ SY2737 @ SV233 )
= SY2737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2348,plain,
! [SV234: $i] :
( ( ! [SY2738: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV234 @ SV234 @ ( tc_fun @ SY2738 @ tc_bool ) )
= SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2349,plain,
! [SV235: $i] :
( ( ! [SY2739: $i] :
( ( c_Relation_OField @ SV235 @ SY2739 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV235 @ SY2739 @ SY2739 ) @ ( c_Relation_ORange @ SV235 @ SY2739 @ SY2739 ) @ ( tc_fun @ SY2739 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2350,plain,
! [SV236: $i] :
( ( ! [SY2740: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV236 )
| ! [SY2741: $i] :
( ( c_lessequals @ SY2740 @ SY2741 @ SV236 )
| ! [SY2742: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2742 @ SY2740 @ SV236 ) @ SY2741 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2351,plain,
! [SV237: $i] :
( ( ! [SY2743: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV237 )
| ! [SY2744: $i] :
( ( c_lessequals @ SY2743 @ SY2744 @ SV237 )
| ! [SY2745: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2743 @ SY2745 @ SV237 ) @ SY2744 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2352,plain,
! [SV238: $i] :
( ( ! [SY2746: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV238 )
| ! [SY2747: $i,SY2748: $i] :
( ( c_lessequals @ SY2746 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2747 @ SY2748 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SY2746 @ SY2748 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2353,plain,
! [SV239: $i] :
( ( ! [SY2749: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV239 )
| ! [SY2750: $i] :
( ! [SY2751: $i] : ( c_lessequals @ SY2749 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2750 @ SY2751 @ SV239 ) @ SV239 )
| ~ ( c_lessequals @ SY2749 @ SY2750 @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2354,plain,
! [SV240: $i] :
( ( ! [SY2752: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV240 )
| ! [SY2753: $i] :
( ( c_lessequals @ SY2752 @ SY2753 @ SV240 )
| ! [SY2754: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2754 @ SY2752 @ SV240 ) @ SY2753 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2355,plain,
! [SV241: $i] :
( ( ! [SY2755: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV241 )
| ! [SY2756: $i] :
( ( c_lessequals @ SY2755 @ SY2756 @ SV241 )
| ! [SY2757: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2755 @ SY2757 @ SV241 ) @ SY2756 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2356,plain,
! [SV242: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ( c_lessequals @ SV242 @ SY2758 @ ( tc_fun @ SY2759 @ tc_bool ) )
| ! [SY2760: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SY2760 @ ( tc_fun @ SY2759 @ tc_bool ) ) @ SY2758 @ ( tc_fun @ SY2759 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2357,plain,
! [SV243: $i] :
( ( ! [SY2761: $i,SY2762: $i] :
( ( c_lessequals @ SV243 @ SY2761 @ ( tc_fun @ SY2762 @ tc_bool ) )
| ! [SY2763: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2763 @ SV243 @ ( tc_fun @ SY2762 @ tc_bool ) ) @ SY2761 @ ( tc_fun @ SY2762 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2358,plain,
! [SV244: $i] :
( ( ! [SY2764: $i] :
( ~ ( class_Orderings_Oorder @ SV244 )
| ! [SY2765: $i] :
( ( c_lessequals @ SY2764 @ SY2765 @ SV244 )
| ! [SY2766: $i] :
( ~ ( c_lessequals @ SY2764 @ SY2766 @ SV244 )
| ~ ( c_lessequals @ SY2766 @ SY2765 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2359,plain,
! [SV245: $i] :
( ( ! [SY2767: $i] :
( ~ ( class_Orderings_Opreorder @ SV245 )
| ! [SY2768: $i] :
( ( c_lessequals @ SY2767 @ SY2768 @ SV245 )
| ! [SY2769: $i] :
( ~ ( c_lessequals @ SY2769 @ SY2768 @ SV245 )
| ~ ( c_lessequals @ SY2767 @ SY2769 @ SV245 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2360,plain,
! [SV246: $i] :
( ( ! [SY2770: $i] : ( c_lessequals @ SV246 @ SV246 @ ( tc_fun @ SY2770 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2361,plain,
! [SV247: $i] :
( ( ! [SY2771: $i] : ( c_lessequals @ SV247 @ SV247 @ ( tc_fun @ SY2771 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2362,plain,
! [SV248: $i] :
( ( ! [SY2772: $i,SY2773: $i] :
( ( c_lessequals @ SV248 @ SY2772 @ ( tc_fun @ SY2773 @ tc_bool ) )
| ! [SY2774: $i] :
( ~ ( c_lessequals @ SY2774 @ SY2772 @ ( tc_fun @ SY2773 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY2774 @ ( tc_fun @ SY2773 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2363,plain,
! [SV249: $i] :
( ( ! [SY2775: $i] :
( ( hBOOL @ ( hAPP @ SV249 @ SY2775 ) )
| ! [SY2776: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2776 @ SY2775 ) )
| ! [SY2777: $i] :
~ ( c_lessequals @ SY2776 @ SV249 @ ( tc_fun @ SY2777 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2364,plain,
! [SV250: $i] :
( ( ! [SY2778: $i] :
( ( c_Wellfounded_Owf @ SV250 @ SY2778 )
| ! [SY2779: $i] :
( ~ ( c_lessequals @ SV250 @ SY2779 @ ( tc_fun @ ( tc_prod @ SY2778 @ SY2778 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2779 @ SY2778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2365,plain,
! [SV251: $i] :
( ( ~ ( class_Orderings_Oorder @ SV251 )
| ! [SY2780: $i] : ( c_lessequals @ SY2780 @ SY2780 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2366,plain,
! [SV252: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV252 )
| ! [SY2781: $i] : ( c_lessequals @ SY2781 @ SY2781 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2367,plain,
! [SV253: $i] :
( ( ! [SY2782: $i] :
( ( c_Relation_Oantisym @ SV253 @ SY2782 )
| ! [SY2783: $i] :
( ~ ( c_Relation_Oantisym @ SY2783 @ SY2782 )
| ~ ( c_lessequals @ SV253 @ SY2783 @ ( tc_fun @ ( tc_prod @ SY2782 @ SY2782 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2368,plain,
! [SV254: $i] :
( ( ! [SY2784: $i] :
( ( hBOOL @ ( hAPP @ SV254 @ SY2784 ) )
| ! [SY2785: $i] :
( ! [SY2786: $i] :
~ ( c_lessequals @ SY2785 @ SV254 @ ( tc_fun @ SY2786 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY2785 @ SY2784 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2369,plain,
! [SV255: $i] :
( ( ! [SY2787: $i] :
( ( c_Wellfounded_Oacyclic @ SV255 @ SY2787 )
| ! [SY2788: $i] :
( ~ ( c_lessequals @ SV255 @ SY2788 @ ( tc_fun @ ( tc_prod @ SY2787 @ SY2787 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY2788 @ SY2787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2370,plain,
! [SV256: $i] :
( ( ! [SY2789: $i,SY2790: $i] :
( ( c_Relation_Osingle__valued @ SV256 @ SY2789 @ SY2790 )
| ! [SY2791: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2791 @ SY2789 @ SY2790 )
| ~ ( c_lessequals @ SV256 @ SY2791 @ ( tc_fun @ ( tc_prod @ SY2789 @ SY2790 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2371,plain,
! [SV257: $i] :
( ( ! [SY2792: $i,SY2793: $i,SY2794: $i,SY2795: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SY2792 @ ( tc_fun @ SY2793 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2794 @ SY2795 @ ( tc_fun @ SY2793 @ tc_bool ) ) @ ( tc_fun @ SY2793 @ tc_bool ) )
| ~ ( c_lessequals @ SY2792 @ SY2795 @ ( tc_fun @ SY2793 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SY2794 @ ( tc_fun @ SY2793 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2372,plain,
! [SV258: $i] :
( ( ! [SY2796: $i] : ( c_in @ SV258 @ ( c_Set_Oinsert @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2796 @ tc_bool ) ) @ SY2796 ) @ SY2796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2373,plain,
! [SV259: $i] :
( ( ! [SY2797: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV259 @ SY2797 ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ SV259 @ SY2797 ) @ ( c_COMBK @ ( c_Relation_OField @ SV259 @ SY2797 ) @ ( tc_fun @ SY2797 @ tc_bool ) @ SY2797 ) @ SY2797 @ SY2797 ) @ ( tc_fun @ ( tc_prod @ SY2797 @ SY2797 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2374,plain,
! [SV260: $i] :
( ( ! [SY2798: $i,SY2799: $i,SY2800: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SY2798 @ SY2799 ) @ ( c_Relation_ODomain @ SY2800 @ SY2798 @ SY2799 ) @ ( tc_fun @ SY2798 @ tc_bool ) )
| ~ ( c_lessequals @ SV260 @ SY2800 @ ( tc_fun @ ( tc_prod @ SY2798 @ SY2799 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2375,plain,
! [SV261: $i] :
( ( ! [SY2801: $i,SY2802: $i] :
( ( SV261
= ( c_Set_Oinsert @ SY2801 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2802 @ tc_bool ) ) @ SY2802 ) )
| ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2802 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SY2801 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2802 @ tc_bool ) ) @ SY2802 ) @ ( tc_fun @ SY2802 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2376,plain,
! [SV262: $i] :
( ( ! [SY2803: $i,SY2804: $i] :
( ( c_Product__Type_OSigma @ SV262 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2803 @ tc_bool ) ) @ ( tc_fun @ SY2803 @ tc_bool ) @ SY2804 ) @ SY2804 @ SY2803 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2804 @ SY2803 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2377,plain,
! [SV263: $i] :
( ( ! [SY2805: $i,SY2806: $i,SY2807: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SY2805 @ ( tc_fun @ SY2806 @ tc_bool ) ) @ SY2807 ) )
| ~ ( hBOOL @ ( hAPP @ SY2805 @ SY2807 ) )
| ~ ( hBOOL @ ( hAPP @ SV263 @ SY2807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2378,plain,
! [SV264: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SY2808 @ SY2809 ) @ ( c_Set_Oinsert @ SV264 @ SY2810 @ SY2809 ) @ ( tc_fun @ SY2809 @ tc_bool ) )
| ~ ( c_lessequals @ SY2808 @ SY2810 @ ( tc_fun @ SY2809 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2379,plain,
! [SV265: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV265 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV265 @ tc_bool ) ) @ ( tc_fun @ SV265 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV265 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2380,plain,
! [SV266: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV266 @ SV266 ) @ tc_bool ) ) @ SV266 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV266 @ SV266 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2381,plain,
! [SV267: $i] :
( ( ! [SY2811: $i,SY2812: $i] :
( ( ( c_Relation_ORange @ SV267 @ SY2811 @ SY2812 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2812 @ tc_bool ) ) )
| ( SV267
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2811 @ SY2812 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2382,plain,
! [SV268: $i] :
( ( ! [SY2813: $i,SY2814: $i,SY2815: $i,SY2816: $i,SY2817: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SY2813 @ SY2814 @ SY2815 ) @ ( c_Relation_OImage @ SY2816 @ SY2817 @ SY2814 @ SY2815 ) @ ( tc_fun @ SY2815 @ tc_bool ) )
| ~ ( c_lessequals @ SY2813 @ SY2817 @ ( tc_fun @ SY2814 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SY2816 @ ( tc_fun @ ( tc_prod @ SY2814 @ SY2815 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2383,plain,
! [SV269: $i] :
( ( ! [SY2818: $i,SY2819: $i] :
( ( c_lessequals @ SV269 @ ( c_Product__Type_OSigma @ SY2818 @ ( c_COMBK @ SY2818 @ ( tc_fun @ SY2819 @ tc_bool ) @ SY2819 ) @ SY2819 @ SY2819 ) @ ( tc_fun @ ( tc_prod @ SY2819 @ SY2819 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY2818 @ SV269 @ SY2819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2384,plain,
! [SV270: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV270 )
| ! [SY2820: $i,SY2821: $i] :
( ( c_lessequals @ SY2820 @ SY2821 @ SV270 )
| ( c_lessequals @ SY2821 @ SY2820 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2385,plain,
! [SV271: $i] :
( ( ! [SY2822: $i,SY2823: $i] :
( ( hBOOL @ ( hAPP @ SV271 @ SY2822 ) )
| ! [SY2824: $i,SY2825: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SY2823 @ SY2824 @ SY2825 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SY2823 @ SY2824 @ SY2825 ) @ SY2825 @ SY2825 ) @ SY2824 @ ( tc_prod @ SY2825 @ SY2825 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SY2823 ) )
| ~ ( c_in @ ( c_Pair @ SY2822 @ SY2823 @ SY2825 @ SY2825 ) @ ( c_Transitive__Closure_Ortrancl @ SY2824 @ SY2825 ) @ ( tc_prod @ SY2825 @ SY2825 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2386,plain,
! [SV272: $i] :
( ( ! [SY2826: $i,SY2827: $i] :
( ( hBOOL @ ( hAPP @ SV272 @ SY2826 ) )
| ! [SY2828: $i,SY2829: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SY2827 @ SY2828 @ SY2829 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SY2827 @ SY2828 @ SY2829 ) @ SY2829 @ SY2829 ) @ SY2828 @ ( tc_prod @ SY2829 @ SY2829 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SY2827 ) )
| ~ ( c_in @ ( c_Pair @ SY2827 @ SY2826 @ SY2829 @ SY2829 ) @ ( c_Transitive__Closure_Ortrancl @ SY2828 @ SY2829 ) @ ( tc_prod @ SY2829 @ SY2829 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2387,plain,
! [SV273: $i] :
( ( ! [SY2830: $i,SY2831: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SY2830 ) @ SY2831 @ ( tc_fun @ ( tc_prod @ SY2830 @ SY2830 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SY2830 ) @ SY2831 @ ( tc_fun @ ( tc_prod @ SY2830 @ SY2830 ) @ tc_bool ) ) @ SV273 @ SY2830 @ SY2830 @ SY2830 ) @ SY2831 @ ( tc_fun @ ( tc_prod @ SY2830 @ SY2830 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SY2830 ) @ SY2831 @ ( tc_fun @ ( tc_prod @ SY2830 @ SY2830 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2388,plain,
! [SV274: $i] :
( ( ! [SY2832: $i,SY2833: $i,SY2834: $i] :
( ( SV274 = SY2832 )
| ! [SY2835: $i,SY2836: $i] :
( ~ ( c_in @ ( c_Pair @ SY2833 @ SY2832 @ SY2834 @ SY2835 ) @ SY2836 @ ( tc_prod @ SY2834 @ SY2835 ) )
| ~ ( c_in @ ( c_Pair @ SY2833 @ SV274 @ SY2834 @ SY2835 ) @ SY2836 @ ( tc_prod @ SY2834 @ SY2835 ) )
| ~ ( c_Relation_Osingle__valued @ SY2836 @ SY2834 @ SY2835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2389,plain,
! [SV275: $i] :
( ( ! [SY2837: $i,SY2838: $i,SY2839: $i,SY2840: $i] :
( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SY2837 @ ( tc_fun @ SY2838 @ tc_bool ) @ SY2839 ) @ SY2839 @ SY2838 )
!= ( c_Product__Type_OSigma @ SY2840 @ ( c_COMBK @ SY2837 @ ( tc_fun @ SY2838 @ tc_bool ) @ SY2839 ) @ SY2839 @ SY2838 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2837 @ SY2838 )
| ( SV275 = SY2840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2390,plain,
! [SV276: $i] :
( ( ! [SY2842: $i,SY2843: $i,SY2844: $i] :
( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2842 @ SY2843 @ ( tc_fun @ ( tc_prod @ SY2844 @ SY2844 ) @ tc_bool ) ) @ SY2844 ) @ ( tc_prod @ SY2844 @ SY2844 ) )
| ~ ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SY2842 @ SY2844 ) @ ( tc_prod @ SY2844 @ SY2844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2391,plain,
! [SV277: $i] :
( ( ! [SY2845: $i,SY2846: $i,SY2847: $i] :
( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2845 @ SY2846 @ ( tc_fun @ ( tc_prod @ SY2847 @ SY2847 ) @ tc_bool ) ) @ SY2847 ) @ ( tc_prod @ SY2847 @ SY2847 ) )
| ~ ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SY2846 @ SY2847 ) @ ( tc_prod @ SY2847 @ SY2847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2392,plain,
! [SV278: $i] :
( ( ! [SY2848: $i,SY2849: $i] :
( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SY2848 @ SY2849 ) @ ( tc_prod @ SY2849 @ SY2849 ) )
| ! [SY2850: $i] :
( ~ ( c_lessequals @ SY2850 @ SY2848 @ ( tc_fun @ ( tc_prod @ SY2849 @ SY2849 ) @ tc_bool ) )
| ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SY2850 @ SY2849 ) @ ( tc_prod @ SY2849 @ SY2849 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2393,plain,
! [SV279: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV279 @ SV279 @ SY2851 @ SY2851 @ SY2851 ) @ ( c_Relation_Orel__comp @ SY2852 @ SV279 @ SY2851 @ SY2851 @ SY2851 ) @ ( tc_fun @ ( tc_prod @ SY2851 @ SY2851 ) @ tc_bool ) ) @ SY2852 @ ( tc_fun @ ( tc_prod @ SY2851 @ SY2851 ) @ tc_bool ) ) @ SY2851 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV279 @ SY2852 @ ( tc_fun @ ( tc_prod @ SY2851 @ SY2851 ) @ tc_bool ) ) @ SY2851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2394,plain,
! [SV280: $i] :
( ( ! [SY2853: $i,SY2854: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV280 @ SY2853 @ ( tc_fun @ ( tc_prod @ SY2854 @ SY2854 ) @ tc_bool ) ) @ SY2854 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV280 @ SV280 @ SY2854 @ SY2854 @ SY2854 ) @ ( c_Relation_Orel__comp @ SY2853 @ SV280 @ SY2854 @ SY2854 @ SY2854 ) @ ( tc_fun @ ( tc_prod @ SY2854 @ SY2854 ) @ tc_bool ) ) @ SY2853 @ ( tc_fun @ ( tc_prod @ SY2854 @ SY2854 ) @ tc_bool ) ) @ SY2854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2395,plain,
! [SV281: $i] :
( ( ! [SY2855: $i] :
( ( ( c_Relation_Orel__comp @ SV281 @ SV281 @ SY2855 @ SY2855 @ SY2855 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2855 @ SY2855 ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ SV281 @ SY2855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2396,plain,
! [SV282: $i] :
( ( ! [SY2856: $i] :
( ( c_Transitive__Closure_Otrancl @ SV282 @ SY2856 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV282 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV282 @ SY2856 ) @ SV282 @ SY2856 @ SY2856 @ SY2856 ) @ ( tc_fun @ ( tc_prod @ SY2856 @ SY2856 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2397,plain,
! [SV283: $i] :
( ( ! [SY2857: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV283 @ SY2857 ) @ ( c_Relation_OId @ SY2857 ) @ ( tc_fun @ ( tc_prod @ SY2857 @ SY2857 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV283 @ SY2857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2398,plain,
! [SV284: $i] :
( ( ! [SY2858: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ ( c_Relation_OId @ SY2858 ) @ ( tc_fun @ ( tc_prod @ SY2858 @ SY2858 ) @ tc_bool ) ) @ SY2858 )
= ( c_Transitive__Closure_Ortrancl @ SV284 @ SY2858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2399,plain,
! [SV285: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV285 @ SV285 ) @ tc_bool ) ) @ SV285 )
= ( c_Relation_OId @ SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2400,plain,
! [SV286: $i] :
( ( ! [SY2859: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SY2859 ) @ SY2859 )
| ~ ( c_Wellfounded_Oacyclic @ SV286 @ SY2859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2401,plain,
! [SV287: $i] :
( ( ! [SY2860: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ ( hAPP @ ( c_Relation_Oconverse @ SY2860 @ SY2860 ) @ SV287 ) @ ( tc_fun @ ( tc_prod @ SY2860 @ SY2860 ) @ tc_bool ) ) @ SY2860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2402,plain,
! [SV288: $i] :
( ( ! [SY2861: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV288 @ ( hAPP @ ( c_Relation_Oconverse @ SY2861 @ SY2861 ) @ SV288 ) @ ( tc_fun @ ( tc_prod @ SY2861 @ SY2861 ) @ tc_bool ) ) @ SY2861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2403,plain,
! [SV289: $i] :
( ( ! [SY2862: $i,SY2863: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV289 @ SY2862 ) @ SY2863 @ SY2862 @ SY2862 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV289 @ SY2863 @ ( tc_fun @ SY2862 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2404,plain,
! [SV290: $i] :
( ( ! [SY2864: $i] :
( ( c_Relation_Oantisym @ SV290 @ SY2864 )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV290 @ ( c_Relation_OId @ SY2864 ) @ ( tc_fun @ ( tc_prod @ SY2864 @ SY2864 ) @ tc_bool ) ) @ SY2864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2405,plain,
! [SV291: $i] :
( ( ! [SY2865: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV291 @ ( c_Relation_OId @ SY2865 ) @ ( tc_fun @ ( tc_prod @ SY2865 @ SY2865 ) @ tc_bool ) ) @ SY2865 )
| ~ ( c_Relation_Oantisym @ SV291 @ SY2865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2406,plain,
! [SV292: $i] :
( ( ! [SY2866: $i,SY2867: $i,SY2868: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2866 @ tc_bool ) ) @ SY2866 ) @ SY2867 @ SY2866 )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY2868 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2866 @ tc_bool ) ) @ SY2866 ) @ SY2867 @ SY2866 ) )
| ! [SY2869: $i] :
( ~ ( c_in @ SY2868 @ SY2869 @ SY2866 )
| ~ ( c_in @ SV292 @ SY2869 @ SY2866 )
| ~ ( c_Equiv__Relations_Oequiv @ SY2869 @ SY2867 @ SY2866 )
| ( c_in @ ( c_Pair @ SV292 @ SY2868 @ SY2866 @ SY2866 ) @ SY2867 @ ( tc_prod @ SY2866 @ SY2866 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2407,plain,
! [SV293: $i] :
( ( ! [SY2870: $i,SY2871: $i] :
( ( c_in @ SV293 @ SY2870 @ SY2871 )
| ! [SY2872: $i] :
( ( SV293 = SY2872 )
| ! [SY2873: $i] :
( ~ ( c_lessequals @ SY2873 @ ( c_Product__Type_OSigma @ SY2870 @ ( c_COMBK @ SY2870 @ ( tc_fun @ SY2871 @ tc_bool ) @ SY2871 ) @ SY2871 @ SY2871 ) @ ( tc_fun @ ( tc_prod @ SY2871 @ SY2871 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SY2872 @ SY2871 @ SY2871 ) @ ( c_Transitive__Closure_Ortrancl @ SY2873 @ SY2871 ) @ ( tc_prod @ SY2871 @ SY2871 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2408,plain,
! [SV294: $i] :
( ( ! [SY2874: $i,SY2875: $i,SY2876: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SY2874 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2875 @ tc_bool ) ) @ SY2875 ) @ SY2875 @ SY2875 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SY2876 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2875 @ tc_bool ) ) @ SY2875 ) @ SY2875 @ SY2875 ) @ ( tc_fun @ SY2875 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SY2874 @ SY2876 @ SY2875 @ SY2875 ) @ SV294 @ ( tc_prod @ SY2875 @ SY2875 ) )
| ! [SY2877: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY2877 @ SV294 @ SY2875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2409,plain,
! [SV295: $i] :
( ( ! [SY2878: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SY2878 ) @ ( c_Transitive__Closure_Ortrancl @ SY2878 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
| ! [SY2879: $i] :
~ ( c_in @ ( c_Pair @ SY2879 @ SY2879 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SY2878 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2410,plain,
! [SV296: $i] :
( ( ! [SY2880: $i,SY2881: $i,SY2882: $i] :
( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SY2880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2881 @ tc_bool ) ) @ SY2881 ) @ SY2881 @ SY2881 )
!= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SY2882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2881 @ tc_bool ) ) @ SY2881 ) @ SY2881 @ SY2881 ) )
| ~ ( c_in @ SY2882 @ ( c_Relation_OField @ SV296 @ SY2881 ) @ SY2881 )
| ~ ( c_in @ SY2880 @ ( c_Relation_OField @ SV296 @ SY2881 ) @ SY2881 )
| ~ ( c_Relation_Oantisym @ SV296 @ SY2881 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SY2881 ) @ SV296 @ SY2881 )
| ( SY2880 = SY2882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2411,plain,
! [SV297: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV297 )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV297 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV297 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV297 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV297 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2412,plain,
! [SV298: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV298 )
| ! [SY2883: $i] : ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV298 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV298 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV298 ) @ SY2883 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2413,plain,
! [SV299: $i] :
( ( ! [SY2884: $i,SY2885: $i,SY2886: $i,SY2887: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SY2884 @ SY2885 @ SY2886 @ SY2887 ) @ SV299 @ SY2886 )
| ~ ( c_in @ SY2885 @ ( c_Product__Type_OSigma @ SV299 @ SY2884 @ SY2886 @ SY2887 ) @ ( tc_prod @ SY2886 @ SY2887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2414,plain,
! [SV300: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SY2888 @ SY2889 @ SY2890 ) @ SY2888 @ SY2890 @ SY2890 ) @ SY2889 @ ( tc_prod @ SY2890 @ SY2890 ) )
| ( SV300 = SY2888 )
| ~ ( c_in @ ( c_Pair @ SV300 @ SY2888 @ SY2890 @ SY2890 ) @ ( c_Transitive__Closure_Ortrancl @ SY2889 @ SY2890 ) @ ( tc_prod @ SY2890 @ SY2890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2415,plain,
! [SV301: $i] :
( ( ! [SY2891: $i,SY2892: $i,SY2893: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SY2891 @ SY2892 @ SY2893 ) @ SY2892 @ SY2893 @ SY2893 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY2893 ) @ ( tc_prod @ SY2893 @ SY2893 ) )
| ( SY2891 = SY2892 )
| ~ ( c_in @ ( c_Pair @ SY2891 @ SY2892 @ SY2893 @ SY2893 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY2893 ) @ ( tc_prod @ SY2893 @ SY2893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2416,plain,
! [SV302: $i] :
( ( ! [SY2894: $i,SY2895: $i,SY2896: $i] :
( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SY2894 @ SV302 @ SY2895 @ SY2896 ) @ SY2896 @ SY2896 ) @ SY2894 @ ( tc_prod @ SY2896 @ SY2896 ) )
| ( SV302 = SY2895 )
| ~ ( c_in @ ( c_Pair @ SV302 @ SY2895 @ SY2896 @ SY2896 ) @ ( c_Transitive__Closure_Ortrancl @ SY2894 @ SY2896 ) @ ( tc_prod @ SY2896 @ SY2896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2417,plain,
! [SV303: $i] :
( ( ! [SY2897: $i,SY2898: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ SY2897 ) )
| ! [SY2899: $i,SY2900: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SY2898 @ SY2899 @ SY2900 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SY2898 ) )
| ~ ( c_in @ ( c_Pair @ SY2897 @ SY2898 @ SY2900 @ SY2900 ) @ ( c_Transitive__Closure_Ortrancl @ SY2899 @ SY2900 ) @ ( tc_prod @ SY2900 @ SY2900 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2418,plain,
! [SV304: $i] :
( ( ! [SY2901: $i,SY2902: $i] :
( ( hBOOL @ ( hAPP @ SV304 @ SY2901 ) )
| ! [SY2903: $i,SY2904: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SY2902 @ SY2903 @ SY2904 ) @ SY2902 @ SY2904 @ SY2904 ) @ ( c_Transitive__Closure_Ortrancl @ SY2903 @ SY2904 ) @ ( tc_prod @ SY2904 @ SY2904 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SY2902 ) )
| ~ ( c_in @ ( c_Pair @ SY2901 @ SY2902 @ SY2904 @ SY2904 ) @ ( c_Transitive__Closure_Ortrancl @ SY2903 @ SY2904 ) @ ( tc_prod @ SY2904 @ SY2904 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2419,plain,
! [SV305: $i] :
( ( ! [SY2905: $i,SY2906: $i] :
( ( hBOOL @ ( hAPP @ SV305 @ SY2905 ) )
| ! [SY2907: $i,SY2908: $i] :
( ( c_in @ ( c_Pair @ SY2906 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SY2906 @ SY2907 @ SY2908 ) @ SY2908 @ SY2908 ) @ ( c_Transitive__Closure_Ortrancl @ SY2907 @ SY2908 ) @ ( tc_prod @ SY2908 @ SY2908 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SY2906 ) )
| ~ ( c_in @ ( c_Pair @ SY2906 @ SY2905 @ SY2908 @ SY2908 ) @ ( c_Transitive__Closure_Ortrancl @ SY2907 @ SY2908 ) @ ( tc_prod @ SY2908 @ SY2908 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2420,plain,
! [SV306: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ( hBOOL @ ( hAPP @ SV306 @ SY2909 ) )
| ! [SY2911: $i,SY2912: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SY2910 @ SY2911 @ SY2912 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SY2910 ) )
| ~ ( c_in @ ( c_Pair @ SY2910 @ SY2909 @ SY2912 @ SY2912 ) @ ( c_Transitive__Closure_Ortrancl @ SY2911 @ SY2912 ) @ ( tc_prod @ SY2912 @ SY2912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2421,plain,
! [SV307: $i] :
( ( ! [SY2913: $i,SY2914: $i,SY2915: $i] :
( ( c_in @ ( c_Pair @ SV307 @ SY2913 @ SY2914 @ SY2914 ) @ ( c_Transitive__Closure_Ortrancl @ SY2915 @ SY2914 ) @ ( tc_prod @ SY2914 @ SY2914 ) )
| ( c_in @ ( c_Pair @ SY2913 @ SV307 @ SY2914 @ SY2914 ) @ ( c_Transitive__Closure_Ortrancl @ SY2915 @ SY2914 ) @ ( tc_prod @ SY2914 @ SY2914 ) )
| ! [SY2916: $i] :
( ~ ( c_in @ ( c_Pair @ SY2916 @ SV307 @ SY2914 @ SY2914 ) @ ( c_Transitive__Closure_Ortrancl @ SY2915 @ SY2914 ) @ ( tc_prod @ SY2914 @ SY2914 ) )
| ~ ( c_in @ ( c_Pair @ SY2916 @ SY2913 @ SY2914 @ SY2914 ) @ ( c_Transitive__Closure_Ortrancl @ SY2915 @ SY2914 ) @ ( tc_prod @ SY2914 @ SY2914 ) )
| ~ ( c_Relation_Osingle__valued @ SY2915 @ SY2914 @ SY2914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2422,plain,
! [SV308: $i] :
( ( ! [SY2917: $i,SY2918: $i] :
( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SY2917 @ SY2918 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY2918 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SY2917 = SV308 )
| ~ ( c_in @ ( c_Pair @ SV308 @ SY2917 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY2918 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2423,plain,
! [SV309: $i] :
( ( ! [SY2919: $i,SY2920: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ SY2919 ) )
| ! [SY2921: $i,SY2922: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SY2920 @ SY2921 @ SY2922 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SY2920 ) )
| ~ ( c_in @ ( c_Pair @ SY2920 @ SY2919 @ SY2922 @ SY2922 ) @ ( c_Transitive__Closure_Ortrancl @ SY2921 @ SY2922 ) @ ( tc_prod @ SY2922 @ SY2922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2424,plain,
! [SV310: $i] :
( ( ! [SY2923: $i,SY2924: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SY2923 @ SY2924 ) @ SY2923 @ t_a @ t_a ) @ SY2924 @ ( tc_prod @ t_a @ t_a ) )
| ( SY2923 = SV310 )
| ~ ( c_in @ ( c_Pair @ SV310 @ SY2923 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY2924 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2425,plain,
! [SV311: $i] :
( ( ! [SY2925: $i,SY2926: $i] :
( ( hBOOL @ ( hAPP @ SV311 @ SY2925 ) )
| ! [SY2927: $i,SY2928: $i] :
( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SY2926 @ SY2927 @ SY2928 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SY2926 ) )
| ~ ( c_in @ ( c_Pair @ SY2925 @ SY2926 @ SY2928 @ SY2928 ) @ ( c_Transitive__Closure_Ortrancl @ SY2927 @ SY2928 ) @ ( tc_prod @ SY2928 @ SY2928 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2426,plain,
! [SV312: $i] :
( ( ! [SY2929: $i,SY2930: $i,SY2931: $i] :
( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SY2929 @ SY2930 @ SY2931 ) @ SY2931 @ SY2931 ) @ ( c_Transitive__Closure_Ortrancl @ SY2930 @ SY2931 ) @ ( tc_prod @ SY2931 @ SY2931 ) )
| ( SV312 = SY2929 )
| ~ ( c_in @ ( c_Pair @ SV312 @ SY2929 @ SY2931 @ SY2931 ) @ ( c_Transitive__Closure_Ortrancl @ SY2930 @ SY2931 ) @ ( tc_prod @ SY2931 @ SY2931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2427,plain,
! [SV313: $i] :
( ( ! [SY2932: $i,SY2933: $i] :
( ( hBOOL @ ( hAPP @ SV313 @ SY2932 ) )
| ( hBOOL @ ( hAPP @ SV313 @ SY2933 ) )
| ! [SY2934: $i,SY2935: $i] :
( ~ ( c_in @ ( c_Pair @ SY2933 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SY2934 @ SY2935 ) @ SY2935 @ SY2935 ) @ SY2934 @ ( tc_prod @ SY2935 @ SY2935 ) )
| ~ ( c_Wellfounded_Owf @ SY2934 @ SY2935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2428,plain,
! [SV314: $i] :
( ( ! [SY2936: $i,SY2937: $i] :
( ( hBOOL @ ( hAPP @ SV314 @ SY2936 ) )
| ( hBOOL @ ( hAPP @ SV314 @ SY2937 ) )
| ! [SY2938: $i,SY2939: $i] :
( ~ ( c_in @ ( c_Pair @ SY2937 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SY2938 @ SY2939 ) @ SY2939 @ SY2939 ) @ SY2938 @ ( tc_prod @ SY2939 @ SY2939 ) )
| ~ ( c_Wellfounded_Owf @ SY2938 @ SY2939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2429,plain,
! [SV315: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ( hBOOL @ ( hAPP @ SV315 @ SY2940 ) )
| ( hBOOL @ ( hAPP @ SV315 @ SY2941 ) )
| ! [SY2942: $i,SY2943: $i] :
( ~ ( c_in @ ( c_Pair @ SY2941 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SY2942 @ SY2943 ) @ SY2943 @ SY2943 ) @ SY2942 @ ( tc_prod @ SY2943 @ SY2943 ) )
| ~ ( c_Wellfounded_Owf @ SY2942 @ SY2943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2430,plain,
! [SV316: $i] :
( ( ! [SY2944: $i,SY2945: $i] :
( ( hBOOL @ ( hAPP @ SV316 @ SY2944 ) )
| ( hBOOL @ ( hAPP @ SV316 @ SY2945 ) )
| ! [SY2946: $i,SY2947: $i] :
( ~ ( c_in @ ( c_Pair @ SY2945 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SY2946 @ SY2947 ) @ SY2947 @ SY2947 ) @ SY2946 @ ( tc_prod @ SY2947 @ SY2947 ) )
| ~ ( c_Wellfounded_Owf @ SY2946 @ SY2947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2431,plain,
! [SV317: $i] :
( ( ! [SY2948: $i,SY2949: $i] :
( ~ ( c_in @ ( c_Pair @ SV317 @ SV317 @ SY2948 @ SY2948 ) @ SY2949 @ ( tc_prod @ SY2948 @ SY2948 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY2949 @ SY2948 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY2949 @ SY2948 ) @ SY2948 @ SY2948 ) @ ( c_Transitive__Closure_Otrancl @ SY2949 @ SY2948 ) @ ( tc_prod @ SY2948 @ SY2948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2432,plain,
! [SV318: $i] :
( ( ! [SY2950: $i,SY2951: $i,SY2952: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SY2950 @ SY2951 @ SY2952 ) @ SY2951 @ SY2952 @ SY2952 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY2952 ) @ ( tc_prod @ SY2952 @ SY2952 ) )
| ( c_in @ ( c_Pair @ SY2950 @ SY2951 @ SY2952 @ SY2952 ) @ SV318 @ ( tc_prod @ SY2952 @ SY2952 ) )
| ~ ( c_in @ ( c_Pair @ SY2950 @ SY2951 @ SY2952 @ SY2952 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY2952 ) @ ( tc_prod @ SY2952 @ SY2952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2433,plain,
! [SV319: $i] :
( ( ! [SY2953: $i,SY2954: $i] :
( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SY2953 @ SY2954 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY2954 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV319 @ SY2953 @ t_a @ t_a ) @ SY2954 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SY2953 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY2954 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2434,plain,
! [SV320: $i] :
( ( ! [SY2955: $i,SY2956: $i] :
( ~ ( c_in @ ( c_Pair @ SV320 @ SV320 @ SY2955 @ SY2955 ) @ ( c_Transitive__Closure_Otrancl @ SY2956 @ SY2955 ) @ ( tc_prod @ SY2955 @ SY2955 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY2956 @ SY2955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2435,plain,
! [SV321: $i] :
( ( ! [SY2957: $i,SY2958: $i,SY2959: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SY2957 @ SY2958 @ SY2959 ) @ SY2957 @ SY2959 @ SY2959 ) @ SY2958 @ ( tc_prod @ SY2959 @ SY2959 ) )
| ( c_in @ ( c_Pair @ SV321 @ SY2957 @ SY2959 @ SY2959 ) @ SY2958 @ ( tc_prod @ SY2959 @ SY2959 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SY2957 @ SY2959 @ SY2959 ) @ ( c_Transitive__Closure_Otrancl @ SY2958 @ SY2959 ) @ ( tc_prod @ SY2959 @ SY2959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2436,plain,
! [SV322: $i] :
( ( ! [SY2960: $i,SY2961: $i,SY2962: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SY2960 @ SY2961 @ SY2962 ) @ SY2962 @ SY2962 ) @ ( c_Transitive__Closure_Otrancl @ SY2961 @ SY2962 ) @ ( tc_prod @ SY2962 @ SY2962 ) )
| ( c_in @ ( c_Pair @ SV322 @ SY2960 @ SY2962 @ SY2962 ) @ SY2961 @ ( tc_prod @ SY2962 @ SY2962 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SY2960 @ SY2962 @ SY2962 ) @ ( c_Transitive__Closure_Otrancl @ SY2961 @ SY2962 ) @ ( tc_prod @ SY2962 @ SY2962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2437,plain,
! [SV323: $i] :
( ( ! [SY2963: $i,SY2964: $i,SY2965: $i] :
( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SY2963 @ SV323 @ SY2964 @ SY2965 ) @ SY2965 @ SY2965 ) @ SY2963 @ ( tc_prod @ SY2965 @ SY2965 ) )
| ( c_in @ ( c_Pair @ SV323 @ SY2964 @ SY2965 @ SY2965 ) @ SY2963 @ ( tc_prod @ SY2965 @ SY2965 ) )
| ~ ( c_in @ ( c_Pair @ SV323 @ SY2964 @ SY2965 @ SY2965 ) @ ( c_Transitive__Closure_Otrancl @ SY2963 @ SY2965 ) @ ( tc_prod @ SY2965 @ SY2965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2438,plain,
! [SV324: $i] :
( ( ! [SY2966: $i,SY2967: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SY2966 @ SY2967 ) @ SY2966 @ t_a @ t_a ) @ SY2967 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV324 @ SY2966 @ t_a @ t_a ) @ SY2967 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV324 @ SY2966 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY2967 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2439,plain,
! [SV325: $i] :
( ( ! [SY2968: $i,SY2969: $i,SY2970: $i] :
( ( c_in @ ( c_Pair @ SV325 @ SY2968 @ SY2969 @ SY2969 ) @ SY2970 @ ( tc_prod @ SY2969 @ SY2969 ) )
| ! [SY2971: $i] :
( ~ ( c_in @ SY2968 @ SY2971 @ SY2969 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY2970 @ ( c_Set_Oinsert @ SY2968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2969 @ tc_bool ) ) @ SY2969 ) @ SY2969 @ SY2969 ) @ ( c_Relation_OImage @ SY2970 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2969 @ tc_bool ) ) @ SY2969 ) @ SY2969 @ SY2969 ) @ ( tc_fun @ SY2969 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY2971 @ SY2970 @ SY2969 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2440,plain,
! [SV326: $i] :
( ( ! [SY2972: $i,SY2973: $i,SY2974: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SY2972 @ SY2973 @ SY2973 ) @ SY2974 @ ( tc_prod @ SY2973 @ SY2973 ) )
| ! [SY2975: $i] :
~ ( c_in @ SY2975 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY2974 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2973 @ tc_bool ) ) @ SY2973 ) @ SY2973 @ SY2973 ) @ ( c_Relation_OImage @ SY2974 @ ( c_Set_Oinsert @ SY2972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2973 @ tc_bool ) ) @ SY2973 ) @ SY2973 @ SY2973 ) @ ( tc_fun @ SY2973 @ tc_bool ) ) @ SY2973 )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ SY2974 @ SY2973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2441,plain,
! [SV327: $i] :
( ( ! [SY2977: $i,SY2978: $i,SY2979: $i,SY2980: $i,SY2981: $i,SY2982: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SY2977 @ SY2978 @ SY2979 @ SY2980 @ SY2981 @ SY2982 ) @ SY2977 @ SY2982 @ SY2981 ) @ SY2979 @ ( tc_prod @ SY2982 @ SY2981 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SY2977 @ SY2980 @ SY2981 ) @ ( c_Relation_Orel__comp @ SY2978 @ SY2979 @ SY2980 @ SY2982 @ SY2981 ) @ ( tc_prod @ SY2980 @ SY2981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2442,plain,
! [SV328: $i] :
( ( ! [SY2983: $i,SY2984: $i,SY2985: $i,SY2986: $i,SY2987: $i,SY2988: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SY2983 @ SY2984 @ SY2985 @ SY2986 @ SY2987 @ SY2988 ) @ SY2986 @ SY2988 ) @ SY2984 @ ( tc_prod @ SY2986 @ SY2988 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SY2983 @ SY2986 @ SY2987 ) @ ( c_Relation_Orel__comp @ SY2984 @ SY2985 @ SY2986 @ SY2988 @ SY2987 ) @ ( tc_prod @ SY2986 @ SY2987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2443,plain,
! [SV329: $i] :
( ( ! [SY2989: $i,SY2990: $i,SY2991: $i,SY2992: $i] :
( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SY2989 @ SY2990 @ SY2991 @ SY2992 ) @ ( tc_fun @ SY2991 @ SY2992 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2989 @ SY2990 @ SV329 @ SY2991 @ SY2992 ) @ SY2989 @ SY2991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2444,plain,
! [SV330: $i] :
( ( ! [SY2993: $i,SY2994: $i,SY2995: $i,SY2996: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SY2993 @ SY2994 @ SY2995 @ SY2996 ) @ ( tc_fun @ SY2995 @ SY2996 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY2993 @ SY2994 @ SV330 @ SY2995 @ SY2996 ) @ SY2993 @ SY2995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2445,plain,
! [SV331: $i] :
( ( ! [SY2997: $i,SY2998: $i,SY2999: $i,SY3000: $i] :
( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SY2997 @ SY2998 @ SY2999 @ SY3000 ) @ ( tc_fun @ SY2999 @ SY3000 ) )
| ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2997 @ SY2998 @ SV331 @ SY2999 @ SY3000 ) ) @ ( hAPP @ SY2998 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2997 @ SY2998 @ SV331 @ SY2999 @ SY3000 ) ) @ SY3000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2446,plain,
! [SV332: $i] :
( ( ! [SY3001: $i,SY3002: $i,SY3003: $i] :
( ( c_in @ ( hAPP @ SV332 @ SY3001 ) @ SY3002 @ SY3003 )
| ! [SY3004: $i,SY3005: $i] :
( ~ ( c_in @ SY3001 @ SY3004 @ SY3005 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY3004 @ ( c_COMBK @ SY3002 @ ( tc_fun @ SY3003 @ tc_bool ) @ SY3005 ) @ SY3005 @ SY3003 ) @ ( tc_fun @ SY3005 @ SY3003 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2447,plain,
! [SV333: $i] :
( ( ! [SY3006: $i,SY3007: $i,SY3008: $i,SY3009: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SY3006 @ SY3007 @ SY3008 @ SY3009 ) @ ( tc_fun @ SY3008 @ SY3009 ) )
| ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY3006 @ SY3007 @ SV333 @ SY3008 @ SY3009 ) ) @ ( hAPP @ SY3007 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY3006 @ SY3007 @ SV333 @ SY3008 @ SY3009 ) ) @ SY3009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2448,plain,
! [SV334: $i] :
( ( ! [SY3010: $i] :
( ( SV334
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SY3010 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SY3010 ) @ SY3010 @ SY3010 ) )
| ~ ( c_in @ SV334 @ ( c_Relation_OId @ SY3010 ) @ ( tc_prod @ SY3010 @ SY3010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2449,plain,
! [SV335: $i] :
( ( ! [SY3011: $i] :
( ( c_Wellfounded_Owf @ SV335 @ SY3011 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV335 @ SY3011 ) @ ( c_Wellfounded_Oacc @ SV335 @ SY3011 ) @ SY3011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2450,plain,
! [SV336: $i] :
( ( ! [SY3012: $i] :
( ( c_Wellfounded_Owf @ SV336 @ SY3012 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV336 @ SY3012 ) @ ( c_Wellfounded_Oacc @ SV336 @ SY3012 ) @ SY3012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2451,plain,
! [SV337: $i] :
( ( ! [SY3013: $i,SY3014: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV337 @ SY3013 @ SY3014 ) @ SV337 @ SY3014 )
| ~ ( c_in @ SY3013 @ ( c_Relation_OId__on @ SV337 @ SY3014 ) @ ( tc_prod @ SY3014 @ SY3014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2452,plain,
! [SV338: $i] :
( ( ! [SY3015: $i,SY3016: $i] :
( ( SV338
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY3015 @ SV338 @ SY3016 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY3015 @ SV338 @ SY3016 ) @ SY3016 @ SY3016 ) )
| ~ ( c_in @ SV338 @ ( c_Relation_OId__on @ SY3015 @ SY3016 ) @ ( tc_prod @ SY3016 @ SY3016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2453,plain,
! [SV339: $i] :
( ( ! [SY3017: $i,SY3018: $i,SY3019: $i,SY3020: $i,SY3021: $i] :
( ( ( c_Recdef_Ocut @ SV339 @ SY3017 @ SY3018 @ SY3019 @ SY3020 )
= ( c_Recdef_Ocut @ SY3021 @ SY3017 @ SY3018 @ SY3019 @ SY3020 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SY3021 @ SY3017 @ SY3018 @ SY3019 @ SY3020 ) @ SY3018 @ SY3019 @ SY3019 ) @ SY3017 @ ( tc_prod @ SY3019 @ SY3019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2454,plain,
! [SV340: $i] :
( ( ! [SY3022: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV340 @ SY3022 ) @ ( c_Relation_OId @ SY3022 ) @ ( tc_fun @ ( tc_prod @ SY3022 @ SY3022 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV340 @ SY3022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2455,plain,
! [SV341: $i] :
( ( ! [SY3023: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV341 @ ( c_Relation_OId @ SY3023 ) @ ( tc_fun @ ( tc_prod @ SY3023 @ SY3023 ) @ tc_bool ) ) @ SY3023 )
= ( c_Transitive__Closure_Ortrancl @ SV341 @ SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2456,plain,
! [SV342: $i] :
( ( ! [SY3024: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV342 @ SY3024 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV342 @ SY3024 ) @ ( c_Relation_OId @ SY3024 ) @ ( tc_fun @ ( tc_prod @ SY3024 @ SY3024 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2457,plain,
! [SV343: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV343 )
| ! [SY3025: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV343 ) @ SY3025 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV343 ) @ SY3025 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2458,plain,
! [SV344: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV344 )
| ! [SY3026: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV344 ) @ SY3026 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV344 ) @ SY3026 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2459,plain,
! [SV345: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV345 )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2460,plain,
! [SV346: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV346 )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2461,plain,
! [SV347: $i] :
( ( ! [SY3027: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV347 @ SY3027 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SY3027 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV347 @ SY3027 ) @ SV347 @ SY3027 @ SY3027 @ SY3027 ) @ ( tc_fun @ ( tc_prod @ SY3027 @ SY3027 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2462,plain,
! [SV348: $i] :
( ( ! [SY3028: $i] :
( ( c_lessequals @ SV348 @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SY3028 @ SY3028 ) @ SV348 ) @ SV348 @ SY3028 @ SY3028 @ SY3028 ) @ ( tc_fun @ ( tc_prod @ SY3028 @ SY3028 ) @ tc_bool ) )
| ! [SY3029: $i] :
~ ( c_Relation_Orefl__on @ SY3029 @ SV348 @ SY3028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2463,plain,
! [SV349: $i] :
( ( ! [SY3030: $i,SY3031: $i,SY3032: $i] :
( ~ ( c_in @ ( c_Pair @ SV349 @ SY3030 @ SY3031 @ SY3031 ) @ ( c_Transitive__Closure_Ortrancl @ SY3032 @ SY3031 ) @ ( tc_prod @ SY3031 @ SY3031 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY3030 @ SV349 @ SY3031 @ SY3031 ) @ SY3032 @ ( tc_prod @ SY3031 @ SY3031 ) ) @ SY3031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2464,plain,
! [SV350: $i] :
( ( ! [SY3033: $i,SY3034: $i,SY3035: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SY3033 @ SY3034 @ SY3034 ) @ SY3035 @ ( tc_prod @ SY3034 @ SY3034 ) ) @ SY3034 )
| ( c_in @ ( c_Pair @ SY3033 @ SV350 @ SY3034 @ SY3034 ) @ ( c_Transitive__Closure_Ortrancl @ SY3035 @ SY3034 ) @ ( tc_prod @ SY3034 @ SY3034 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY3035 @ SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2465,plain,
! [SV351: $i] :
( ( ! [SY3036: $i,SY3037: $i] :
( ( c_in @ SV351 @ ( c_Relation_OImage @ SY3036 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3037 @ tc_bool ) ) @ SY3037 ) @ SY3037 @ SY3037 ) @ SY3037 )
| ! [SY3038: $i] :
( ~ ( c_in @ SV351 @ SY3038 @ SY3037 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3038 @ SY3036 @ SY3037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2466,plain,
! [SV352: $i] :
( ( ! [SY3039: $i,SY3040: $i,SY3041: $i,SY3042: $i] :
( ( c_in @ ( c_Pair @ SV352 @ SY3039 @ SY3040 @ SY3041 ) @ SY3042 @ ( tc_prod @ SY3040 @ SY3041 ) )
| ~ ( c_in @ SY3039 @ ( c_Relation_OImage @ SY3042 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3040 @ tc_bool ) ) @ SY3040 ) @ SY3040 @ SY3041 ) @ SY3041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2467,plain,
! [SV353: $i] :
( ( ! [SY3043: $i,SY3044: $i,SY3045: $i,SY3046: $i] :
( ( c_in @ SV353 @ ( c_Relation_OImage @ SY3043 @ ( c_Set_Oinsert @ SY3044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3045 @ tc_bool ) ) @ SY3045 ) @ SY3045 @ SY3046 ) @ SY3046 )
| ~ ( c_in @ ( c_Pair @ SY3044 @ SV353 @ SY3045 @ SY3046 ) @ SY3043 @ ( tc_prod @ SY3045 @ SY3046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2468,plain,
! [SV354: $i] :
( ( ! [SY3047: $i,SY3048: $i,SY3049: $i] :
( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SY3047 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3048 @ tc_bool ) ) @ SY3048 ) @ SY3048 @ SY3048 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SY3049 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3048 @ tc_bool ) ) @ SY3048 ) @ SY3048 @ SY3048 ) )
| ~ ( c_in @ ( c_Pair @ SY3047 @ SY3049 @ SY3048 @ SY3048 ) @ SV354 @ ( tc_prod @ SY3048 @ SY3048 ) )
| ! [SY3050: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3050 @ SV354 @ SY3048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2469,plain,
! [SV355: $i] :
( ( ! [SY3051: $i,SY3052: $i,SY3053: $i] :
( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SY3051 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3052 @ tc_bool ) ) @ SY3052 ) @ SY3052 @ SY3052 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SY3053 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3052 @ tc_bool ) ) @ SY3052 ) @ SY3052 @ SY3052 ) )
| ~ ( c_in @ ( c_Pair @ SY3051 @ SY3053 @ SY3052 @ SY3052 ) @ SV355 @ ( tc_prod @ SY3052 @ SY3052 ) )
| ! [SY3054: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3054 @ SV355 @ SY3052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2470,plain,
! [SV356: $i] :
( ( ! [SY3055: $i,SY3056: $i,SY3057: $i] :
( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SY3055 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3056 @ tc_bool ) ) @ SY3056 ) @ SY3056 @ SY3056 )
!= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SY3057 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3056 @ tc_bool ) ) @ SY3056 ) @ SY3056 @ SY3056 ) )
| ( c_in @ ( c_Pair @ SY3055 @ SY3057 @ SY3056 @ SY3056 ) @ SV356 @ ( tc_prod @ SY3056 @ SY3056 ) )
| ! [SY3058: $i] :
( ~ ( c_in @ SY3057 @ SY3058 @ SY3056 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3058 @ SV356 @ SY3056 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2471,plain,
! [SV357: $i] :
( ( ! [SY3059: $i,SY3060: $i,SY3061: $i] :
( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SY3059 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3060 @ tc_bool ) ) @ SY3060 ) @ SY3060 @ SY3060 )
!= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SY3061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3060 @ tc_bool ) ) @ SY3060 ) @ SY3060 @ SY3060 ) )
| ! [SY3062: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY3062 @ SV357 @ SY3060 )
| ( c_in @ ( c_Pair @ SY3059 @ SY3061 @ SY3060 @ SY3060 ) @ SV357 @ ( tc_prod @ SY3060 @ SY3060 ) )
| ~ ( c_in @ SY3061 @ SY3062 @ SY3060 )
| ~ ( c_in @ SY3059 @ SY3062 @ SY3060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2472,plain,
! [SV358: $i] :
( ( ! [SY3063: $i,SY3064: $i,SY3065: $i] :
( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SY3063 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3064 @ tc_bool ) ) @ SY3064 ) @ SY3064 @ SY3064 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SY3065 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3064 @ tc_bool ) ) @ SY3064 ) @ SY3064 @ SY3064 ) )
| ~ ( c_in @ ( c_Pair @ SY3063 @ SY3065 @ SY3064 @ SY3064 ) @ SV358 @ ( tc_prod @ SY3064 @ SY3064 ) )
| ! [SY3066: $i] :
( ~ ( c_in @ SY3065 @ SY3066 @ SY3064 )
| ~ ( c_in @ SY3063 @ SY3066 @ SY3064 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3066 @ SV358 @ SY3064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2473,plain,
! [SV359: $i] :
( ( ! [SY3067: $i,SY3068: $i,SY3069: $i] :
( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SY3067 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3068 @ tc_bool ) ) @ SY3068 ) @ SY3068 @ SY3068 )
!= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SY3069 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3068 @ tc_bool ) ) @ SY3068 ) @ SY3068 @ SY3068 ) )
| ! [SY3070: $i] :
( ~ ( c_in @ SY3069 @ SY3070 @ SY3068 )
| ~ ( c_in @ SY3067 @ SY3070 @ SY3068 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3070 @ SV359 @ SY3068 )
| ( c_in @ ( c_Pair @ SY3067 @ SY3069 @ SY3068 @ SY3068 ) @ SV359 @ ( tc_prod @ SY3068 @ SY3068 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2474,plain,
! [SV360: $i] :
( ( ! [SY3071: $i,SY3072: $i,SY3073: $i] :
( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SY3071 @ SV360 @ SY3072 @ SY3073 ) @ SY3073 @ SY3073 ) @ SY3071 @ ( tc_prod @ SY3073 @ SY3073 ) )
| ~ ( c_in @ ( c_Pair @ SV360 @ SY3072 @ SY3073 @ SY3073 ) @ ( c_Transitive__Closure_Otrancl @ SY3071 @ SY3073 ) @ ( tc_prod @ SY3073 @ SY3073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2475,plain,
! [SV361: $i] :
( ( ! [SY3074: $i,SY3075: $i,SY3076: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SY3074 @ SY3075 @ SY3076 ) @ SY3075 @ SY3076 @ SY3076 ) @ SV361 @ ( tc_prod @ SY3076 @ SY3076 ) )
| ~ ( c_in @ ( c_Pair @ SY3074 @ SY3075 @ SY3076 @ SY3076 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SY3076 ) @ ( tc_prod @ SY3076 @ SY3076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2476,plain,
! [SV362: $i] :
( ( ! [SY3077: $i] :
( ( hBOOL @ ( hAPP @ SV362 @ SY3077 ) )
| ! [SY3078: $i,SY3079: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SY3078 @ SY3079 ) @ ( c_Wellfounded_Oacc @ SY3078 @ SY3079 ) @ SY3079 )
| ~ ( c_in @ SY3077 @ ( c_Wellfounded_Oacc @ SY3078 @ SY3079 ) @ SY3079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2477,plain,
! [SV363: $i] :
( ( ! [SY3080: $i,SY3081: $i] :
( ( c_in @ SV363 @ ( c_Wellfounded_Oacc @ SY3080 @ SY3081 ) @ SY3081 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY3080 @ SV363 @ SY3081 ) @ ( c_Wellfounded_Oacc @ SY3080 @ SY3081 ) @ SY3081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2478,plain,
! [SV364: $i] :
( ( ! [SY3082: $i] :
( ( hBOOL @ ( hAPP @ SV364 @ SY3082 ) )
| ! [SY3083: $i] :
( ~ ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SY3083 ) ) )
| ~ ( c_in @ SY3082 @ ( c_Wellfounded_Oacc @ SY3083 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2479,plain,
! [SV365: $i] :
( ( ! [SY3084: $i] :
( ( hBOOL @ ( hAPP @ SV365 @ SY3084 ) )
| ! [SY3085: $i,SY3086: $i] :
( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SY3085 @ SY3086 ) ) )
| ~ ( c_in @ SY3084 @ ( c_Wellfounded_Oacc @ SY3085 @ SY3086 ) @ SY3086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2480,plain,
! [SV366: $i] :
( ( ! [SY3087: $i,SY3088: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV366 @ SY3087 @ SY3088 ) @ ( c_Wellfounded_Oacc @ SV366 @ SY3088 ) @ SY3088 )
| ( c_in @ SY3087 @ ( c_Wellfounded_Oacc @ SV366 @ SY3088 ) @ SY3088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2481,plain,
! [SV367: $i] :
( ( ! [SY3089: $i] :
( ( hBOOL @ ( hAPP @ SV367 @ SY3089 ) )
| ! [SY3090: $i,SY3091: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SY3090 @ SY3091 ) @ ( c_Wellfounded_Oacc @ SY3090 @ SY3091 ) @ SY3091 )
| ~ ( c_in @ SY3089 @ ( c_Wellfounded_Oacc @ SY3090 @ SY3091 ) @ SY3091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2482,plain,
! [SV368: $i] :
( ( ! [SY3092: $i] :
( ( hBOOL @ ( hAPP @ SV368 @ SY3092 ) )
| ! [SY3093: $i] :
( ~ ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SY3093 ) ) )
| ~ ( c_in @ SY3092 @ ( c_Wellfounded_Oacc @ SY3093 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2483,plain,
! [SV369: $i] :
( ( ! [SY3094: $i] :
( ( hBOOL @ ( hAPP @ SV369 @ SY3094 ) )
| ! [SY3095: $i,SY3096: $i] :
( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SY3095 @ SY3096 ) ) )
| ~ ( c_in @ SY3094 @ ( c_Wellfounded_Oacc @ SY3095 @ SY3096 ) @ SY3096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2484,plain,
! [SV370: $i] :
( ( ! [SY3097: $i,SY3098: $i,SY3099: $i,SY3100: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SY3097 @ SY3098 @ SY3099 @ SY3100 ) @ SV370 @ SY3099 )
| ~ ( c_in @ SY3097 @ ( c_Relation_OImage @ SY3098 @ SV370 @ SY3099 @ SY3100 ) @ SY3100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2485,plain,
! [SV371: $i] :
( ( ! [SY3101: $i,SY3102: $i,SY3103: $i,SY3104: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SY3101 @ SY3102 @ SY3103 @ SY3104 ) @ SV371 @ SY3103 )
| ~ ( c_in @ SY3101 @ ( c_Relation_OImage @ SY3102 @ SV371 @ SY3103 @ SY3104 ) @ SY3104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2486,plain,
! [SV372: $i] :
( ( ! [SY3105: $i] :
( ( c_Wellfounded_Owf @ SV372 @ SY3105 )
| ! [SY3106: $i,SY3107: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY3106 @ SY3107 @ SY3105 @ SY3105 ) @ SV372 @ ( tc_prod @ SY3105 @ SY3105 ) ) @ SY3105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2487,plain,
! [SV373: $i] :
( ( ! [SY3108: $i,SY3109: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SY3108 @ SY3109 ) @ SV373 @ SY3109 )
| ! [SY3110: $i] :
~ ( c_in @ SY3110 @ SV373 @ SY3109 )
| ~ ( c_Wellfounded_Owf @ SY3108 @ SY3109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2488,plain,
! [SV374: $i] :
( ( ! [SY3111: $i,SY3112: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SY3111 @ SY3112 ) @ SV374 @ SY3112 )
| ! [SY3113: $i] :
~ ( c_in @ SY3113 @ SV374 @ SY3112 )
| ~ ( c_Wellfounded_Owf @ SY3111 @ SY3112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2489,plain,
! [SV375: $i] :
( ( ! [SY3114: $i,SY3115: $i,SY3116: $i,SY3117: $i,SY3118: $i,SY3119: $i,SY3120: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SY3114 ) @ SY3115 )
= ( hAPP @ ( hAPP @ SV375 @ SY3116 ) @ SY3117 ) )
| ~ ( c_in @ ( c_Pair @ SY3115 @ SY3117 @ SY3118 @ SY3118 ) @ SY3119 @ ( tc_prod @ SY3118 @ SY3118 ) )
| ! [SY3121: $i] :
( ~ ( c_in @ ( c_Pair @ SY3114 @ SY3116 @ SY3120 @ SY3120 ) @ SY3121 @ ( tc_prod @ SY3120 @ SY3120 ) )
| ! [SY3122: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY3121 @ SY3119 @ SV375 @ SY3120 @ SY3118 @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2490,plain,
! [SV376: $i] :
( ( ! [SY3123: $i] :
( ( ( hAPP @ SV376 @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SY3123 ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SY3123 ) @ SY3123 ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ SV376 @ SY3123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2491,plain,
! [SV377: $i] :
( ( ! [SY3124: $i,SY3125: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV377 @ SY3124 @ SY3125 ) @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2492,plain,
! [SV378: $i] :
( ( ! [SY3126: $i,SY3127: $i,SY3128: $i,SY3129: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV378 @ SY3126 @ SY3127 @ SY3128 ) @ SY3129 @ ( tc_prod @ SY3127 @ SY3128 ) ) @ SY3127 @ SY3128 )
= ( c_Set_Oinsert @ SV378 @ ( c_Relation_ODomain @ SY3129 @ SY3127 @ SY3128 ) @ SY3127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2493,plain,
! [SV379: $i] :
( ( ! [SY3130: $i] :
( ( hBOOL @ ( hAPP @ SV379 @ SY3130 ) )
| ! [SY3131: $i] :
( ( SY3131 = SY3130 )
| ! [SY3132: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3131 @ SV379 @ SY3132 ) @ SY3130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2494,plain,
! [SV380: $i] :
( ( ! [SY3133: $i,SY3134: $i] :
( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV380 @ SY3133 @ SY3134 ) @ SY3134 )
= ( c_Set_Oinsert @ SV380 @ SY3133 @ SY3134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2495,plain,
! [SV381: $i] :
( ( ! [SY3135: $i,SY3136: $i,SY3137: $i] :
( ( c_Set_Oinsert @ SV381 @ ( c_Set_Oinsert @ SY3135 @ SY3136 @ SY3137 ) @ SY3137 )
= ( c_Set_Oinsert @ SY3135 @ ( c_Set_Oinsert @ SV381 @ SY3136 @ SY3137 ) @ SY3137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2496,plain,
! [SV382: $i] :
( ( ! [SY3138: $i,SY3139: $i,SY3140: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SY3138 @ SY3139 ) @ SY3140 ) )
| ~ ( hBOOL @ ( hAPP @ SY3138 @ SY3140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2497,plain,
! [SV383: $i] :
( ( ! [SY3141: $i,SY3142: $i,SY3143: $i,SY3144: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV383 @ SY3141 @ SY3142 @ SY3143 ) @ SY3144 @ ( tc_prod @ SY3142 @ SY3143 ) ) @ SY3142 @ SY3143 )
= ( c_Set_Oinsert @ SY3141 @ ( c_Relation_ORange @ SY3144 @ SY3142 @ SY3143 ) @ SY3143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2498,plain,
! [SV384: $i] :
( ( ! [SY3145: $i,SY3146: $i,SY3147: $i] :
( ( c_in @ SV384 @ ( c_Set_Oinsert @ SY3145 @ SY3146 @ SY3147 ) @ SY3147 )
| ~ ( c_in @ SV384 @ SY3146 @ SY3147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2499,plain,
! [SV385: $i] :
( ( ! [SY3148: $i,SY3149: $i,SY3150: $i] :
( ( c_in @ SV385 @ ( c_Set_Oinsert @ SY3148 @ SY3149 @ SY3150 ) @ SY3150 )
| ~ ( c_in @ SV385 @ SY3149 @ SY3150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2500,plain,
! [SV386: $i] :
( ( ! [SY3151: $i,SY3152: $i] :
( ( c_in @ SV386 @ SY3151 @ SY3152 )
| ! [SY3153: $i] :
( ( SV386 = SY3153 )
| ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SY3153 @ SY3151 @ SY3152 ) @ SY3152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2501,plain,
! [SV387: $i] :
( ( ! [SY3154: $i,SY3155: $i] : ( c_in @ SV387 @ ( c_Set_Oinsert @ SV387 @ SY3154 @ SY3155 ) @ SY3155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2502,plain,
! [SV388: $i] :
( ( ! [SY3156: $i,SY3157: $i] : ( c_in @ SV388 @ ( c_Set_Oinsert @ SV388 @ SY3156 @ SY3157 ) @ SY3157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2503,plain,
! [SV389: $i] :
( ( ! [SY3158: $i,SY3159: $i] : ( c_in @ SV389 @ ( c_Set_Oinsert @ SV389 @ SY3158 @ SY3159 ) @ SY3159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2504,plain,
! [SV390: $i] :
( ( ! [SY3160: $i,SY3161: $i,SY3162: $i] :
( ( ( c_Set_Oinsert @ SV390 @ SY3160 @ SY3161 )
!= ( c_Set_Oinsert @ SV390 @ SY3162 @ SY3161 ) )
| ( c_in @ SV390 @ SY3162 @ SY3161 )
| ( SY3160 = SY3162 )
| ( c_in @ SV390 @ SY3160 @ SY3161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2505,plain,
! [SV391: $i] :
( ( ! [SY3163: $i,SY3164: $i] :
( ( ( c_Set_Oinsert @ SV391 @ SY3163 @ SY3164 )
= SY3163 )
| ~ ( c_in @ SV391 @ SY3163 @ SY3164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2506,plain,
! [SV392: $i] :
( ( ! [SY3165: $i,SY3166: $i,SY3167: $i,SY3168: $i,SY3169: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SY3165 @ SY3166 ) @ SY3167 @ SY3168 )
| ! [SY3170: $i] :
( ~ ( c_in @ SY3166 @ SY3169 @ SY3170 )
| ! [SY3171: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY3171 @ SV392 @ SY3165 @ SY3170 @ SY3167 @ SY3168 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3169 @ SY3171 @ SY3170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2507,plain,
! [SV393: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV393 )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV393 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2508,plain,
! [SV394: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV394 )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV394 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2509,plain,
! [SV395: $i] :
( ( ! [SY3172: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ SV395 @ SY3172 )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV395 @ SY3172 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2510,plain,
! [SV396: $i] :
( ( ! [SY3173: $i] :
( ( c_Nitpick_Orefl_H @ SV396 @ SY3173 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SY3173 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SY3173 ) @ SY3173 @ SY3173 ) @ SV396 @ ( tc_prod @ SY3173 @ SY3173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2511,plain,
! [SV397: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV397 )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV397 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2512,plain,
! [SV398: $i] :
( ( ! [SY3174: $i,SY3175: $i] :
( ~ ( c_in @ SV398 @ SY3174 @ SY3175 )
| ! [SY3176: $i] :
( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SY3174 @ SY3176 @ SY3175 ) @ SY3175 @ SY3175 ) @ SY3176 @ ( tc_prod @ SY3175 @ SY3175 ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ SY3174 @ SY3175 )
| ~ ( c_Wellfounded_Owf @ SY3176 @ SY3175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2513,plain,
! [SV399: $i] :
( ( ! [SY3178: $i,SY3179: $i] :
( ~ ( c_in @ SV399 @ SY3178 @ SY3179 )
| ! [SY3180: $i] :
( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SY3178 @ SY3180 @ SY3179 ) @ SY3179 @ SY3179 ) @ SY3180 @ ( tc_prod @ SY3179 @ SY3179 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY3178 @ SY3179 )
| ~ ( c_Wellfounded_Owf @ SY3180 @ SY3179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2514,plain,
! [SV400: $i] :
( ( ! [SY3182: $i,SY3183: $i,SY3184: $i,SY3185: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SY3182 @ SY3183 @ SY3184 @ SY3185 ) @ SY3182 @ SY3184 @ SY3185 ) @ SY3183 @ ( tc_prod @ SY3184 @ SY3185 ) )
| ~ ( c_in @ SY3182 @ ( c_Relation_OImage @ SY3183 @ SV400 @ SY3184 @ SY3185 ) @ SY3185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2515,plain,
! [SV401: $i] :
( ( ! [SY3186: $i,SY3187: $i,SY3188: $i,SY3189: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SY3186 @ SY3187 @ SY3188 @ SY3189 ) @ SY3186 @ SY3188 @ SY3189 ) @ SY3187 @ ( tc_prod @ SY3188 @ SY3189 ) )
| ~ ( c_in @ SY3186 @ ( c_Relation_OImage @ SY3187 @ SV401 @ SY3188 @ SY3189 ) @ SY3189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2516,plain,
! [SV402: $i] :
( ( ! [SY3190: $i,SY3191: $i,SY3192: $i] :
( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SY3190 @ SY3191 @ SY3192 ) @ SY3191 @ SY3192 ) @ SY3190 @ ( tc_prod @ SY3191 @ SY3192 ) )
| ~ ( c_in @ SV402 @ ( c_Relation_ODomain @ SY3190 @ SY3191 @ SY3192 ) @ SY3191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2517,plain,
! [SV403: $i] :
( ( ! [SY3193: $i,SY3194: $i,SY3195: $i] :
( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SY3193 @ SY3194 @ SY3195 ) @ SY3194 @ SY3195 ) @ SY3193 @ ( tc_prod @ SY3194 @ SY3195 ) )
| ~ ( c_in @ SV403 @ ( c_Relation_ODomain @ SY3193 @ SY3194 @ SY3195 ) @ SY3194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2518,plain,
! [SV404: $i] :
( ( ! [SY3196: $i] :
( ( hBOOL @ ( hAPP @ SV404 @ SY3196 ) )
| ! [SY3197: $i,SY3198: $i] :
( ( c_in @ SY3197 @ ( c_Wellfounded_Oacc @ SY3198 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY3197 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SY3198 ) @ t_a @ t_a ) @ SY3198 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3196 @ ( c_Wellfounded_Oacc @ SY3198 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2519,plain,
! [SV405: $i] :
( ( ! [SY3199: $i] :
( ( hBOOL @ ( hAPP @ SV405 @ SY3199 ) )
| ! [SY3200: $i,SY3201: $i] :
( ( c_in @ SY3200 @ ( c_Wellfounded_Oacc @ SY3201 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY3200 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SY3201 ) @ t_a @ t_a ) @ SY3201 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3199 @ ( c_Wellfounded_Oacc @ SY3201 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2520,plain,
! [SV406: $i] :
( ( ! [SY3202: $i,SY3203: $i] :
( ( c_in @ SV406 @ ( c_Wellfounded_Oacc @ SY3202 @ SY3203 ) @ SY3203 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY3202 @ SV406 @ SY3203 ) @ SV406 @ SY3203 @ SY3203 ) @ SY3202 @ ( tc_prod @ SY3203 @ SY3203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2521,plain,
! [SV407: $i] :
( ( ! [SY3204: $i,SY3205: $i] :
( ( hBOOL @ ( hAPP @ SV407 @ SY3204 ) )
| ( hBOOL @ ( hAPP @ SV407 @ SY3205 ) )
| ! [SY3206: $i,SY3207: $i] :
( ~ ( c_in @ ( c_Pair @ SY3205 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SY3206 @ SY3207 ) @ SY3207 @ SY3207 ) @ SY3206 @ ( tc_prod @ SY3207 @ SY3207 ) )
| ~ ( c_in @ SY3204 @ ( c_Wellfounded_Oacc @ SY3206 @ SY3207 ) @ SY3207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2522,plain,
! [SV408: $i] :
( ( ! [SY3208: $i] :
( ( hBOOL @ ( hAPP @ SV408 @ SY3208 ) )
| ! [SY3209: $i] :
( ( hBOOL @ ( hAPP @ SV408 @ SY3209 ) )
| ! [SY3210: $i] :
( ~ ( c_in @ ( c_Pair @ SY3209 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SY3210 ) @ t_a @ t_a ) @ SY3210 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3208 @ ( c_Wellfounded_Oacc @ SY3210 @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2523,plain,
! [SV409: $i] :
( ( ! [SY3211: $i] :
( ( hBOOL @ ( hAPP @ SV409 @ SY3211 ) )
| ! [SY3212: $i] :
( ( hBOOL @ ( hAPP @ SV409 @ SY3212 ) )
| ! [SY3213: $i] :
( ~ ( c_in @ ( c_Pair @ SY3212 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SY3213 ) @ t_a @ t_a ) @ SY3213 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3211 @ ( c_Wellfounded_Oacc @ SY3213 @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2524,plain,
! [SV410: $i] :
( ( ! [SY3214: $i,SY3215: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ SY3214 ) )
| ( hBOOL @ ( hAPP @ SV410 @ SY3215 ) )
| ! [SY3216: $i,SY3217: $i] :
( ~ ( c_in @ ( c_Pair @ SY3215 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SY3216 @ SY3217 ) @ SY3217 @ SY3217 ) @ SY3216 @ ( tc_prod @ SY3217 @ SY3217 ) )
| ~ ( c_in @ SY3214 @ ( c_Wellfounded_Oacc @ SY3216 @ SY3217 ) @ SY3217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2525,plain,
! [SV411: $i] :
( ( ! [SY3218: $i,SY3219: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV411 @ SY3218 @ SY3219 ) @ SY3218 @ SY3219 @ SY3219 ) @ SV411 @ ( tc_prod @ SY3219 @ SY3219 ) )
| ( c_in @ SY3218 @ ( c_Wellfounded_Oacc @ SV411 @ SY3219 ) @ SY3219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2526,plain,
! [SV412: $i] :
( ( ! [SY3220: $i,SY3221: $i,SY3222: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SY3220 @ SY3221 @ SY3221 ) @ SY3222 @ ( tc_prod @ SY3221 @ SY3221 ) ) @ SY3221 )
| ( c_in @ ( c_Pair @ SY3220 @ SV412 @ SY3221 @ SY3221 ) @ ( c_Transitive__Closure_Ortrancl @ SY3222 @ SY3221 ) @ ( tc_prod @ SY3221 @ SY3221 ) )
| ~ ( c_Wellfounded_Owf @ SY3222 @ SY3221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2527,plain,
! [SV413: $i] :
( ( ! [SY3223: $i,SY3224: $i,SY3225: $i] :
( ~ ( c_in @ ( c_Pair @ SV413 @ SY3223 @ SY3224 @ SY3224 ) @ ( c_Transitive__Closure_Ortrancl @ SY3225 @ SY3224 ) @ ( tc_prod @ SY3224 @ SY3224 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY3223 @ SV413 @ SY3224 @ SY3224 ) @ SY3225 @ ( tc_prod @ SY3224 @ SY3224 ) ) @ SY3224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2528,plain,
! [SV414: $i] :
( ( ! [SY3226: $i,SY3227: $i,SY3228: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SY3226 @ SY3227 @ SY3228 ) @ SV414 @ SY3228 @ SY3227 ) @ SY3226 @ ( tc_prod @ SY3228 @ SY3227 ) )
| ~ ( c_in @ SV414 @ ( c_Relation_ORange @ SY3226 @ SY3228 @ SY3227 ) @ SY3227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2529,plain,
! [SV415: $i] :
( ( ! [SY3229: $i,SY3230: $i,SY3231: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SY3229 @ SY3230 @ SY3231 ) @ SV415 @ SY3231 @ SY3230 ) @ SY3229 @ ( tc_prod @ SY3231 @ SY3230 ) )
| ~ ( c_in @ SV415 @ ( c_Relation_ORange @ SY3229 @ SY3231 @ SY3230 ) @ SY3230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2530,plain,
! [SV416: $i] :
( ( ! [SY3232: $i,SY3233: $i,SY3234: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SY3232 @ SY3233 @ SY3234 ) @ SY3233 @ SY3234 @ SY3234 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SY3234 ) @ ( tc_prod @ SY3234 @ SY3234 ) )
| ~ ( c_in @ ( c_Pair @ SY3232 @ SY3233 @ SY3234 @ SY3234 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SY3234 ) @ ( tc_prod @ SY3234 @ SY3234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2531,plain,
! [SV417: $i] :
( ( ! [SY3235: $i,SY3236: $i,SY3237: $i] :
( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SY3235 @ SV417 @ SY3236 @ SY3237 ) @ SY3237 @ SY3237 ) @ ( c_Transitive__Closure_Ortrancl @ SY3235 @ SY3237 ) @ ( tc_prod @ SY3237 @ SY3237 ) )
| ~ ( c_in @ ( c_Pair @ SV417 @ SY3236 @ SY3237 @ SY3237 ) @ ( c_Transitive__Closure_Otrancl @ SY3235 @ SY3237 ) @ ( tc_prod @ SY3237 @ SY3237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2532,plain,
! [SV418: $i] :
( ( ! [SY3238: $i,SY3239: $i,SY3240: $i] :
( ( c_in @ ( c_Pair @ SV418 @ SY3238 @ SY3239 @ SY3239 ) @ ( c_Transitive__Closure_Ortrancl @ SY3240 @ SY3239 ) @ ( tc_prod @ SY3239 @ SY3239 ) )
| ! [SY3241: $i] :
( ~ ( c_in @ ( c_Pair @ SY3241 @ SY3238 @ SY3239 @ SY3239 ) @ SY3240 @ ( tc_prod @ SY3239 @ SY3239 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SY3241 @ SY3239 @ SY3239 ) @ ( c_Transitive__Closure_Ortrancl @ SY3240 @ SY3239 ) @ ( tc_prod @ SY3239 @ SY3239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2533,plain,
! [SV419: $i] :
( ( ! [SY3242: $i,SY3243: $i,SY3244: $i] :
( ( c_in @ ( c_Pair @ SV419 @ SY3242 @ SY3243 @ SY3243 ) @ ( c_Transitive__Closure_Otrancl @ SY3244 @ SY3243 ) @ ( tc_prod @ SY3243 @ SY3243 ) )
| ! [SY3245: $i] :
( ~ ( c_in @ ( c_Pair @ SY3245 @ SY3242 @ SY3243 @ SY3243 ) @ ( c_Transitive__Closure_Otrancl @ SY3244 @ SY3243 ) @ ( tc_prod @ SY3243 @ SY3243 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SY3245 @ SY3243 @ SY3243 ) @ SY3244 @ ( tc_prod @ SY3243 @ SY3243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2534,plain,
! [SV420: $i] :
( ( ! [SY3246: $i,SY3247: $i,SY3248: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SY3246 @ SY3247 @ SY3247 ) @ ( c_Transitive__Closure_Otrancl @ SY3248 @ SY3247 ) @ ( tc_prod @ SY3247 @ SY3247 ) )
| ! [SY3249: $i] :
( ~ ( c_in @ ( c_Pair @ SY3249 @ SY3246 @ SY3247 @ SY3247 ) @ SY3248 @ ( tc_prod @ SY3247 @ SY3247 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SY3249 @ SY3247 @ SY3247 ) @ ( c_Transitive__Closure_Otrancl @ SY3248 @ SY3247 ) @ ( tc_prod @ SY3247 @ SY3247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2535,plain,
! [SV421: $i] :
( ( ! [SY3250: $i,SY3251: $i,SY3252: $i,SY3253: $i,SY3254: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SY3250 @ SY3251 @ SY3252 @ SY3253 ) @ SY3254 )
= ( hAPP @ SV421 @ SY3254 ) )
| ~ ( c_in @ ( c_Pair @ SY3254 @ SY3251 @ SY3252 @ SY3252 ) @ SY3250 @ ( tc_prod @ SY3252 @ SY3252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2536,plain,
! [SV422: $i] :
( ( ! [SY3255: $i,SY3256: $i,SY3257: $i,SY3258: $i,SY3259: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SY3255 @ SY3256 @ SY3257 @ SY3258 ) @ SY3259 )
= ( hAPP @ SV422 @ SY3259 ) )
| ~ ( c_in @ ( c_Pair @ SY3259 @ SY3256 @ SY3257 @ SY3257 ) @ SY3255 @ ( tc_prod @ SY3257 @ SY3257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2537,plain,
! [SV423: $i] :
( ( ! [SY3260: $i] :
( ( SV423 = SY3260 )
| ! [SY3261: $i,SY3262: $i] :
( ~ ( c_in @ ( c_Pair @ SV423 @ SY3260 @ SY3261 @ SY3261 ) @ ( c_Transitive__Closure_Ortrancl @ SY3262 @ SY3261 ) @ ( tc_prod @ SY3261 @ SY3261 ) )
| ( c_in @ SV423 @ ( c_Relation_ODomain @ SY3262 @ SY3261 @ SY3261 ) @ SY3261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2538,plain,
! [SV424: $i] :
( ( ! [SY3263: $i,SY3264: $i] :
( ( c_in @ SV424 @ ( c_Relation_ODomain @ SY3263 @ SY3264 @ SY3264 ) @ SY3264 )
| ( c_in @ ( c_Pair @ SV424 @ SV424 @ SY3264 @ SY3264 ) @ ( c_Transitive__Closure_Ortrancl @ SY3263 @ SY3264 ) @ ( tc_prod @ SY3264 @ SY3264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2539,plain,
! [SV425: $i] :
( ( ! [SY3265: $i,SY3266: $i] :
( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SY3265 @ SY3266 ) @ SY3266 )
| ! [SY3267: $i] :
( ~ ( c_in @ ( c_Pair @ SV425 @ SY3267 @ SY3266 @ SY3266 ) @ ( c_Transitive__Closure_Ortrancl @ SY3265 @ SY3266 ) @ ( tc_prod @ SY3266 @ SY3266 ) )
| ~ ( c_in @ SY3267 @ ( c_Wellfounded_Oacc @ SY3265 @ SY3266 ) @ SY3266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2540,plain,
! [SV426: $i] :
( ( ! [SY3268: $i,SY3269: $i] :
( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SY3268 @ SY3269 ) @ SY3269 )
| ! [SY3270: $i] :
( ~ ( c_in @ SY3270 @ ( c_Wellfounded_Oacc @ SY3268 @ SY3269 ) @ SY3269 )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY3270 @ SY3269 @ SY3269 ) @ ( c_Transitive__Closure_Ortrancl @ SY3268 @ SY3269 ) @ ( tc_prod @ SY3269 @ SY3269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2541,plain,
! [SV427: $i] :
( ( ! [SY3271: $i] :
( ( c_Relation_Osym @ SV427 @ SY3271 )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SY3271 @ SY3271 ) @ SV427 ) @ SY3271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2542,plain,
! [SV428: $i] :
( ( ! [SY3272: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV428 @ SV428 ) @ SY3272 ) @ SV428 )
| ~ ( c_Relation_Osym @ SY3272 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2543,plain,
! [SV429: $i] :
( ( ! [SY3273: $i,SY3274: $i] :
( ( c_Relation_Orefl__on @ SV429 @ SY3273 @ SY3274 )
| ~ ( c_Relation_Orefl__on @ SV429 @ ( hAPP @ ( c_Relation_Oconverse @ SY3274 @ SY3274 ) @ SY3273 ) @ SY3274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2544,plain,
! [SV430: $i] :
( ( ! [SY3275: $i,SY3276: $i] :
( ( c_Relation_Orefl__on @ SV430 @ ( hAPP @ ( c_Relation_Oconverse @ SY3275 @ SY3275 ) @ SY3276 ) @ SY3275 )
| ~ ( c_Relation_Orefl__on @ SV430 @ SY3276 @ SY3275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2545,plain,
! [SV431: $i] :
( ( ! [SY3277: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV431 @ SV431 ) @ SY3277 )
= SY3277 )
| ~ ( c_Relation_Osym @ SY3277 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2546,plain,
! [SV432: $i] :
( ( ! [SY3278: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV432 @ SV432 ) @ SY3278 )
!= SY3278 )
| ( c_Relation_Osym @ SY3278 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2547,plain,
! [SV433: $i] :
( ( ! [SY3279: $i,SY3280: $i,SY3281: $i,SY3282: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SY3279 ) @ ( c_Relation_Orel__comp @ SY3280 @ SY3281 @ SV433 @ SY3282 @ SY3279 ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SY3282 @ SY3279 ) @ SY3281 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SY3282 ) @ SY3280 ) @ SY3279 @ SY3282 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2548,plain,
! [SV434: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV434 @ SV434 ) @ ( c_Relation_OId @ SV434 ) )
= ( c_Relation_OId @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2549,plain,
! [SV435: $i] :
( ( ! [SY3283: $i,SY3284: $i,SY3285: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV435 @ SV435 ) @ ( c_Relation_Oinv__image @ SY3283 @ SY3284 @ SY3285 @ SV435 ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ SY3285 @ SY3285 ) @ SY3283 ) @ SY3284 @ SY3285 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2550,plain,
! [SV436: $i] :
( ( ! [SY3286: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV436 @ SV436 ) @ SY3286 ) @ SV436 )
= ( hAPP @ ( c_Relation_Oconverse @ SV436 @ SV436 ) @ ( c_Transitive__Closure_Otrancl @ SY3286 @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2551,plain,
! [SV437: $i] :
( ( ! [SY3287: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV437 @ SV437 ) @ ( c_Relation_OId__on @ SY3287 @ SV437 ) )
= ( c_Relation_OId__on @ SY3287 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2552,plain,
! [SV438: $i] :
( ( ! [SY3288: $i] :
( ( c_Relation_Oantisym @ SV438 @ SY3288 )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SY3288 @ SY3288 ) @ SV438 ) @ SY3288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2553,plain,
! [SV439: $i] :
( ( ! [SY3289: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV439 @ SV439 ) @ SY3289 ) @ SV439 )
| ~ ( c_Relation_Oantisym @ SY3289 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2554,plain,
! [SV440: $i] :
( ( ! [SY3290: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV440 @ SV440 ) @ SY3290 ) @ SV440 )
= ( hAPP @ ( c_Relation_Oconverse @ SV440 @ SV440 ) @ ( c_Transitive__Closure_Ortrancl @ SY3290 @ SV440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2555,plain,
! [SV441: $i] :
( ( ! [SY3291: $i,SY3292: $i] :
( ( c_Relation_Ototal__on @ SV441 @ SY3291 @ SY3292 )
| ~ ( c_Relation_Ototal__on @ SV441 @ ( hAPP @ ( c_Relation_Oconverse @ SY3292 @ SY3292 ) @ SY3291 ) @ SY3292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2556,plain,
! [SV442: $i] :
( ( ! [SY3293: $i,SY3294: $i] :
( ( c_Relation_Ototal__on @ SV442 @ ( hAPP @ ( c_Relation_Oconverse @ SY3293 @ SY3293 ) @ SY3294 ) @ SY3293 )
| ~ ( c_Relation_Ototal__on @ SV442 @ SY3294 @ SY3293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2557,plain,
! [SV443: $i] :
( ( ! [SY3295: $i,SY3296: $i] :
( ( c_in @ SV443 @ ( c_Transitive__Closure_Ortrancl @ SY3295 @ SY3296 ) @ ( tc_prod @ SY3296 @ SY3296 ) )
| ~ ( c_in @ SV443 @ SY3295 @ ( tc_prod @ SY3296 @ SY3296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2558,plain,
! [SV444: $i] :
( ( ! [SY3297: $i,SY3298: $i] :
( ( c_in @ SV444 @ ( c_Transitive__Closure_Otrancl @ SY3297 @ SY3298 ) @ ( tc_prod @ SY3298 @ SY3298 ) )
| ~ ( c_in @ SV444 @ SY3297 @ ( tc_prod @ SY3298 @ SY3298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2559,plain,
! [SV445: $i] :
( ( ! [SY3299: $i,SY3300: $i,SY3301: $i] :
( ( c_in @ ( c_Pair @ SV445 @ SY3299 @ SY3300 @ SY3300 ) @ ( c_Transitive__Closure_Otrancl @ SY3301 @ SY3300 ) @ ( tc_prod @ SY3300 @ SY3300 ) )
| ! [SY3302: $i] :
( ~ ( c_in @ ( c_Pair @ SY3302 @ SY3299 @ SY3300 @ SY3300 ) @ ( c_Transitive__Closure_Ortrancl @ SY3301 @ SY3300 ) @ ( tc_prod @ SY3300 @ SY3300 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SY3302 @ SY3300 @ SY3300 ) @ SY3301 @ ( tc_prod @ SY3300 @ SY3300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2560,plain,
! [SV446: $i] :
( ( ! [SY3303: $i,SY3304: $i,SY3305: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SY3303 @ SY3304 @ SY3304 ) @ ( c_Transitive__Closure_Otrancl @ SY3305 @ SY3304 ) @ ( tc_prod @ SY3304 @ SY3304 ) )
| ! [SY3306: $i] :
( ~ ( c_in @ ( c_Pair @ SY3306 @ SY3303 @ SY3304 @ SY3304 ) @ SY3305 @ ( tc_prod @ SY3304 @ SY3304 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY3306 @ SY3304 @ SY3304 ) @ ( c_Transitive__Closure_Ortrancl @ SY3305 @ SY3304 ) @ ( tc_prod @ SY3304 @ SY3304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2561,plain,
! [SV447: $i] :
( ( ! [SY3307: $i,SY3308: $i,SY3309: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SY3307 @ SY3308 @ SY3308 ) @ ( c_Transitive__Closure_Ortrancl @ SY3309 @ SY3308 ) @ ( tc_prod @ SY3308 @ SY3308 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY3307 @ SY3308 @ SY3308 ) @ ( c_Transitive__Closure_Otrancl @ SY3309 @ SY3308 ) @ ( tc_prod @ SY3308 @ SY3308 ) )
| ( SV447 = SY3307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2562,plain,
! [SV448: $i] :
( ( ! [SY3310: $i,SY3311: $i,SY3312: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SY3310 @ SY3311 @ SY3311 ) @ ( c_Transitive__Closure_Otrancl @ SY3312 @ SY3311 ) @ ( tc_prod @ SY3311 @ SY3311 ) )
| ( SV448 = SY3310 )
| ~ ( c_in @ ( c_Pair @ SV448 @ SY3310 @ SY3311 @ SY3311 ) @ ( c_Transitive__Closure_Ortrancl @ SY3312 @ SY3311 ) @ ( tc_prod @ SY3311 @ SY3311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2563,plain,
! [SV449: $i] :
( ( ! [SY3313: $i,SY3314: $i,SY3315: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SY3313 @ SY3314 @ SY3314 ) @ ( c_Transitive__Closure_Otrancl @ SY3315 @ SY3314 ) @ ( tc_prod @ SY3314 @ SY3314 ) )
| ( SV449 = SY3313 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SY3313 @ SY3314 @ SY3314 ) @ ( c_Transitive__Closure_Ortrancl @ SY3315 @ SY3314 ) @ ( tc_prod @ SY3314 @ SY3314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2564,plain,
! [SV450: $i] :
( ( ! [SY3316: $i,SY3317: $i,SY3318: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SY3316 @ SY3317 @ SY3317 ) @ ( c_Transitive__Closure_Ortrancl @ SY3318 @ SY3317 ) @ ( tc_prod @ SY3317 @ SY3317 ) )
| ~ ( c_in @ ( c_Pair @ SV450 @ SY3316 @ SY3317 @ SY3317 ) @ ( c_Transitive__Closure_Otrancl @ SY3318 @ SY3317 ) @ ( tc_prod @ SY3317 @ SY3317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2565,plain,
! [SV451: $i] :
( ( ! [SY3319: $i,SY3320: $i,SY3321: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SY3319 @ SY3320 @ SY3320 ) @ ( c_Transitive__Closure_Otrancl @ SY3321 @ SY3320 ) @ ( tc_prod @ SY3320 @ SY3320 ) )
| ! [SY3322: $i] :
( ~ ( c_in @ ( c_Pair @ SY3322 @ SY3319 @ SY3320 @ SY3320 ) @ ( c_Transitive__Closure_Ortrancl @ SY3321 @ SY3320 ) @ ( tc_prod @ SY3320 @ SY3320 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SY3322 @ SY3320 @ SY3320 ) @ ( c_Transitive__Closure_Otrancl @ SY3321 @ SY3320 ) @ ( tc_prod @ SY3320 @ SY3320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2566,plain,
! [SV452: $i] :
( ( ! [SY3323: $i,SY3324: $i,SY3325: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SY3323 @ SY3324 @ SY3324 ) @ ( c_Transitive__Closure_Otrancl @ SY3325 @ SY3324 ) @ ( tc_prod @ SY3324 @ SY3324 ) )
| ! [SY3326: $i] :
( ~ ( c_in @ ( c_Pair @ SY3326 @ SY3323 @ SY3324 @ SY3324 ) @ ( c_Transitive__Closure_Otrancl @ SY3325 @ SY3324 ) @ ( tc_prod @ SY3324 @ SY3324 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SY3326 @ SY3324 @ SY3324 ) @ ( c_Transitive__Closure_Ortrancl @ SY3325 @ SY3324 ) @ ( tc_prod @ SY3324 @ SY3324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2567,plain,
! [SV453: $i] :
( ( ! [SY3327: $i,SY3328: $i] :
( ( c_in @ SV453 @ ( c_Wellfounded_Oacc @ SY3327 @ SY3328 ) @ SY3328 )
| ~ ( c_Wellfounded_Owf @ SY3327 @ SY3328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2568,plain,
! [SV454: $i] :
( ( ! [SY3329: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV454 @ SY3329 ) @ SY3329 )
| ~ ( c_Relation_Osym @ SV454 @ SY3329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2569,plain,
! [SV455: $i] :
( ( ! [SY3330: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV455 @ SY3330 ) @ SY3330 @ SY3330 )
= ( c_Relation_ODomain @ SV455 @ SY3330 @ SY3330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2570,plain,
! [SV456: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId @ SV456 ) @ SV456 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2571,plain,
! [SV457: $i] :
( ( ! [SY3331: $i,SY3332: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV457 ) @ SY3331 @ SV457 @ SV457 @ SY3332 )
= SY3331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2572,plain,
! [SV458: $i] :
( ( ! [SY3333: $i,SY3334: $i] :
( ( c_Relation_Orel__comp @ SV458 @ ( c_Relation_OId @ SY3333 ) @ SY3334 @ SY3333 @ SY3333 )
= SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2573,plain,
! [SV459: $i] :
( ( ! [SY3335: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ SV459 @ SY3335 ) @ SY3335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2574,plain,
! [SV460: $i] :
( ( ! [SY3336: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ ( c_Transitive__Closure_Otrancl @ SY3336 @ SV460 ) ) @ SV460 )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ SY3336 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2575,plain,
! [SV461: $i] :
( ( ! [SY3337: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV461 @ SY3337 ) @ SY3337 )
| ~ ( c_Relation_Osym @ SV461 @ SY3337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2576,plain,
! [SV462: $i] :
( ( ! [SY3338: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV462 @ SV462 @ SY3338 @ SY3338 @ SY3338 ) @ SY3338 )
| ~ ( c_Wellfounded_Owf @ SV462 @ SY3338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2577,plain,
! [SV463: $i] :
( ( ! [SY3339: $i] :
( ( c_Wellfounded_Owf @ SV463 @ SY3339 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV463 @ SV463 @ SY3339 @ SY3339 @ SY3339 ) @ SY3339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2578,plain,
! [SV464: $i] :
( ( ! [SY3340: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ SV464 ) @ SY3340 @ SV464 @ SV464 )
= SY3340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2579,plain,
! [SV465: $i] :
( ( ! [SY3341: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV465 @ SY3341 ) @ SY3341 @ SY3341 )
= SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2580,plain,
! [SV466: $i] :
( ( ! [SY3342: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV466 @ SY3342 ) @ SY3342 @ SY3342 )
= ( c_Relation_ORange @ SV466 @ SY3342 @ SY3342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2581,plain,
! [SV467: $i] :
( ( ! [SY3343: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ SV467 @ SY3343 ) @ SY3343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2582,plain,
! [SV468: $i] :
( ( ! [SY3344: $i] : ( c_Relation_Orefl__on @ SV468 @ ( c_Relation_OId__on @ SV468 @ SY3344 ) @ SY3344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2583,plain,
! [SV469: $i] :
( ( ! [SY3345: $i,SY3346: $i] :
( ! [SY3347: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SY3345 @ SY3346 @ SY3347 ) @ SY3347 )
| ~ ( c_Wellfounded_Owf @ SV469 @ SY3346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2584,plain,
! [SV470: $i] :
( ( ! [SY3348: $i] :
( ( c_Relation_Orel__comp @ SV470 @ ( c_Transitive__Closure_Ortrancl @ SV470 @ SY3348 ) @ SY3348 @ SY3348 @ SY3348 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV470 @ SY3348 ) @ SV470 @ SY3348 @ SY3348 @ SY3348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2585,plain,
! [SV471: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ! [SY3351: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SY3349 @ SY3350 @ SY3351 ) @ SY3351 )
| ~ ( c_Relation_Osym @ SV471 @ SY3350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2586,plain,
! [SV472: $i] :
( ( ! [SY3352: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV472 @ SY3352 ) @ SY3352 )
= ( c_Transitive__Closure_Ortrancl @ SV472 @ SY3352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2587,plain,
! [SV473: $i] :
( ( ! [SY3353: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV473 @ SY3353 ) @ SY3353 )
| ~ ( c_Wellfounded_Owf @ SV473 @ SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2588,plain,
! [SV474: $i] :
( ( ! [SY3354: $i,SY3355: $i,SY3356: $i,SY3357: $i,SY3358: $i,SY3359: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SY3354 @ SY3355 @ SY3356 @ SY3357 ) @ SY3358 @ SY3355 @ SY3357 @ SY3359 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SY3354 @ SY3358 @ SY3356 @ SY3357 @ SY3359 ) @ SY3355 @ SY3356 @ SY3359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2589,plain,
! [SV475: $i] :
( ( ! [SY3360: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV475 @ SV475 ) @ SY3360 ) @ SY3360 @ SV475 @ SV475 @ SV475 )
!= SY3360 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SY3360 @ SV475 @ SV475 ) @ SY3360 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2590,plain,
! [SV476: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_OId @ SV476 ) @ SV476 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2591,plain,
! [SV477: $i] :
( ( ! [SY3361: $i,SY3362: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ SV477 @ SY3361 ) @ SY3362 ) @ SY3361 @ SV477 )
= ( c_Relation_ODomain @ SY3362 @ SV477 @ SY3361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2592,plain,
! [SV478: $i] :
( ( ! [SY3363: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV478 @ SY3363 ) @ SY3363 @ SY3363 )
= SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2593,plain,
! [SV479: $i] :
( ( ! [SY3364: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV479 @ SV479 ) @ SY3364 ) @ SY3364 @ SV479 @ SV479 @ SV479 )
= SY3364 )
| ! [SY3365: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3365 @ SY3364 @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2594,plain,
! [SV480: $i] :
( ( ! [SY3366: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV480 @ SY3366 ) @ ( c_Transitive__Closure_Ortrancl @ SV480 @ SY3366 ) @ SY3366 @ SY3366 @ SY3366 )
= ( c_Transitive__Closure_Ortrancl @ SV480 @ SY3366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2595,plain,
! [SV481: $i] :
( ( ! [SY3367: $i,SY3368: $i] :
( ( c_Relation_Orefl__on @ SV481 @ SY3367 @ SY3368 )
| ~ ( c_Equiv__Relations_Oequiv @ SV481 @ SY3367 @ SY3368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2596,plain,
! [SV482: $i] :
( ( ! [SY3369: $i] :
( ( c_Relation_Osym @ SV482 @ SY3369 )
| ! [SY3370: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3370 @ SV482 @ SY3369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2597,plain,
! [SV483: $i] :
( ( ! [SY3371: $i,SY3372: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SV483 @ SY3371 ) @ SY3372 ) @ SY3371 @ SV483 )
= ( c_Relation_ORange @ SY3372 @ SV483 @ SY3371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2598,plain,
! [SV484: $i] :
( ( ! [SY3373: $i] :
( ( c_Transitive__Closure_Otrancl @ SV484 @ SY3373 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SY3373 ) @ SV484 @ SY3373 @ SY3373 @ SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2599,plain,
! [SV485: $i] :
( ( ! [SY3374: $i] :
( ( c_Transitive__Closure_Otrancl @ SV485 @ SY3374 )
= ( c_Relation_Orel__comp @ SV485 @ ( c_Transitive__Closure_Ortrancl @ SV485 @ SY3374 ) @ SY3374 @ SY3374 @ SY3374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2600,plain,
! [SV486: $i] :
( ( ! [SY3375: $i,SY3376: $i] :
( ( c_Relation_ORange @ SV486 @ SY3375 @ SY3376 )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SY3375 @ SY3376 ) @ SV486 ) @ SY3376 @ SY3375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2601,plain,
! [SV487: $i] :
( ( ! [SY3377: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV487 @ SY3377 ) @ SY3377 )
= ( c_Transitive__Closure_Ortrancl @ SV487 @ SY3377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2602,plain,
! [SV488: $i] :
( ( ! [SY3378: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SY3378 ) @ SY3378 )
= ( c_Transitive__Closure_Ortrancl @ SV488 @ SY3378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2603,plain,
! [SV489: $i] :
( ( ! [SY3379: $i,SY3380: $i,SY3381: $i] :
( ( c_in @ ( c_Pair @ SV489 @ SY3379 @ SY3380 @ SY3380 ) @ ( c_Transitive__Closure_Ortrancl @ SY3381 @ SY3380 ) @ ( tc_prod @ SY3380 @ SY3380 ) )
| ! [SY3382: $i] :
( ~ ( c_in @ ( c_Pair @ SY3382 @ SY3379 @ SY3380 @ SY3380 ) @ ( c_Transitive__Closure_Ortrancl @ SY3381 @ SY3380 ) @ ( tc_prod @ SY3380 @ SY3380 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SY3382 @ SY3380 @ SY3380 ) @ SY3381 @ ( tc_prod @ SY3380 @ SY3380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2604,plain,
! [SV490: $i] :
( ( ! [SY3383: $i,SY3384: $i,SY3385: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SY3383 @ SY3384 @ SY3384 ) @ ( c_Transitive__Closure_Otrancl @ SY3385 @ SY3384 ) @ ( tc_prod @ SY3384 @ SY3384 ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SY3383 @ SY3384 @ SY3384 ) @ SY3385 @ ( tc_prod @ SY3384 @ SY3384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2605,plain,
! [SV491: $i] :
( ( ! [SY3386: $i,SY3387: $i,SY3388: $i] :
( ( c_in @ ( c_Pair @ SV491 @ SY3386 @ SY3387 @ SY3387 ) @ ( c_Transitive__Closure_Ortrancl @ SY3388 @ SY3387 ) @ ( tc_prod @ SY3387 @ SY3387 ) )
| ! [SY3389: $i] :
( ~ ( c_in @ ( c_Pair @ SY3389 @ SY3386 @ SY3387 @ SY3387 ) @ ( c_Transitive__Closure_Ortrancl @ SY3388 @ SY3387 ) @ ( tc_prod @ SY3387 @ SY3387 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SY3389 @ SY3387 @ SY3387 ) @ ( c_Transitive__Closure_Ortrancl @ SY3388 @ SY3387 ) @ ( tc_prod @ SY3387 @ SY3387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2606,plain,
! [SV492: $i] :
( ( ! [SY3390: $i,SY3391: $i] : ( c_in @ ( c_Pair @ SV492 @ SV492 @ SY3390 @ SY3390 ) @ ( c_Transitive__Closure_Ortrancl @ SY3391 @ SY3390 ) @ ( tc_prod @ SY3390 @ SY3390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2607,plain,
! [SV493: $i] :
( ( ! [SY3392: $i,SY3393: $i] : ( c_in @ ( c_Pair @ SV493 @ SV493 @ SY3392 @ SY3392 ) @ ( c_Transitive__Closure_Ortrancl @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3392 @ SY3392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2608,plain,
! [SV494: $i] :
( ( ! [SY3394: $i,SY3395: $i,SY3396: $i] :
( ~ ( c_in @ ( c_Pair @ SV494 @ SY3394 @ SY3395 @ SY3395 ) @ SY3396 @ ( tc_prod @ SY3395 @ SY3395 ) )
| ~ ( c_in @ ( c_Pair @ SY3394 @ SV494 @ SY3395 @ SY3395 ) @ SY3396 @ ( tc_prod @ SY3395 @ SY3395 ) )
| ~ ( c_Wellfounded_Owf @ SY3396 @ SY3395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2609,plain,
! [SV495: $i] :
( ( ! [SY3397: $i] :
( ( SV495 = SY3397 )
| ! [SY3398: $i,SY3399: $i] :
( ~ ( c_in @ ( c_Pair @ SY3397 @ SV495 @ SY3398 @ SY3398 ) @ SY3399 @ ( tc_prod @ SY3398 @ SY3398 ) )
| ~ ( c_in @ ( c_Pair @ SV495 @ SY3397 @ SY3398 @ SY3398 ) @ SY3399 @ ( tc_prod @ SY3398 @ SY3398 ) )
| ~ ( c_Relation_Oantisym @ SY3399 @ SY3398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2610,plain,
! [SV496: $i] :
( ( ! [SY3400: $i] :
( ( SV496 = SY3400 )
| ! [SY3401: $i,SY3402: $i] :
( ~ ( c_in @ ( c_Pair @ SY3400 @ SV496 @ SY3401 @ SY3401 ) @ SY3402 @ ( tc_prod @ SY3401 @ SY3401 ) )
| ~ ( c_in @ ( c_Pair @ SV496 @ SY3400 @ SY3401 @ SY3401 ) @ SY3402 @ ( tc_prod @ SY3401 @ SY3401 ) )
| ~ ( c_Relation_Oantisym @ SY3402 @ SY3401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2611,plain,
! [SV497: $i] :
( ( ! [SY3403: $i,SY3404: $i,SY3405: $i] :
( ( ( hAPP @ SV497 @ SY3403 )
= ( hAPP @ SV497 @ SY3404 ) )
| ! [SY3406: $i] :
( ~ ( c_in @ ( c_Pair @ SY3403 @ SY3404 @ SY3405 @ SY3405 ) @ SY3406 @ ( tc_prod @ SY3405 @ SY3405 ) )
| ! [SY3407: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY3406 @ SV497 @ SY3405 @ SY3407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2612,plain,
! [SV498: $i] :
( ( ! [SY3408: $i] :
( ( SV498 = SY3408 )
| ! [SY3409: $i,SY3410: $i] :
~ ( c_in @ ( c_Pair @ SV498 @ SY3408 @ SY3409 @ SY3409 ) @ ( c_Relation_OId__on @ SY3410 @ SY3409 ) @ ( tc_prod @ SY3409 @ SY3409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2613,plain,
! [SV499: $i] :
( ( ! [SY3411: $i,SY3412: $i,SY3413: $i,SY3414: $i,SY3415: $i] :
( ( ( c_Recdef_Ocut @ SV499 @ SY3411 @ SY3412 @ SY3413 @ SY3414 )
!= ( c_Recdef_Ocut @ SY3415 @ SY3411 @ SY3412 @ SY3413 @ SY3414 ) )
| ! [SY3416: $i] :
( ( ( hAPP @ SV499 @ SY3416 )
= ( hAPP @ SY3415 @ SY3416 ) )
| ~ ( c_in @ ( c_Pair @ SY3416 @ SY3412 @ SY3413 @ SY3413 ) @ SY3411 @ ( tc_prod @ SY3413 @ SY3413 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2614,plain,
! [SV500: $i] :
( ( ! [SY3417: $i] :
( ( SV500 = SY3417 )
| ! [SY3418: $i] :
~ ( c_in @ ( c_Pair @ SV500 @ SY3417 @ SY3418 @ SY3418 ) @ ( c_Relation_OId @ SY3418 ) @ ( tc_prod @ SY3418 @ SY3418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2615,plain,
! [SV501: $i] :
( ( ! [SY3419: $i,SY3420: $i] :
( ( c_in @ ( c_Pair @ SV501 @ SV501 @ SY3419 @ SY3419 ) @ SY3420 @ ( tc_prod @ SY3419 @ SY3419 ) )
| ~ ( c_Nitpick_Orefl_H @ SY3420 @ SY3419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2616,plain,
! [SV502: $i] :
( ( ! [SY3421: $i,SY3422: $i] :
( ~ ( c_in @ ( c_Pair @ SV502 @ SV502 @ SY3421 @ SY3421 ) @ SY3422 @ ( tc_prod @ SY3421 @ SY3421 ) )
| ~ ( c_Wellfounded_Owf @ SY3422 @ SY3421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2617,plain,
! [SV503: $i] :
( ( ! [SY3423: $i,SY3424: $i,SY3425: $i,SY3426: $i,SY3427: $i] :
( ( c_in @ ( c_Pair @ SV503 @ SY3423 @ SY3424 @ SY3424 ) @ ( c_Relation_Oinv__image @ SY3425 @ SY3426 @ SY3427 @ SY3424 ) @ ( tc_prod @ SY3424 @ SY3424 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY3426 @ SV503 ) @ ( hAPP @ SY3426 @ SY3423 ) @ SY3427 @ SY3427 ) @ SY3425 @ ( tc_prod @ SY3427 @ SY3427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2618,plain,
! [SV504: $i] :
( ( ! [SY3428: $i,SY3429: $i,SY3430: $i,SY3431: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SY3428 ) @ ( hAPP @ SV504 @ SY3429 ) @ SY3430 @ SY3430 ) @ SY3431 @ ( tc_prod @ SY3430 @ SY3430 ) )
| ! [SY3432: $i] :
~ ( c_in @ ( c_Pair @ SY3428 @ SY3429 @ SY3432 @ SY3432 ) @ ( c_Relation_Oinv__image @ SY3431 @ SV504 @ SY3430 @ SY3432 ) @ ( tc_prod @ SY3432 @ SY3432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2619,plain,
! [SV505: $i] :
( ( ! [SY3433: $i,SY3434: $i,SY3435: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SY3433 @ SY3434 @ SY3434 ) @ SY3435 @ ( tc_prod @ SY3434 @ SY3434 ) )
| ~ ( c_in @ ( c_Pair @ SY3433 @ SV505 @ SY3434 @ SY3434 ) @ SY3435 @ ( tc_prod @ SY3434 @ SY3434 ) )
| ~ ( c_Relation_Osym @ SY3435 @ SY3434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2620,plain,
! [SV506: $i] :
( ( ! [SY3436: $i,SY3437: $i,SY3438: $i] :
( ( c_in @ ( c_Pair @ SV506 @ SY3436 @ SY3437 @ SY3437 ) @ SY3438 @ ( tc_prod @ SY3437 @ SY3437 ) )
| ~ ( c_in @ ( c_Pair @ SY3436 @ SV506 @ SY3437 @ SY3437 ) @ SY3438 @ ( tc_prod @ SY3437 @ SY3437 ) )
| ~ ( c_Relation_Osym @ SY3438 @ SY3437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2621,plain,
! [SV507: $i] :
( ( ! [SY3439: $i,SY3440: $i,SY3441: $i,SY3442: $i,SY3443: $i,SY3444: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SY3439 @ SY3440 @ SY3441 ) @ ( c_Relation_Orel__comp @ SY3442 @ SY3443 @ SY3440 @ SY3444 @ SY3441 ) @ ( tc_prod @ SY3440 @ SY3441 ) )
| ! [SY3445: $i] :
( ~ ( c_in @ ( c_Pair @ SY3445 @ SY3439 @ SY3444 @ SY3441 ) @ SY3443 @ ( tc_prod @ SY3444 @ SY3441 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY3445 @ SY3440 @ SY3444 ) @ SY3442 @ ( tc_prod @ SY3440 @ SY3444 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2622,plain,
! [SV508: $i] :
( ( ! [SY3446: $i,SY3447: $i,SY3448: $i] :
( ( c_in @ ( c_Pair @ SV508 @ SY3446 @ SY3447 @ SY3447 ) @ ( c_Transitive__Closure_Otrancl @ SY3448 @ SY3447 ) @ ( tc_prod @ SY3447 @ SY3447 ) )
| ! [SY3449: $i] :
( ~ ( c_in @ ( c_Pair @ SY3449 @ SY3446 @ SY3447 @ SY3447 ) @ SY3448 @ ( tc_prod @ SY3447 @ SY3447 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SY3449 @ SY3447 @ SY3447 ) @ SY3448 @ ( tc_prod @ SY3447 @ SY3447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2623,plain,
! [SV509: $i] :
( ( ! [SY3450: $i,SY3451: $i,SY3452: $i] :
( ( c_in @ ( c_Pair @ SV509 @ SY3450 @ SY3451 @ SY3451 ) @ ( c_Transitive__Closure_Otrancl @ SY3452 @ SY3451 ) @ ( tc_prod @ SY3451 @ SY3451 ) )
| ! [SY3453: $i] :
( ~ ( c_in @ ( c_Pair @ SY3453 @ SY3450 @ SY3451 @ SY3451 ) @ ( c_Transitive__Closure_Otrancl @ SY3452 @ SY3451 ) @ ( tc_prod @ SY3451 @ SY3451 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SY3453 @ SY3451 @ SY3451 ) @ ( c_Transitive__Closure_Otrancl @ SY3452 @ SY3451 ) @ ( tc_prod @ SY3451 @ SY3451 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2624,plain,
! [SV510: $i] :
( ( ! [SY3454: $i] : ( c_in @ ( c_Pair @ SV510 @ SV510 @ SY3454 @ SY3454 ) @ ( c_Relation_OId @ SY3454 ) @ ( tc_prod @ SY3454 @ SY3454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2625,plain,
! [SV511: $i] :
( ( ! [SY3455: $i] : ( c_in @ ( c_Pair @ SV511 @ SV511 @ SY3455 @ SY3455 ) @ ( c_Relation_OId @ SY3455 ) @ ( tc_prod @ SY3455 @ SY3455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2626,plain,
! [SV512: $i] :
( ( ! [SY3456: $i,SY3457: $i,SY3458: $i] :
( ( c_in @ ( hAPP @ SV512 @ SY3456 ) @ ( hAPP @ SY3457 @ SY3456 ) @ SY3458 )
| ! [SY3459: $i,SY3460: $i] :
( ~ ( c_in @ SY3456 @ SY3459 @ SY3460 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SY3459 @ SY3457 @ SY3460 @ SY3458 ) @ ( tc_fun @ SY3460 @ SY3458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2627,plain,
! [SV513: $i] :
( ( ! [SY3461: $i,SY3462: $i,SY3463: $i] :
( ~ ( c_in @ SV513 @ SY3461 @ SY3462 )
| ! [SY3464: $i,SY3465: $i] :
( ( c_in @ ( hAPP @ SY3463 @ SV513 ) @ ( hAPP @ SY3464 @ SV513 ) @ SY3465 )
| ~ ( c_in @ SY3463 @ ( c_FuncSet_OPi @ SY3461 @ SY3464 @ SY3462 @ SY3465 ) @ ( tc_fun @ SY3462 @ SY3465 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2628,plain,
! [SV514: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i] :
( ( c_in @ ( c_Pair @ SV514 @ SY3466 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3467 @ SY3468 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV514 @ SY3466 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV514 = SY3466 )
| ( SV514 = SY3468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2629,plain,
! [SV515: $i] :
( ( ! [SY3469: $i,SY3470: $i,SY3471: $i] :
( ( c_in @ ( c_Pair @ SV515 @ SY3469 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3470 @ SY3471 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV515 @ SY3469 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3469 = SY3471 )
| ( SV515 = SY3471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2630,plain,
! [SV516: $i] :
( ( ! [SY3472: $i] :
~ ( c_in @ ( c_Pair @ SV516 @ SV516 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3472 @ SV516 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2631,plain,
! [SV517: $i] :
( ( ! [SY3473: $i,SY3474: $i] :
~ ( c_in @ ( c_Pair @ SV517 @ SY3473 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3474 @ SV517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2632,plain,
! [SV518: $i] :
( ( ! [SY3475: $i,SY3476: $i] :
( ( c_in @ ( c_Pair @ SV518 @ SY3475 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3476 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3477: $i] :
( ( SY3475 = SY3477 )
| ~ ( c_in @ ( c_Pair @ SV518 @ SY3475 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3476 @ SY3477 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2633,plain,
! [SV519: $i] :
( ( ! [SY3478: $i] :
( ( SV519 = SY3478 )
| ( SY3478 = SV519 )
| ! [SY3479: $i] : ( c_in @ ( c_Pair @ SV519 @ SY3478 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3479 @ SV519 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2634,plain,
! [SV520: $i] :
( ( ! [SY3480: $i] :
~ ( c_in @ ( c_Pair @ SV520 @ SV520 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3480 @ SV520 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2635,plain,
! [SV521: $i] :
( ( ! [SY3481: $i,SY3482: $i] :
~ ( c_in @ ( c_Pair @ SV521 @ SY3481 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3482 @ SY3481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2636,plain,
! [SV522: $i] :
( ( ! [SY3483: $i,SY3484: $i,SY3485: $i] :
( ( c_in @ ( c_Pair @ SV522 @ SY3483 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3484 @ SY3485 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV522 @ SY3483 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV522 = SY3483 )
| ( SY3483 = SY3485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2637,plain,
! [SV523: $i] :
( ( ! [SY3486: $i,SY3487: $i,SY3488: $i] :
( ( c_in @ ( c_Pair @ SV523 @ SY3486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3487 @ SY3488 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV523 @ SY3486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV523 = SY3488 )
| ( SY3486 = SY3488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2638,plain,
! [SV524: $i] :
( ( ! [SY3489: $i] :
( ( SV524 = SY3489 )
| ( SV524 = SY3489 )
| ! [SY3490: $i] : ( c_in @ ( c_Pair @ SV524 @ SY3489 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3490 @ SY3489 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2639,plain,
! [SV525: $i] :
( ( ! [SY3491: $i,SY3492: $i] :
( ( c_in @ ( c_Pair @ SV525 @ SY3491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3493: $i] :
( ( SV525 = SY3493 )
| ~ ( c_in @ ( c_Pair @ SV525 @ SY3491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3492 @ SY3493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2640,plain,
! [SV526: $i] :
( ( ! [SY3494: $i] :
( ( SV526 = SY3494 )
| ( c_in @ ( c_Pair @ SV526 @ SY3494 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV526 @ SY3494 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2641,plain,
! [SV527: $i] :
( ( ! [SY3495: $i,SY3496: $i] :
( ( c_in @ ( c_Pair @ SV527 @ SY3495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3496 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3497: $i] :
( ~ ( c_in @ ( c_Pair @ SY3495 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3497 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3495 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3497 @ ( v_sko__local__X3__1 @ SY3496 @ SY3497 @ SV527 @ SY3495 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SY3495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3496 @ ( v_sko__local__X3__1 @ SY3496 @ SY3497 @ SV527 @ SY3495 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3497 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3496 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SY3495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2642,plain,
! [SV528: $i] :
( ( ! [SY3498: $i,SY3499: $i] :
( ( c_in @ ( c_Pair @ SV528 @ SY3498 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3499 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3500: $i] :
( ~ ( c_in @ ( c_Pair @ SY3498 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3500 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV528 @ SY3498 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3499 @ ( v_sko__local__X3__1 @ SY3500 @ SY3499 @ SY3498 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3498 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3500 @ ( v_sko__local__X3__1 @ SY3500 @ SY3499 @ SY3498 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3499 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3500 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3498 = SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2643,plain,
! [SV529: $i] :
( ( ! [SY3501: $i,SY3502: $i] :
( ( c_in @ ( c_Pair @ SV529 @ SY3501 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3502 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3503: $i] :
( ~ ( c_in @ ( c_Pair @ SY3501 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3503 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3501 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3503 @ ( v_sko__local__X3__1 @ SY3502 @ SY3503 @ SV529 @ SY3501 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SY3501 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3502 @ ( v_sko__local__X3__1 @ SY3502 @ SY3503 @ SV529 @ SY3501 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3503 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3502 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SY3501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2644,plain,
! [SV530: $i] :
( ( ! [SY3504: $i,SY3505: $i] :
( ( c_in @ ( c_Pair @ SV530 @ SY3504 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3505 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3506: $i] :
( ~ ( c_in @ ( c_Pair @ SY3504 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3506 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV530 @ SY3504 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3505 @ ( v_sko__local__X3__1 @ SY3506 @ SY3505 @ SY3504 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3504 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3506 @ ( v_sko__local__X3__1 @ SY3506 @ SY3505 @ SY3504 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3505 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3506 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3504 = SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2645,plain,
! [SV531: $i] :
( ( ! [SY3507: $i,SY3508: $i,SY3509: $i] :
( ( c_in @ ( c_Pair @ SV531 @ SY3507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3508 @ SY3509 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3510: $i] :
( ~ ( c_in @ ( c_Pair @ SV531 @ SY3507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3508 @ SY3510 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SY3507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3510 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SY3507 @ SY3509 @ SY3510 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SY3507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3509 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SY3507 @ SY3509 @ SY3510 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3510 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3509 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY3508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2646,plain,
! [SV532: $i] :
( ( ! [SY3511: $i,SY3512: $i,SY3513: $i] :
( ( c_in @ ( c_Pair @ SV532 @ SY3511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3512 @ SY3513 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3514: $i] :
( ~ ( c_in @ ( c_Pair @ SV532 @ SY3511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3512 @ SY3514 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SY3511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3513 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SY3511 @ SY3514 @ SY3513 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SY3511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3514 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SY3511 @ SY3514 @ SY3513 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3513 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3514 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY3512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2647,plain,
! [SV533: $i] :
( ( ! [SY3515: $i,SY3516: $i,SY3517: $i] :
( ( c_in @ ( c_Pair @ SV533 @ SY3515 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3516 @ SY3517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3518: $i] :
( ~ ( c_in @ ( c_Pair @ SV533 @ SY3515 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3516 @ SY3518 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SY3515 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3518 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SY3515 @ SY3517 @ SY3518 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SY3515 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3517 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SY3515 @ SY3517 @ SY3518 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3518 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3517 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY3516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2648,plain,
! [SV534: $i] :
( ( ! [SY3519: $i,SY3520: $i,SY3521: $i] :
( ( c_in @ ( c_Pair @ SV534 @ SY3519 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3520 @ SY3521 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3522: $i] :
( ~ ( c_in @ ( c_Pair @ SV534 @ SY3519 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3520 @ SY3522 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SY3519 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3521 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SY3519 @ SY3522 @ SY3521 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SY3519 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3522 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SY3519 @ SY3522 @ SY3521 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3521 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3522 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY3520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2649,plain,
! [SV535: $i] :
( ( ! [SY3523: $i,SY3524: $i,SY3525: $i] :
( ( c_in @ ( c_Pair @ SV535 @ SY3523 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3524 @ SY3525 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV535 @ SY3523 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3525 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SY3523 @ SY3525 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3525 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY3524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2650,plain,
! [SV536: $i] :
( ( ! [SY3526: $i,SY3527: $i,SY3528: $i] :
( ( c_in @ ( c_Pair @ SV536 @ SY3526 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3527 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3529: $i,SY3530: $i] :
( ~ ( c_in @ ( c_Pair @ SY3528 @ SY3529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3530 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3528 @ SY3529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3530 @ ( v_sko__local__X2__1 @ SY3527 @ SY3530 @ SV536 @ SY3528 @ SY3526 @ SY3529 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SY3526 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3527 @ ( v_sko__local__X2__1 @ SY3527 @ SY3530 @ SV536 @ SY3528 @ SY3526 @ SY3529 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3530 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3527 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3526 = SY3528 )
| ( SV536 = SY3529 )
| ( SY3528 = SY3529 )
| ( SV536 = SY3526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2651,plain,
! [SV537: $i] :
( ( ! [SY3531: $i,SY3532: $i,SY3533: $i] :
( ( c_in @ ( c_Pair @ SV537 @ SY3531 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3532 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3534: $i,SY3535: $i] :
( ~ ( c_in @ ( c_Pair @ SY3533 @ SY3534 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3535 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SY3531 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3532 @ ( v_sko__local__X2__1 @ SY3535 @ SY3532 @ SY3533 @ SV537 @ SY3534 @ SY3531 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3533 @ SY3534 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3535 @ ( v_sko__local__X2__1 @ SY3535 @ SY3532 @ SY3533 @ SV537 @ SY3534 @ SY3531 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3532 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3535 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3534 = SV537 )
| ( SY3533 = SY3531 )
| ( SV537 = SY3531 )
| ( SY3533 = SY3534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2652,plain,
! [SV538: $i] :
( ( ! [SY3536: $i,SY3537: $i,SY3538: $i] :
( ( c_in @ ( c_Pair @ SV538 @ SY3536 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3537 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3539: $i,SY3540: $i] :
( ~ ( c_in @ ( c_Pair @ SY3538 @ SY3539 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3540 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3538 @ SY3539 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3540 @ ( v_sko__local__X2__1 @ SY3537 @ SY3540 @ SV538 @ SY3538 @ SY3536 @ SY3539 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SY3536 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3537 @ ( v_sko__local__X2__1 @ SY3537 @ SY3540 @ SV538 @ SY3538 @ SY3536 @ SY3539 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3540 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3537 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3536 = SY3538 )
| ( SV538 = SY3539 )
| ( SY3538 = SY3539 )
| ( SV538 = SY3536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2653,plain,
! [SV539: $i] :
( ( ! [SY3541: $i,SY3542: $i,SY3543: $i] :
( ( c_in @ ( c_Pair @ SV539 @ SY3541 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3542 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3544: $i,SY3545: $i] :
( ~ ( c_in @ ( c_Pair @ SY3543 @ SY3544 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3545 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SY3541 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3542 @ ( v_sko__local__X2__1 @ SY3545 @ SY3542 @ SY3543 @ SV539 @ SY3544 @ SY3541 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3543 @ SY3544 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3545 @ ( v_sko__local__X2__1 @ SY3545 @ SY3542 @ SY3543 @ SV539 @ SY3544 @ SY3541 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3542 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3545 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3544 = SV539 )
| ( SY3543 = SY3541 )
| ( SV539 = SY3541 )
| ( SY3543 = SY3544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2654,plain,
! [SV540: $i] :
( ( ! [SY3546: $i,SY3547: $i,SY3548: $i] :
( ( c_in @ ( c_Pair @ SV540 @ SY3546 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3547 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3549: $i,SY3550: $i] :
( ~ ( c_in @ ( c_Pair @ SY3548 @ SY3549 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3550 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SY3546 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3547 @ ( v_sko__local__X1__1 @ SY3550 @ SY3547 @ SY3548 @ SV540 @ SY3549 @ SY3546 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3548 @ SY3549 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3550 @ ( v_sko__local__X1__1 @ SY3550 @ SY3547 @ SY3548 @ SV540 @ SY3549 @ SY3546 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3547 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3550 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3549 = SV540 )
| ( SY3548 = SY3546 )
| ( SV540 = SY3546 )
| ( SY3548 = SY3549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2655,plain,
! [SV541: $i] :
( ( ! [SY3551: $i,SY3552: $i,SY3553: $i] :
( ( c_in @ ( c_Pair @ SV541 @ SY3551 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3552 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3554: $i,SY3555: $i] :
( ~ ( c_in @ ( c_Pair @ SY3553 @ SY3554 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY3555 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SY3551 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3552 @ ( v_sko__local__X1__1 @ SY3555 @ SY3552 @ SY3553 @ SV541 @ SY3554 @ SY3551 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3553 @ SY3554 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY3555 @ ( v_sko__local__X1__1 @ SY3555 @ SY3552 @ SY3553 @ SV541 @ SY3554 @ SY3551 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3552 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY3555 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY3554 = SV541 )
| ( SY3553 = SY3551 )
| ( SV541 = SY3551 )
| ( SY3553 = SY3554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2656,plain,
! [SV542: $i] :
( ( ! [SY3556: $i,SY3557: $i] :
( ( ( hAPP @ SV542 @ SY3556 )
= ( hAPP @ SY3556 @ SY3557 ) )
| ~ ( c_in @ SY3556 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV542 @ SY3557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2657,plain,
! [SV543: $i] :
( ( ! [SY3558: $i,SY3559: $i,SY3560: $i,SY3561: $i,SY3562: $i] :
( ( c_in @ ( c_Pair @ SV543 @ SY3558 @ SY3559 @ SY3560 ) @ ( c_Product__Type_OSigma @ SY3561 @ SY3562 @ SY3559 @ SY3560 ) @ ( tc_prod @ SY3559 @ SY3560 ) )
| ~ ( c_in @ SY3558 @ ( hAPP @ SY3562 @ SV543 ) @ SY3560 )
| ~ ( c_in @ SV543 @ SY3561 @ SY3559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2658,plain,
! [SV544: $i] :
( ( ! [SY3563: $i,SY3564: $i,SY3565: $i,SY3566: $i,SY3567: $i] :
( ( c_in @ ( c_Pair @ SV544 @ SY3563 @ SY3564 @ SY3565 ) @ ( c_Product__Type_OSigma @ SY3566 @ SY3567 @ SY3564 @ SY3565 ) @ ( tc_prod @ SY3564 @ SY3565 ) )
| ~ ( c_in @ SY3563 @ ( hAPP @ SY3567 @ SV544 ) @ SY3565 )
| ~ ( c_in @ SV544 @ SY3566 @ SY3564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2659,plain,
! [SV545: $i] :
( ( ! [SY3568: $i,SY3569: $i] :
( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SY3568 @ SY3569 ) @ SY3569 )
| ! [SY3570: $i] :
( ~ ( c_in @ ( c_Pair @ SV545 @ SY3570 @ SY3569 @ SY3569 ) @ SY3568 @ ( tc_prod @ SY3569 @ SY3569 ) )
| ~ ( c_in @ SY3570 @ ( c_Wellfounded_Oacc @ SY3568 @ SY3569 ) @ SY3569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2660,plain,
! [SV546: $i] :
( ( ! [SY3571: $i,SY3572: $i] :
( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SY3571 @ SY3572 ) @ SY3572 )
| ! [SY3573: $i] :
( ~ ( c_in @ ( c_Pair @ SV546 @ SY3573 @ SY3572 @ SY3572 ) @ SY3571 @ ( tc_prod @ SY3572 @ SY3572 ) )
| ~ ( c_in @ SY3573 @ ( c_Wellfounded_Oacc @ SY3571 @ SY3572 ) @ SY3572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2661,plain,
! [SV547: $i] :
( ( ! [SY3574: $i,SY3575: $i,SY3576: $i,SY3577: $i] :
( ( c_in @ SV547 @ ( c_Relation_OImage @ SY3574 @ SY3575 @ SY3576 @ SY3577 ) @ SY3577 )
| ! [SY3578: $i] :
( ~ ( c_in @ ( c_Pair @ SY3578 @ SV547 @ SY3576 @ SY3577 ) @ SY3574 @ ( tc_prod @ SY3576 @ SY3577 ) )
| ~ ( c_in @ SY3578 @ SY3575 @ SY3576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2662,plain,
! [SV548: $i] :
( ( ! [SY3579: $i,SY3580: $i,SY3581: $i,SY3582: $i] :
( ( c_in @ SV548 @ ( c_Relation_OImage @ SY3579 @ SY3580 @ SY3581 @ SY3582 ) @ SY3582 )
| ! [SY3583: $i] :
( ~ ( c_in @ ( c_Pair @ SY3583 @ SV548 @ SY3581 @ SY3582 ) @ SY3579 @ ( tc_prod @ SY3581 @ SY3582 ) )
| ~ ( c_in @ SY3583 @ SY3580 @ SY3581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2663,plain,
! [SV549: $i] :
( ( ! [SY3584: $i,SY3585: $i] :
( ( c_in @ SV549 @ SY3584 @ SY3585 )
| ! [SY3586: $i] :
~ ( c_in @ ( c_Pair @ SV549 @ SY3586 @ SY3585 @ SY3585 ) @ ( c_Relation_OId__on @ SY3584 @ SY3585 ) @ ( tc_prod @ SY3585 @ SY3585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2664,plain,
! [SV550: $i] :
( ( ! [SY3587: $i,SY3588: $i] :
( ( c_in @ ( c_Pair @ SV550 @ SV550 @ SY3587 @ SY3587 ) @ ( c_Relation_OId__on @ SY3588 @ SY3587 ) @ ( tc_prod @ SY3587 @ SY3587 ) )
| ~ ( c_in @ SV550 @ SY3588 @ SY3587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2665,plain,
! [SV551: $i] :
( ( ! [SY3589: $i,SY3590: $i] :
( ( c_in @ SV551 @ SY3589 @ SY3590 )
| ! [SY3591: $i,SY3592: $i] :
( ~ ( c_in @ ( c_Pair @ SY3591 @ SV551 @ SY3590 @ SY3590 ) @ SY3592 @ ( tc_prod @ SY3590 @ SY3590 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3589 @ SY3592 @ SY3590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2666,plain,
! [SV552: $i] :
( ( ! [SY3593: $i,SY3594: $i] :
( ( c_in @ SV552 @ SY3593 @ SY3594 )
| ! [SY3595: $i,SY3596: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY3595 @ SY3594 @ SY3594 ) @ SY3596 @ ( tc_prod @ SY3594 @ SY3594 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3593 @ SY3596 @ SY3594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2667,plain,
! [SV553: $i] :
( ( ! [SY3597: $i,SY3598: $i,SY3599: $i] :
( ( c_in @ SV553 @ ( c_Relation_ORange @ SY3597 @ SY3598 @ SY3599 ) @ SY3599 )
| ! [SY3600: $i] :
~ ( c_in @ ( c_Pair @ SY3600 @ SV553 @ SY3598 @ SY3599 ) @ SY3597 @ ( tc_prod @ SY3598 @ SY3599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2668,plain,
! [SV554: $i] :
( ( ! [SY3601: $i,SY3602: $i,SY3603: $i] :
( ( c_in @ SV554 @ ( c_Relation_ORange @ SY3601 @ SY3602 @ SY3603 ) @ SY3603 )
| ! [SY3604: $i] :
~ ( c_in @ ( c_Pair @ SY3604 @ SV554 @ SY3602 @ SY3603 ) @ SY3601 @ ( tc_prod @ SY3602 @ SY3603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2669,plain,
! [SV555: $i] :
( ( ! [SY3605: $i,SY3606: $i,SY3607: $i] :
( ( c_in @ SV555 @ ( c_Relation_ODomain @ SY3605 @ SY3606 @ SY3607 ) @ SY3606 )
| ! [SY3608: $i] :
~ ( c_in @ ( c_Pair @ SV555 @ SY3608 @ SY3606 @ SY3607 ) @ SY3605 @ ( tc_prod @ SY3606 @ SY3607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2670,plain,
! [SV556: $i] :
( ( ! [SY3609: $i,SY3610: $i,SY3611: $i] :
( ( c_in @ SV556 @ ( c_Relation_ODomain @ SY3609 @ SY3610 @ SY3611 ) @ SY3610 )
| ! [SY3612: $i] :
~ ( c_in @ ( c_Pair @ SV556 @ SY3612 @ SY3610 @ SY3611 ) @ SY3609 @ ( tc_prod @ SY3610 @ SY3611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2671,plain,
! [SV557: $i] :
( ( ! [SY3613: $i,SY3614: $i,SY3615: $i] :
( ( c_in @ SV557 @ ( hAPP @ SY3613 @ SY3614 ) @ SY3615 )
| ! [SY3616: $i,SY3617: $i] :
~ ( c_in @ ( c_Pair @ SY3614 @ SV557 @ SY3616 @ SY3615 ) @ ( c_Product__Type_OSigma @ SY3617 @ SY3613 @ SY3616 @ SY3615 ) @ ( tc_prod @ SY3616 @ SY3615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2672,plain,
! [SV558: $i] :
( ( ! [SY3618: $i,SY3619: $i,SY3620: $i] :
( ( c_in @ SV558 @ SY3618 @ SY3619 )
| ! [SY3621: $i,SY3622: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SY3620 @ SY3619 @ SY3621 ) @ ( c_Product__Type_OSigma @ SY3618 @ SY3622 @ SY3619 @ SY3621 ) @ ( tc_prod @ SY3619 @ SY3621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2673,plain,
! [SV559: $i] :
( ( ! [SY3623: $i,SY3624: $i,SY3625: $i] :
( ( c_in @ ( c_Pair @ SV559 @ SY3623 @ SY3624 @ SY3624 ) @ SY3625 @ ( tc_prod @ SY3624 @ SY3624 ) )
| ( c_in @ ( c_Pair @ SY3623 @ SV559 @ SY3624 @ SY3624 ) @ SY3625 @ ( tc_prod @ SY3624 @ SY3624 ) )
| ( SY3623 = SV559 )
| ! [SY3626: $i] :
( ~ ( c_in @ SV559 @ SY3626 @ SY3624 )
| ~ ( c_in @ SY3623 @ SY3626 @ SY3624 )
| ~ ( c_Relation_Ototal__on @ SY3626 @ SY3625 @ SY3624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2674,plain,
! [SV560: $i] :
( ( ! [SY3627: $i,SY3628: $i] :
( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SY3627 @ SY3627 ) @ SY3628 @ ( tc_prod @ SY3627 @ SY3627 ) )
| ! [SY3629: $i] :
( ~ ( c_in @ SV560 @ SY3629 @ SY3627 )
| ~ ( c_Relation_Orefl__on @ SY3629 @ SY3628 @ SY3627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2675,plain,
! [SV561: $i] :
( ( ! [SY3630: $i,SY3631: $i] :
( ( c_in @ SV561 @ SY3630 @ SY3631 )
| ! [SY3632: $i,SY3633: $i] :
( ~ ( c_in @ ( c_Pair @ SY3632 @ SV561 @ SY3631 @ SY3631 ) @ SY3633 @ ( tc_prod @ SY3631 @ SY3631 ) )
| ~ ( c_Relation_Orefl__on @ SY3630 @ SY3633 @ SY3631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2676,plain,
! [SV562: $i] :
( ( ! [SY3634: $i,SY3635: $i] :
( ( c_in @ SV562 @ SY3634 @ SY3635 )
| ! [SY3636: $i,SY3637: $i] :
( ~ ( c_in @ ( c_Pair @ SV562 @ SY3636 @ SY3635 @ SY3635 ) @ SY3637 @ ( tc_prod @ SY3635 @ SY3635 ) )
| ~ ( c_Relation_Orefl__on @ SY3634 @ SY3637 @ SY3635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2677,plain,
! [SV563: $i] :
( ( ! [SY3638: $i,SY3639: $i] :
( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SY3638 @ SY3638 ) @ SY3639 @ ( tc_prod @ SY3638 @ SY3638 ) )
| ! [SY3640: $i] :
( ~ ( c_in @ SV563 @ SY3640 @ SY3638 )
| ~ ( c_Relation_Orefl__on @ SY3640 @ SY3639 @ SY3638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2678,plain,
! [SV564: $i] :
( ( ! [SY3641: $i,SY3642: $i,SY3643: $i] :
( ( c_in @ ( c_Pair @ SV564 @ SY3641 @ SY3642 @ SY3642 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY3642 @ SY3642 ) @ SY3643 ) @ SY3642 ) @ ( tc_prod @ SY3642 @ SY3642 ) )
| ~ ( c_in @ ( c_Pair @ SV564 @ SY3641 @ SY3642 @ SY3642 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3642 @ SY3642 ) @ ( c_Transitive__Closure_Otrancl @ SY3643 @ SY3642 ) ) @ ( tc_prod @ SY3642 @ SY3642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2679,plain,
! [SV565: $i] :
( ( ! [SY3644: $i,SY3645: $i,SY3646: $i] :
( ( c_in @ ( c_Pair @ SV565 @ SY3644 @ SY3645 @ SY3645 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3645 @ SY3645 ) @ ( c_Transitive__Closure_Otrancl @ SY3646 @ SY3645 ) ) @ ( tc_prod @ SY3645 @ SY3645 ) )
| ~ ( c_in @ ( c_Pair @ SV565 @ SY3644 @ SY3645 @ SY3645 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY3645 @ SY3645 ) @ SY3646 ) @ SY3645 ) @ ( tc_prod @ SY3645 @ SY3645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2680,plain,
! [SV566: $i] :
( ( ! [SY3647: $i,SY3648: $i,SY3649: $i] :
( ( c_in @ ( c_Pair @ SV566 @ SY3647 @ SY3648 @ SY3648 ) @ ( c_Transitive__Closure_Ortrancl @ SY3649 @ SY3648 ) @ ( tc_prod @ SY3648 @ SY3648 ) )
| ~ ( c_in @ ( c_Pair @ SY3647 @ SV566 @ SY3648 @ SY3648 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY3648 @ SY3648 ) @ SY3649 ) @ SY3648 ) @ ( tc_prod @ SY3648 @ SY3648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2681,plain,
! [SV567: $i] :
( ( ! [SY3650: $i,SY3651: $i,SY3652: $i] :
( ( c_in @ ( c_Pair @ SV567 @ SY3650 @ SY3651 @ SY3651 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY3651 @ SY3651 ) @ SY3652 ) @ SY3651 ) @ ( tc_prod @ SY3651 @ SY3651 ) )
| ~ ( c_in @ ( c_Pair @ SY3650 @ SV567 @ SY3651 @ SY3651 ) @ ( c_Transitive__Closure_Ortrancl @ SY3652 @ SY3651 ) @ ( tc_prod @ SY3651 @ SY3651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2682,plain,
( ( v_a____ = v_b____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2683,plain,
! [SV568: $i] :
( ( ! [SY3653: $i,SY3654: $i,SY3655: $i,SY3656: $i,SY3657: $i,SY3658: $i,SY3659: $i,SY3660: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SY3653 @ SY3654 ) )
!= ( hAPP @ SY3655 @ ( hAPP @ SY3656 @ SY3657 ) ) )
| ! [SY3661: $i,SY3662: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SY3653 @ SY3658 @ SY3659 @ SY3660 ) @ SY3654 )
= ( hAPP @ ( c_Fun_Ocomp @ SY3655 @ SY3656 @ SY3661 @ SY3659 @ SY3662 ) @ SY3657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2684,plain,
! [SV569: $i] :
( ( ! [SY3663: $i,SY3664: $i,SY3665: $i,SY3666: $i,SY3667: $i,SY3668: $i] :
( ! [SY3669: $i] :
( ( c_Fun_Ocomp @ SV569 @ SY3663 @ SY3664 @ SY3665 @ SY3666 )
!= ( c_Fun_Ocomp @ SY3667 @ SY3668 @ SY3669 @ SY3665 @ SY3666 ) )
| ! [SY3670: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SY3663 @ SY3670 ) )
= ( hAPP @ SY3667 @ ( hAPP @ SY3668 @ SY3670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2685,plain,
! [SV570: $i] :
( ( ! [SY3671: $i,SY3672: $i,SY3673: $i,SY3674: $i,SY3675: $i] :
( ( ( c_Pair @ SV570 @ SY3671 @ SY3672 @ SY3673 )
!= ( c_Pair @ SY3674 @ SY3675 @ SY3672 @ SY3673 ) )
| ( SY3671 = SY3675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2686,plain,
! [SV571: $i] :
( ( ! [SY3676: $i,SY3677: $i,SY3678: $i,SY3679: $i] :
( ! [SY3680: $i] :
( ( c_Pair @ SV571 @ SY3676 @ SY3677 @ SY3678 )
!= ( c_Pair @ SY3679 @ SY3680 @ SY3677 @ SY3678 ) )
| ( SV571 = SY3679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2687,plain,
! [SV572: $i] :
( ( ! [SY3681: $i,SY3682: $i,SY3683: $i,SY3684: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SY3681 @ SY3682 @ SY3683 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3683 @ SY3682 ) @ SY3684 ) @ ( tc_prod @ SY3682 @ SY3683 ) )
| ~ ( c_in @ ( c_Pair @ SY3681 @ SV572 @ SY3683 @ SY3682 ) @ SY3684 @ ( tc_prod @ SY3683 @ SY3682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2688,plain,
! [SV573: $i] :
( ( ! [SY3685: $i,SY3686: $i,SY3687: $i,SY3688: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SY3685 @ SY3686 @ SY3687 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3687 @ SY3686 ) @ SY3688 ) @ ( tc_prod @ SY3686 @ SY3687 ) )
| ~ ( c_in @ ( c_Pair @ SY3685 @ SV573 @ SY3687 @ SY3686 ) @ SY3688 @ ( tc_prod @ SY3687 @ SY3686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2689,plain,
! [SV574: $i] :
( ( ! [SY3689: $i,SY3690: $i,SY3691: $i,SY3692: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SY3689 @ SY3690 @ SY3691 ) @ SY3692 @ ( tc_prod @ SY3690 @ SY3691 ) )
| ~ ( c_in @ ( c_Pair @ SY3689 @ SV574 @ SY3691 @ SY3690 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3690 @ SY3691 ) @ SY3692 ) @ ( tc_prod @ SY3691 @ SY3690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2690,plain,
! [SV575: $i] :
( ( ! [SY3693: $i,SY3694: $i,SY3695: $i,SY3696: $i,SY3697: $i,SY3698: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SY3693 @ SY3694 @ SY3695 @ SY3696 @ SY3697 ) @ SY3696 @ SY3698 @ SY3697 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SY3693 @ SY3696 @ SY3698 @ SY3695 ) @ SY3694 @ SY3695 @ SY3698 @ SY3697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2691,plain,
! [SV576: $i] :
( ( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ SV576 ) @ ( 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____ @ SV576 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2692,plain,
! [SV577: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV577 ) @ ( 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____ @ SV577 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2693,plain,
( ( v_b____ = v_c____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2694,plain,
! [SV578: $i] :
( ( ! [SY3699: $i,SY3700: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV578 @ SY3699 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY3699 @ SV578 ) @ SY3700 ) )
= SY3700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2695,plain,
! [SV579: $i] :
( ( ! [SY3701: $i,SY3702: $i,SY3703: $i,SY3704: $i,SY3705: $i] :
( ( hAPP @ SV579 @ ( hAPP @ SY3701 @ SY3702 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SY3701 @ SY3703 @ SY3704 @ SY3705 ) @ SY3702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2696,plain,
! [SV580: $i] :
( ( ! [SY3706: $i,SY3707: $i,SY3708: $i,SY3709: $i,SY3710: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SY3706 @ SY3707 @ SY3708 @ SY3709 ) @ SY3710 )
= ( hAPP @ SV580 @ ( hAPP @ SY3706 @ SY3710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2697,plain,
! [SV581: $i] :
( ( ! [SY3711: $i] :
( ! [SY3712: $i] : ( c_in @ SV581 @ SY3711 @ SY3712 )
| ~ ( hBOOL @ ( hAPP @ SY3711 @ SV581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2698,plain,
! [SV582: $i] :
( ( ! [SY3713: $i] :
( ( hBOOL @ ( hAPP @ SV582 @ SY3713 ) )
| ! [SY3714: $i] :
~ ( c_in @ SY3713 @ SV582 @ SY3714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2699,plain,
( ( v_a____ = v_c____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2700,plain,
! [SV583: $i] :
( ( ! [SY3715: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV583 @ SY3715 ) )
| ~ ( class_Lattices_Olattice @ SY3715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2701,plain,
! [SV584: $i] :
( ( ! [SY3716: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV584 @ SY3716 ) )
| ~ ( class_Lattices_Olattice @ SY3716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2702,plain,
! [SV585: $i] :
( ( ! [SY3717: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV585 @ SY3717 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY3717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2703,plain,
! [SV586: $i] :
( ( ! [SY3718: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV586 @ SY3718 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY3718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2704,plain,
! [SV587: $i] :
( ( ! [SY3719: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV587 @ SY3719 ) )
| ~ ( class_Orderings_Opreorder @ SY3719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2705,plain,
! [SV588: $i] :
( ( ! [SY3720: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV588 @ SY3720 ) )
| ~ ( class_Lattices_Olattice @ SY3720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2706,plain,
! [SV589: $i] :
( ( ! [SY3721: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV589 @ SY3721 ) )
| ~ ( class_Orderings_Oorder @ SY3721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2707,plain,
! [SV590: $i] :
( ( ! [SY3722: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV590 @ SY3722 ) )
| ~ ( class_Orderings_Obot @ SY3722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2708,plain,
! [SV591: $i] :
( ( ! [SY3723: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV591 @ SY3723 ) )
| ~ ( class_HOL_Oord @ SY3723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2709,plain,
! [SV592: $i] :
( ( ! [SY3724: $i] : ( c_fequal @ SV592 @ SV592 @ SY3724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2710,plain,
! [SV593: $i] :
( ( ! [SY3725: $i] :
( ( SV593 = SY3725 )
| ! [SY3726: $i] :
~ ( c_fequal @ SV593 @ SY3725 @ SY3726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2711,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2712,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV1 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( 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 ) @ SV1 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2713,plain,
! [SV2: $i] :
( ( ( 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 ) @ SV2 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV2 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2714,plain,
! [SV594: $i,SV3: $i] :
( ( ! [SY3727: $i,SY3728: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SV594 @ ( tc_fun @ SY3727 @ tc_bool ) ) @ SY3728 @ ( tc_fun @ SY3727 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SY3728 @ ( tc_fun @ SY3727 @ tc_bool ) ) @ ( tc_fun @ SY3727 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2715,plain,
! [SV595: $i,SV4: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ SY3729 @ ( tc_fun @ SY3730 @ tc_bool ) ) @ ( tc_fun @ SY3730 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ SY3729 @ ( tc_fun @ SY3730 @ tc_bool ) ) @ ( tc_fun @ SY3730 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2716,plain,
! [SV596: $i,SV5: $i] :
( ( ! [SY3731: $i,SY3732: $i,SY3733: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SY3731 @ SY3732 ) @ SY3733 @ ( tc_fun @ SY3732 @ tc_bool ) )
| ! [SY2170: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY2170 @ ( c_COMBK @ SY3733 @ ( tc_fun @ SY3732 @ tc_bool ) @ SY3731 ) @ SY3731 @ SY3732 ) @ ( tc_fun @ ( tc_prod @ SY3731 @ SY3732 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2717,plain,
! [SV597: $i,SV6: $i] :
( ( ! [SY3735: $i] :
( ( c_Set_Oinsert @ SV6 @ ( c_Set_Oinsert @ SV597 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3735 @ tc_bool ) ) @ SY3735 ) @ SY3735 )
= ( c_Set_Oinsert @ SV597 @ ( c_Set_Oinsert @ SV6 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3735 @ tc_bool ) ) @ SY3735 ) @ SY3735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2718,plain,
! [SV598: $i,SV8: $i] :
( ( ! [SY3736: $i,SY3737: $i] :
( ( hAPP @ ( c_COMBK @ SV8 @ SV598 @ SY3736 ) @ SY3737 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2719,plain,
! [SV599: $i,SV9: $i] :
( ( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SV599 ) @ tc_bool ) ) @ SV9 @ SV599 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV9 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2720,plain,
! [SV600: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
| ! [SY2178: $i,SY2179: $i] :
( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SY2178 @ SY2179 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2178 @ SY2179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2721,plain,
! [SV601: $i,SV11: $i] :
( ( ! [SY3740: $i,SY3741: $i,SY3742: $i] :
( ( c_Relation_OImage @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV601 @ SY3740 @ ( tc_fun @ SY3741 @ tc_bool ) ) @ SY3741 @ SY3742 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV11 @ SV601 @ SY3741 @ SY3742 ) @ ( c_Relation_OImage @ SV11 @ SY3740 @ SY3741 @ SY3742 ) @ ( tc_fun @ SY3742 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2722,plain,
! [SV602: $i,SV12: $i] :
( ( ! [SY3743: $i,SY3744: $i,SY3745: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV12 @ SV602 @ ( tc_fun @ ( tc_prod @ SY3743 @ SY3744 ) @ tc_bool ) ) @ SY3745 @ SY3743 @ SY3744 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV12 @ SY3745 @ SY3743 @ SY3744 ) @ ( c_Relation_OImage @ SV602 @ SY3745 @ SY3743 @ SY3744 ) @ ( tc_fun @ SY3744 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2723,plain,
! [SV603: $i,SV13: $i] :
( ( ! [SY3746: $i,SY3747: $i,SY3748: $i,SY3749: $i,SY3750: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SY3746 @ SY3747 @ SY3748 ) @ ( c_Relation_Orel__comp @ SY3749 @ SY3750 @ SY3746 @ SY3747 @ SY3748 ) @ ( tc_fun @ ( tc_prod @ SY3746 @ SY3748 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SY3750 @ ( tc_fun @ ( tc_prod @ SY3747 @ SY3748 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SY3749 @ ( tc_fun @ ( tc_prod @ SY3746 @ SY3747 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2724,plain,
! [SV14: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV14 ) )
= $true )
| ( ( ! [SY2194: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2194 @ SY2194 @ SV14 )
= SY2194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2725,plain,
! [SV604: $i,SV15: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV15 @ SV15 @ ( tc_fun @ SV604 @ tc_bool ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2726,plain,
! [SV605: $i,SV16: $i] :
( ( ! [SY3751: $i] :
( ( c_lessequals @ SV16 @ ( c_Product__Type_OSigma @ SV605 @ ( c_COMBK @ SV605 @ ( tc_fun @ SY3751 @ tc_bool ) @ SY3751 ) @ SY3751 @ SY3751 ) @ ( tc_fun @ ( tc_prod @ SY3751 @ SY3751 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV605 @ SV16 @ SY3751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2727,plain,
! [SV606: $i,SV17: $i] :
( ( c_lessequals @ ( c_Relation_OId__on @ SV17 @ SV606 ) @ ( c_Product__Type_OSigma @ SV17 @ ( c_COMBK @ SV17 @ ( tc_fun @ SV606 @ tc_bool ) @ SV606 ) @ SV606 @ SV606 ) @ ( tc_fun @ ( tc_prod @ SV606 @ SV606 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2728,plain,
! [SV607: $i,SV18: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV18 )
| ! [SY3752: $i,SY3753: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SY3752 @ SV18 ) @ SY3753 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV607 @ SY3753 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3752 @ SY3753 @ SV18 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2729,plain,
! [SV608: $i,SV19: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV19 )
| ! [SY3754: $i,SY3755: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3754 @ SY3755 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3754 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3755 @ SV19 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2730,plain,
! [SV609: $i,SV20: $i] :
( ( ! [SY3756: $i,SY3757: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV609 @ SY3756 @ ( tc_fun @ SY3757 @ tc_bool ) ) @ ( tc_fun @ SY3757 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV609 @ ( tc_fun @ SY3757 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY3756 @ ( tc_fun @ SY3757 @ tc_bool ) ) @ ( tc_fun @ SY3757 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2731,plain,
! [SV610: $i,SV21: $i] :
( ( ! [SY3758: $i,SY3759: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV610 @ ( tc_fun @ SY3758 @ tc_bool ) ) @ SY3759 @ ( tc_fun @ SY3758 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV21 @ SY3759 @ ( tc_fun @ SY3758 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV610 @ SY3759 @ ( tc_fun @ SY3758 @ tc_bool ) ) @ ( tc_fun @ SY3758 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2732,plain,
! [SV611: $i,SV22: $i] :
( ( ( SV22 = SV611 )
| ! [SY3760: $i] :
~ ( c_in @ SV22 @ ( c_Set_Oinsert @ SV611 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3760 @ tc_bool ) ) @ SY3760 ) @ SY3760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2733,plain,
! [SV612: $i,SV23: $i] :
( ( ! [SY3761: $i,SY3762: $i,SY3763: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV23 @ SV612 @ ( tc_fun @ SY3761 @ tc_bool ) ) @ SY3762 @ SY3761 @ SY3763 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV23 @ SY3762 @ SY3761 @ SY3763 ) @ ( c_Product__Type_OSigma @ SV612 @ SY3762 @ SY3761 @ SY3763 ) @ ( tc_fun @ ( tc_prod @ SY3761 @ SY3763 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2734,plain,
! [SV613: $i,SV24: $i] :
( ( ! [SY3764: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SY3764 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SY3764 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SY3764 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV24 @ SY3764 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2735,plain,
! [SV614: $i,SV25: $i] :
( ( ! [SY3765: $i,SY3766: $i] :
( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SY3765 @ tc_bool ) )
| ! [SY3767: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SY3766 @ ( tc_fun @ SY3767 @ tc_bool ) @ SY3765 ) @ SY3765 @ SY3767 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SY3766 @ ( tc_fun @ SY3767 @ tc_bool ) @ SY3765 ) @ SY3765 @ SY3767 ) @ ( tc_fun @ ( tc_prod @ SY3765 @ SY3767 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY3766 @ SY3767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2736,plain,
! [SV615: $i,SV26: $i] :
( ( ! [SY3769: $i,SY3770: $i,SY3771: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SY3769 @ tc_bool ) @ SY3770 ) @ SY3770 @ SY3769 ) @ ( c_Product__Type_OSigma @ SY3771 @ ( c_COMBK @ SV615 @ ( tc_fun @ SY3769 @ tc_bool ) @ SY3770 ) @ SY3770 @ SY3769 ) @ ( tc_fun @ ( tc_prod @ SY3770 @ SY3769 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV26 @ SY3771 @ ( tc_fun @ SY3770 @ tc_bool ) )
| ! [SY3772: $i] :
~ ( c_in @ SY3772 @ SV615 @ SY3769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2737,plain,
! [SV616: $i,SV27: $i] :
( ( ! [SY3773: $i] :
( ( c_lessequals @ SV27 @ SV616 @ ( tc_fun @ SY3773 @ tc_bool ) )
| ! [SY3774: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY3774 @ SV27 @ SY3773 ) @ SV616 @ ( tc_fun @ SY3773 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2738,plain,
! [SV617: $i,SV28: $i] :
( ( ! [SY3775: $i,SY3776: $i] :
( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SV617 @ SY3775 @ SY3776 ) @ ( tc_fun @ SY3776 @ tc_bool ) )
| ~ ( c_lessequals @ SV28 @ SY3775 @ ( tc_fun @ SY3776 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2739,plain,
! [SV618: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
| ! [SY2236: $i,SY2237: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SY2236 @ SY2237 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2236 @ SY2237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2740,plain,
! [SV619: $i,SV30: $i] :
( ( ! [SY3779: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV30 @ SV619 ) @ ( c_Transitive__Closure_Ortrancl @ SY3779 @ SV619 ) @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV30 @ SY3779 @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) ) @ SV619 ) @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2741,plain,
! [SV620: $i,SV31: $i] :
( ( ! [SY3780: $i,SY3781: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV31 @ SV620 @ SY3780 ) @ SY3781 @ ( tc_fun @ SY3780 @ tc_bool ) )
= ( c_Set_Oinsert @ SV31 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SY3781 @ ( tc_fun @ SY3780 @ tc_bool ) ) @ SY3780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2742,plain,
! [SV621: $i,SV32: $i] :
( ( ! [SY3782: $i,SY3783: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Set_Oinsert @ SV621 @ SY3782 @ SY3783 ) @ ( tc_fun @ SY3783 @ tc_bool ) )
= ( c_Set_Oinsert @ SV621 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SY3782 @ ( tc_fun @ SY3783 @ tc_bool ) ) @ SY3783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2743,plain,
! [SV622: $i,SV33: $i] :
( ( ! [SY3784: $i,SY3785: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SV622 ) @ tc_bool ) ) @ SY3784 @ SV33 @ SV622 @ SY3785 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SY3785 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2744,plain,
! [SV623: $i,SV34: $i] :
( ( ! [SY3786: $i,SY3787: $i] :
( ( c_Relation_Orel__comp @ SV34 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV623 @ SY3786 ) @ tc_bool ) ) @ SY3787 @ SV623 @ SY3786 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3787 @ SY3786 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2745,plain,
! [SV624: $i,SV35: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV35 @ tc_bool ) ) @ SV624 @ ( tc_fun @ SV35 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2746,plain,
! [SV625: $i,SV36: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV36 @ SV36 ) @ tc_bool ) ) @ SV625 @ ( tc_fun @ ( tc_prod @ SV36 @ SV36 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2747,plain,
! [SV37: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV37 ) )
= $true )
| ( ( ! [SY2254: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV37 ) @ SY2254 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2748,plain,
! [SV626: $i,SV38: $i] :
( ( ! [SY3788: $i] :
( ( c_Set_Oinsert @ SV38 @ SV626 @ SY3788 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3788 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2749,plain,
! [SV627: $i,SV39: $i] :
( ( ! [SY3789: $i,SY3790: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV39 @ SV627 @ SY3789 ) @ ( c_Set_Oinsert @ SV39 @ SY3790 @ SY3789 ) @ ( tc_fun @ SY3789 @ tc_bool ) )
= ( c_Set_Oinsert @ SV39 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV627 @ SY3790 @ ( tc_fun @ SY3789 @ tc_bool ) ) @ SY3789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2750,plain,
! [SV628: $i,SV40: $i] :
( ( ! [SY3791: $i] :
( ( c_Relation_OImage @ SV40 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV628 @ tc_bool ) ) @ SV628 @ SY3791 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3791 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2751,plain,
! [SV629: $i,SV41: $i] :
( ( ! [SY3792: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SY3792 @ SY3792 ) @ tc_bool ) ) @ SY3792 )
| ~ ( c_Relation_Osym @ SV629 @ SY3792 )
| ~ ( c_Relation_Osym @ SV41 @ SY3792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2752,plain,
! [SV630: $i,SV42: $i] :
( ( ! [SY3793: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV42 @ SV630 ) @ ( c_Transitive__Closure_Ortrancl @ SY3793 @ SV630 ) @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV42 @ SY3793 @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2753,plain,
! [SV631: $i,SV43: $i] :
( ( ! [SY3794: $i,SY3795: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV43 @ SV631 @ ( tc_fun @ ( tc_prod @ SY3794 @ SY3795 ) @ tc_bool ) ) @ SY3794 @ SY3795 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV43 @ SY3794 @ SY3795 ) @ ( c_Relation_ODomain @ SV631 @ SY3794 @ SY3795 ) @ ( tc_fun @ SY3794 @ tc_bool ) ) @ ( tc_fun @ SY3794 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2754,plain,
! [SV44: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV44 ) )
= $true )
| ( ( ! [SY2269: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2269 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= ( c_Orderings_Obot__class_Obot @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2755,plain,
! [SV45: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV45 ) )
= $true )
| ( ( ! [SY2270: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV45 ) @ SY2270 @ SV45 )
= ( c_Orderings_Obot__class_Obot @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2756,plain,
! [SV632: $i,SV46: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV46 @ tc_bool ) ) @ SV632 @ ( tc_fun @ SV46 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV46 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2757,plain,
! [SV633: $i,SV47: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV47 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV633 @ tc_bool ) ) @ ( tc_fun @ SV633 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV633 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2758,plain,
! [SV634: $i,SV48: $i] :
( ( ! [SY3796: $i] : ( c_lessequals @ SV48 @ ( c_Set_Oinsert @ SV634 @ SV48 @ SY3796 ) @ ( tc_fun @ SY3796 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2759,plain,
! [SV635: $i,SV49: $i] :
( ( ! [SY3797: $i,SY3798: $i,SY3799: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV49 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SY3797 @ ( tc_fun @ SY3798 @ tc_bool ) ) @ SY3798 @ SY3799 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV49 @ SV635 @ SY3798 @ SY3799 ) @ ( c_Relation_OImage @ SV49 @ SY3797 @ SY3798 @ SY3799 ) @ ( tc_fun @ SY3799 @ tc_bool ) ) @ ( tc_fun @ SY3799 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2760,plain,
! [SV636: $i,SV50: $i] :
( ( ! [SY3800: $i,SY3801: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SV636 @ ( tc_fun @ SY3800 @ tc_bool ) ) @ SY3801 @ ( tc_fun @ SY3800 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV636 @ SY3801 @ ( tc_fun @ SY3800 @ tc_bool ) ) @ ( tc_fun @ SY3800 @ tc_bool ) ) )
| ( c_lessequals @ SY3801 @ SV50 @ ( tc_fun @ SY3800 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2761,plain,
! [SV637: $i,SV51: $i] :
( ( ! [SY3802: $i,SY3803: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SV637 @ ( tc_fun @ SY3802 @ tc_bool ) ) @ SY3803 @ ( tc_fun @ SY3802 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV637 @ SY3803 @ ( tc_fun @ SY3802 @ tc_bool ) ) @ ( tc_fun @ SY3802 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY3803 @ SV51 @ ( tc_fun @ SY3802 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2762,plain,
! [SV638: $i,SV52: $i] :
( ( ! [SY3804: $i,SY3805: $i,SY3806: $i,SY3807: $i,SY3808: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SY3804 @ SY3805 @ SY3806 ) @ ( c_Product__Type_OSigma @ SY3807 @ ( c_COMBK @ SY3808 @ ( tc_fun @ SY3806 @ tc_bool ) @ SY3804 ) @ SY3804 @ SY3806 ) @ ( tc_fun @ ( tc_prod @ SY3804 @ SY3806 ) @ tc_bool ) )
| ! [SY3809: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY3809 @ ( c_COMBK @ SY3808 @ ( tc_fun @ SY3806 @ tc_bool ) @ SY3805 ) @ SY3805 @ SY3806 ) @ ( tc_fun @ ( tc_prod @ SY3805 @ SY3806 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SY3807 @ ( c_COMBK @ SY3809 @ ( tc_fun @ SY3805 @ tc_bool ) @ SY3804 ) @ SY3804 @ SY3805 ) @ ( tc_fun @ ( tc_prod @ SY3804 @ SY3805 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2763,plain,
! [SV639: $i,SV53: $i] :
( ( ! [SY3810: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SY3810 @ SY3810 ) @ tc_bool ) ) @ SY3810 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SY3810 @ SY3810 @ SY3810 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SY3810 @ SY3810 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV639 @ SY3810 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SY3810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2764,plain,
! [SV640: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
| ! [SY3811: $i] :
( ( hBOOL @ ( hAPP @ SY3811 @ SV640 ) )
| ! [SY3812: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3811 @ SV54 @ ( tc_fun @ SY3812 @ tc_bool ) ) @ SV640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2765,plain,
! [SV641: $i,SV55: $i] :
( ( ! [SY3813: $i,SY3814: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV641 @ ( tc_fun @ SY3813 @ tc_bool ) ) @ SY3814 ) )
| ~ ( hBOOL @ ( hAPP @ SV641 @ SY3814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2766,plain,
! [SV642: $i,SV56: $i] :
( ( ! [SY3815: $i,SY3816: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV642 @ ( tc_fun @ SY3815 @ tc_bool ) ) @ SY3816 ) )
| ~ ( hBOOL @ ( hAPP @ SV56 @ SY3816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2767,plain,
! [SV643: $i,SV57: $i] :
( ( ! [SY3817: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SY3817 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SY3817 @ SV643 )
| ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SY3817 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2768,plain,
! [SV644: $i,SV58: $i] :
( ( ! [SY3818: $i,SY3819: $i,SY3820: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV644 @ ( tc_fun @ SY3818 @ tc_bool ) ) @ ( c_COMBK @ SY3819 @ ( tc_fun @ SY3820 @ tc_bool ) @ SY3818 ) @ SY3818 @ SY3820 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV58 @ ( c_COMBK @ SY3819 @ ( tc_fun @ SY3820 @ tc_bool ) @ SY3818 ) @ SY3818 @ SY3820 ) @ ( c_Product__Type_OSigma @ SV644 @ ( c_COMBK @ SY3819 @ ( tc_fun @ SY3820 @ tc_bool ) @ SY3818 ) @ SY3818 @ SY3820 ) @ ( tc_fun @ ( tc_prod @ SY3818 @ SY3820 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2769,plain,
! [SV645: $i,SV59: $i] :
( ( ! [SY3821: $i,SY3822: $i,SY3823: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SY3821 @ SY3822 @ SY3823 ) @ SY3821 @ SY3823 )
| ~ ( c_Relation_Osingle__valued @ SV645 @ SY3822 @ SY3823 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SY3821 @ SY3822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2770,plain,
! [SV646: $i,SV60: $i] :
( ( ! [SY3824: $i,SY3825: $i,SY3826: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SY3824 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3825 @ SY3826 @ ( tc_fun @ ( tc_prod @ SY3824 @ SY3824 ) @ tc_bool ) ) @ SY3824 )
| ~ ( c_Relation_Orefl__on @ SV646 @ SY3826 @ SY3824 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SY3825 @ SY3824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2771,plain,
! [SV647: $i,SV61: $i] :
( ( ~ ( class_Lattices_Olattice @ SV61 )
| ! [SY3827: $i,SY3828: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SY3827 @ SV61 ) @ SY3828 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3827 @ SY3828 @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2772,plain,
! [SV648: $i,SV62: $i] :
( ( ~ ( class_Lattices_Olattice @ SV62 )
| ! [SY3829: $i,SY3830: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ SY3830 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ SY3830 @ SV62 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2773,plain,
! [SV649: $i,SV63: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV63 )
| ! [SY3831: $i,SY3832: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ SY3832 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ SY3832 @ SV63 ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2774,plain,
! [SV650: $i,SV64: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV64 )
| ! [SY3833: $i,SY3834: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ SY3833 @ SV64 ) @ SY3834 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3833 @ SY3834 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2775,plain,
! [SV651: $i,SV65: $i] :
( ( ! [SY3835: $i,SY3836: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ SV651 @ ( tc_fun @ SY3835 @ tc_bool ) ) @ SY3836 @ ( tc_fun @ SY3835 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV651 @ SY3836 @ ( tc_fun @ SY3835 @ tc_bool ) ) @ ( tc_fun @ SY3835 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2776,plain,
! [SV652: $i,SV66: $i] :
( ( ! [SY3837: $i,SY3838: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ SY3837 @ ( tc_fun @ SY3838 @ tc_bool ) ) @ ( tc_fun @ SY3838 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ SY3837 @ ( tc_fun @ SY3838 @ tc_bool ) ) @ ( tc_fun @ SY3838 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2777,plain,
! [SV67: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV67 ) )
= $true )
| ( ( ! [SY2335: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2335 @ ( c_Orderings_Obot__class_Obot @ SV67 ) @ SV67 )
= SY2335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2778,plain,
! [SV68: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV68 ) )
= $true )
| ( ( ! [SY2336: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV68 ) @ SY2336 @ SV68 )
= SY2336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2779,plain,
! [SV653: $i,SV69: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV69 @ tc_bool ) ) @ SV653 @ ( tc_fun @ SV69 @ tc_bool ) )
= SV653 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2780,plain,
! [SV654: $i,SV70: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV654 @ tc_bool ) ) @ ( tc_fun @ SV654 @ tc_bool ) )
= SV70 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2781,plain,
! [SV655: $i,SV71: $i] :
( ( ! [SY3839: $i,SY3840: $i,SY3841: $i,SY3842: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SY3839 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY3840 @ SY3841 @ SY3842 ) @ ( tc_fun @ SY3842 @ tc_bool ) @ SY3839 ) @ SY3839 @ SY3842 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SY3840 @ SY3839 @ SY3842 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV655 @ ( c_COMBK @ ( c_Set_Oinsert @ SY3840 @ SY3841 @ SY3842 ) @ ( tc_fun @ SY3842 @ tc_bool ) @ SY3839 ) @ SY3839 @ SY3842 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SY3839 ) @ ( c_COMBK @ SY3841 @ ( tc_fun @ SY3842 @ tc_bool ) @ SY3839 ) @ SY3839 @ SY3842 ) @ ( tc_fun @ ( tc_prod @ SY3839 @ SY3842 ) @ tc_bool ) ) @ ( tc_prod @ SY3839 @ SY3842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2782,plain,
! [SV656: $i,SV72: $i] :
( ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
| ! [SY3843: $i] :
( ~ ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SY3843 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY3843 @ SV656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2783,plain,
! [SV657: $i,SV73: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV73 @ tc_bool ) ) @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2784,plain,
! [SV658: $i,SV74: $i] :
( ( ! [SY3844: $i] :
( ~ ( c_in @ SV74 @ SV658 @ SY3844 )
| ! [SY3845: $i] :
( ~ ( c_in @ SV74 @ SY3845 @ SY3844 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3845 @ SV658 @ ( tc_fun @ SY3844 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3844 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2785,plain,
! [SV659: $i,SV75: $i] :
( ( ~ ( class_Lattices_Olattice @ SV75 )
| ! [SY3846: $i,SY3847: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3846 @ SY3847 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3846 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3847 @ SV75 ) @ SV75 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2786,plain,
! [SV76: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV76 ) )
= $true )
| ( ( ! [SY2353: $i,SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2353 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2353 @ SY2354 @ SV76 ) @ SV76 )
= SY2353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2787,plain,
! [SV660: $i,SV77: $i] :
( ( ! [SY3848: $i] :
( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SY3848 @ SY3848 @ SY3848 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3848 @ SY3848 ) @ tc_bool ) ) )
| ! [SY3849: $i] :
( ( ( c_Relation_Orel__comp @ SY3849 @ SV660 @ SY3848 @ SY3848 @ SY3848 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3848 @ SY3848 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3849 @ SV77 @ ( tc_fun @ ( tc_prod @ SY3848 @ SY3848 ) @ tc_bool ) ) @ SV660 @ SY3848 @ SY3848 @ SY3848 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3848 @ SY3848 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2788,plain,
! [SV661: $i,SV78: $i] :
( ( ! [SY3850: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SY3850 @ SY3850 @ SY3850 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3850 @ SY3850 ) @ tc_bool ) ) )
| ! [SY3851: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY3851 @ SY3850 @ SY3850 @ SY3850 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3850 @ SY3850 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3851 @ SV661 @ ( tc_fun @ ( tc_prod @ SY3850 @ SY3850 ) @ tc_bool ) ) @ SY3850 @ SY3850 @ SY3850 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3850 @ SY3850 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2789,plain,
! [SV662: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
| ! [SY2362: $i,SY2363: $i] :
( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SY2362 @ SY2363 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2362 @ SY2363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2790,plain,
! [SV663: $i,SV80: $i] :
( ( ( SV80 = SV663 )
| ! [SY3854: $i] :
( ~ ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SY3854 @ tc_bool ) )
| ~ ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SY3854 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2791,plain,
! [SV664: $i,SV81: $i] :
( ( ( SV81 = SV664 )
| ! [SY3855: $i] :
( ~ ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SY3855 @ tc_bool ) )
| ~ ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SY3855 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2792,plain,
! [SV82: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV82 ) )
= $true )
| ( ( ! [SY2368: $i,SY2369: $i] :
( ( SY2368 = SY2369 )
| ~ ( c_lessequals @ SY2369 @ SY2368 @ SV82 )
| ~ ( c_lessequals @ SY2368 @ SY2369 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2793,plain,
! [SV83: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV83 ) )
= $true )
| ( ( ! [SY2370: $i,SY2371: $i] :
( ( SY2370 = SY2371 )
| ~ ( c_lessequals @ SY2371 @ SY2370 @ SV83 )
| ~ ( c_lessequals @ SY2370 @ SY2371 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2794,plain,
! [SV84: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV84 ) )
= $true )
| ( ( ! [SY2372: $i,SY2373: $i] :
( ( SY2372 = SY2373 )
| ~ ( c_lessequals @ SY2372 @ SY2373 @ SV84 )
| ~ ( c_lessequals @ SY2373 @ SY2372 @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2795,plain,
! [SV85: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV85 ) )
= $true )
| ( ( ! [SY2374: $i,SY2375: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2374 @ SY2375 @ SV85 ) @ SV85 )
= SY2374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2796,plain,
! [SV86: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV86 ) )
= $true )
| ( ( ! [SY2376: $i,SY2377: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2376 @ SY2377 @ SV86 )
= SY2376 )
| ~ ( c_lessequals @ SY2377 @ SY2376 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2797,plain,
! [SV87: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV87 ) )
= $true )
| ( ( ! [SY2378: $i,SY2379: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2378 @ SY2379 @ SV87 )
!= SY2379 )
| ( c_lessequals @ SY2378 @ SY2379 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2798,plain,
! [SV88: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 ) )
= $true )
| ( ( ! [SY2380: $i,SY2381: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2380 @ SY2381 @ SV88 )
= SY2381 )
| ~ ( c_lessequals @ SY2380 @ SY2381 @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2799,plain,
! [SV665: $i,SV89: $i] :
( ( ! [SY3856: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV89 @ SV665 @ ( tc_fun @ SY3856 @ tc_bool ) )
= SV665 )
| ~ ( c_lessequals @ SV89 @ SV665 @ ( tc_fun @ SY3856 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2800,plain,
! [SV666: $i,SV90: $i] :
( ( ! [SY3857: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV90 @ SV666 @ ( tc_fun @ SY3857 @ tc_bool ) )
= SV90 )
| ~ ( c_lessequals @ SV666 @ SV90 @ ( tc_fun @ SY3857 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2801,plain,
! [SV667: $i,SV91: $i] :
( ( ! [SY3858: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV91 @ SV667 @ ( tc_fun @ SY3858 @ tc_bool ) )
!= SV667 )
| ( c_lessequals @ SV91 @ SV667 @ ( tc_fun @ SY3858 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2802,plain,
! [SV668: $i,SV92: $i] :
( ( ! [SY3859: $i,SY3860: $i,SY3861: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SY3859 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3860 @ SY3861 @ ( tc_fun @ ( tc_prod @ SY3859 @ SY3859 ) @ tc_bool ) ) @ SY3859 )
| ~ ( c_Relation_Orefl__on @ SV668 @ SY3861 @ SY3859 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SY3860 @ SY3859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2803,plain,
! [SV669: $i,SV93: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV93 )
| ! [SY3862: $i,SY3863: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ SY3862 @ SV93 ) @ SY3863 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3862 @ SY3863 @ SV93 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2804,plain,
! [SV670: $i,SV94: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV94 )
| ! [SY3864: $i,SY3865: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ SY3865 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ SY3865 @ SV94 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2805,plain,
! [SV671: $i,SV95: $i] :
( ( ~ ( class_Lattices_Olattice @ SV95 )
| ! [SY3866: $i,SY3867: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ SY3867 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SY3867 @ SV95 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2806,plain,
! [SV672: $i,SV96: $i] :
( ( ~ ( class_Lattices_Olattice @ SV96 )
| ! [SY3868: $i,SY3869: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SY3868 @ SV96 ) @ SY3869 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3868 @ SY3869 @ SV96 ) @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2807,plain,
! [SV673: $i,SV97: $i] :
( ( ! [SY3870: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV97 @ SV673 @ ( tc_fun @ SY3870 @ tc_bool ) )
= SV97 )
| ~ ( c_lessequals @ SV97 @ SV673 @ ( tc_fun @ SY3870 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2808,plain,
! [SV674: $i,SV98: $i] :
( ( ! [SY3871: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV674 @ ( tc_fun @ SY3871 @ tc_bool ) )
= SV674 )
| ~ ( c_lessequals @ SV674 @ SV98 @ ( tc_fun @ SY3871 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2809,plain,
! [SV99: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV99 ) )
= $true )
| ( ( ! [SY2408: $i,SY2409: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2408 @ SY2409 @ SV99 )
= SY2408 )
| ~ ( c_lessequals @ SY2408 @ SY2409 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2810,plain,
! [SV100: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV100 ) )
= $true )
| ( ( ! [SY2410: $i,SY2411: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2410 @ SY2411 @ SV100 )
!= SY2410 )
| ( c_lessequals @ SY2410 @ SY2411 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2811,plain,
! [SV101: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV101 ) )
= $true )
| ( ( ! [SY2412: $i,SY2413: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2412 @ SY2413 @ SV101 )
= SY2413 )
| ~ ( c_lessequals @ SY2413 @ SY2412 @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2812,plain,
! [SV675: $i,SV102: $i] :
( ( ! [SY3872: $i,SY3873: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SY3872 @ tc_bool ) ) @ SY3873 @ ( tc_fun @ SY3872 @ tc_bool ) )
| ~ ( c_lessequals @ SV675 @ SY3873 @ ( tc_fun @ SY3872 @ tc_bool ) )
| ~ ( c_lessequals @ SV102 @ SY3873 @ ( tc_fun @ SY3872 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2813,plain,
! [SV676: $i,SV103: $i] :
( ( ! [SY3874: $i] : ( c_lessequals @ SV103 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ SV103 @ ( tc_fun @ SY3874 @ tc_bool ) ) @ ( tc_fun @ SY3874 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2814,plain,
! [SV677: $i,SV104: $i] :
( ( ! [SY3875: $i] : ( c_lessequals @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV677 @ ( tc_fun @ SY3875 @ tc_bool ) ) @ ( tc_fun @ SY3875 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2815,plain,
! [SV678: $i,SV105: $i] :
( ( ! [SY3876: $i,SY3877: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SY3876 @ tc_bool ) ) @ SY3877 @ ( tc_fun @ SY3876 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SY3877 @ ( tc_fun @ SY3876 @ tc_bool ) )
| ~ ( c_lessequals @ SV105 @ SY3877 @ ( tc_fun @ SY3876 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2816,plain,
! [SV679: $i,SV106: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV106 )
| ! [SY3878: $i,SY3879: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SY3878 @ SV106 ) @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SY3878 @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SY3879 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2817,plain,
! [SV107: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV107 ) )
= $true )
| ( ( ! [SY2427: $i,SY2428: $i] : ( c_lessequals @ SY2427 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2427 @ SY2428 @ SV107 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2818,plain,
! [SV108: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV108 ) )
= $true )
| ( ( ! [SY2429: $i,SY2430: $i] : ( c_lessequals @ SY2429 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2430 @ SY2429 @ SV108 ) @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2819,plain,
! [SV680: $i,SV109: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV109 )
| ! [SY3880: $i,SY3881: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SY3880 @ SV109 ) @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SY3880 @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SY3881 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2820,plain,
! [SV681: $i,SV110: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV110 )
| ! [SY3882: $i,SY3883: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SY3882 @ SV110 ) @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SY3882 @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SY3883 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2821,plain,
! [SV111: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV111 ) )
= $true )
| ( ( ! [SY2437: $i,SY2438: $i] : ( c_lessequals @ SY2437 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2438 @ SY2437 @ SV111 ) @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2822,plain,
! [SV112: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV112 ) )
= $true )
| ( ( ! [SY2439: $i,SY2440: $i] : ( c_lessequals @ SY2439 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2439 @ SY2440 @ SV112 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2823,plain,
! [SV682: $i,SV113: $i] :
( ( ! [SY3884: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV113 @ SV682 @ ( tc_fun @ SY3884 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV682 @ SV113 @ ( tc_fun @ SY3884 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2824,plain,
! [SV114: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV114 ) )
= $true )
| ( ( ! [SY2443: $i,SY2444: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2443 @ SY2444 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2444 @ SY2443 @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2825,plain,
! [SV115: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV115 ) )
= $true )
| ( ( ! [SY2445: $i,SY2446: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2445 @ SY2446 @ SV115 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2446 @ SY2445 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2826,plain,
! [SV683: $i,SV116: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV116 @ SV683 )
| ~ ( c_Wellfounded_Owf @ SV116 @ SV683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2827,plain,
! [SV684: $i,SV117: $i] :
( ( ~ ( class_Lattices_Olattice @ SV117 )
| ! [SY3885: $i,SY3886: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3885 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3886 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3885 @ SY3886 @ SV117 ) @ SV117 ) @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2828,plain,
! [SV685: $i,SV118: $i] :
( ( ! [SY3887: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SY3887 @ SV685 ) )
| ~ ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SY3887 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY3887 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2829,plain,
! [SV686: $i,SV119: $i] :
( ( ! [SY3888: $i] :
( ( ( c_Set_Oinsert @ SV119 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 )
!= ( c_Set_Oinsert @ SY3888 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 ) )
| ( SV119 = SY3888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2830,plain,
! [SV687: $i,SV120: $i] :
( ( ! [SY3889: $i,SY3890: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV120 @ SV687 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SY3890 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3890 @ SV120 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( tc_fun @ SY3889 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV687 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ SY3890 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3890 @ SV120 @ ( tc_fun @ SY3889 @ tc_bool ) ) @ ( tc_fun @ SY3889 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2831,plain,
! [SV688: $i,SV122: $i] :
( ( ! [SY3891: $i,SY3892: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV688 @ SY3891 @ SY3891 ) @ SY3892 @ ( tc_prod @ SY3891 @ SY3891 ) ) @ SY3891 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV122 @ ( c_Set_Oinsert @ SV688 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3891 @ tc_bool ) ) @ SY3891 ) @ SY3891 ) @ ( c_Relation_OField @ SY3892 @ SY3891 ) @ ( tc_fun @ SY3891 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2832,plain,
! [SV689: $i,SV123: $i] :
( ( ! [SY3893: $i] :
( ( ( c_Set_Oinsert @ SV123 @ SV689 @ SY3893 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3893 @ tc_bool ) ) )
| ( c_in @ SV123 @ SV689 @ SY3893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2833,plain,
! [SV690: $i,SV125: $i] :
( ( ! [SY3894: $i] :
( ( c_in @ SV125 @ SV690 @ SY3894 )
| ! [SY3895: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SY3895 @ SY3894 ) @ SV690 @ ( tc_fun @ SY3894 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2834,plain,
! [SV691: $i,SV126: $i] :
( ( ! [SY3896: $i,SY3897: $i,SY3898: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV691 @ ( tc_fun @ SY3896 @ tc_bool ) ) @ SY3897 @ SY3896 @ SY3898 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV126 @ SY3897 @ SY3896 @ SY3898 ) @ ( c_Product__Type_OSigma @ SV691 @ SY3897 @ SY3896 @ SY3898 ) @ ( tc_fun @ ( tc_prod @ SY3896 @ SY3898 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2835,plain,
! [SV692: $i,SV127: $i] :
( ( ! [SY3899: $i,SY3900: $i] :
( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SY3899 @ SY3900 ) @ ( tc_fun @ SY3900 @ tc_bool ) )
| ~ ( c_lessequals @ SV127 @ SY3899 @ ( tc_fun @ SY3900 @ tc_bool ) )
| ( c_in @ SV692 @ SV127 @ SY3900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2836,plain,
! [SV693: $i,SV128: $i] :
( ( ! [SY3901: $i] :
( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SY3901 @ tc_bool ) )
| ! [SY3902: $i] :
( ( c_in @ SY3902 @ SV128 @ SY3901 )
| ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SY3902 @ SV693 @ SY3901 ) @ ( tc_fun @ SY3901 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2837,plain,
! [SV694: $i,SV129: $i] :
( ( ! [SY3903: $i,SY3904: $i] :
( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SY3903 @ SY3904 ) @ ( tc_fun @ SY3904 @ tc_bool ) )
| ~ ( c_lessequals @ SV129 @ SY3903 @ ( tc_fun @ SY3904 @ tc_bool ) )
| ( c_in @ SV694 @ SV129 @ SY3904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2838,plain,
! [SV695: $i,SV130: $i] :
( ( ! [SY3905: $i] :
( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SY3905 @ tc_bool ) )
| ! [SY3906: $i] :
( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SY3906 @ SV695 @ SY3905 ) @ ( tc_fun @ SY3905 @ tc_bool ) )
| ( c_in @ SY3906 @ SV130 @ SY3905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2839,plain,
! [SV696: $i,SV131: $i] :
( ( ! [SY3907: $i,SY3908: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ ( c_Set_Oinsert @ SV696 @ SY3907 @ SY3908 ) @ ( tc_fun @ SY3908 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SY3907 @ ( tc_fun @ SY3908 @ tc_bool ) ) )
| ( c_in @ SV696 @ SV131 @ SY3908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2840,plain,
! [SV697: $i,SV132: $i] :
( ( ! [SY3909: $i,SY3910: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV132 @ SV697 @ SY3909 ) @ SY3910 @ ( tc_fun @ SY3909 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV697 @ SY3910 @ ( tc_fun @ SY3909 @ tc_bool ) ) )
| ( c_in @ SV132 @ SY3910 @ SY3909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2841,plain,
! [SV698: $i,SV133: $i] :
( ( ! [SY3911: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 @ SV698 @ ( tc_fun @ SY3911 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3911 @ tc_bool ) ) )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3911 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2842,plain,
! [SV699: $i,SV134: $i] :
( ( ! [SY3912: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ SV699 @ ( tc_fun @ SY3912 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3912 @ tc_bool ) ) )
| ( SV134
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3912 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2843,plain,
! [SV135: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV135 ) )
= $true )
| ( ( ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2492 @ SY2493 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) )
| ( SY2492
= ( c_Orderings_Obot__class_Obot @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2844,plain,
! [SV136: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV136 ) )
= $true )
| ( ( ! [SY2494: $i,SY2495: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2494 @ SY2495 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
| ( SY2495
= ( c_Orderings_Obot__class_Obot @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2845,plain,
! [SV700: $i,SV137: $i] :
( ( ! [SY3913: $i,SY3914: $i,SY3915: $i,SY3916: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV700 @ ( tc_fun @ ( tc_prod @ SY3913 @ SY3914 ) @ tc_bool ) ) @ SY3915 @ SY3913 @ SY3914 @ SY3916 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SY3915 @ SY3913 @ SY3914 @ SY3916 ) @ ( c_Relation_Orel__comp @ SV700 @ SY3915 @ SY3913 @ SY3914 @ SY3916 ) @ ( tc_fun @ ( tc_prod @ SY3913 @ SY3916 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2846,plain,
! [SV701: $i,SV138: $i] :
( ( ! [SY3917: $i,SY3918: $i,SY3919: $i,SY3920: $i] :
( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV701 @ SY3917 @ ( tc_fun @ ( tc_prod @ SY3918 @ SY3919 ) @ tc_bool ) ) @ SY3920 @ SY3918 @ SY3919 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SV701 @ SY3920 @ SY3918 @ SY3919 ) @ ( c_Relation_Orel__comp @ SV138 @ SY3917 @ SY3920 @ SY3918 @ SY3919 ) @ ( tc_fun @ ( tc_prod @ SY3920 @ SY3919 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2847,plain,
! [SV702: $i,SV139: $i] :
( ( ! [SY3921: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV139 @ SV702 @ ( tc_fun @ ( tc_prod @ SY3921 @ SY3921 ) @ tc_bool ) ) @ SY3921 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV139 @ SY3921 ) @ ( c_Relation_OField @ SV702 @ SY3921 ) @ ( tc_fun @ SY3921 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2848,plain,
! [SV703: $i,SV140: $i] :
( ( ! [SY3922: $i] :
( ( c_lessequals @ SV140 @ SV703 @ ( tc_fun @ SY3922 @ tc_bool ) )
| ! [SY3923: $i] :
~ ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3923 @ SV703 @ ( tc_fun @ SY3922 @ tc_bool ) ) @ ( tc_fun @ SY3922 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2849,plain,
! [SV704: $i,SV141: $i] :
( ( ! [SY3924: $i] :
( ( c_lessequals @ SV141 @ SV704 @ ( tc_fun @ SY3924 @ tc_bool ) )
| ! [SY3925: $i] :
~ ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV704 @ SY3925 @ ( tc_fun @ SY3924 @ tc_bool ) ) @ ( tc_fun @ SY3924 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2850,plain,
! [SV705: $i,SV142: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV142 )
| ! [SY3926: $i] :
( ( c_lessequals @ SV705 @ SY3926 @ SV142 )
| ! [SY3927: $i] :
~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3926 @ SY3927 @ SV142 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2851,plain,
! [SV706: $i,SV143: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ! [SY3928: $i] :
( ( c_lessequals @ SV706 @ SY3928 @ SV143 )
| ! [SY3929: $i] :
~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3929 @ SY3928 @ SV143 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2852,plain,
! [SV707: $i,SV144: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ! [SY3930: $i,SY3931: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SY3930 @ SV144 ) @ SY3931 @ SV144 )
| ~ ( c_lessequals @ SV707 @ SY3931 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2853,plain,
! [SV708: $i,SV145: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV145 )
| ! [SY3932: $i,SY3933: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SY3932 @ SV145 ) @ SY3933 @ SV145 )
| ~ ( c_lessequals @ SY3932 @ SY3933 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2854,plain,
! [SV709: $i,SV146: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV146 )
| ! [SY3934: $i] :
( ( c_lessequals @ SV709 @ SY3934 @ SV146 )
| ! [SY3935: $i] :
~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3934 @ SY3935 @ SV146 ) @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2855,plain,
! [SV710: $i,SV147: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV147 )
| ! [SY3936: $i] :
( ( c_lessequals @ SV710 @ SY3936 @ SV147 )
| ! [SY3937: $i] :
~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3937 @ SY3936 @ SV147 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2856,plain,
! [SV711: $i,SV148: $i] :
( ( ! [SY3938: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV148 @ SV711 @ ( tc_fun @ SY3938 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SV148 @ ( tc_fun @ SY3938 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2857,plain,
! [SV149: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV149 ) )
= $true )
| ( ( ! [SY2534: $i,SY2535: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2534 @ SY2535 @ SV149 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2535 @ SY2534 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2858,plain,
! [SV150: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV150 ) )
= $true )
| ( ( ! [SY2536: $i,SY2537: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2536 @ SY2537 @ SV150 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2537 @ SY2536 @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2859,plain,
! [SV712: $i,SV151: $i] :
( ( ! [SY3939: $i,SY3940: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV712 @ ( tc_fun @ ( tc_prod @ SY3939 @ SY3940 ) @ tc_bool ) ) @ SY3939 @ SY3940 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV151 @ SY3939 @ SY3940 ) @ ( c_Relation_ODomain @ SV712 @ SY3939 @ SY3940 ) @ ( tc_fun @ SY3939 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2860,plain,
! [SV713: $i,SV152: $i] :
( ( ! [SY3941: $i] :
( ( c_Set_Oinsert @ SV152 @ SV713 @ SY3941 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV152 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3941 @ tc_bool ) ) @ SY3941 ) @ SV713 @ ( tc_fun @ SY3941 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2861,plain,
! [SV714: $i,SV153: $i] :
( ( ! [SY3942: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV153 @ tc_bool ) ) @ SV714 @ SV153 @ SY3942 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV153 @ SY3942 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2862,plain,
! [SV715: $i,SV154: $i] :
( ( ! [SY3943: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV154 @ SV715 ) @ ( c_Wellfounded_Oacc @ SY3943 @ SV715 ) @ ( tc_fun @ SV715 @ tc_bool ) )
| ~ ( c_lessequals @ SY3943 @ SV154 @ ( tc_fun @ ( tc_prod @ SV715 @ SV715 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2863,plain,
! [SV716: $i,SV155: $i] :
( ( ! [SY3944: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SV716 @ ( tc_fun @ SY3944 @ tc_bool ) ) @ ( tc_fun @ SY3944 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SV716 @ ( tc_fun @ SY3944 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2864,plain,
! [SV156: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV156 ) )
= $true )
| ( ( ! [SY2549: $i,SY2550: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) @ SV156 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2865,plain,
! [SV157: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV157 ) )
= $true )
| ( ( ! [SY2551: $i,SY2552: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) @ SV157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2866,plain,
! [SV717: $i,SV158: $i] :
( ( ! [SY3945: $i] :
( ( ( c_Relation_ODomain @ SV158 @ SV717 @ SY3945 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV717 @ tc_bool ) ) )
| ( SV158
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV717 @ SY3945 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2867,plain,
! [SV718: $i,SV159: $i] :
( ( ! [SY3946: $i,SY3947: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV718 @ ( tc_fun @ ( tc_prod @ SY3946 @ SY3947 ) @ tc_bool ) ) @ SY3946 @ SY3947 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV159 @ SY3946 @ SY3947 ) @ ( c_Relation_ORange @ SV718 @ SY3946 @ SY3947 ) @ ( tc_fun @ SY3947 @ tc_bool ) ) @ ( tc_fun @ SY3947 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2868,plain,
! [SV719: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
| ! [SY2559: $i,SY2560: $i] :
( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SY2559 @ SY2560 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2559 @ SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2869,plain,
! [SV720: $i,SV162: $i] :
( ( ! [SY3950: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV162 @ SV720 ) @ ( c_Transitive__Closure_Ortrancl @ SY3950 @ SV720 ) @ ( tc_fun @ ( tc_prod @ SV720 @ SV720 ) @ tc_bool ) ) @ SV720 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV162 @ SY3950 @ ( tc_fun @ ( tc_prod @ SV720 @ SV720 ) @ tc_bool ) ) @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2870,plain,
! [SV721: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV721 ) )
| ! [SY3951: $i,SY3952: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3951 @ SV163 @ ( tc_fun @ SY3952 @ tc_bool ) ) @ SV721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2871,plain,
! [SV722: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ SV164 @ SV722 ) )
| ! [SY3953: $i,SY3954: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SY3953 @ ( tc_fun @ SY3954 @ tc_bool ) ) @ SV722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2872,plain,
! [SV723: $i,SV165: $i] :
( ( ! [SY3955: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SY3955 @ SY3955 ) @ tc_bool ) ) @ SY3955 )
| ~ ( c_Relation_Osym @ SV723 @ SY3955 )
| ~ ( c_Relation_Osym @ SV165 @ SY3955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2873,plain,
! [SV724: $i,SV166: $i] :
( ( ! [SY3956: $i,SY3957: $i,SY3958: $i,SY3959: $i] :
( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SY3956 @ SY3957 @ SY3958 @ SY3959 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SY3956 @ SY3957 @ SY3958 @ SY3959 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SY3956 @ SY3957 @ SY3958 @ SY3959 )
= ( c_Recdef_Ocut @ SV724 @ SY3956 @ SY3957 @ SY3958 @ SY3959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2874,plain,
! [SV725: $i,SV167: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ SV167 @ SV725 ) @ SV725 @ SV725 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2875,plain,
! [SV726: $i,SV168: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV168 @ SV726 )
| ! [SY3960: $i,SY3961: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY3960 @ SY3961 @ SV726 @ SV726 ) @ SV168 @ ( tc_prod @ SV726 @ SV726 ) ) @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2876,plain,
! [SV727: $i,SV169: $i] :
( ( ! [SY3962: $i] :
( ~ ( class_HOL_Oord @ SV169 )
| ! [SY3963: $i] :
( ( c_lessequals @ ( hAPP @ SV727 @ SY3962 ) @ ( hAPP @ SY3963 @ SY3962 ) @ SV169 )
| ! [SY3964: $i] :
~ ( c_lessequals @ SV727 @ SY3963 @ ( tc_fun @ SY3964 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2877,plain,
! [SV728: $i,SV170: $i] :
( ( ! [SY3965: $i,SY3966: $i] :
( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SY3965 @ ( tc_fun @ SY3966 @ tc_bool ) ) @ SY3966 )
| ~ ( c_in @ SV170 @ SY3965 @ SY3966 )
| ~ ( c_in @ SV170 @ SV728 @ SY3966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2878,plain,
! [SV729: $i,SV171: $i] :
( ( ! [SY3967: $i,SY3968: $i] :
( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SY3967 @ ( tc_fun @ SY3968 @ tc_bool ) ) @ SY3968 )
| ~ ( c_in @ SV171 @ SY3967 @ SY3968 )
| ~ ( c_in @ SV171 @ SV729 @ SY3968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2879,plain,
! [SV730: $i,SV172: $i] :
( ( ! [SY3969: $i] :
( ( c_in @ SV172 @ SV730 @ SY3969 )
| ! [SY3970: $i] :
( ~ ( c_in @ SV172 @ SY3970 @ SY3969 )
| ~ ( c_lessequals @ SY3970 @ SV730 @ ( tc_fun @ SY3969 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2880,plain,
! [SV731: $i,SV173: $i] :
( ( ! [SY3971: $i] :
( ( c_in @ SV173 @ SV731 @ SY3971 )
| ! [SY3972: $i] :
( ~ ( c_lessequals @ SY3972 @ SV731 @ ( tc_fun @ SY3971 @ tc_bool ) )
| ~ ( c_in @ SV173 @ SY3972 @ SY3971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2881,plain,
! [SV732: $i,SV174: $i] :
( ( ! [SY3973: $i] :
( ( c_in @ SV174 @ SV732 @ SY3973 )
| ! [SY3974: $i] :
( ~ ( c_in @ SV174 @ SY3974 @ SY3973 )
| ~ ( c_lessequals @ SY3974 @ SV732 @ ( tc_fun @ SY3973 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2882,plain,
! [SV733: $i,SV175: $i] :
( ( ! [SY3975: $i] :
( ( c_in @ SV175 @ SV733 @ SY3975 )
| ! [SY3976: $i] :
( ~ ( c_in @ SV175 @ SY3976 @ SY3975 )
| ~ ( c_lessequals @ SY3976 @ SV733 @ ( tc_fun @ SY3975 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2883,plain,
! [SV734: $i,SV176: $i] :
( ( ! [SY3977: $i,SY3978: $i] :
( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV734 @ SY3977 @ ( tc_fun @ SY3978 @ tc_bool ) ) @ SY3978 )
| ~ ( c_in @ SV176 @ SV734 @ SY3978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2884,plain,
! [SV735: $i,SV177: $i] :
( ( ! [SY3979: $i,SY3980: $i] :
( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SY3979 @ ( tc_fun @ SY3980 @ tc_bool ) ) @ SY3980 )
| ~ ( c_in @ SV177 @ SY3979 @ SY3980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2885,plain,
! [SV736: $i,SV178: $i] :
( ( ~ ( c_in @ SV178 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV736 @ tc_bool ) ) @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2886,plain,
! [SV737: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ SV179 @ SV737 ) )
| ! [SY3981: $i] :
~ ( c_in @ SV737 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3981 @ tc_bool ) ) @ SY3981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2887,plain,
! [SV738: $i,SV180: $i] :
( ( ~ ( c_in @ SV180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV738 @ tc_bool ) ) @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2888,plain,
! [SV739: $i,SV181: $i] :
( ( ~ ( c_in @ SV181 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV739 @ tc_bool ) ) @ SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2889,plain,
! [SV740: $i,SV182: $i] :
( ( ! [SY3982: $i] :
( ( c_in @ SV182 @ SV740 @ SY3982 )
| ! [SY3983: $i] :
( ( c_in @ SV182 @ SY3983 @ SY3982 )
| ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3983 @ SV740 @ ( tc_fun @ SY3982 @ tc_bool ) ) @ SY3982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2890,plain,
! [SV741: $i,SV183: $i] :
( ( ! [SY3984: $i] :
( ( c_in @ SV183 @ SV741 @ SY3984 )
| ! [SY3985: $i] :
~ ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3985 @ SV741 @ ( tc_fun @ SY3984 @ tc_bool ) ) @ SY3984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2891,plain,
! [SV742: $i,SV184: $i] :
( ( ! [SY3986: $i] :
( ( c_in @ SV184 @ SV742 @ SY3986 )
| ! [SY3987: $i] :
~ ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV742 @ SY3987 @ ( tc_fun @ SY3986 @ tc_bool ) ) @ SY3986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2892,plain,
! [SV743: $i,SV185: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV185 @ SV743 ) )
| ! [SY3988: $i] :
~ ( c_in @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3988 @ tc_bool ) ) @ SY3988 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2893,plain,
! [SV744: $i,SV186: $i] :
( ( ! [SY3989: $i,SY3990: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3989 @ SY3990 @ ( tc_fun @ ( tc_prod @ SV186 @ SV744 ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SY3989 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SY3990 ) @ ( tc_fun @ ( tc_prod @ SV744 @ SV186 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2894,plain,
! [SV745: $i,SV187: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV187 @ SV187 ) @ SV745 ) @ SV187 )
| ~ ( c_Wellfounded_Oacyclic @ SV745 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2895,plain,
! [SV746: $i,SV188: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV188 @ SV746 )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV746 @ SV746 ) @ SV188 ) @ SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2896,plain,
! [SV747: $i,SV189: $i] :
( ( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ SV189 @ SV189 ) @ SV747 ) @ SV189 )
= ( c_Relation_OField @ SV747 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2897,plain,
! [SV748: $i,SV190: $i] :
( ( ! [SY3991: $i,SY3992: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3991 @ SY3992 @ ( tc_fun @ ( tc_prod @ SV190 @ SV748 ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SY3991 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SY3992 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV190 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2898,plain,
! [SV749: $i,SV191: $i] :
( ( ! [SY3993: $i,SY3994: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SY3993 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY3994 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SY3993 @ SV749 ) )
| ~ ( c_in @ ( c_Pair @ SV191 @ SY3994 @ SV749 @ SV749 ) @ SY3993 @ ( tc_prod @ SV749 @ SV749 ) )
| ! [SY3995: $i] :
( ~ ( c_in @ SY3994 @ SY3995 @ SV749 )
| ~ ( c_in @ SV191 @ SY3995 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3995 @ SY3993 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2899,plain,
! [SV750: $i,SV193: $i] :
( ( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV193 @ SV750 ) @ tc_bool ) ) @ SV193 @ SV750 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV750 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2900,plain,
! [SV751: $i,SV194: $i] :
( ( ! [SY3996: $i,SY3997: $i,SY3998: $i] :
( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3996 @ tc_bool ) ) @ SY3996 ) @ SY3996 )
!= ( c_Set_Oinsert @ SY3997 @ ( c_Set_Oinsert @ SY3998 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3996 @ tc_bool ) ) @ SY3996 ) @ SY3996 ) )
| ( SV194 = SY3998 )
| ( SV194 = SY3997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2901,plain,
! [SV752: $i,SV195: $i] :
( ( ! [SY3999: $i,SY4000: $i] :
( ! [SY4001: $i] :
( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3999 @ tc_bool ) ) @ SY3999 ) @ SY3999 )
!= ( c_Set_Oinsert @ SY4000 @ ( c_Set_Oinsert @ SY4001 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3999 @ tc_bool ) ) @ SY3999 ) @ SY3999 ) )
| ( SV752 = SY4000 )
| ( SV195 = SY4000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2902,plain,
! [SV753: $i,SV196: $i] :
( ( ! [SY4002: $i,SY4003: $i,SY4004: $i] :
( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4002 @ tc_bool ) ) @ SY4002 ) @ SY4002 )
!= ( c_Set_Oinsert @ SY4003 @ ( c_Set_Oinsert @ SY4004 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4002 @ tc_bool ) ) @ SY4002 ) @ SY4002 ) )
| ( SV196 = SY4004 )
| ( SV753 = SY4004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2903,plain,
! [SV754: $i,SV197: $i] :
( ( ! [SY4005: $i,SY4006: $i,SY4007: $i] :
( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4005 @ tc_bool ) ) @ SY4005 ) @ SY4005 )
!= ( c_Set_Oinsert @ SY4006 @ ( c_Set_Oinsert @ SY4007 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4005 @ tc_bool ) ) @ SY4005 ) @ SY4005 ) )
| ( SV754 = SY4006 )
| ( SV754 = SY4007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2904,plain,
! [SV755: $i,SV198: $i] :
( ( ! [SY4008: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV198 @ SV755 ) @ ( c_Product__Type_OSigma @ SY4008 @ ( c_COMBK @ SY4008 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV198 @ ( c_Product__Type_OSigma @ SY4008 @ ( c_COMBK @ SY4008 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2905,plain,
! [SV756: $i,SV199: $i] :
( ( ! [SY4009: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV199 @ SV756 ) @ ( c_Transitive__Closure_Ortrancl @ SY4009 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ ( c_Transitive__Closure_Ortrancl @ SY4009 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2906,plain,
! [SV757: $i,SV200: $i] :
( ( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) @ ( tc_fun @ SV757 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2907,plain,
! [SV758: $i,SV202: $i] :
( ( ! [SY4010: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV758 @ SY4010 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2908,plain,
! [SV759: $i,SV204: $i] :
( ( ! [SY4011: $i,SY4012: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SV759 @ SY4011 ) @ SY4012 @ ( tc_fun @ SY4011 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV759 @ SY4012 @ ( tc_fun @ SY4011 @ tc_bool ) ) @ SY4011 ) )
| ~ ( c_in @ SV204 @ SY4012 @ SY4011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2909,plain,
! [SV760: $i,SV205: $i] :
( ( ! [SY4013: $i,SY4014: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SV760 @ SY4013 @ SY4014 ) @ ( tc_fun @ SY4014 @ tc_bool ) )
= ( c_Set_Oinsert @ SV760 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SY4013 @ ( tc_fun @ SY4014 @ tc_bool ) ) @ SY4014 ) )
| ~ ( c_in @ SV760 @ SV205 @ SY4014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2910,plain,
! [SV761: $i,SV206: $i] :
( ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV206 @ tc_bool ) ) @ SV761 @ SV206 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2911,plain,
! [SV762: $i,SV207: $i] :
( ( ! [SY4015: $i,SY4016: $i,SY4017: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SY4015 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4016 @ SY4017 @ ( tc_fun @ SY4015 @ tc_bool ) ) @ ( tc_fun @ SY4015 @ tc_bool ) )
| ~ ( c_lessequals @ SV762 @ SY4017 @ ( tc_fun @ SY4015 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SY4016 @ ( tc_fun @ SY4015 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2912,plain,
! [SV208: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV208 ) )
= $true )
| ( ( ! [SY2672: $i,SY2673: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2672 @ SY2673 @ SV208 ) @ SY2672 @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2913,plain,
! [SV209: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV209 ) )
= $true )
| ( ( ! [SY2674: $i,SY2675: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2674 @ SY2675 @ SV209 ) @ SY2675 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2914,plain,
! [SV763: $i,SV210: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV210 )
| ! [SY4018: $i,SY4019: $i] :
( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4018 @ SY4019 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4019 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4018 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2915,plain,
! [SV764: $i,SV211: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV211 )
| ! [SY4020: $i,SY4021: $i] :
( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4020 @ SY4021 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4021 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4020 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2916,plain,
! [SV765: $i,SV212: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV212 )
| ! [SY4022: $i,SY4023: $i] :
( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4022 @ SY4023 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4023 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4022 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2917,plain,
! [SV213: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV213 ) )
= $true )
| ( ( ! [SY2685: $i,SY2686: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2685 @ SY2686 @ SV213 ) @ SY2686 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2918,plain,
! [SV214: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV214 ) )
= $true )
| ( ( ! [SY2687: $i,SY2688: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2687 @ SY2688 @ SV214 ) @ SY2687 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2919,plain,
! [SV766: $i,SV215: $i] :
( ( ! [SY4024: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 @ SV766 @ ( tc_fun @ SY4024 @ tc_bool ) ) @ SV215 @ ( tc_fun @ SY4024 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2920,plain,
! [SV767: $i,SV216: $i] :
( ( ! [SY4025: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV216 @ SV767 @ ( tc_fun @ SY4025 @ tc_bool ) ) @ SV767 @ ( tc_fun @ SY4025 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2921,plain,
! [SV768: $i,SV217: $i] :
( ( ! [SY4026: $i,SY4027: $i] :
( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SY4026 @ ( tc_fun @ SY4027 @ tc_bool ) ) @ ( tc_fun @ SY4027 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SY4026 @ ( tc_fun @ SY4027 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SY4027 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2922,plain,
! [SV769: $i,SV218: $i] :
( ( ! [SY4028: $i,SY4029: $i] :
( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SY4028 @ ( tc_fun @ SY4029 @ tc_bool ) ) @ ( tc_fun @ SY4029 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SY4028 @ ( tc_fun @ SY4029 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SY4029 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2923,plain,
! [SV770: $i,SV219: $i] :
( ( ! [SY4030: $i,SY4031: $i,SY4032: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV770 @ ( tc_fun @ SY4030 @ tc_bool ) ) @ ( c_COMBK @ SY4031 @ ( tc_fun @ SY4032 @ tc_bool ) @ SY4030 ) @ SY4030 @ SY4032 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV219 @ ( c_COMBK @ SY4031 @ ( tc_fun @ SY4032 @ tc_bool ) @ SY4030 ) @ SY4030 @ SY4032 ) @ ( c_Product__Type_OSigma @ SV770 @ ( c_COMBK @ SY4031 @ ( tc_fun @ SY4032 @ tc_bool ) @ SY4030 ) @ SY4030 @ SY4032 ) @ ( tc_fun @ ( tc_prod @ SY4030 @ SY4032 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2924,plain,
! [SV771: $i,SV220: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV220 )
| ! [SY4033: $i,SY4034: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV771 @ SY4033 @ SV220 ) @ SY4034 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV771 @ SY4034 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4033 @ SY4034 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2925,plain,
! [SV772: $i,SV221: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV221 )
| ! [SY4035: $i,SY4036: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4035 @ SY4036 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4035 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4036 @ SV221 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2926,plain,
! [SV773: $i,SV222: $i] :
( ( ! [SY4037: $i,SY4038: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV773 @ SY4037 @ ( tc_fun @ SY4038 @ tc_bool ) ) @ ( tc_fun @ SY4038 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV773 @ ( tc_fun @ SY4038 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SY4037 @ ( tc_fun @ SY4038 @ tc_bool ) ) @ ( tc_fun @ SY4038 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2927,plain,
! [SV774: $i,SV223: $i] :
( ( ! [SY4039: $i,SY4040: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV223 @ SV774 @ ( tc_fun @ SY4039 @ tc_bool ) ) @ SY4040 @ ( tc_fun @ SY4039 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV223 @ SY4040 @ ( tc_fun @ SY4039 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV774 @ SY4040 @ ( tc_fun @ SY4039 @ tc_bool ) ) @ ( tc_fun @ SY4039 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2928,plain,
! [SV775: $i,SV224: $i] :
( ( ! [SY4041: $i,SY4042: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SY4041 ) @ SY4042 @ ( tc_fun @ SY4041 @ tc_bool ) )
| ~ ( c_lessequals @ SV775 @ SY4042 @ ( tc_fun @ SY4041 @ tc_bool ) )
| ~ ( c_in @ SV224 @ SY4042 @ SY4041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2929,plain,
! [SV225: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV225 ) )
= $true )
| ( ( ! [SY2718: $i,SY2719: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) @ SV225 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2930,plain,
! [SV226: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV226 ) )
= $true )
| ( ( ! [SY2720: $i,SY2721: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) @ SV226 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2931,plain,
! [SV776: $i,SV227: $i] :
( ( ! [SY4043: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SV776 @ ( tc_fun @ SY4043 @ tc_bool ) ) @ ( tc_fun @ SY4043 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SV776 @ ( tc_fun @ SY4043 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2932,plain,
! [SV777: $i,SV228: $i] :
( ( ! [SY4044: $i] :
( ( c_lessequals @ ( c_Relation_OField @ SV228 @ SV777 ) @ ( c_Relation_OField @ SY4044 @ SV777 ) @ ( tc_fun @ SV777 @ tc_bool ) )
| ~ ( c_lessequals @ SV228 @ SY4044 @ ( tc_fun @ ( tc_prod @ SV777 @ SV777 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2933,plain,
! [SV778: $i,SV229: $i] :
( ( ! [SY4045: $i,SY4046: $i,SY4047: $i] :
( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SY4045 @ ( tc_fun @ SY4046 @ tc_bool ) ) @ SY4046 @ SY4047 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SY4046 @ SY4047 ) @ ( c_Relation_OImage @ SV229 @ SY4045 @ SY4046 @ SY4047 ) @ ( tc_fun @ SY4047 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SY4046 @ SY4047 ) @ SV229 ) @ SY4047 @ SY4046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2934,plain,
! [SV779: $i,SV230: $i] :
( ( ! [SY4048: $i,SY4049: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV779 @ ( tc_fun @ ( tc_prod @ SY4048 @ SY4049 ) @ tc_bool ) ) @ SY4048 @ SY4049 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV230 @ SY4048 @ SY4049 ) @ ( c_Relation_ORange @ SV779 @ SY4048 @ SY4049 ) @ ( tc_fun @ SY4049 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2935,plain,
! [SV780: $i,SV231: $i] :
( ( ! [SY4050: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV231 @ SV780 @ ( tc_fun @ ( tc_prod @ SY4050 @ SY4050 ) @ tc_bool ) ) @ SY4050 )
| ~ ( c_Wellfounded_Owf @ SV231 @ SY4050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2936,plain,
! [SV781: $i,SV232: $i] :
( ( ! [SY4051: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV232 @ SV781 @ ( tc_fun @ ( tc_prod @ SY4051 @ SY4051 ) @ tc_bool ) ) @ SY4051 )
| ~ ( c_Wellfounded_Owf @ SV781 @ SY4051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2937,plain,
! [SV233: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV233 ) )
= $true )
| ( ( ! [SY2737: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2737 @ SY2737 @ SV233 )
= SY2737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2938,plain,
! [SV782: $i,SV234: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV234 @ SV234 @ ( tc_fun @ SV782 @ tc_bool ) )
= SV234 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2939,plain,
! [SV783: $i,SV235: $i] :
( ( ( c_Relation_OField @ SV235 @ SV783 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV235 @ SV783 @ SV783 ) @ ( c_Relation_ORange @ SV235 @ SV783 @ SV783 ) @ ( tc_fun @ SV783 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2940,plain,
! [SV784: $i,SV236: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV236 )
| ! [SY4052: $i] :
( ( c_lessequals @ SV784 @ SY4052 @ SV236 )
| ! [SY4053: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4053 @ SV784 @ SV236 ) @ SY4052 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2941,plain,
! [SV785: $i,SV237: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV237 )
| ! [SY4054: $i] :
( ( c_lessequals @ SV785 @ SY4054 @ SV237 )
| ! [SY4055: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SY4055 @ SV237 ) @ SY4054 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2942,plain,
! [SV786: $i,SV238: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV238 )
| ! [SY4056: $i,SY4057: $i] :
( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4056 @ SY4057 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SV786 @ SY4057 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2943,plain,
! [SV787: $i,SV239: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV239 )
| ! [SY4058: $i] :
( ! [SY4059: $i] : ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4058 @ SY4059 @ SV239 ) @ SV239 )
| ~ ( c_lessequals @ SV787 @ SY4058 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2944,plain,
! [SV788: $i,SV240: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV240 )
| ! [SY4060: $i] :
( ( c_lessequals @ SV788 @ SY4060 @ SV240 )
| ! [SY4061: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4061 @ SV788 @ SV240 ) @ SY4060 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2945,plain,
! [SV789: $i,SV241: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV241 )
| ! [SY4062: $i] :
( ( c_lessequals @ SV789 @ SY4062 @ SV241 )
| ! [SY4063: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SY4063 @ SV241 ) @ SY4062 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2946,plain,
! [SV790: $i,SV242: $i] :
( ( ! [SY4064: $i] :
( ( c_lessequals @ SV242 @ SV790 @ ( tc_fun @ SY4064 @ tc_bool ) )
| ! [SY4065: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SY4065 @ ( tc_fun @ SY4064 @ tc_bool ) ) @ SV790 @ ( tc_fun @ SY4064 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2947,plain,
! [SV791: $i,SV243: $i] :
( ( ! [SY4066: $i] :
( ( c_lessequals @ SV243 @ SV791 @ ( tc_fun @ SY4066 @ tc_bool ) )
| ! [SY4067: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4067 @ SV243 @ ( tc_fun @ SY4066 @ tc_bool ) ) @ SV791 @ ( tc_fun @ SY4066 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2948,plain,
! [SV792: $i,SV244: $i] :
( ( ~ ( class_Orderings_Oorder @ SV244 )
| ! [SY4068: $i] :
( ( c_lessequals @ SV792 @ SY4068 @ SV244 )
| ! [SY4069: $i] :
( ~ ( c_lessequals @ SV792 @ SY4069 @ SV244 )
| ~ ( c_lessequals @ SY4069 @ SY4068 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2949,plain,
! [SV793: $i,SV245: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV245 )
| ! [SY4070: $i] :
( ( c_lessequals @ SV793 @ SY4070 @ SV245 )
| ! [SY4071: $i] :
( ~ ( c_lessequals @ SY4071 @ SY4070 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SY4071 @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2950,plain,
! [SV794: $i,SV246: $i] :
( ( c_lessequals @ SV246 @ SV246 @ ( tc_fun @ SV794 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2951,plain,
! [SV795: $i,SV247: $i] :
( ( c_lessequals @ SV247 @ SV247 @ ( tc_fun @ SV795 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2952,plain,
! [SV796: $i,SV248: $i] :
( ( ! [SY4072: $i] :
( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SY4072 @ tc_bool ) )
| ! [SY4073: $i] :
( ~ ( c_lessequals @ SY4073 @ SV796 @ ( tc_fun @ SY4072 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY4073 @ ( tc_fun @ SY4072 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2953,plain,
! [SV797: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
| ! [SY4074: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4074 @ SV797 ) )
| ! [SY2777: $i] :
~ ( c_lessequals @ SY4074 @ SV249 @ ( tc_fun @ SY2777 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2954,plain,
! [SV798: $i,SV250: $i] :
( ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
| ! [SY4076: $i] :
( ~ ( c_lessequals @ SV250 @ SY4076 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4076 @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2955,plain,
! [SV251: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV251 ) )
= $true )
| ( ( ! [SY2780: $i] : ( c_lessequals @ SY2780 @ SY2780 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2956,plain,
! [SV252: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV252 ) )
= $true )
| ( ( ! [SY2781: $i] : ( c_lessequals @ SY2781 @ SY2781 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2957,plain,
! [SV799: $i,SV253: $i] :
( ( ( c_Relation_Oantisym @ SV253 @ SV799 )
| ! [SY4077: $i] :
( ~ ( c_Relation_Oantisym @ SY4077 @ SV799 )
| ~ ( c_lessequals @ SV253 @ SY4077 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2958,plain,
! [SV800: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
| ! [SY4078: $i] :
( ! [SY2786: $i] :
~ ( c_lessequals @ SY4078 @ SV254 @ ( tc_fun @ SY2786 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4078 @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2959,plain,
! [SV801: $i,SV255: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
| ! [SY4080: $i] :
( ~ ( c_lessequals @ SV255 @ SY4080 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4080 @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2960,plain,
! [SV802: $i,SV256: $i] :
( ( ! [SY4081: $i] :
( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SY4081 )
| ! [SY4082: $i] :
( ~ ( c_Relation_Osingle__valued @ SY4082 @ SV802 @ SY4081 )
| ~ ( c_lessequals @ SV256 @ SY4082 @ ( tc_fun @ ( tc_prod @ SV802 @ SY4081 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2961,plain,
! [SV803: $i,SV257: $i] :
( ( ! [SY4083: $i,SY4084: $i,SY4085: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SY4083 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4084 @ SY4085 @ ( tc_fun @ SY4083 @ tc_bool ) ) @ ( tc_fun @ SY4083 @ tc_bool ) )
| ~ ( c_lessequals @ SV803 @ SY4085 @ ( tc_fun @ SY4083 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SY4084 @ ( tc_fun @ SY4083 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2962,plain,
! [SV804: $i,SV258: $i] :
( ( c_in @ SV258 @ ( c_Set_Oinsert @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV804 @ tc_bool ) ) @ SV804 ) @ SV804 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2963,plain,
! [SV805: $i,SV259: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV259 @ SV805 ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ SV259 @ SV805 ) @ ( c_COMBK @ ( c_Relation_OField @ SV259 @ SV805 ) @ ( tc_fun @ SV805 @ tc_bool ) @ SV805 ) @ SV805 @ SV805 ) @ ( tc_fun @ ( tc_prod @ SV805 @ SV805 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2964,plain,
! [SV806: $i,SV260: $i] :
( ( ! [SY4086: $i,SY4087: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SV806 @ SY4086 ) @ ( c_Relation_ODomain @ SY4087 @ SV806 @ SY4086 ) @ ( tc_fun @ SV806 @ tc_bool ) )
| ~ ( c_lessequals @ SV260 @ SY4087 @ ( tc_fun @ ( tc_prod @ SV806 @ SY4086 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2965,plain,
! [SV807: $i,SV261: $i] :
( ( ! [SY4088: $i] :
( ( SV261
= ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4088 @ tc_bool ) ) @ SY4088 ) )
| ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4088 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4088 @ tc_bool ) ) @ SY4088 ) @ ( tc_fun @ SY4088 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2966,plain,
! [SV808: $i,SV262: $i] :
( ( ! [SY4089: $i] :
( ( c_Product__Type_OSigma @ SV262 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV808 @ tc_bool ) ) @ ( tc_fun @ SV808 @ tc_bool ) @ SY4089 ) @ SY4089 @ SV808 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4089 @ SV808 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2967,plain,
! [SV809: $i,SV263: $i] :
( ( ! [SY4090: $i,SY4091: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SY4090 @ tc_bool ) ) @ SY4091 ) )
| ~ ( hBOOL @ ( hAPP @ SV809 @ SY4091 ) )
| ~ ( hBOOL @ ( hAPP @ SV263 @ SY4091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2968,plain,
! [SV810: $i,SV264: $i] :
( ( ! [SY4092: $i,SY4093: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SV810 @ SY4092 ) @ ( c_Set_Oinsert @ SV264 @ SY4093 @ SY4092 ) @ ( tc_fun @ SY4092 @ tc_bool ) )
| ~ ( c_lessequals @ SV810 @ SY4093 @ ( tc_fun @ SY4092 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2969,plain,
! [SV811: $i,SV267: $i] :
( ( ! [SY4094: $i] :
( ( ( c_Relation_ORange @ SV267 @ SV811 @ SY4094 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4094 @ tc_bool ) ) )
| ( SV267
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV811 @ SY4094 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2970,plain,
! [SV812: $i,SV268: $i] :
( ( ! [SY4095: $i,SY4096: $i,SY4097: $i,SY4098: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SY4095 @ SY4096 ) @ ( c_Relation_OImage @ SY4097 @ SY4098 @ SY4095 @ SY4096 ) @ ( tc_fun @ SY4096 @ tc_bool ) )
| ~ ( c_lessequals @ SV812 @ SY4098 @ ( tc_fun @ SY4095 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SY4097 @ ( tc_fun @ ( tc_prod @ SY4095 @ SY4096 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2971,plain,
! [SV813: $i,SV269: $i] :
( ( ! [SY4099: $i] :
( ( c_lessequals @ SV269 @ ( c_Product__Type_OSigma @ SV813 @ ( c_COMBK @ SV813 @ ( tc_fun @ SY4099 @ tc_bool ) @ SY4099 ) @ SY4099 @ SY4099 ) @ ( tc_fun @ ( tc_prod @ SY4099 @ SY4099 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV813 @ SV269 @ SY4099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2972,plain,
! [SV270: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV270 ) )
= $true )
| ( ( ! [SY2820: $i,SY2821: $i] :
( ( c_lessequals @ SY2820 @ SY2821 @ SV270 )
| ( c_lessequals @ SY2821 @ SY2820 @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2973,plain,
! [SV814: $i,SV271: $i] :
( ( ! [SY4100: $i] :
( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
| ! [SY4101: $i,SY4102: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SY4100 @ SY4101 @ SY4102 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SY4100 @ SY4101 @ SY4102 ) @ SY4102 @ SY4102 ) @ SY4101 @ ( tc_prod @ SY4102 @ SY4102 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SY4100 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SY4100 @ SY4102 @ SY4102 ) @ ( c_Transitive__Closure_Ortrancl @ SY4101 @ SY4102 ) @ ( tc_prod @ SY4102 @ SY4102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2974,plain,
! [SV815: $i,SV272: $i] :
( ( ! [SY4103: $i] :
( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
| ! [SY4104: $i,SY4105: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SY4103 @ SY4104 @ SY4105 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SY4103 @ SY4104 @ SY4105 ) @ SY4105 @ SY4105 ) @ SY4104 @ ( tc_prod @ SY4105 @ SY4105 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SY4103 ) )
| ~ ( c_in @ ( c_Pair @ SY4103 @ SV815 @ SY4105 @ SY4105 ) @ ( c_Transitive__Closure_Ortrancl @ SY4104 @ SY4105 ) @ ( tc_prod @ SY4105 @ SY4105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2975,plain,
! [SV816: $i,SV273: $i] :
( ( ! [SY4106: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SY4106 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SY4106 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SY4106 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SY4106 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2976,plain,
! [SV817: $i,SV274: $i] :
( ( ! [SY4107: $i,SY4108: $i] :
( ( SV274 = SV817 )
| ! [SY4109: $i,SY4110: $i] :
( ~ ( c_in @ ( c_Pair @ SY4107 @ SV817 @ SY4108 @ SY4109 ) @ SY4110 @ ( tc_prod @ SY4108 @ SY4109 ) )
| ~ ( c_in @ ( c_Pair @ SY4107 @ SV274 @ SY4108 @ SY4109 ) @ SY4110 @ ( tc_prod @ SY4108 @ SY4109 ) )
| ~ ( c_Relation_Osingle__valued @ SY4110 @ SY4108 @ SY4109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2977,plain,
! [SV818: $i,SV275: $i] :
( ( ! [SY4111: $i,SY4112: $i,SY4113: $i] :
( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SY4111 @ tc_bool ) @ SY4112 ) @ SY4112 @ SY4111 )
!= ( c_Product__Type_OSigma @ SY4113 @ ( c_COMBK @ SV818 @ ( tc_fun @ SY4111 @ tc_bool ) @ SY4112 ) @ SY4112 @ SY4111 ) )
| ! [SY4114: $i] :
~ ( c_in @ SY4114 @ SV818 @ SY4111 )
| ( SV275 = SY4113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2978,plain,
! [SV819: $i,SV276: $i] :
( ( ! [SY4115: $i,SY4116: $i] :
( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV819 @ SY4115 @ ( tc_fun @ ( tc_prod @ SY4116 @ SY4116 ) @ tc_bool ) ) @ SY4116 ) @ ( tc_prod @ SY4116 @ SY4116 ) )
| ~ ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SV819 @ SY4116 ) @ ( tc_prod @ SY4116 @ SY4116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2979,plain,
! [SV820: $i,SV277: $i] :
( ( ! [SY4117: $i,SY4118: $i] :
( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SY4117 @ ( tc_fun @ ( tc_prod @ SY4118 @ SY4118 ) @ tc_bool ) ) @ SY4118 ) @ ( tc_prod @ SY4118 @ SY4118 ) )
| ~ ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SY4117 @ SY4118 ) @ ( tc_prod @ SY4118 @ SY4118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2980,plain,
! [SV821: $i,SV278: $i] :
( ( ! [SY4119: $i] :
( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SY4119 ) @ ( tc_prod @ SY4119 @ SY4119 ) )
| ! [SY4120: $i] :
( ~ ( c_lessequals @ SY4120 @ SV821 @ ( tc_fun @ ( tc_prod @ SY4119 @ SY4119 ) @ tc_bool ) )
| ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SY4120 @ SY4119 ) @ ( tc_prod @ SY4119 @ SY4119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2981,plain,
! [SV822: $i,SV279: $i] :
( ( ! [SY4121: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV279 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( c_Relation_Orel__comp @ SY4121 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SY4121 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV279 @ SY4121 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2982,plain,
! [SV823: $i,SV280: $i] :
( ( ! [SY4122: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV280 @ SV823 @ ( tc_fun @ ( tc_prod @ SY4122 @ SY4122 ) @ tc_bool ) ) @ SY4122 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV280 @ SV280 @ SY4122 @ SY4122 @ SY4122 ) @ ( c_Relation_Orel__comp @ SV823 @ SV280 @ SY4122 @ SY4122 @ SY4122 ) @ ( tc_fun @ ( tc_prod @ SY4122 @ SY4122 ) @ tc_bool ) ) @ SV823 @ ( tc_fun @ ( tc_prod @ SY4122 @ SY4122 ) @ tc_bool ) ) @ SY4122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2983,plain,
! [SV824: $i,SV281: $i] :
( ( ( ( c_Relation_Orel__comp @ SV281 @ SV281 @ SV824 @ SV824 @ SV824 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ SV281 @ SV824 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2984,plain,
! [SV825: $i,SV282: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV282 @ SV825 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV282 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV282 @ SV825 ) @ SV282 @ SV825 @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2985,plain,
! [SV826: $i,SV283: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV283 @ SV826 ) @ ( c_Relation_OId @ SV826 ) @ ( tc_fun @ ( tc_prod @ SV826 @ SV826 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV283 @ SV826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2986,plain,
! [SV827: $i,SV284: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ ( c_Relation_OId @ SV827 ) @ ( tc_fun @ ( tc_prod @ SV827 @ SV827 ) @ tc_bool ) ) @ SV827 )
= ( c_Transitive__Closure_Ortrancl @ SV284 @ SV827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2987,plain,
! [SV828: $i,SV286: $i] :
( ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV828 ) @ SV828 )
| ~ ( c_Wellfounded_Oacyclic @ SV286 @ SV828 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2988,plain,
! [SV829: $i,SV287: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ ( hAPP @ ( c_Relation_Oconverse @ SV829 @ SV829 ) @ SV287 ) @ ( tc_fun @ ( tc_prod @ SV829 @ SV829 ) @ tc_bool ) ) @ SV829 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2989,plain,
! [SV830: $i,SV288: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV288 @ ( hAPP @ ( c_Relation_Oconverse @ SV830 @ SV830 ) @ SV288 ) @ ( tc_fun @ ( tc_prod @ SV830 @ SV830 ) @ tc_bool ) ) @ SV830 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2990,plain,
! [SV831: $i,SV289: $i] :
( ( ! [SY4123: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV289 @ SV831 ) @ SY4123 @ SV831 @ SV831 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV289 @ SY4123 @ ( tc_fun @ SV831 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2991,plain,
! [SV832: $i,SV290: $i] :
( ( ( c_Relation_Oantisym @ SV290 @ SV832 )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV290 @ ( c_Relation_OId @ SV832 ) @ ( tc_fun @ ( tc_prod @ SV832 @ SV832 ) @ tc_bool ) ) @ SV832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2992,plain,
! [SV833: $i,SV291: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV291 @ ( c_Relation_OId @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) @ SV833 )
| ~ ( c_Relation_Oantisym @ SV291 @ SV833 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2993,plain,
! [SV834: $i,SV292: $i] :
( ( ! [SY4124: $i,SY4125: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SY4124 @ SV834 )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY4125 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SY4124 @ SV834 ) )
| ! [SY4126: $i] :
( ~ ( c_in @ SY4125 @ SY4126 @ SV834 )
| ~ ( c_in @ SV292 @ SY4126 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4126 @ SY4124 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SY4125 @ SV834 @ SV834 ) @ SY4124 @ ( tc_prod @ SV834 @ SV834 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2994,plain,
! [SV835: $i,SV293: $i] :
( ( ! [SY4127: $i] :
( ( c_in @ SV293 @ SV835 @ SY4127 )
| ! [SY4128: $i] :
( ( SV293 = SY4128 )
| ! [SY4129: $i] :
( ~ ( c_lessequals @ SY4129 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SY4127 @ tc_bool ) @ SY4127 ) @ SY4127 @ SY4127 ) @ ( tc_fun @ ( tc_prod @ SY4127 @ SY4127 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SY4128 @ SY4127 @ SY4127 ) @ ( c_Transitive__Closure_Ortrancl @ SY4129 @ SY4127 ) @ ( tc_prod @ SY4127 @ SY4127 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2995,plain,
! [SV836: $i,SV294: $i] :
( ( ! [SY4130: $i,SY4131: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4130 @ tc_bool ) ) @ SY4130 ) @ SY4130 @ SY4130 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SY4131 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4130 @ tc_bool ) ) @ SY4130 ) @ SY4130 @ SY4130 ) @ ( tc_fun @ SY4130 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV836 @ SY4131 @ SY4130 @ SY4130 ) @ SV294 @ ( tc_prod @ SY4130 @ SY4130 ) )
| ! [SY2877: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY2877 @ SV294 @ SY4130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2996,plain,
! [SV837: $i,SV295: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SV837 ) @ ( c_Transitive__Closure_Ortrancl @ SV837 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
| ! [SY4133: $i] :
~ ( c_in @ ( c_Pair @ SY4133 @ SY4133 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SV837 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2997,plain,
! [SV838: $i,SV296: $i] :
( ( ! [SY4134: $i,SY4135: $i] :
( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4134 @ tc_bool ) ) @ SY4134 ) @ SY4134 @ SY4134 )
!= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SY4135 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4134 @ tc_bool ) ) @ SY4134 ) @ SY4134 @ SY4134 ) )
| ~ ( c_in @ SY4135 @ ( c_Relation_OField @ SV296 @ SY4134 ) @ SY4134 )
| ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SY4134 ) @ SY4134 )
| ~ ( c_Relation_Oantisym @ SV296 @ SY4134 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SY4134 ) @ SV296 @ SY4134 )
| ( SV838 = SY4135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2998,plain,
! [SV297: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV297 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV297 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV297 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV297 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV297 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2999,plain,
! [SV298: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV298 )
= $true )
| ( ( ! [SY2883: $i] : ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV298 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV298 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV298 ) @ SY2883 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(3000,plain,
! [SV839: $i,SV299: $i] :
( ( ! [SY4136: $i,SY4137: $i,SY4138: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SY4136 @ SY4137 @ SY4138 ) @ SV299 @ SY4137 )
| ~ ( c_in @ SY4136 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SY4137 @ SY4138 ) @ ( tc_prod @ SY4137 @ SY4138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3001,plain,
! [SV840: $i,SV300: $i] :
( ( ! [SY4139: $i,SY4140: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SY4139 @ SY4140 ) @ SV840 @ SY4140 @ SY4140 ) @ SY4139 @ ( tc_prod @ SY4140 @ SY4140 ) )
| ( SV300 = SV840 )
| ~ ( c_in @ ( c_Pair @ SV300 @ SV840 @ SY4140 @ SY4140 ) @ ( c_Transitive__Closure_Ortrancl @ SY4139 @ SY4140 ) @ ( tc_prod @ SY4140 @ SY4140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3002,plain,
! [SV841: $i,SV301: $i] :
( ( ! [SY4141: $i,SY4142: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SY4141 @ SY4142 ) @ SY4141 @ SY4142 @ SY4142 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY4142 ) @ ( tc_prod @ SY4142 @ SY4142 ) )
| ( SV841 = SY4141 )
| ~ ( c_in @ ( c_Pair @ SV841 @ SY4141 @ SY4142 @ SY4142 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY4142 ) @ ( tc_prod @ SY4142 @ SY4142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3003,plain,
! [SV842: $i,SV302: $i] :
( ( ! [SY4143: $i,SY4144: $i] :
( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SY4143 @ SY4144 ) @ SY4144 @ SY4144 ) @ SV842 @ ( tc_prod @ SY4144 @ SY4144 ) )
| ( SV302 = SY4143 )
| ~ ( c_in @ ( c_Pair @ SV302 @ SY4143 @ SY4144 @ SY4144 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SY4144 ) @ ( tc_prod @ SY4144 @ SY4144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3004,plain,
! [SV843: $i,SV303: $i] :
( ( ! [SY4145: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
| ! [SY4146: $i,SY4147: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SY4145 @ SY4146 @ SY4147 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SY4145 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SY4145 @ SY4147 @ SY4147 ) @ ( c_Transitive__Closure_Ortrancl @ SY4146 @ SY4147 ) @ ( tc_prod @ SY4147 @ SY4147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3005,plain,
! [SV844: $i,SV304: $i] :
( ( ! [SY4148: $i] :
( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
| ! [SY4149: $i,SY4150: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SY4148 @ SY4149 @ SY4150 ) @ SY4148 @ SY4150 @ SY4150 ) @ ( c_Transitive__Closure_Ortrancl @ SY4149 @ SY4150 ) @ ( tc_prod @ SY4150 @ SY4150 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SY4148 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SY4148 @ SY4150 @ SY4150 ) @ ( c_Transitive__Closure_Ortrancl @ SY4149 @ SY4150 ) @ ( tc_prod @ SY4150 @ SY4150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3006,plain,
! [SV845: $i,SV305: $i] :
( ( ! [SY4151: $i] :
( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
| ! [SY4152: $i,SY4153: $i] :
( ( c_in @ ( c_Pair @ SY4151 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SY4151 @ SY4152 @ SY4153 ) @ SY4153 @ SY4153 ) @ ( c_Transitive__Closure_Ortrancl @ SY4152 @ SY4153 ) @ ( tc_prod @ SY4153 @ SY4153 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SY4151 ) )
| ~ ( c_in @ ( c_Pair @ SY4151 @ SV845 @ SY4153 @ SY4153 ) @ ( c_Transitive__Closure_Ortrancl @ SY4152 @ SY4153 ) @ ( tc_prod @ SY4153 @ SY4153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3007,plain,
! [SV846: $i,SV306: $i] :
( ( ! [SY4154: $i] :
( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
| ! [SY4155: $i,SY4156: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SY4154 @ SY4155 @ SY4156 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SY4154 ) )
| ~ ( c_in @ ( c_Pair @ SY4154 @ SV846 @ SY4156 @ SY4156 ) @ ( c_Transitive__Closure_Ortrancl @ SY4155 @ SY4156 ) @ ( tc_prod @ SY4156 @ SY4156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3008,plain,
! [SV847: $i,SV307: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SY4157 @ SY4157 ) @ ( c_Transitive__Closure_Ortrancl @ SY4158 @ SY4157 ) @ ( tc_prod @ SY4157 @ SY4157 ) )
| ( c_in @ ( c_Pair @ SV847 @ SV307 @ SY4157 @ SY4157 ) @ ( c_Transitive__Closure_Ortrancl @ SY4158 @ SY4157 ) @ ( tc_prod @ SY4157 @ SY4157 ) )
| ! [SY4159: $i] :
( ~ ( c_in @ ( c_Pair @ SY4159 @ SV307 @ SY4157 @ SY4157 ) @ ( c_Transitive__Closure_Ortrancl @ SY4158 @ SY4157 ) @ ( tc_prod @ SY4157 @ SY4157 ) )
| ~ ( c_in @ ( c_Pair @ SY4159 @ SV847 @ SY4157 @ SY4157 ) @ ( c_Transitive__Closure_Ortrancl @ SY4158 @ SY4157 ) @ ( tc_prod @ SY4157 @ SY4157 ) )
| ~ ( c_Relation_Osingle__valued @ SY4158 @ SY4157 @ SY4157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3009,plain,
! [SV848: $i,SV308: $i] :
( ( ! [SY4160: $i] :
( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SV848 @ SY4160 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4160 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SV848 = SV308 )
| ~ ( c_in @ ( c_Pair @ SV308 @ SV848 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4160 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3010,plain,
! [SV849: $i,SV309: $i] :
( ( ! [SY4161: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
| ! [SY4162: $i,SY4163: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SY4161 @ SY4162 @ SY4163 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SY4161 ) )
| ~ ( c_in @ ( c_Pair @ SY4161 @ SV849 @ SY4163 @ SY4163 ) @ ( c_Transitive__Closure_Ortrancl @ SY4162 @ SY4163 ) @ ( tc_prod @ SY4163 @ SY4163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3011,plain,
! [SV850: $i,SV310: $i] :
( ( ! [SY4164: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SV850 @ SY4164 ) @ SV850 @ t_a @ t_a ) @ SY4164 @ ( tc_prod @ t_a @ t_a ) )
| ( SV850 = SV310 )
| ~ ( c_in @ ( c_Pair @ SV310 @ SV850 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4164 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3012,plain,
! [SV851: $i,SV311: $i] :
( ( ! [SY4165: $i] :
( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
| ! [SY4166: $i,SY4167: $i] :
( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SY4165 @ SY4166 @ SY4167 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SY4165 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SY4165 @ SY4167 @ SY4167 ) @ ( c_Transitive__Closure_Ortrancl @ SY4166 @ SY4167 ) @ ( tc_prod @ SY4167 @ SY4167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3013,plain,
! [SV852: $i,SV312: $i] :
( ( ! [SY4168: $i,SY4169: $i] :
( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SY4168 @ SY4169 ) @ SY4169 @ SY4169 ) @ ( c_Transitive__Closure_Ortrancl @ SY4168 @ SY4169 ) @ ( tc_prod @ SY4169 @ SY4169 ) )
| ( SV312 = SV852 )
| ~ ( c_in @ ( c_Pair @ SV312 @ SV852 @ SY4169 @ SY4169 ) @ ( c_Transitive__Closure_Ortrancl @ SY4168 @ SY4169 ) @ ( tc_prod @ SY4169 @ SY4169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3014,plain,
! [SV853: $i,SV313: $i] :
( ( ! [SY4170: $i] :
( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
| ( hBOOL @ ( hAPP @ SV313 @ SY4170 ) )
| ! [SY2934: $i,SY2935: $i] :
( ~ ( c_in @ ( c_Pair @ SY4170 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SY2934 @ SY2935 ) @ SY2935 @ SY2935 ) @ SY2934 @ ( tc_prod @ SY2935 @ SY2935 ) )
| ~ ( c_Wellfounded_Owf @ SY2934 @ SY2935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3015,plain,
! [SV854: $i,SV314: $i] :
( ( ! [SY4173: $i] :
( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
| ( hBOOL @ ( hAPP @ SV314 @ SY4173 ) )
| ! [SY2938: $i,SY2939: $i] :
( ~ ( c_in @ ( c_Pair @ SY4173 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SY2938 @ SY2939 ) @ SY2939 @ SY2939 ) @ SY2938 @ ( tc_prod @ SY2939 @ SY2939 ) )
| ~ ( c_Wellfounded_Owf @ SY2938 @ SY2939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3016,plain,
! [SV855: $i,SV315: $i] :
( ( ! [SY4176: $i] :
( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
| ( hBOOL @ ( hAPP @ SV315 @ SY4176 ) )
| ! [SY2942: $i,SY2943: $i] :
( ~ ( c_in @ ( c_Pair @ SY4176 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SY2942 @ SY2943 ) @ SY2943 @ SY2943 ) @ SY2942 @ ( tc_prod @ SY2943 @ SY2943 ) )
| ~ ( c_Wellfounded_Owf @ SY2942 @ SY2943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3017,plain,
! [SV856: $i,SV316: $i] :
( ( ! [SY4179: $i] :
( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
| ( hBOOL @ ( hAPP @ SV316 @ SY4179 ) )
| ! [SY2946: $i,SY2947: $i] :
( ~ ( c_in @ ( c_Pair @ SY4179 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SY2946 @ SY2947 ) @ SY2947 @ SY2947 ) @ SY2946 @ ( tc_prod @ SY2947 @ SY2947 ) )
| ~ ( c_Wellfounded_Owf @ SY2946 @ SY2947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3018,plain,
! [SV857: $i,SV317: $i] :
( ( ! [SY4182: $i] :
( ~ ( c_in @ ( c_Pair @ SV317 @ SV317 @ SV857 @ SV857 ) @ SY4182 @ ( tc_prod @ SV857 @ SV857 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY4182 @ SV857 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY4182 @ SV857 ) @ SV857 @ SV857 ) @ ( c_Transitive__Closure_Otrancl @ SY4182 @ SV857 ) @ ( tc_prod @ SV857 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3019,plain,
! [SV858: $i,SV318: $i] :
( ( ! [SY4183: $i,SY4184: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SY4183 @ SY4184 ) @ SY4183 @ SY4184 @ SY4184 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY4184 ) @ ( tc_prod @ SY4184 @ SY4184 ) )
| ( c_in @ ( c_Pair @ SV858 @ SY4183 @ SY4184 @ SY4184 ) @ SV318 @ ( tc_prod @ SY4184 @ SY4184 ) )
| ~ ( c_in @ ( c_Pair @ SV858 @ SY4183 @ SY4184 @ SY4184 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY4184 ) @ ( tc_prod @ SY4184 @ SY4184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3020,plain,
! [SV859: $i,SV319: $i] :
( ( ! [SY4185: $i] :
( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SV859 @ SY4185 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4185 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ SY4185 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4185 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3021,plain,
! [SV860: $i,SV320: $i] :
( ( ! [SY4186: $i] :
( ~ ( c_in @ ( c_Pair @ SV320 @ SV320 @ SV860 @ SV860 ) @ ( c_Transitive__Closure_Otrancl @ SY4186 @ SV860 ) @ ( tc_prod @ SV860 @ SV860 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4186 @ SV860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3022,plain,
! [SV861: $i,SV321: $i] :
( ( ! [SY4187: $i,SY4188: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SY4187 @ SY4188 ) @ SV861 @ SY4188 @ SY4188 ) @ SY4187 @ ( tc_prod @ SY4188 @ SY4188 ) )
| ( c_in @ ( c_Pair @ SV321 @ SV861 @ SY4188 @ SY4188 ) @ SY4187 @ ( tc_prod @ SY4188 @ SY4188 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV861 @ SY4188 @ SY4188 ) @ ( c_Transitive__Closure_Otrancl @ SY4187 @ SY4188 ) @ ( tc_prod @ SY4188 @ SY4188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3023,plain,
! [SV862: $i,SV322: $i] :
( ( ! [SY4189: $i,SY4190: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SY4189 @ SY4190 ) @ SY4190 @ SY4190 ) @ ( c_Transitive__Closure_Otrancl @ SY4189 @ SY4190 ) @ ( tc_prod @ SY4190 @ SY4190 ) )
| ( c_in @ ( c_Pair @ SV322 @ SV862 @ SY4190 @ SY4190 ) @ SY4189 @ ( tc_prod @ SY4190 @ SY4190 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV862 @ SY4190 @ SY4190 ) @ ( c_Transitive__Closure_Otrancl @ SY4189 @ SY4190 ) @ ( tc_prod @ SY4190 @ SY4190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3024,plain,
! [SV863: $i,SV323: $i] :
( ( ! [SY4191: $i,SY4192: $i] :
( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SY4191 @ SY4192 ) @ SY4192 @ SY4192 ) @ SV863 @ ( tc_prod @ SY4192 @ SY4192 ) )
| ( c_in @ ( c_Pair @ SV323 @ SY4191 @ SY4192 @ SY4192 ) @ SV863 @ ( tc_prod @ SY4192 @ SY4192 ) )
| ~ ( c_in @ ( c_Pair @ SV323 @ SY4191 @ SY4192 @ SY4192 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SY4192 ) @ ( tc_prod @ SY4192 @ SY4192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3025,plain,
! [SV864: $i,SV324: $i] :
( ( ! [SY4193: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SV864 @ SY4193 ) @ SV864 @ t_a @ t_a ) @ SY4193 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ SY4193 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4193 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3026,plain,
! [SV865: $i,SV325: $i] :
( ( ! [SY4194: $i,SY4195: $i] :
( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SY4194 @ SY4194 ) @ SY4195 @ ( tc_prod @ SY4194 @ SY4194 ) )
| ! [SY4196: $i] :
( ~ ( c_in @ SV865 @ SY4196 @ SY4194 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY4195 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4194 @ tc_bool ) ) @ SY4194 ) @ SY4194 @ SY4194 ) @ ( c_Relation_OImage @ SY4195 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4194 @ tc_bool ) ) @ SY4194 ) @ SY4194 @ SY4194 ) @ ( tc_fun @ SY4194 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4196 @ SY4195 @ SY4194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3027,plain,
! [SV866: $i,SV326: $i] :
( ( ! [SY4197: $i,SY4198: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SY4197 @ SY4197 ) @ SY4198 @ ( tc_prod @ SY4197 @ SY4197 ) )
| ! [SY4199: $i] :
~ ( c_in @ SY4199 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY4198 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4197 @ tc_bool ) ) @ SY4197 ) @ SY4197 @ SY4197 ) @ ( c_Relation_OImage @ SY4198 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4197 @ tc_bool ) ) @ SY4197 ) @ SY4197 @ SY4197 ) @ ( tc_fun @ SY4197 @ tc_bool ) ) @ SY4197 )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ SY4198 @ SY4197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3028,plain,
! [SV867: $i,SV327: $i] :
( ( ! [SY4201: $i,SY4202: $i,SY4203: $i,SY4204: $i,SY4205: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SY4201 @ SY4202 @ SY4203 @ SY4204 @ SY4205 ) @ SV867 @ SY4205 @ SY4204 ) @ SY4202 @ ( tc_prod @ SY4205 @ SY4204 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SY4203 @ SY4204 ) @ ( c_Relation_Orel__comp @ SY4201 @ SY4202 @ SY4203 @ SY4205 @ SY4204 ) @ ( tc_prod @ SY4203 @ SY4204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3029,plain,
! [SV868: $i,SV328: $i] :
( ( ! [SY4206: $i,SY4207: $i,SY4208: $i,SY4209: $i,SY4210: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SY4206 @ SY4207 @ SY4208 @ SY4209 @ SY4210 ) @ SY4208 @ SY4210 ) @ SY4206 @ ( tc_prod @ SY4208 @ SY4210 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SY4208 @ SY4209 ) @ ( c_Relation_Orel__comp @ SY4206 @ SY4207 @ SY4208 @ SY4210 @ SY4209 ) @ ( tc_prod @ SY4208 @ SY4209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3030,plain,
! [SV869: $i,SV329: $i] :
( ( ! [SY4211: $i,SY4212: $i,SY4213: $i] :
( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SV869 @ SY4211 @ SY4212 @ SY4213 ) @ ( tc_fun @ SY4212 @ SY4213 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV869 @ SY4211 @ SV329 @ SY4212 @ SY4213 ) @ SV869 @ SY4212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3031,plain,
! [SV870: $i,SV330: $i] :
( ( ! [SY4214: $i,SY4215: $i,SY4216: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV870 @ SY4214 @ SY4215 @ SY4216 ) @ ( tc_fun @ SY4215 @ SY4216 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV870 @ SY4214 @ SV330 @ SY4215 @ SY4216 ) @ SV870 @ SY4215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3032,plain,
! [SV871: $i,SV331: $i] :
( ( ! [SY4217: $i,SY4218: $i,SY4219: $i] :
( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SY4217 @ SY4218 @ SY4219 ) @ ( tc_fun @ SY4218 @ SY4219 ) )
| ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SY4217 @ SV331 @ SY4218 @ SY4219 ) ) @ ( hAPP @ SY4217 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SY4217 @ SV331 @ SY4218 @ SY4219 ) ) @ SY4219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3033,plain,
! [SV872: $i,SV332: $i] :
( ( ! [SY4220: $i,SY4221: $i] :
( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SY4220 @ SY4221 )
| ! [SY4222: $i,SY4223: $i] :
( ~ ( c_in @ SV872 @ SY4222 @ SY4223 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY4222 @ ( c_COMBK @ SY4220 @ ( tc_fun @ SY4221 @ tc_bool ) @ SY4223 ) @ SY4223 @ SY4221 ) @ ( tc_fun @ SY4223 @ SY4221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3034,plain,
! [SV873: $i,SV333: $i] :
( ( ! [SY4224: $i,SY4225: $i,SY4226: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SY4224 @ SY4225 @ SY4226 ) @ ( tc_fun @ SY4225 @ SY4226 ) )
| ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SY4224 @ SV333 @ SY4225 @ SY4226 ) ) @ ( hAPP @ SY4224 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SY4224 @ SV333 @ SY4225 @ SY4226 ) ) @ SY4226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3035,plain,
! [SV874: $i,SV334: $i] :
( ( ( SV334
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ SV874 @ SV874 ) )
| ~ ( c_in @ SV334 @ ( c_Relation_OId @ SV874 ) @ ( tc_prod @ SV874 @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3036,plain,
! [SV875: $i,SV335: $i] :
( ( ( c_Wellfounded_Owf @ SV335 @ SV875 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV335 @ SV875 ) @ ( c_Wellfounded_Oacc @ SV335 @ SV875 ) @ SV875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3037,plain,
! [SV876: $i,SV336: $i] :
( ( ( c_Wellfounded_Owf @ SV336 @ SV876 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV336 @ SV876 ) @ ( c_Wellfounded_Oacc @ SV336 @ SV876 ) @ SV876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3038,plain,
! [SV877: $i,SV337: $i] :
( ( ! [SY4227: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV337 @ SV877 @ SY4227 ) @ SV337 @ SY4227 )
| ~ ( c_in @ SV877 @ ( c_Relation_OId__on @ SV337 @ SY4227 ) @ ( tc_prod @ SY4227 @ SY4227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3039,plain,
! [SV878: $i,SV338: $i] :
( ( ! [SY4228: $i] :
( ( SV338
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SY4228 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SY4228 ) @ SY4228 @ SY4228 ) )
| ~ ( c_in @ SV338 @ ( c_Relation_OId__on @ SV878 @ SY4228 ) @ ( tc_prod @ SY4228 @ SY4228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3040,plain,
! [SV879: $i,SV339: $i] :
( ( ! [SY4229: $i,SY4230: $i,SY4231: $i,SY4232: $i] :
( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SY4229 @ SY4230 @ SY4231 )
= ( c_Recdef_Ocut @ SY4232 @ SV879 @ SY4229 @ SY4230 @ SY4231 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SY4232 @ SV879 @ SY4229 @ SY4230 @ SY4231 ) @ SY4229 @ SY4230 @ SY4230 ) @ SV879 @ ( tc_prod @ SY4230 @ SY4230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3041,plain,
! [SV880: $i,SV340: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV340 @ SV880 ) @ ( c_Relation_OId @ SV880 ) @ ( tc_fun @ ( tc_prod @ SV880 @ SV880 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV340 @ SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3042,plain,
! [SV881: $i,SV341: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV341 @ ( c_Relation_OId @ SV881 ) @ ( tc_fun @ ( tc_prod @ SV881 @ SV881 ) @ tc_bool ) ) @ SV881 )
= ( c_Transitive__Closure_Ortrancl @ SV341 @ SV881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3043,plain,
! [SV882: $i,SV342: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV342 @ SV882 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV342 @ SV882 ) @ ( c_Relation_OId @ SV882 ) @ ( tc_fun @ ( tc_prod @ SV882 @ SV882 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3044,plain,
! [SV343: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV343 )
= $true )
| ( ( ! [SY3025: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV343 ) @ SY3025 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV343 ) @ SY3025 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(3045,plain,
! [SV344: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV344 )
= $true )
| ( ( ! [SY3026: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV344 ) @ SY3026 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV344 ) @ SY3026 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(3046,plain,
! [SV345: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV345 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(3047,plain,
! [SV346: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV346 )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(3048,plain,
! [SV883: $i,SV347: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV347 @ SV883 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SV883 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV347 @ SV883 ) @ SV347 @ SV883 @ SV883 @ SV883 ) @ ( tc_fun @ ( tc_prod @ SV883 @ SV883 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3049,plain,
! [SV884: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV884 @ SV884 ) @ SV348 ) @ SV348 @ SV884 @ SV884 @ SV884 ) @ ( tc_fun @ ( tc_prod @ SV884 @ SV884 ) @ tc_bool ) )
| ! [SY4233: $i] :
~ ( c_Relation_Orefl__on @ SY4233 @ SV348 @ SV884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3050,plain,
! [SV885: $i,SV349: $i] :
( ( ! [SY4234: $i,SY4235: $i] :
( ~ ( c_in @ ( c_Pair @ SV349 @ SV885 @ SY4234 @ SY4234 ) @ ( c_Transitive__Closure_Ortrancl @ SY4235 @ SY4234 ) @ ( tc_prod @ SY4234 @ SY4234 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SY4234 @ SY4234 ) @ SY4235 @ ( tc_prod @ SY4234 @ SY4234 ) ) @ SY4234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3051,plain,
! [SV886: $i,SV350: $i] :
( ( ! [SY4236: $i,SY4237: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SY4236 @ SY4236 ) @ SY4237 @ ( tc_prod @ SY4236 @ SY4236 ) ) @ SY4236 )
| ( c_in @ ( c_Pair @ SV886 @ SV350 @ SY4236 @ SY4236 ) @ ( c_Transitive__Closure_Ortrancl @ SY4237 @ SY4236 ) @ ( tc_prod @ SY4236 @ SY4236 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4237 @ SY4236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3052,plain,
! [SV887: $i,SV351: $i] :
( ( ! [SY4238: $i] :
( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4238 @ tc_bool ) ) @ SY4238 ) @ SY4238 @ SY4238 ) @ SY4238 )
| ! [SY4239: $i] :
( ~ ( c_in @ SV351 @ SY4239 @ SY4238 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4239 @ SV887 @ SY4238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3053,plain,
! [SV888: $i,SV352: $i] :
( ( ! [SY4240: $i,SY4241: $i,SY4242: $i] :
( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SY4240 @ SY4241 ) @ SY4242 @ ( tc_prod @ SY4240 @ SY4241 ) )
| ~ ( c_in @ SV888 @ ( c_Relation_OImage @ SY4242 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4240 @ tc_bool ) ) @ SY4240 ) @ SY4240 @ SY4241 ) @ SY4241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3054,plain,
! [SV889: $i,SV353: $i] :
( ( ! [SY4243: $i,SY4244: $i,SY4245: $i] :
( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SY4243 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4244 @ tc_bool ) ) @ SY4244 ) @ SY4244 @ SY4245 ) @ SY4245 )
| ~ ( c_in @ ( c_Pair @ SY4243 @ SV353 @ SY4244 @ SY4245 ) @ SV889 @ ( tc_prod @ SY4244 @ SY4245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3055,plain,
! [SV890: $i,SV354: $i] :
( ( ! [SY4246: $i,SY4247: $i] :
( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4246 @ tc_bool ) ) @ SY4246 ) @ SY4246 @ SY4246 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SY4247 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4246 @ tc_bool ) ) @ SY4246 ) @ SY4246 @ SY4246 ) )
| ~ ( c_in @ ( c_Pair @ SV890 @ SY4247 @ SY4246 @ SY4246 ) @ SV354 @ ( tc_prod @ SY4246 @ SY4246 ) )
| ! [SY3050: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3050 @ SV354 @ SY4246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3056,plain,
! [SV891: $i,SV355: $i] :
( ( ! [SY4249: $i,SY4250: $i] :
( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4249 @ tc_bool ) ) @ SY4249 ) @ SY4249 @ SY4249 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SY4250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4249 @ tc_bool ) ) @ SY4249 ) @ SY4249 @ SY4249 ) )
| ~ ( c_in @ ( c_Pair @ SV891 @ SY4250 @ SY4249 @ SY4249 ) @ SV355 @ ( tc_prod @ SY4249 @ SY4249 ) )
| ! [SY3054: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3054 @ SV355 @ SY4249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3057,plain,
! [SV892: $i,SV356: $i] :
( ( ! [SY4252: $i,SY4253: $i] :
( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4252 @ tc_bool ) ) @ SY4252 ) @ SY4252 @ SY4252 )
!= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SY4253 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4252 @ tc_bool ) ) @ SY4252 ) @ SY4252 @ SY4252 ) )
| ( c_in @ ( c_Pair @ SV892 @ SY4253 @ SY4252 @ SY4252 ) @ SV356 @ ( tc_prod @ SY4252 @ SY4252 ) )
| ! [SY3058: $i] :
( ~ ( c_in @ SY4253 @ SY3058 @ SY4252 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3058 @ SV356 @ SY4252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3058,plain,
! [SV893: $i,SV357: $i] :
( ( ! [SY4255: $i,SY4256: $i] :
( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4255 @ tc_bool ) ) @ SY4255 ) @ SY4255 @ SY4255 )
!= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SY4256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4255 @ tc_bool ) ) @ SY4255 ) @ SY4255 @ SY4255 ) )
| ! [SY4257: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY4257 @ SV357 @ SY4255 )
| ( c_in @ ( c_Pair @ SV893 @ SY4256 @ SY4255 @ SY4255 ) @ SV357 @ ( tc_prod @ SY4255 @ SY4255 ) )
| ~ ( c_in @ SY4256 @ SY4257 @ SY4255 )
| ~ ( c_in @ SV893 @ SY4257 @ SY4255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3059,plain,
! [SV894: $i,SV358: $i] :
( ( ! [SY4258: $i,SY4259: $i] :
( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4258 @ tc_bool ) ) @ SY4258 ) @ SY4258 @ SY4258 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SY4259 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4258 @ tc_bool ) ) @ SY4258 ) @ SY4258 @ SY4258 ) )
| ~ ( c_in @ ( c_Pair @ SV894 @ SY4259 @ SY4258 @ SY4258 ) @ SV358 @ ( tc_prod @ SY4258 @ SY4258 ) )
| ! [SY4260: $i] :
( ~ ( c_in @ SY4259 @ SY4260 @ SY4258 )
| ~ ( c_in @ SV894 @ SY4260 @ SY4258 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4260 @ SV358 @ SY4258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3060,plain,
! [SV895: $i,SV359: $i] :
( ( ! [SY4261: $i,SY4262: $i] :
( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4261 @ tc_bool ) ) @ SY4261 ) @ SY4261 @ SY4261 )
!= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SY4262 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4261 @ tc_bool ) ) @ SY4261 ) @ SY4261 @ SY4261 ) )
| ! [SY4263: $i] :
( ~ ( c_in @ SY4262 @ SY4263 @ SY4261 )
| ~ ( c_in @ SV895 @ SY4263 @ SY4261 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4263 @ SV359 @ SY4261 )
| ( c_in @ ( c_Pair @ SV895 @ SY4262 @ SY4261 @ SY4261 ) @ SV359 @ ( tc_prod @ SY4261 @ SY4261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3061,plain,
! [SV896: $i,SV360: $i] :
( ( ! [SY4264: $i,SY4265: $i] :
( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV896 @ SV360 @ SY4264 @ SY4265 ) @ SY4265 @ SY4265 ) @ SV896 @ ( tc_prod @ SY4265 @ SY4265 ) )
| ~ ( c_in @ ( c_Pair @ SV360 @ SY4264 @ SY4265 @ SY4265 ) @ ( c_Transitive__Closure_Otrancl @ SV896 @ SY4265 ) @ ( tc_prod @ SY4265 @ SY4265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3062,plain,
! [SV897: $i,SV361: $i] :
( ( ! [SY4266: $i,SY4267: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SV897 @ SY4266 @ SY4267 ) @ SY4266 @ SY4267 @ SY4267 ) @ SV361 @ ( tc_prod @ SY4267 @ SY4267 ) )
| ~ ( c_in @ ( c_Pair @ SV897 @ SY4266 @ SY4267 @ SY4267 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SY4267 ) @ ( tc_prod @ SY4267 @ SY4267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3063,plain,
! [SV898: $i,SV362: $i] :
( ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
| ! [SY4268: $i,SY4269: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SY4268 @ SY4269 ) @ ( c_Wellfounded_Oacc @ SY4268 @ SY4269 ) @ SY4269 )
| ~ ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SY4268 @ SY4269 ) @ SY4269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3064,plain,
! [SV899: $i,SV363: $i] :
( ( ! [SY4270: $i] :
( ( c_in @ SV363 @ ( c_Wellfounded_Oacc @ SV899 @ SY4270 ) @ SY4270 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV899 @ SV363 @ SY4270 ) @ ( c_Wellfounded_Oacc @ SV899 @ SY4270 ) @ SY4270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3065,plain,
! [SV900: $i,SV364: $i] :
( ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
| ! [SY4271: $i] :
( ~ ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SY4271 ) ) )
| ~ ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SY4271 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3066,plain,
! [SV901: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
| ! [SY4272: $i,SY4273: $i] :
( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SY4272 @ SY4273 ) ) )
| ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SY4272 @ SY4273 ) @ SY4273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3067,plain,
! [SV902: $i,SV366: $i] :
( ( ! [SY4274: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV366 @ SV902 @ SY4274 ) @ ( c_Wellfounded_Oacc @ SV366 @ SY4274 ) @ SY4274 )
| ( c_in @ SV902 @ ( c_Wellfounded_Oacc @ SV366 @ SY4274 ) @ SY4274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3068,plain,
! [SV903: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
| ! [SY4275: $i,SY4276: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SY4275 @ SY4276 ) @ ( c_Wellfounded_Oacc @ SY4275 @ SY4276 ) @ SY4276 )
| ~ ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SY4275 @ SY4276 ) @ SY4276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3069,plain,
! [SV904: $i,SV368: $i] :
( ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
| ! [SY4277: $i] :
( ~ ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SY4277 ) ) )
| ~ ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SY4277 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3070,plain,
! [SV905: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
| ! [SY4278: $i,SY4279: $i] :
( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SY4278 @ SY4279 ) ) )
| ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SY4278 @ SY4279 ) @ SY4279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3071,plain,
! [SV906: $i,SV370: $i] :
( ( ! [SY4280: $i,SY4281: $i,SY4282: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SY4280 @ SY4281 @ SY4282 ) @ SV370 @ SY4281 )
| ~ ( c_in @ SV906 @ ( c_Relation_OImage @ SY4280 @ SV370 @ SY4281 @ SY4282 ) @ SY4282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3072,plain,
! [SV907: $i,SV371: $i] :
( ( ! [SY4283: $i,SY4284: $i,SY4285: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SY4283 @ SY4284 @ SY4285 ) @ SV371 @ SY4284 )
| ~ ( c_in @ SV907 @ ( c_Relation_OImage @ SY4283 @ SV371 @ SY4284 @ SY4285 ) @ SY4285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3073,plain,
! [SV908: $i,SV372: $i] :
( ( ( c_Wellfounded_Owf @ SV372 @ SV908 )
| ! [SY4286: $i,SY4287: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY4286 @ SY4287 @ SV908 @ SV908 ) @ SV372 @ ( tc_prod @ SV908 @ SV908 ) ) @ SV908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3074,plain,
! [SV909: $i,SV373: $i] :
( ( ! [SY4288: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SY4288 ) @ SV373 @ SY4288 )
| ! [SY3110: $i] :
~ ( c_in @ SY3110 @ SV373 @ SY4288 )
| ~ ( c_Wellfounded_Owf @ SV909 @ SY4288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3075,plain,
! [SV910: $i,SV374: $i] :
( ( ! [SY4290: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SY4290 ) @ SV374 @ SY4290 )
| ! [SY3113: $i] :
~ ( c_in @ SY3113 @ SV374 @ SY4290 )
| ~ ( c_Wellfounded_Owf @ SV910 @ SY4290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3076,plain,
! [SV911: $i,SV375: $i] :
( ( ! [SY4292: $i,SY4293: $i,SY4294: $i,SY4295: $i,SY4296: $i,SY4297: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SY4292 )
= ( hAPP @ ( hAPP @ SV375 @ SY4293 ) @ SY4294 ) )
| ~ ( c_in @ ( c_Pair @ SY4292 @ SY4294 @ SY4295 @ SY4295 ) @ SY4296 @ ( tc_prod @ SY4295 @ SY4295 ) )
| ! [SY4298: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SY4293 @ SY4297 @ SY4297 ) @ SY4298 @ ( tc_prod @ SY4297 @ SY4297 ) )
| ! [SY3122: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY4298 @ SY4296 @ SV375 @ SY4297 @ SY4295 @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3077,plain,
! [SV912: $i,SV376: $i] :
( ( ( ( hAPP @ SV376 @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) @ SV912 ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ SV376 @ SV912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3078,plain,
! [SV913: $i,SV377: $i] :
( ( ! [SY4300: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV377 @ SV913 @ SY4300 ) @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3079,plain,
! [SV914: $i,SV378: $i] :
( ( ! [SY4301: $i,SY4302: $i,SY4303: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV378 @ SV914 @ SY4301 @ SY4302 ) @ SY4303 @ ( tc_prod @ SY4301 @ SY4302 ) ) @ SY4301 @ SY4302 )
= ( c_Set_Oinsert @ SV378 @ ( c_Relation_ODomain @ SY4303 @ SY4301 @ SY4302 ) @ SY4301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3080,plain,
! [SV915: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
| ! [SY4304: $i] :
( ( SY4304 = SV915 )
| ! [SY4305: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY4304 @ SV379 @ SY4305 ) @ SV915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3081,plain,
! [SV916: $i,SV380: $i] :
( ( ! [SY4306: $i] :
( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV380 @ SV916 @ SY4306 ) @ SY4306 )
= ( c_Set_Oinsert @ SV380 @ SV916 @ SY4306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3082,plain,
! [SV917: $i,SV381: $i] :
( ( ! [SY4307: $i,SY4308: $i] :
( ( c_Set_Oinsert @ SV381 @ ( c_Set_Oinsert @ SV917 @ SY4307 @ SY4308 ) @ SY4308 )
= ( c_Set_Oinsert @ SV917 @ ( c_Set_Oinsert @ SV381 @ SY4307 @ SY4308 ) @ SY4308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3083,plain,
! [SV918: $i,SV382: $i] :
( ( ! [SY4309: $i,SY4310: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SV918 @ SY4309 ) @ SY4310 ) )
| ~ ( hBOOL @ ( hAPP @ SV918 @ SY4310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3084,plain,
! [SV919: $i,SV383: $i] :
( ( ! [SY4311: $i,SY4312: $i,SY4313: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV383 @ SV919 @ SY4311 @ SY4312 ) @ SY4313 @ ( tc_prod @ SY4311 @ SY4312 ) ) @ SY4311 @ SY4312 )
= ( c_Set_Oinsert @ SV919 @ ( c_Relation_ORange @ SY4313 @ SY4311 @ SY4312 ) @ SY4312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3085,plain,
! [SV920: $i,SV384: $i] :
( ( ! [SY4314: $i,SY4315: $i] :
( ( c_in @ SV384 @ ( c_Set_Oinsert @ SV920 @ SY4314 @ SY4315 ) @ SY4315 )
| ~ ( c_in @ SV384 @ SY4314 @ SY4315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3086,plain,
! [SV921: $i,SV385: $i] :
( ( ! [SY4316: $i,SY4317: $i] :
( ( c_in @ SV385 @ ( c_Set_Oinsert @ SV921 @ SY4316 @ SY4317 ) @ SY4317 )
| ~ ( c_in @ SV385 @ SY4316 @ SY4317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3087,plain,
! [SV922: $i,SV386: $i] :
( ( ! [SY4318: $i] :
( ( c_in @ SV386 @ SV922 @ SY4318 )
| ! [SY4319: $i] :
( ( SV386 = SY4319 )
| ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SY4319 @ SV922 @ SY4318 ) @ SY4318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3088,plain,
! [SV923: $i,SV387: $i] :
( ( ! [SY4320: $i] : ( c_in @ SV387 @ ( c_Set_Oinsert @ SV387 @ SV923 @ SY4320 ) @ SY4320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3089,plain,
! [SV924: $i,SV388: $i] :
( ( ! [SY4321: $i] : ( c_in @ SV388 @ ( c_Set_Oinsert @ SV388 @ SV924 @ SY4321 ) @ SY4321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3090,plain,
! [SV925: $i,SV389: $i] :
( ( ! [SY4322: $i] : ( c_in @ SV389 @ ( c_Set_Oinsert @ SV389 @ SV925 @ SY4322 ) @ SY4322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3091,plain,
! [SV926: $i,SV390: $i] :
( ( ! [SY4323: $i,SY4324: $i] :
( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SY4323 )
!= ( c_Set_Oinsert @ SV390 @ SY4324 @ SY4323 ) )
| ( c_in @ SV390 @ SY4324 @ SY4323 )
| ( SV926 = SY4324 )
| ( c_in @ SV390 @ SV926 @ SY4323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3092,plain,
! [SV927: $i,SV391: $i] :
( ( ! [SY4325: $i] :
( ( ( c_Set_Oinsert @ SV391 @ SV927 @ SY4325 )
= SV927 )
| ~ ( c_in @ SV391 @ SV927 @ SY4325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3093,plain,
! [SV928: $i,SV392: $i] :
( ( ! [SY4326: $i,SY4327: $i,SY4328: $i,SY4329: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SY4326 ) @ SY4327 @ SY4328 )
| ! [SY4330: $i] :
( ~ ( c_in @ SY4326 @ SY4329 @ SY4330 )
| ! [SY4331: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY4331 @ SV392 @ SV928 @ SY4330 @ SY4327 @ SY4328 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4329 @ SY4331 @ SY4330 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3094,plain,
! [SV393: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV393 )
= $true )
| ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV393 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(3095,plain,
! [SV394: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV394 )
= $true )
| ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV394 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(3096,plain,
! [SV929: $i,SV395: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ SV395 @ SV929 )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV395 @ SV929 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3097,plain,
! [SV930: $i,SV396: $i] :
( ( ( c_Nitpick_Orefl_H @ SV396 @ SV930 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ SV930 @ SV930 ) @ SV396 @ ( tc_prod @ SV930 @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3098,plain,
! [SV397: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV397 )
= $true )
| ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV397 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(3099,plain,
! [SV931: $i,SV398: $i] :
( ( ! [SY4332: $i] :
( ~ ( c_in @ SV398 @ SV931 @ SY4332 )
| ! [SY4333: $i] :
( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SY4333 @ SY4332 ) @ SY4332 @ SY4332 ) @ SY4333 @ ( tc_prod @ SY4332 @ SY4332 ) )
| ! [SY4334: $i] :
~ ( c_in @ SY4334 @ SV931 @ SY4332 )
| ~ ( c_Wellfounded_Owf @ SY4333 @ SY4332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3100,plain,
! [SV932: $i,SV399: $i] :
( ( ! [SY4335: $i] :
( ~ ( c_in @ SV399 @ SV932 @ SY4335 )
| ! [SY4336: $i] :
( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SY4336 @ SY4335 ) @ SY4335 @ SY4335 ) @ SY4336 @ ( tc_prod @ SY4335 @ SY4335 ) )
| ! [SY4337: $i] :
~ ( c_in @ SY4337 @ SV932 @ SY4335 )
| ~ ( c_Wellfounded_Owf @ SY4336 @ SY4335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(3101,plain,
! [SV933: $i,SV400: $i] :
( ( ! [SY4338: $i,SY4339: $i,SY4340: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SY4338 @ SY4339 @ SY4340 ) @ SV933 @ SY4339 @ SY4340 ) @ SY4338 @ ( tc_prod @ SY4339 @ SY4340 ) )
| ~ ( c_in @ SV933 @ ( c_Relation_OImage @ SY4338 @ SV400 @ SY4339 @ SY4340 ) @ SY4340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3102,plain,
! [SV934: $i,SV401: $i] :
( ( ! [SY4341: $i,SY4342: $i,SY4343: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SY4341 @ SY4342 @ SY4343 ) @ SV934 @ SY4342 @ SY4343 ) @ SY4341 @ ( tc_prod @ SY4342 @ SY4343 ) )
| ~ ( c_in @ SV934 @ ( c_Relation_OImage @ SY4341 @ SV401 @ SY4342 @ SY4343 ) @ SY4343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3103,plain,
! [SV935: $i,SV402: $i] :
( ( ! [SY4344: $i,SY4345: $i] :
( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SV935 @ SY4344 @ SY4345 ) @ SY4344 @ SY4345 ) @ SV935 @ ( tc_prod @ SY4344 @ SY4345 ) )
| ~ ( c_in @ SV402 @ ( c_Relation_ODomain @ SV935 @ SY4344 @ SY4345 ) @ SY4344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3104,plain,
! [SV936: $i,SV403: $i] :
( ( ! [SY4346: $i,SY4347: $i] :
( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SV936 @ SY4346 @ SY4347 ) @ SY4346 @ SY4347 ) @ SV936 @ ( tc_prod @ SY4346 @ SY4347 ) )
| ~ ( c_in @ SV403 @ ( c_Relation_ODomain @ SV936 @ SY4346 @ SY4347 ) @ SY4346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3105,plain,
! [SV937: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
| ! [SY4348: $i,SY4349: $i] :
( ( c_in @ SY4348 @ ( c_Wellfounded_Oacc @ SY4349 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4348 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SY4349 ) @ t_a @ t_a ) @ SY4349 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SY4349 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3106,plain,
! [SV938: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
| ! [SY4350: $i,SY4351: $i] :
( ( c_in @ SY4350 @ ( c_Wellfounded_Oacc @ SY4351 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4350 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SY4351 ) @ t_a @ t_a ) @ SY4351 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SY4351 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3107,plain,
! [SV939: $i,SV406: $i] :
( ( ! [SY4352: $i] :
( ( c_in @ SV406 @ ( c_Wellfounded_Oacc @ SV939 @ SY4352 ) @ SY4352 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV939 @ SV406 @ SY4352 ) @ SV406 @ SY4352 @ SY4352 ) @ SV939 @ ( tc_prod @ SY4352 @ SY4352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3108,plain,
! [SV940: $i,SV407: $i] :
( ( ! [SY4353: $i] :
( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
| ( hBOOL @ ( hAPP @ SV407 @ SY4353 ) )
| ! [SY4354: $i,SY4355: $i] :
( ~ ( c_in @ ( c_Pair @ SY4353 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SY4354 @ SY4355 ) @ SY4355 @ SY4355 ) @ SY4354 @ ( tc_prod @ SY4355 @ SY4355 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SY4354 @ SY4355 ) @ SY4355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3109,plain,
! [SV941: $i,SV408: $i] :
( ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
| ! [SY4356: $i] :
( ( hBOOL @ ( hAPP @ SV408 @ SY4356 ) )
| ! [SY4357: $i] :
( ~ ( c_in @ ( c_Pair @ SY4356 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SY4357 ) @ t_a @ t_a ) @ SY4357 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SY4357 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3110,plain,
! [SV942: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
| ! [SY4358: $i] :
( ( hBOOL @ ( hAPP @ SV409 @ SY4358 ) )
| ! [SY4359: $i] :
( ~ ( c_in @ ( c_Pair @ SY4358 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SY4359 ) @ t_a @ t_a ) @ SY4359 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SY4359 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3111,plain,
! [SV943: $i,SV410: $i] :
( ( ! [SY4360: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
| ( hBOOL @ ( hAPP @ SV410 @ SY4360 ) )
| ! [SY4361: $i,SY4362: $i] :
( ~ ( c_in @ ( c_Pair @ SY4360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SY4361 @ SY4362 ) @ SY4362 @ SY4362 ) @ SY4361 @ ( tc_prod @ SY4362 @ SY4362 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SY4361 @ SY4362 ) @ SY4362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3112,plain,
! [SV944: $i,SV411: $i] :
( ( ! [SY4363: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV411 @ SV944 @ SY4363 ) @ SV944 @ SY4363 @ SY4363 ) @ SV411 @ ( tc_prod @ SY4363 @ SY4363 ) )
| ( c_in @ SV944 @ ( c_Wellfounded_Oacc @ SV411 @ SY4363 ) @ SY4363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3113,plain,
! [SV945: $i,SV412: $i] :
( ( ! [SY4364: $i,SY4365: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SY4364 @ SY4364 ) @ SY4365 @ ( tc_prod @ SY4364 @ SY4364 ) ) @ SY4364 )
| ( c_in @ ( c_Pair @ SV945 @ SV412 @ SY4364 @ SY4364 ) @ ( c_Transitive__Closure_Ortrancl @ SY4365 @ SY4364 ) @ ( tc_prod @ SY4364 @ SY4364 ) )
| ~ ( c_Wellfounded_Owf @ SY4365 @ SY4364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3114,plain,
! [SV946: $i,SV413: $i] :
( ( ! [SY4366: $i,SY4367: $i] :
( ~ ( c_in @ ( c_Pair @ SV413 @ SV946 @ SY4366 @ SY4366 ) @ ( c_Transitive__Closure_Ortrancl @ SY4367 @ SY4366 ) @ ( tc_prod @ SY4366 @ SY4366 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SY4366 @ SY4366 ) @ SY4367 @ ( tc_prod @ SY4366 @ SY4366 ) ) @ SY4366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3115,plain,
! [SV947: $i,SV414: $i] :
( ( ! [SY4368: $i,SY4369: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SV947 @ SY4368 @ SY4369 ) @ SV414 @ SY4369 @ SY4368 ) @ SV947 @ ( tc_prod @ SY4369 @ SY4368 ) )
| ~ ( c_in @ SV414 @ ( c_Relation_ORange @ SV947 @ SY4369 @ SY4368 ) @ SY4368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3116,plain,
! [SV948: $i,SV415: $i] :
( ( ! [SY4370: $i,SY4371: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SV948 @ SY4370 @ SY4371 ) @ SV415 @ SY4371 @ SY4370 ) @ SV948 @ ( tc_prod @ SY4371 @ SY4370 ) )
| ~ ( c_in @ SV415 @ ( c_Relation_ORange @ SV948 @ SY4371 @ SY4370 ) @ SY4370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3117,plain,
! [SV949: $i,SV416: $i] :
( ( ! [SY4372: $i,SY4373: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SV949 @ SY4372 @ SY4373 ) @ SY4372 @ SY4373 @ SY4373 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SY4373 ) @ ( tc_prod @ SY4373 @ SY4373 ) )
| ~ ( c_in @ ( c_Pair @ SV949 @ SY4372 @ SY4373 @ SY4373 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SY4373 ) @ ( tc_prod @ SY4373 @ SY4373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3118,plain,
! [SV950: $i,SV417: $i] :
( ( ! [SY4374: $i,SY4375: $i] :
( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV950 @ SV417 @ SY4374 @ SY4375 ) @ SY4375 @ SY4375 ) @ ( c_Transitive__Closure_Ortrancl @ SV950 @ SY4375 ) @ ( tc_prod @ SY4375 @ SY4375 ) )
| ~ ( c_in @ ( c_Pair @ SV417 @ SY4374 @ SY4375 @ SY4375 ) @ ( c_Transitive__Closure_Otrancl @ SV950 @ SY4375 ) @ ( tc_prod @ SY4375 @ SY4375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3119,plain,
! [SV951: $i,SV418: $i] :
( ( ! [SY4376: $i,SY4377: $i] :
( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SY4376 @ SY4376 ) @ ( c_Transitive__Closure_Ortrancl @ SY4377 @ SY4376 ) @ ( tc_prod @ SY4376 @ SY4376 ) )
| ! [SY4378: $i] :
( ~ ( c_in @ ( c_Pair @ SY4378 @ SV951 @ SY4376 @ SY4376 ) @ SY4377 @ ( tc_prod @ SY4376 @ SY4376 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SY4378 @ SY4376 @ SY4376 ) @ ( c_Transitive__Closure_Ortrancl @ SY4377 @ SY4376 ) @ ( tc_prod @ SY4376 @ SY4376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3120,plain,
! [SV952: $i,SV419: $i] :
( ( ! [SY4379: $i,SY4380: $i] :
( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SY4379 @ SY4379 ) @ ( c_Transitive__Closure_Otrancl @ SY4380 @ SY4379 ) @ ( tc_prod @ SY4379 @ SY4379 ) )
| ! [SY4381: $i] :
( ~ ( c_in @ ( c_Pair @ SY4381 @ SV952 @ SY4379 @ SY4379 ) @ ( c_Transitive__Closure_Otrancl @ SY4380 @ SY4379 ) @ ( tc_prod @ SY4379 @ SY4379 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SY4381 @ SY4379 @ SY4379 ) @ SY4380 @ ( tc_prod @ SY4379 @ SY4379 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3121,plain,
! [SV953: $i,SV420: $i] :
( ( ! [SY4382: $i,SY4383: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SY4382 @ SY4382 ) @ ( c_Transitive__Closure_Otrancl @ SY4383 @ SY4382 ) @ ( tc_prod @ SY4382 @ SY4382 ) )
| ! [SY4384: $i] :
( ~ ( c_in @ ( c_Pair @ SY4384 @ SV953 @ SY4382 @ SY4382 ) @ SY4383 @ ( tc_prod @ SY4382 @ SY4382 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SY4384 @ SY4382 @ SY4382 ) @ ( c_Transitive__Closure_Otrancl @ SY4383 @ SY4382 ) @ ( tc_prod @ SY4382 @ SY4382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3122,plain,
! [SV954: $i,SV421: $i] :
( ( ! [SY4385: $i,SY4386: $i,SY4387: $i,SY4388: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SY4385 @ SY4386 @ SY4387 ) @ SY4388 )
= ( hAPP @ SV421 @ SY4388 ) )
| ~ ( c_in @ ( c_Pair @ SY4388 @ SY4385 @ SY4386 @ SY4386 ) @ SV954 @ ( tc_prod @ SY4386 @ SY4386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3123,plain,
! [SV955: $i,SV422: $i] :
( ( ! [SY4389: $i,SY4390: $i,SY4391: $i,SY4392: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SY4389 @ SY4390 @ SY4391 ) @ SY4392 )
= ( hAPP @ SV422 @ SY4392 ) )
| ~ ( c_in @ ( c_Pair @ SY4392 @ SY4389 @ SY4390 @ SY4390 ) @ SV955 @ ( tc_prod @ SY4390 @ SY4390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3124,plain,
! [SV956: $i,SV423: $i] :
( ( ( SV423 = SV956 )
| ! [SY4393: $i,SY4394: $i] :
( ~ ( c_in @ ( c_Pair @ SV423 @ SV956 @ SY4393 @ SY4393 ) @ ( c_Transitive__Closure_Ortrancl @ SY4394 @ SY4393 ) @ ( tc_prod @ SY4393 @ SY4393 ) )
| ( c_in @ SV423 @ ( c_Relation_ODomain @ SY4394 @ SY4393 @ SY4393 ) @ SY4393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3125,plain,
! [SV957: $i,SV424: $i] :
( ( ! [SY4395: $i] :
( ( c_in @ SV424 @ ( c_Relation_ODomain @ SV957 @ SY4395 @ SY4395 ) @ SY4395 )
| ( c_in @ ( c_Pair @ SV424 @ SV424 @ SY4395 @ SY4395 ) @ ( c_Transitive__Closure_Ortrancl @ SV957 @ SY4395 ) @ ( tc_prod @ SY4395 @ SY4395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3126,plain,
! [SV958: $i,SV425: $i] :
( ( ! [SY4396: $i] :
( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SY4396 ) @ SY4396 )
| ! [SY4397: $i] :
( ~ ( c_in @ ( c_Pair @ SV425 @ SY4397 @ SY4396 @ SY4396 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SY4396 ) @ ( tc_prod @ SY4396 @ SY4396 ) )
| ~ ( c_in @ SY4397 @ ( c_Wellfounded_Oacc @ SV958 @ SY4396 ) @ SY4396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3127,plain,
! [SV959: $i,SV426: $i] :
( ( ! [SY4398: $i] :
( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SY4398 ) @ SY4398 )
| ! [SY4399: $i] :
( ~ ( c_in @ SY4399 @ ( c_Wellfounded_Oacc @ SV959 @ SY4398 ) @ SY4398 )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4399 @ SY4398 @ SY4398 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SY4398 ) @ ( tc_prod @ SY4398 @ SY4398 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3128,plain,
! [SV960: $i,SV427: $i] :
( ( ( c_Relation_Osym @ SV427 @ SV960 )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV960 @ SV960 ) @ SV427 ) @ SV960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3129,plain,
! [SV961: $i,SV428: $i] :
( ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV428 @ SV428 ) @ SV961 ) @ SV428 )
| ~ ( c_Relation_Osym @ SV961 @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3130,plain,
! [SV962: $i,SV429: $i] :
( ( ! [SY4400: $i] :
( ( c_Relation_Orefl__on @ SV429 @ SV962 @ SY4400 )
| ~ ( c_Relation_Orefl__on @ SV429 @ ( hAPP @ ( c_Relation_Oconverse @ SY4400 @ SY4400 ) @ SV962 ) @ SY4400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3131,plain,
! [SV963: $i,SV430: $i] :
( ( ! [SY4401: $i] :
( ( c_Relation_Orefl__on @ SV430 @ ( hAPP @ ( c_Relation_Oconverse @ SV963 @ SV963 ) @ SY4401 ) @ SV963 )
| ~ ( c_Relation_Orefl__on @ SV430 @ SY4401 @ SV963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3132,plain,
! [SV964: $i,SV431: $i] :
( ( ( ( hAPP @ ( c_Relation_Oconverse @ SV431 @ SV431 ) @ SV964 )
= SV964 )
| ~ ( c_Relation_Osym @ SV964 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3133,plain,
! [SV965: $i,SV432: $i] :
( ( ( ( hAPP @ ( c_Relation_Oconverse @ SV432 @ SV432 ) @ SV965 )
!= SV965 )
| ( c_Relation_Osym @ SV965 @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3134,plain,
! [SV966: $i,SV433: $i] :
( ( ! [SY4402: $i,SY4403: $i,SY4404: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SV966 ) @ ( c_Relation_Orel__comp @ SY4402 @ SY4403 @ SV433 @ SY4404 @ SV966 ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SY4404 @ SV966 ) @ SY4403 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SY4404 ) @ SY4402 ) @ SV966 @ SY4404 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3135,plain,
! [SV967: $i,SV435: $i] :
( ( ! [SY4405: $i,SY4406: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV435 @ SV435 ) @ ( c_Relation_Oinv__image @ SV967 @ SY4405 @ SY4406 @ SV435 ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ SY4406 @ SY4406 ) @ SV967 ) @ SY4405 @ SY4406 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3136,plain,
! [SV968: $i,SV436: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV436 @ SV436 ) @ SV968 ) @ SV436 )
= ( hAPP @ ( c_Relation_Oconverse @ SV436 @ SV436 ) @ ( c_Transitive__Closure_Otrancl @ SV968 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3137,plain,
! [SV969: $i,SV437: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV437 @ SV437 ) @ ( c_Relation_OId__on @ SV969 @ SV437 ) )
= ( c_Relation_OId__on @ SV969 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3138,plain,
! [SV970: $i,SV438: $i] :
( ( ( c_Relation_Oantisym @ SV438 @ SV970 )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV970 @ SV970 ) @ SV438 ) @ SV970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3139,plain,
! [SV971: $i,SV439: $i] :
( ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV439 @ SV439 ) @ SV971 ) @ SV439 )
| ~ ( c_Relation_Oantisym @ SV971 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3140,plain,
! [SV972: $i,SV440: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV440 @ SV440 ) @ SV972 ) @ SV440 )
= ( hAPP @ ( c_Relation_Oconverse @ SV440 @ SV440 ) @ ( c_Transitive__Closure_Ortrancl @ SV972 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3141,plain,
! [SV973: $i,SV441: $i] :
( ( ! [SY4407: $i] :
( ( c_Relation_Ototal__on @ SV441 @ SV973 @ SY4407 )
| ~ ( c_Relation_Ototal__on @ SV441 @ ( hAPP @ ( c_Relation_Oconverse @ SY4407 @ SY4407 ) @ SV973 ) @ SY4407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3142,plain,
! [SV974: $i,SV442: $i] :
( ( ! [SY4408: $i] :
( ( c_Relation_Ototal__on @ SV442 @ ( hAPP @ ( c_Relation_Oconverse @ SV974 @ SV974 ) @ SY4408 ) @ SV974 )
| ~ ( c_Relation_Ototal__on @ SV442 @ SY4408 @ SV974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3143,plain,
! [SV975: $i,SV443: $i] :
( ( ! [SY4409: $i] :
( ( c_in @ SV443 @ ( c_Transitive__Closure_Ortrancl @ SV975 @ SY4409 ) @ ( tc_prod @ SY4409 @ SY4409 ) )
| ~ ( c_in @ SV443 @ SV975 @ ( tc_prod @ SY4409 @ SY4409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3144,plain,
! [SV976: $i,SV444: $i] :
( ( ! [SY4410: $i] :
( ( c_in @ SV444 @ ( c_Transitive__Closure_Otrancl @ SV976 @ SY4410 ) @ ( tc_prod @ SY4410 @ SY4410 ) )
| ~ ( c_in @ SV444 @ SV976 @ ( tc_prod @ SY4410 @ SY4410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3145,plain,
! [SV977: $i,SV445: $i] :
( ( ! [SY4411: $i,SY4412: $i] :
( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SY4411 @ SY4411 ) @ ( c_Transitive__Closure_Otrancl @ SY4412 @ SY4411 ) @ ( tc_prod @ SY4411 @ SY4411 ) )
| ! [SY4413: $i] :
( ~ ( c_in @ ( c_Pair @ SY4413 @ SV977 @ SY4411 @ SY4411 ) @ ( c_Transitive__Closure_Ortrancl @ SY4412 @ SY4411 ) @ ( tc_prod @ SY4411 @ SY4411 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SY4413 @ SY4411 @ SY4411 ) @ SY4412 @ ( tc_prod @ SY4411 @ SY4411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3146,plain,
! [SV978: $i,SV446: $i] :
( ( ! [SY4414: $i,SY4415: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SY4414 @ SY4414 ) @ ( c_Transitive__Closure_Otrancl @ SY4415 @ SY4414 ) @ ( tc_prod @ SY4414 @ SY4414 ) )
| ! [SY4416: $i] :
( ~ ( c_in @ ( c_Pair @ SY4416 @ SV978 @ SY4414 @ SY4414 ) @ SY4415 @ ( tc_prod @ SY4414 @ SY4414 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY4416 @ SY4414 @ SY4414 ) @ ( c_Transitive__Closure_Ortrancl @ SY4415 @ SY4414 ) @ ( tc_prod @ SY4414 @ SY4414 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3147,plain,
! [SV979: $i,SV447: $i] :
( ( ! [SY4417: $i,SY4418: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SY4417 @ SY4417 ) @ ( c_Transitive__Closure_Ortrancl @ SY4418 @ SY4417 ) @ ( tc_prod @ SY4417 @ SY4417 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SV979 @ SY4417 @ SY4417 ) @ ( c_Transitive__Closure_Otrancl @ SY4418 @ SY4417 ) @ ( tc_prod @ SY4417 @ SY4417 ) )
| ( SV447 = SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3148,plain,
! [SV980: $i,SV448: $i] :
( ( ! [SY4419: $i,SY4420: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SY4419 @ SY4419 ) @ ( c_Transitive__Closure_Otrancl @ SY4420 @ SY4419 ) @ ( tc_prod @ SY4419 @ SY4419 ) )
| ( SV448 = SV980 )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV980 @ SY4419 @ SY4419 ) @ ( c_Transitive__Closure_Ortrancl @ SY4420 @ SY4419 ) @ ( tc_prod @ SY4419 @ SY4419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3149,plain,
! [SV981: $i,SV449: $i] :
( ( ! [SY4421: $i,SY4422: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SY4421 @ SY4421 ) @ ( c_Transitive__Closure_Otrancl @ SY4422 @ SY4421 ) @ ( tc_prod @ SY4421 @ SY4421 ) )
| ( SV449 = SV981 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV981 @ SY4421 @ SY4421 ) @ ( c_Transitive__Closure_Ortrancl @ SY4422 @ SY4421 ) @ ( tc_prod @ SY4421 @ SY4421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3150,plain,
! [SV982: $i,SV450: $i] :
( ( ! [SY4423: $i,SY4424: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SY4423 @ SY4423 ) @ ( c_Transitive__Closure_Ortrancl @ SY4424 @ SY4423 ) @ ( tc_prod @ SY4423 @ SY4423 ) )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV982 @ SY4423 @ SY4423 ) @ ( c_Transitive__Closure_Otrancl @ SY4424 @ SY4423 ) @ ( tc_prod @ SY4423 @ SY4423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3151,plain,
! [SV983: $i,SV451: $i] :
( ( ! [SY4425: $i,SY4426: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SY4425 @ SY4425 ) @ ( c_Transitive__Closure_Otrancl @ SY4426 @ SY4425 ) @ ( tc_prod @ SY4425 @ SY4425 ) )
| ! [SY4427: $i] :
( ~ ( c_in @ ( c_Pair @ SY4427 @ SV983 @ SY4425 @ SY4425 ) @ ( c_Transitive__Closure_Ortrancl @ SY4426 @ SY4425 ) @ ( tc_prod @ SY4425 @ SY4425 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SY4427 @ SY4425 @ SY4425 ) @ ( c_Transitive__Closure_Otrancl @ SY4426 @ SY4425 ) @ ( tc_prod @ SY4425 @ SY4425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3152,plain,
! [SV984: $i,SV452: $i] :
( ( ! [SY4428: $i,SY4429: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SY4428 @ SY4428 ) @ ( c_Transitive__Closure_Otrancl @ SY4429 @ SY4428 ) @ ( tc_prod @ SY4428 @ SY4428 ) )
| ! [SY4430: $i] :
( ~ ( c_in @ ( c_Pair @ SY4430 @ SV984 @ SY4428 @ SY4428 ) @ ( c_Transitive__Closure_Otrancl @ SY4429 @ SY4428 ) @ ( tc_prod @ SY4428 @ SY4428 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SY4430 @ SY4428 @ SY4428 ) @ ( c_Transitive__Closure_Ortrancl @ SY4429 @ SY4428 ) @ ( tc_prod @ SY4428 @ SY4428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3153,plain,
! [SV985: $i,SV453: $i] :
( ( ! [SY4431: $i] :
( ( c_in @ SV453 @ ( c_Wellfounded_Oacc @ SV985 @ SY4431 ) @ SY4431 )
| ~ ( c_Wellfounded_Owf @ SV985 @ SY4431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3154,plain,
! [SV986: $i,SV454: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV454 @ SV986 ) @ SV986 )
| ~ ( c_Relation_Osym @ SV454 @ SV986 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3155,plain,
! [SV987: $i,SV455: $i] :
( ( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV455 @ SV987 ) @ SV987 @ SV987 )
= ( c_Relation_ODomain @ SV455 @ SV987 @ SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3156,plain,
! [SV988: $i,SV457: $i] :
( ( ! [SY4432: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV457 ) @ SV988 @ SV457 @ SV457 @ SY4432 )
= SV988 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3157,plain,
! [SV989: $i,SV458: $i] :
( ( ! [SY4433: $i] :
( ( c_Relation_Orel__comp @ SV458 @ ( c_Relation_OId @ SV989 ) @ SY4433 @ SV989 @ SV989 )
= SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3158,plain,
! [SV990: $i,SV459: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_OId__on @ SV459 @ SV990 ) @ SV990 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3159,plain,
! [SV991: $i,SV460: $i] :
( ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ ( c_Transitive__Closure_Otrancl @ SV991 @ SV460 ) ) @ SV460 )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ SV991 ) @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3160,plain,
! [SV992: $i,SV461: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV461 @ SV992 ) @ SV992 )
| ~ ( c_Relation_Osym @ SV461 @ SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3161,plain,
! [SV993: $i,SV462: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV462 @ SV462 @ SV993 @ SV993 @ SV993 ) @ SV993 )
| ~ ( c_Wellfounded_Owf @ SV462 @ SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3162,plain,
! [SV994: $i,SV463: $i] :
( ( ( c_Wellfounded_Owf @ SV463 @ SV994 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV463 @ SV463 @ SV994 @ SV994 @ SV994 ) @ SV994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3163,plain,
! [SV995: $i,SV464: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId @ SV464 ) @ SV995 @ SV464 @ SV464 )
= SV995 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3164,plain,
! [SV996: $i,SV465: $i] :
( ( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV465 @ SV996 ) @ SV996 @ SV996 )
= SV465 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3165,plain,
! [SV997: $i,SV466: $i] :
( ( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV466 @ SV997 ) @ SV997 @ SV997 )
= ( c_Relation_ORange @ SV466 @ SV997 @ SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3166,plain,
! [SV998: $i,SV467: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId__on @ SV467 @ SV998 ) @ SV998 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3167,plain,
! [SV999: $i,SV468: $i] :
( ( c_Relation_Orefl__on @ SV468 @ ( c_Relation_OId__on @ SV468 @ SV999 ) @ SV999 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3168,plain,
! [SV1000: $i,SV469: $i] :
( ( ! [SY4434: $i] :
( ! [SY4435: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SV1000 @ SY4434 @ SY4435 ) @ SY4435 )
| ~ ( c_Wellfounded_Owf @ SV469 @ SY4434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3169,plain,
! [SV1001: $i,SV470: $i] :
( ( ( c_Relation_Orel__comp @ SV470 @ ( c_Transitive__Closure_Ortrancl @ SV470 @ SV1001 ) @ SV1001 @ SV1001 @ SV1001 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV470 @ SV1001 ) @ SV470 @ SV1001 @ SV1001 @ SV1001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3170,plain,
! [SV1002: $i,SV471: $i] :
( ( ! [SY4436: $i] :
( ! [SY4437: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SV1002 @ SY4436 @ SY4437 ) @ SY4437 )
| ~ ( c_Relation_Osym @ SV471 @ SY4436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3171,plain,
! [SV1003: $i,SV472: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV472 @ SV1003 ) @ SV1003 )
= ( c_Transitive__Closure_Ortrancl @ SV472 @ SV1003 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3172,plain,
! [SV1004: $i,SV473: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV473 @ SV1004 ) @ SV1004 )
| ~ ( c_Wellfounded_Owf @ SV473 @ SV1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3173,plain,
! [SV1005: $i,SV474: $i] :
( ( ! [SY4438: $i,SY4439: $i,SY4440: $i,SY4441: $i,SY4442: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SY4438 @ SY4439 @ SY4440 ) @ SY4441 @ SY4438 @ SY4440 @ SY4442 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SY4441 @ SY4439 @ SY4440 @ SY4442 ) @ SY4438 @ SY4439 @ SY4442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3174,plain,
! [SV1006: $i,SV475: $i] :
( ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV475 @ SV475 ) @ SV1006 ) @ SV1006 @ SV475 @ SV475 @ SV475 )
!= SV1006 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV1006 @ SV475 @ SV475 ) @ SV1006 @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3175,plain,
! [SV1007: $i,SV477: $i] :
( ( ! [SY4443: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ SV477 @ SV1007 ) @ SY4443 ) @ SV1007 @ SV477 )
= ( c_Relation_ODomain @ SY4443 @ SV477 @ SV1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3176,plain,
! [SV1008: $i,SV478: $i] :
( ( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV478 @ SV1008 ) @ SV1008 @ SV1008 )
= SV478 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3177,plain,
! [SV1009: $i,SV479: $i] :
( ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV479 @ SV479 ) @ SV1009 ) @ SV1009 @ SV479 @ SV479 @ SV479 )
= SV1009 )
| ! [SY4444: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4444 @ SV1009 @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3178,plain,
! [SV1010: $i,SV480: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV480 @ SV1010 ) @ ( c_Transitive__Closure_Ortrancl @ SV480 @ SV1010 ) @ SV1010 @ SV1010 @ SV1010 )
= ( c_Transitive__Closure_Ortrancl @ SV480 @ SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3179,plain,
! [SV1011: $i,SV481: $i] :
( ( ! [SY4445: $i] :
( ( c_Relation_Orefl__on @ SV481 @ SV1011 @ SY4445 )
| ~ ( c_Equiv__Relations_Oequiv @ SV481 @ SV1011 @ SY4445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3180,plain,
! [SV1012: $i,SV482: $i] :
( ( ( c_Relation_Osym @ SV482 @ SV1012 )
| ! [SY4446: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4446 @ SV482 @ SV1012 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3181,plain,
! [SV1013: $i,SV483: $i] :
( ( ! [SY4447: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SV483 @ SV1013 ) @ SY4447 ) @ SV1013 @ SV483 )
= ( c_Relation_ORange @ SY4447 @ SV483 @ SV1013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3182,plain,
! [SV1014: $i,SV484: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV484 @ SV1014 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV1014 ) @ SV484 @ SV1014 @ SV1014 @ SV1014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3183,plain,
! [SV1015: $i,SV485: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV485 @ SV1015 )
= ( c_Relation_Orel__comp @ SV485 @ ( c_Transitive__Closure_Ortrancl @ SV485 @ SV1015 ) @ SV1015 @ SV1015 @ SV1015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3184,plain,
! [SV1016: $i,SV486: $i] :
( ( ! [SY4448: $i] :
( ( c_Relation_ORange @ SV486 @ SV1016 @ SY4448 )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SV1016 @ SY4448 ) @ SV486 ) @ SY4448 @ SV1016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3185,plain,
! [SV1017: $i,SV487: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV487 @ SV1017 ) @ SV1017 )
= ( c_Transitive__Closure_Ortrancl @ SV487 @ SV1017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3186,plain,
! [SV1018: $i,SV488: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV1018 ) @ SV1018 )
= ( c_Transitive__Closure_Ortrancl @ SV488 @ SV1018 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3187,plain,
! [SV1019: $i,SV489: $i] :
( ( ! [SY4449: $i,SY4450: $i] :
( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SY4449 @ SY4449 ) @ ( c_Transitive__Closure_Ortrancl @ SY4450 @ SY4449 ) @ ( tc_prod @ SY4449 @ SY4449 ) )
| ! [SY4451: $i] :
( ~ ( c_in @ ( c_Pair @ SY4451 @ SV1019 @ SY4449 @ SY4449 ) @ ( c_Transitive__Closure_Ortrancl @ SY4450 @ SY4449 ) @ ( tc_prod @ SY4449 @ SY4449 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SY4451 @ SY4449 @ SY4449 ) @ SY4450 @ ( tc_prod @ SY4449 @ SY4449 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3188,plain,
! [SV1020: $i,SV490: $i] :
( ( ! [SY4452: $i,SY4453: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SY4452 @ SY4452 ) @ ( c_Transitive__Closure_Otrancl @ SY4453 @ SY4452 ) @ ( tc_prod @ SY4452 @ SY4452 ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SY4452 @ SY4452 ) @ SY4453 @ ( tc_prod @ SY4452 @ SY4452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3189,plain,
! [SV1021: $i,SV491: $i] :
( ( ! [SY4454: $i,SY4455: $i] :
( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SY4454 @ SY4454 ) @ ( c_Transitive__Closure_Ortrancl @ SY4455 @ SY4454 ) @ ( tc_prod @ SY4454 @ SY4454 ) )
| ! [SY4456: $i] :
( ~ ( c_in @ ( c_Pair @ SY4456 @ SV1021 @ SY4454 @ SY4454 ) @ ( c_Transitive__Closure_Ortrancl @ SY4455 @ SY4454 ) @ ( tc_prod @ SY4454 @ SY4454 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SY4456 @ SY4454 @ SY4454 ) @ ( c_Transitive__Closure_Ortrancl @ SY4455 @ SY4454 ) @ ( tc_prod @ SY4454 @ SY4454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3190,plain,
! [SV1022: $i,SV492: $i] :
( ( ! [SY4457: $i] : ( c_in @ ( c_Pair @ SV492 @ SV492 @ SV1022 @ SV1022 ) @ ( c_Transitive__Closure_Ortrancl @ SY4457 @ SV1022 ) @ ( tc_prod @ SV1022 @ SV1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3191,plain,
! [SV1023: $i,SV493: $i] :
( ( ! [SY4458: $i] : ( c_in @ ( c_Pair @ SV493 @ SV493 @ SV1023 @ SV1023 ) @ ( c_Transitive__Closure_Ortrancl @ SY4458 @ SV1023 ) @ ( tc_prod @ SV1023 @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3192,plain,
! [SV1024: $i,SV494: $i] :
( ( ! [SY4459: $i,SY4460: $i] :
( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SY4459 @ SY4459 ) @ SY4460 @ ( tc_prod @ SY4459 @ SY4459 ) )
| ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SY4459 @ SY4459 ) @ SY4460 @ ( tc_prod @ SY4459 @ SY4459 ) )
| ~ ( c_Wellfounded_Owf @ SY4460 @ SY4459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3193,plain,
! [SV1025: $i,SV495: $i] :
( ( ( SV495 = SV1025 )
| ! [SY4461: $i,SY4462: $i] :
( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SY4461 @ SY4461 ) @ SY4462 @ ( tc_prod @ SY4461 @ SY4461 ) )
| ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SY4461 @ SY4461 ) @ SY4462 @ ( tc_prod @ SY4461 @ SY4461 ) )
| ~ ( c_Relation_Oantisym @ SY4462 @ SY4461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3194,plain,
! [SV1026: $i,SV496: $i] :
( ( ( SV496 = SV1026 )
| ! [SY4463: $i,SY4464: $i] :
( ~ ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SY4463 @ SY4463 ) @ SY4464 @ ( tc_prod @ SY4463 @ SY4463 ) )
| ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SY4463 @ SY4463 ) @ SY4464 @ ( tc_prod @ SY4463 @ SY4463 ) )
| ~ ( c_Relation_Oantisym @ SY4464 @ SY4463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3195,plain,
! [SV1027: $i,SV497: $i] :
( ( ! [SY4465: $i,SY4466: $i] :
( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SY4465 ) )
| ! [SY4467: $i] :
( ~ ( c_in @ ( c_Pair @ SV1027 @ SY4465 @ SY4466 @ SY4466 ) @ SY4467 @ ( tc_prod @ SY4466 @ SY4466 ) )
| ! [SY3407: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY4467 @ SV497 @ SY4466 @ SY3407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3196,plain,
! [SV1028: $i,SV498: $i] :
( ( ( SV498 = SV1028 )
| ! [SY4469: $i,SY4470: $i] :
~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ SY4469 @ SY4469 ) @ ( c_Relation_OId__on @ SY4470 @ SY4469 ) @ ( tc_prod @ SY4469 @ SY4469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3197,plain,
! [SV1029: $i,SV499: $i] :
( ( ! [SY4471: $i,SY4472: $i,SY4473: $i,SY4474: $i] :
( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SY4471 @ SY4472 @ SY4473 )
!= ( c_Recdef_Ocut @ SY4474 @ SV1029 @ SY4471 @ SY4472 @ SY4473 ) )
| ! [SY4475: $i] :
( ( ( hAPP @ SV499 @ SY4475 )
= ( hAPP @ SY4474 @ SY4475 ) )
| ~ ( c_in @ ( c_Pair @ SY4475 @ SY4471 @ SY4472 @ SY4472 ) @ SV1029 @ ( tc_prod @ SY4472 @ SY4472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3198,plain,
! [SV1030: $i,SV500: $i] :
( ( ( SV500 = SV1030 )
| ! [SY4476: $i] :
~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ SY4476 @ SY4476 ) @ ( c_Relation_OId @ SY4476 ) @ ( tc_prod @ SY4476 @ SY4476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3199,plain,
! [SV1031: $i,SV501: $i] :
( ( ! [SY4477: $i] :
( ( c_in @ ( c_Pair @ SV501 @ SV501 @ SV1031 @ SV1031 ) @ SY4477 @ ( tc_prod @ SV1031 @ SV1031 ) )
| ~ ( c_Nitpick_Orefl_H @ SY4477 @ SV1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3200,plain,
! [SV1032: $i,SV502: $i] :
( ( ! [SY4478: $i] :
( ~ ( c_in @ ( c_Pair @ SV502 @ SV502 @ SV1032 @ SV1032 ) @ SY4478 @ ( tc_prod @ SV1032 @ SV1032 ) )
| ~ ( c_Wellfounded_Owf @ SY4478 @ SV1032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3201,plain,
! [SV1033: $i,SV503: $i] :
( ( ! [SY4479: $i,SY4480: $i,SY4481: $i,SY4482: $i] :
( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SY4479 @ SY4479 ) @ ( c_Relation_Oinv__image @ SY4480 @ SY4481 @ SY4482 @ SY4479 ) @ ( tc_prod @ SY4479 @ SY4479 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY4481 @ SV503 ) @ ( hAPP @ SY4481 @ SV1033 ) @ SY4482 @ SY4482 ) @ SY4480 @ ( tc_prod @ SY4482 @ SY4482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3202,plain,
! [SV1034: $i,SV504: $i] :
( ( ! [SY4483: $i,SY4484: $i,SY4485: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SY4483 ) @ SY4484 @ SY4484 ) @ SY4485 @ ( tc_prod @ SY4484 @ SY4484 ) )
| ! [SY4486: $i] :
~ ( c_in @ ( c_Pair @ SV1034 @ SY4483 @ SY4486 @ SY4486 ) @ ( c_Relation_Oinv__image @ SY4485 @ SV504 @ SY4484 @ SY4486 ) @ ( tc_prod @ SY4486 @ SY4486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3203,plain,
! [SV1035: $i,SV505: $i] :
( ( ! [SY4487: $i,SY4488: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SY4487 @ SY4487 ) @ SY4488 @ ( tc_prod @ SY4487 @ SY4487 ) )
| ~ ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SY4487 @ SY4487 ) @ SY4488 @ ( tc_prod @ SY4487 @ SY4487 ) )
| ~ ( c_Relation_Osym @ SY4488 @ SY4487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3204,plain,
! [SV1036: $i,SV506: $i] :
( ( ! [SY4489: $i,SY4490: $i] :
( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SY4489 @ SY4489 ) @ SY4490 @ ( tc_prod @ SY4489 @ SY4489 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SY4489 @ SY4489 ) @ SY4490 @ ( tc_prod @ SY4489 @ SY4489 ) )
| ~ ( c_Relation_Osym @ SY4490 @ SY4489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3205,plain,
! [SV1037: $i,SV507: $i] :
( ( ! [SY4491: $i,SY4492: $i,SY4493: $i,SY4494: $i,SY4495: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SY4491 @ SY4492 ) @ ( c_Relation_Orel__comp @ SY4493 @ SY4494 @ SY4491 @ SY4495 @ SY4492 ) @ ( tc_prod @ SY4491 @ SY4492 ) )
| ! [SY4496: $i] :
( ~ ( c_in @ ( c_Pair @ SY4496 @ SV1037 @ SY4495 @ SY4492 ) @ SY4494 @ ( tc_prod @ SY4495 @ SY4492 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY4496 @ SY4491 @ SY4495 ) @ SY4493 @ ( tc_prod @ SY4491 @ SY4495 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3206,plain,
! [SV1038: $i,SV508: $i] :
( ( ! [SY4497: $i,SY4498: $i] :
( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SY4497 @ SY4497 ) @ ( c_Transitive__Closure_Otrancl @ SY4498 @ SY4497 ) @ ( tc_prod @ SY4497 @ SY4497 ) )
| ! [SY4499: $i] :
( ~ ( c_in @ ( c_Pair @ SY4499 @ SV1038 @ SY4497 @ SY4497 ) @ SY4498 @ ( tc_prod @ SY4497 @ SY4497 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SY4499 @ SY4497 @ SY4497 ) @ SY4498 @ ( tc_prod @ SY4497 @ SY4497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3207,plain,
! [SV1039: $i,SV509: $i] :
( ( ! [SY4500: $i,SY4501: $i] :
( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SY4500 @ SY4500 ) @ ( c_Transitive__Closure_Otrancl @ SY4501 @ SY4500 ) @ ( tc_prod @ SY4500 @ SY4500 ) )
| ! [SY4502: $i] :
( ~ ( c_in @ ( c_Pair @ SY4502 @ SV1039 @ SY4500 @ SY4500 ) @ ( c_Transitive__Closure_Otrancl @ SY4501 @ SY4500 ) @ ( tc_prod @ SY4500 @ SY4500 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SY4502 @ SY4500 @ SY4500 ) @ ( c_Transitive__Closure_Otrancl @ SY4501 @ SY4500 ) @ ( tc_prod @ SY4500 @ SY4500 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3208,plain,
! [SV1040: $i,SV510: $i] :
( ( c_in @ ( c_Pair @ SV510 @ SV510 @ SV1040 @ SV1040 ) @ ( c_Relation_OId @ SV1040 ) @ ( tc_prod @ SV1040 @ SV1040 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3209,plain,
! [SV1041: $i,SV511: $i] :
( ( c_in @ ( c_Pair @ SV511 @ SV511 @ SV1041 @ SV1041 ) @ ( c_Relation_OId @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3210,plain,
! [SV1042: $i,SV512: $i] :
( ( ! [SY4503: $i,SY4504: $i] :
( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SY4503 @ SV1042 ) @ SY4504 )
| ! [SY4505: $i,SY4506: $i] :
( ~ ( c_in @ SV1042 @ SY4505 @ SY4506 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SY4505 @ SY4503 @ SY4506 @ SY4504 ) @ ( tc_fun @ SY4506 @ SY4504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3211,plain,
! [SV1043: $i,SV513: $i] :
( ( ! [SY4507: $i,SY4508: $i] :
( ~ ( c_in @ SV513 @ SV1043 @ SY4507 )
| ! [SY4509: $i,SY4510: $i] :
( ( c_in @ ( hAPP @ SY4508 @ SV513 ) @ ( hAPP @ SY4509 @ SV513 ) @ SY4510 )
| ~ ( c_in @ SY4508 @ ( c_FuncSet_OPi @ SV1043 @ SY4509 @ SY4507 @ SY4510 ) @ ( tc_fun @ SY4507 @ SY4510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3212,plain,
! [SV1044: $i,SV514: $i] :
( ( ! [SY4511: $i,SY4512: $i] :
( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4511 @ SY4512 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4511 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV514 = SV1044 )
| ( SV514 = SY4512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3213,plain,
! [SV1045: $i,SV515: $i] :
( ( ! [SY4513: $i,SY4514: $i] :
( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4513 @ SY4514 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4513 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1045 = SY4514 )
| ( SV515 = SY4514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3214,plain,
! [SV1046: $i,SV516: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV516 @ SV516 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1046 @ SV516 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3215,plain,
! [SV1047: $i,SV517: $i] :
( ( ! [SY4515: $i] :
~ ( c_in @ ( c_Pair @ SV517 @ SV1047 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4515 @ SV517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3216,plain,
! [SV1048: $i,SV518: $i] :
( ( ! [SY4516: $i] :
( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4516 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4517: $i] :
( ( SV1048 = SY4517 )
| ~ ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4516 @ SY4517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3217,plain,
! [SV1049: $i,SV519: $i] :
( ( ( SV519 = SV1049 )
| ( SV1049 = SV519 )
| ! [SY4518: $i] : ( c_in @ ( c_Pair @ SV519 @ SV1049 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4518 @ SV519 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3218,plain,
! [SV1050: $i,SV520: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV520 @ SV520 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1050 @ SV520 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3219,plain,
! [SV1051: $i,SV521: $i] :
( ( ! [SY4519: $i] :
~ ( c_in @ ( c_Pair @ SV521 @ SV1051 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4519 @ SV1051 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3220,plain,
! [SV1052: $i,SV522: $i] :
( ( ! [SY4520: $i,SY4521: $i] :
( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4520 @ SY4521 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4520 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV522 = SV1052 )
| ( SV1052 = SY4521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3221,plain,
! [SV1053: $i,SV523: $i] :
( ( ! [SY4522: $i,SY4523: $i] :
( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4522 @ SY4523 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4522 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV523 = SY4523 )
| ( SV1053 = SY4523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3222,plain,
! [SV1054: $i,SV524: $i] :
( ( ( SV524 = SV1054 )
| ( SV524 = SV1054 )
| ! [SY4524: $i] : ( c_in @ ( c_Pair @ SV524 @ SV1054 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4524 @ SV1054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3223,plain,
! [SV1055: $i,SV525: $i] :
( ( ! [SY4525: $i] :
( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4525 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4526: $i] :
( ( SV525 = SY4526 )
| ~ ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4525 @ SY4526 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3224,plain,
! [SV1056: $i,SV526: $i] :
( ( ( SV526 = SV1056 )
| ( c_in @ ( c_Pair @ SV526 @ SV1056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV526 @ SV1056 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3225,plain,
! [SV1057: $i,SV527: $i] :
( ( ! [SY4527: $i] :
( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4527 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4528: $i] :
( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4528 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4528 @ ( v_sko__local__X3__1 @ SY4527 @ SY4528 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4527 @ ( v_sko__local__X3__1 @ SY4527 @ SY4528 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4528 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4527 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3226,plain,
! [SV1058: $i,SV528: $i] :
( ( ! [SY4529: $i] :
( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4529 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4530: $i] :
( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4530 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4529 @ ( v_sko__local__X3__1 @ SY4530 @ SY4529 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4530 @ ( v_sko__local__X3__1 @ SY4530 @ SY4529 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4529 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4530 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3227,plain,
! [SV1059: $i,SV529: $i] :
( ( ! [SY4531: $i] :
( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4531 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4532: $i] :
( ~ ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4532 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4532 @ ( v_sko__local__X3__1 @ SY4531 @ SY4532 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4531 @ ( v_sko__local__X3__1 @ SY4531 @ SY4532 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4532 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4531 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3228,plain,
! [SV1060: $i,SV530: $i] :
( ( ! [SY4533: $i] :
( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4533 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4534: $i] :
( ~ ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4534 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4533 @ ( v_sko__local__X3__1 @ SY4534 @ SY4533 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4534 @ ( v_sko__local__X3__1 @ SY4534 @ SY4533 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4533 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4534 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3229,plain,
! [SV1061: $i,SV531: $i] :
( ( ! [SY4535: $i,SY4536: $i] :
( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4535 @ SY4536 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4537: $i] :
( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4535 @ SY4537 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4537 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SY4536 @ SY4537 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4536 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SY4536 @ SY4537 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4537 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4536 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY4535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3230,plain,
! [SV1062: $i,SV532: $i] :
( ( ! [SY4538: $i,SY4539: $i] :
( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4538 @ SY4539 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4540: $i] :
( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4538 @ SY4540 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4539 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY4540 @ SY4539 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4540 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY4540 @ SY4539 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4539 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4540 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY4538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3231,plain,
! [SV1063: $i,SV533: $i] :
( ( ! [SY4541: $i,SY4542: $i] :
( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4541 @ SY4542 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4543: $i] :
( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4541 @ SY4543 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4543 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SY4542 @ SY4543 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4542 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SY4542 @ SY4543 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4543 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4542 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY4541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3232,plain,
! [SV1064: $i,SV534: $i] :
( ( ! [SY4544: $i,SY4545: $i] :
( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4544 @ SY4545 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4546: $i] :
( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4544 @ SY4546 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4545 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY4546 @ SY4545 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4546 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY4546 @ SY4545 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4545 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4546 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY4544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3233,plain,
! [SV1065: $i,SV535: $i] :
( ( ! [SY4547: $i,SY4548: $i] :
( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4547 @ SY4548 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4548 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SY4548 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4548 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SY4547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3234,plain,
! [SV1066: $i,SV536: $i] :
( ( ! [SY4549: $i,SY4550: $i] :
( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4549 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4551: $i,SY4552: $i] :
( ~ ( c_in @ ( c_Pair @ SY4550 @ SY4551 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4552 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4550 @ SY4551 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4552 @ ( v_sko__local__X2__1 @ SY4549 @ SY4552 @ SV536 @ SY4550 @ SV1066 @ SY4551 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4549 @ ( v_sko__local__X2__1 @ SY4549 @ SY4552 @ SV536 @ SY4550 @ SV1066 @ SY4551 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4552 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4549 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SY4550 )
| ( SV536 = SY4551 )
| ( SY4550 = SY4551 )
| ( SV536 = SV1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3235,plain,
! [SV1067: $i,SV537: $i] :
( ( ! [SY4553: $i,SY4554: $i] :
( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4553 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4555: $i,SY4556: $i] :
( ~ ( c_in @ ( c_Pair @ SY4554 @ SY4555 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4556 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4553 @ ( v_sko__local__X2__1 @ SY4556 @ SY4553 @ SY4554 @ SV537 @ SY4555 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4554 @ SY4555 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4556 @ ( v_sko__local__X2__1 @ SY4556 @ SY4553 @ SY4554 @ SV537 @ SY4555 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4553 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4556 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY4555 = SV537 )
| ( SY4554 = SV1067 )
| ( SV537 = SV1067 )
| ( SY4554 = SY4555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3236,plain,
! [SV1068: $i,SV538: $i] :
( ( ! [SY4557: $i,SY4558: $i] :
( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4557 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4559: $i,SY4560: $i] :
( ~ ( c_in @ ( c_Pair @ SY4558 @ SY4559 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4560 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY4558 @ SY4559 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4560 @ ( v_sko__local__X2__1 @ SY4557 @ SY4560 @ SV538 @ SY4558 @ SV1068 @ SY4559 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4557 @ ( v_sko__local__X2__1 @ SY4557 @ SY4560 @ SV538 @ SY4558 @ SV1068 @ SY4559 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4560 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4557 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SY4558 )
| ( SV538 = SY4559 )
| ( SY4558 = SY4559 )
| ( SV538 = SV1068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3237,plain,
! [SV1069: $i,SV539: $i] :
( ( ! [SY4561: $i,SY4562: $i] :
( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4561 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4563: $i,SY4564: $i] :
( ~ ( c_in @ ( c_Pair @ SY4562 @ SY4563 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4564 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4561 @ ( v_sko__local__X2__1 @ SY4564 @ SY4561 @ SY4562 @ SV539 @ SY4563 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY4562 @ SY4563 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4564 @ ( v_sko__local__X2__1 @ SY4564 @ SY4561 @ SY4562 @ SV539 @ SY4563 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4561 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4564 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY4563 = SV539 )
| ( SY4562 = SV1069 )
| ( SV539 = SV1069 )
| ( SY4562 = SY4563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3238,plain,
! [SV1070: $i,SV540: $i] :
( ( ! [SY4565: $i,SY4566: $i] :
( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4565 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4567: $i,SY4568: $i] :
( ~ ( c_in @ ( c_Pair @ SY4566 @ SY4567 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4568 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4565 @ ( v_sko__local__X1__1 @ SY4568 @ SY4565 @ SY4566 @ SV540 @ SY4567 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4566 @ SY4567 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4568 @ ( v_sko__local__X1__1 @ SY4568 @ SY4565 @ SY4566 @ SV540 @ SY4567 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4565 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4568 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY4567 = SV540 )
| ( SY4566 = SV1070 )
| ( SV540 = SV1070 )
| ( SY4566 = SY4567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3239,plain,
! [SV1071: $i,SV541: $i] :
( ( ! [SY4569: $i,SY4570: $i] :
( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4569 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY4571: $i,SY4572: $i] :
( ~ ( c_in @ ( c_Pair @ SY4570 @ SY4571 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY4572 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4569 @ ( v_sko__local__X1__1 @ SY4572 @ SY4569 @ SY4570 @ SV541 @ SY4571 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY4570 @ SY4571 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY4572 @ ( v_sko__local__X1__1 @ SY4572 @ SY4569 @ SY4570 @ SV541 @ SY4571 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4569 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY4572 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY4571 = SV541 )
| ( SY4570 = SV1071 )
| ( SV541 = SV1071 )
| ( SY4570 = SY4571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3240,plain,
! [SV1072: $i,SV542: $i] :
( ( ! [SY4573: $i] :
( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SY4573 ) )
| ~ ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV542 @ SY4573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3241,plain,
! [SV1073: $i,SV543: $i] :
( ( ! [SY4574: $i,SY4575: $i,SY4576: $i,SY4577: $i] :
( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SY4574 @ SY4575 ) @ ( c_Product__Type_OSigma @ SY4576 @ SY4577 @ SY4574 @ SY4575 ) @ ( tc_prod @ SY4574 @ SY4575 ) )
| ~ ( c_in @ SV1073 @ ( hAPP @ SY4577 @ SV543 ) @ SY4575 )
| ~ ( c_in @ SV543 @ SY4576 @ SY4574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3242,plain,
! [SV1074: $i,SV544: $i] :
( ( ! [SY4578: $i,SY4579: $i,SY4580: $i,SY4581: $i] :
( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SY4578 @ SY4579 ) @ ( c_Product__Type_OSigma @ SY4580 @ SY4581 @ SY4578 @ SY4579 ) @ ( tc_prod @ SY4578 @ SY4579 ) )
| ~ ( c_in @ SV1074 @ ( hAPP @ SY4581 @ SV544 ) @ SY4579 )
| ~ ( c_in @ SV544 @ SY4580 @ SY4578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3243,plain,
! [SV1075: $i,SV545: $i] :
( ( ! [SY4582: $i] :
( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SY4582 ) @ SY4582 )
| ! [SY4583: $i] :
( ~ ( c_in @ ( c_Pair @ SV545 @ SY4583 @ SY4582 @ SY4582 ) @ SV1075 @ ( tc_prod @ SY4582 @ SY4582 ) )
| ~ ( c_in @ SY4583 @ ( c_Wellfounded_Oacc @ SV1075 @ SY4582 ) @ SY4582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3244,plain,
! [SV1076: $i,SV546: $i] :
( ( ! [SY4584: $i] :
( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SY4584 ) @ SY4584 )
| ! [SY4585: $i] :
( ~ ( c_in @ ( c_Pair @ SV546 @ SY4585 @ SY4584 @ SY4584 ) @ SV1076 @ ( tc_prod @ SY4584 @ SY4584 ) )
| ~ ( c_in @ SY4585 @ ( c_Wellfounded_Oacc @ SV1076 @ SY4584 ) @ SY4584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3245,plain,
! [SV1077: $i,SV547: $i] :
( ( ! [SY4586: $i,SY4587: $i,SY4588: $i] :
( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SY4586 @ SY4587 @ SY4588 ) @ SY4588 )
| ! [SY4589: $i] :
( ~ ( c_in @ ( c_Pair @ SY4589 @ SV547 @ SY4587 @ SY4588 ) @ SV1077 @ ( tc_prod @ SY4587 @ SY4588 ) )
| ~ ( c_in @ SY4589 @ SY4586 @ SY4587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3246,plain,
! [SV1078: $i,SV548: $i] :
( ( ! [SY4590: $i,SY4591: $i,SY4592: $i] :
( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SY4590 @ SY4591 @ SY4592 ) @ SY4592 )
| ! [SY4593: $i] :
( ~ ( c_in @ ( c_Pair @ SY4593 @ SV548 @ SY4591 @ SY4592 ) @ SV1078 @ ( tc_prod @ SY4591 @ SY4592 ) )
| ~ ( c_in @ SY4593 @ SY4590 @ SY4591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3247,plain,
! [SV1079: $i,SV549: $i] :
( ( ! [SY4594: $i] :
( ( c_in @ SV549 @ SV1079 @ SY4594 )
| ! [SY4595: $i] :
~ ( c_in @ ( c_Pair @ SV549 @ SY4595 @ SY4594 @ SY4594 ) @ ( c_Relation_OId__on @ SV1079 @ SY4594 ) @ ( tc_prod @ SY4594 @ SY4594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3248,plain,
! [SV1080: $i,SV550: $i] :
( ( ! [SY4596: $i] :
( ( c_in @ ( c_Pair @ SV550 @ SV550 @ SV1080 @ SV1080 ) @ ( c_Relation_OId__on @ SY4596 @ SV1080 ) @ ( tc_prod @ SV1080 @ SV1080 ) )
| ~ ( c_in @ SV550 @ SY4596 @ SV1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3249,plain,
! [SV1081: $i,SV551: $i] :
( ( ! [SY4597: $i] :
( ( c_in @ SV551 @ SV1081 @ SY4597 )
| ! [SY4598: $i,SY4599: $i] :
( ~ ( c_in @ ( c_Pair @ SY4598 @ SV551 @ SY4597 @ SY4597 ) @ SY4599 @ ( tc_prod @ SY4597 @ SY4597 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SY4599 @ SY4597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3250,plain,
! [SV1082: $i,SV552: $i] :
( ( ! [SY4600: $i] :
( ( c_in @ SV552 @ SV1082 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY4601 @ SY4600 @ SY4600 ) @ SY4602 @ ( tc_prod @ SY4600 @ SY4600 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SY4602 @ SY4600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3251,plain,
! [SV1083: $i,SV553: $i] :
( ( ! [SY4603: $i,SY4604: $i] :
( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SY4603 @ SY4604 ) @ SY4604 )
| ! [SY4605: $i] :
~ ( c_in @ ( c_Pair @ SY4605 @ SV553 @ SY4603 @ SY4604 ) @ SV1083 @ ( tc_prod @ SY4603 @ SY4604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3252,plain,
! [SV1084: $i,SV554: $i] :
( ( ! [SY4606: $i,SY4607: $i] :
( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SY4606 @ SY4607 ) @ SY4607 )
| ! [SY4608: $i] :
~ ( c_in @ ( c_Pair @ SY4608 @ SV554 @ SY4606 @ SY4607 ) @ SV1084 @ ( tc_prod @ SY4606 @ SY4607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3253,plain,
! [SV1085: $i,SV555: $i] :
( ( ! [SY4609: $i,SY4610: $i] :
( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SY4609 @ SY4610 ) @ SY4609 )
| ! [SY4611: $i] :
~ ( c_in @ ( c_Pair @ SV555 @ SY4611 @ SY4609 @ SY4610 ) @ SV1085 @ ( tc_prod @ SY4609 @ SY4610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3254,plain,
! [SV1086: $i,SV556: $i] :
( ( ! [SY4612: $i,SY4613: $i] :
( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SY4612 @ SY4613 ) @ SY4612 )
| ! [SY4614: $i] :
~ ( c_in @ ( c_Pair @ SV556 @ SY4614 @ SY4612 @ SY4613 ) @ SV1086 @ ( tc_prod @ SY4612 @ SY4613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3255,plain,
! [SV1087: $i,SV557: $i] :
( ( ! [SY4615: $i,SY4616: $i] :
( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SY4615 ) @ SY4616 )
| ! [SY4617: $i,SY4618: $i] :
~ ( c_in @ ( c_Pair @ SY4615 @ SV557 @ SY4617 @ SY4616 ) @ ( c_Product__Type_OSigma @ SY4618 @ SV1087 @ SY4617 @ SY4616 ) @ ( tc_prod @ SY4617 @ SY4616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3256,plain,
! [SV1088: $i,SV558: $i] :
( ( ! [SY4619: $i,SY4620: $i] :
( ( c_in @ SV558 @ SV1088 @ SY4619 )
| ! [SY4621: $i,SY4622: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SY4620 @ SY4619 @ SY4621 ) @ ( c_Product__Type_OSigma @ SV1088 @ SY4622 @ SY4619 @ SY4621 ) @ ( tc_prod @ SY4619 @ SY4621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3257,plain,
! [SV1089: $i,SV559: $i] :
( ( ! [SY4623: $i,SY4624: $i] :
( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SY4623 @ SY4623 ) @ SY4624 @ ( tc_prod @ SY4623 @ SY4623 ) )
| ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SY4623 @ SY4623 ) @ SY4624 @ ( tc_prod @ SY4623 @ SY4623 ) )
| ( SV1089 = SV559 )
| ! [SY4625: $i] :
( ~ ( c_in @ SV559 @ SY4625 @ SY4623 )
| ~ ( c_in @ SV1089 @ SY4625 @ SY4623 )
| ~ ( c_Relation_Ototal__on @ SY4625 @ SY4624 @ SY4623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3258,plain,
! [SV1090: $i,SV560: $i] :
( ( ! [SY4626: $i] :
( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SY4626 @ ( tc_prod @ SV1090 @ SV1090 ) )
| ! [SY4627: $i] :
( ~ ( c_in @ SV560 @ SY4627 @ SV1090 )
| ~ ( c_Relation_Orefl__on @ SY4627 @ SY4626 @ SV1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3259,plain,
! [SV1091: $i,SV561: $i] :
( ( ! [SY4628: $i] :
( ( c_in @ SV561 @ SV1091 @ SY4628 )
| ! [SY4629: $i,SY4630: $i] :
( ~ ( c_in @ ( c_Pair @ SY4629 @ SV561 @ SY4628 @ SY4628 ) @ SY4630 @ ( tc_prod @ SY4628 @ SY4628 ) )
| ~ ( c_Relation_Orefl__on @ SV1091 @ SY4630 @ SY4628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3260,plain,
! [SV1092: $i,SV562: $i] :
( ( ! [SY4631: $i] :
( ( c_in @ SV562 @ SV1092 @ SY4631 )
| ! [SY4632: $i,SY4633: $i] :
( ~ ( c_in @ ( c_Pair @ SV562 @ SY4632 @ SY4631 @ SY4631 ) @ SY4633 @ ( tc_prod @ SY4631 @ SY4631 ) )
| ~ ( c_Relation_Orefl__on @ SV1092 @ SY4633 @ SY4631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3261,plain,
! [SV1093: $i,SV563: $i] :
( ( ! [SY4634: $i] :
( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SY4634 @ ( tc_prod @ SV1093 @ SV1093 ) )
| ! [SY4635: $i] :
( ~ ( c_in @ SV563 @ SY4635 @ SV1093 )
| ~ ( c_Relation_Orefl__on @ SY4635 @ SY4634 @ SV1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3262,plain,
! [SV1094: $i,SV564: $i] :
( ( ! [SY4636: $i,SY4637: $i] :
( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SY4636 @ SY4636 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY4636 @ SY4636 ) @ SY4637 ) @ SY4636 ) @ ( tc_prod @ SY4636 @ SY4636 ) )
| ~ ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SY4636 @ SY4636 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY4636 @ SY4636 ) @ ( c_Transitive__Closure_Otrancl @ SY4637 @ SY4636 ) ) @ ( tc_prod @ SY4636 @ SY4636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3263,plain,
! [SV1095: $i,SV565: $i] :
( ( ! [SY4638: $i,SY4639: $i] :
( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SY4638 @ SY4638 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY4638 @ SY4638 ) @ ( c_Transitive__Closure_Otrancl @ SY4639 @ SY4638 ) ) @ ( tc_prod @ SY4638 @ SY4638 ) )
| ~ ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SY4638 @ SY4638 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY4638 @ SY4638 ) @ SY4639 ) @ SY4638 ) @ ( tc_prod @ SY4638 @ SY4638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3264,plain,
! [SV1096: $i,SV566: $i] :
( ( ! [SY4640: $i,SY4641: $i] :
( ( c_in @ ( c_Pair @ SV566 @ SV1096 @ SY4640 @ SY4640 ) @ ( c_Transitive__Closure_Ortrancl @ SY4641 @ SY4640 ) @ ( tc_prod @ SY4640 @ SY4640 ) )
| ~ ( c_in @ ( c_Pair @ SV1096 @ SV566 @ SY4640 @ SY4640 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY4640 @ SY4640 ) @ SY4641 ) @ SY4640 ) @ ( tc_prod @ SY4640 @ SY4640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3265,plain,
! [SV1097: $i,SV567: $i] :
( ( ! [SY4642: $i,SY4643: $i] :
( ( c_in @ ( c_Pair @ SV567 @ SV1097 @ SY4642 @ SY4642 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SY4642 @ SY4642 ) @ SY4643 ) @ SY4642 ) @ ( tc_prod @ SY4642 @ SY4642 ) )
| ~ ( c_in @ ( c_Pair @ SV1097 @ SV567 @ SY4642 @ SY4642 ) @ ( c_Transitive__Closure_Ortrancl @ SY4643 @ SY4642 ) @ ( tc_prod @ SY4642 @ SY4642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3266,plain,
! [SV1098: $i,SV568: $i] :
( ( ! [SY4644: $i,SY4645: $i,SY4646: $i,SY4647: $i,SY4648: $i,SY4649: $i,SY4650: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SY4644 ) )
!= ( hAPP @ SY4645 @ ( hAPP @ SY4646 @ SY4647 ) ) )
| ! [SY4651: $i,SY4652: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SY4648 @ SY4649 @ SY4650 ) @ SY4644 )
= ( hAPP @ ( c_Fun_Ocomp @ SY4645 @ SY4646 @ SY4651 @ SY4649 @ SY4652 ) @ SY4647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3267,plain,
! [SV1099: $i,SV569: $i] :
( ( ! [SY4653: $i,SY4654: $i,SY4655: $i,SY4656: $i,SY4657: $i] :
( ! [SY4658: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SY4653 @ SY4654 @ SY4655 )
!= ( c_Fun_Ocomp @ SY4656 @ SY4657 @ SY4658 @ SY4654 @ SY4655 ) )
| ! [SY4659: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY4659 ) )
= ( hAPP @ SY4656 @ ( hAPP @ SY4657 @ SY4659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3268,plain,
! [SV1100: $i,SV570: $i] :
( ( ! [SY4660: $i,SY4661: $i,SY4662: $i,SY4663: $i] :
( ( ( c_Pair @ SV570 @ SV1100 @ SY4660 @ SY4661 )
!= ( c_Pair @ SY4662 @ SY4663 @ SY4660 @ SY4661 ) )
| ( SV1100 = SY4663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3269,plain,
! [SV1101: $i,SV571: $i] :
( ( ! [SY4664: $i,SY4665: $i,SY4666: $i] :
( ! [SY4667: $i] :
( ( c_Pair @ SV571 @ SV1101 @ SY4664 @ SY4665 )
!= ( c_Pair @ SY4666 @ SY4667 @ SY4664 @ SY4665 ) )
| ( SV571 = SY4666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3270,plain,
! [SV1102: $i,SV572: $i] :
( ( ! [SY4668: $i,SY4669: $i,SY4670: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SY4668 @ SY4669 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY4669 @ SY4668 ) @ SY4670 ) @ ( tc_prod @ SY4668 @ SY4669 ) )
| ~ ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SY4669 @ SY4668 ) @ SY4670 @ ( tc_prod @ SY4669 @ SY4668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3271,plain,
! [SV1103: $i,SV573: $i] :
( ( ! [SY4671: $i,SY4672: $i,SY4673: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SY4671 @ SY4672 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY4672 @ SY4671 ) @ SY4673 ) @ ( tc_prod @ SY4671 @ SY4672 ) )
| ~ ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SY4672 @ SY4671 ) @ SY4673 @ ( tc_prod @ SY4672 @ SY4671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3272,plain,
! [SV1104: $i,SV574: $i] :
( ( ! [SY4674: $i,SY4675: $i,SY4676: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SY4674 @ SY4675 ) @ SY4676 @ ( tc_prod @ SY4674 @ SY4675 ) )
| ~ ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SY4675 @ SY4674 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY4674 @ SY4675 ) @ SY4676 ) @ ( tc_prod @ SY4675 @ SY4674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3273,plain,
! [SV1105: $i,SV575: $i] :
( ( ! [SY4677: $i,SY4678: $i,SY4679: $i,SY4680: $i,SY4681: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SY4677 @ SY4678 @ SY4679 @ SY4680 ) @ SY4679 @ SY4681 @ SY4680 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SY4679 @ SY4681 @ SY4678 ) @ SY4677 @ SY4678 @ SY4681 @ SY4680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3274,plain,
! [SV576: $i] :
( ( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ SV576 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV576 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2691]) ).
thf(3275,plain,
! [SV577: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV577 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ SV577 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2692]) ).
thf(3276,plain,
! [SV1106: $i,SV578: $i] :
( ( ! [SY4682: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV578 @ SV1106 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1106 @ SV578 ) @ SY4682 ) )
= SY4682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3277,plain,
! [SV1107: $i,SV579: $i] :
( ( ! [SY4683: $i,SY4684: $i,SY4685: $i,SY4686: $i] :
( ( hAPP @ SV579 @ ( hAPP @ SV1107 @ SY4683 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SV1107 @ SY4684 @ SY4685 @ SY4686 ) @ SY4683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3278,plain,
! [SV1108: $i,SV580: $i] :
( ( ! [SY4687: $i,SY4688: $i,SY4689: $i,SY4690: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SV1108 @ SY4687 @ SY4688 @ SY4689 ) @ SY4690 )
= ( hAPP @ SV580 @ ( hAPP @ SV1108 @ SY4690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3279,plain,
! [SV1109: $i,SV581: $i] :
( ( ! [SY4691: $i] : ( c_in @ SV581 @ SV1109 @ SY4691 )
| ~ ( hBOOL @ ( hAPP @ SV1109 @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3280,plain,
! [SV1110: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ SV582 @ SV1110 ) )
| ! [SY4692: $i] :
~ ( c_in @ SV1110 @ SV582 @ SY4692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3281,plain,
! [SV1111: $i,SV583: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV583 @ SV1111 ) )
| ~ ( class_Lattices_Olattice @ SV1111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3282,plain,
! [SV1112: $i,SV584: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV584 @ SV1112 ) )
| ~ ( class_Lattices_Olattice @ SV1112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3283,plain,
! [SV1113: $i,SV585: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV585 @ SV1113 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV1113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3284,plain,
! [SV1114: $i,SV586: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV586 @ SV1114 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV1114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3285,plain,
! [SV1115: $i,SV587: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV587 @ SV1115 ) )
| ~ ( class_Orderings_Opreorder @ SV1115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3286,plain,
! [SV1116: $i,SV588: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV588 @ SV1116 ) )
| ~ ( class_Lattices_Olattice @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3287,plain,
! [SV1117: $i,SV589: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV589 @ SV1117 ) )
| ~ ( class_Orderings_Oorder @ SV1117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3288,plain,
! [SV1118: $i,SV590: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV590 @ SV1118 ) )
| ~ ( class_Orderings_Obot @ SV1118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3289,plain,
! [SV1119: $i,SV591: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV591 @ SV1119 ) )
| ~ ( class_HOL_Oord @ SV1119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3290,plain,
! [SV1120: $i,SV592: $i] :
( ( c_fequal @ SV592 @ SV592 @ SV1120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3291,plain,
! [SV1121: $i,SV593: $i] :
( ( ( SV593 = SV1121 )
| ! [SY4693: $i] :
~ ( c_fequal @ SV593 @ SV1121 @ SY4693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3292,plain,
! [SV1: $i] :
( ( ( 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 ) @ SV1 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV1 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(3293,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV2 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( 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 ) @ SV2 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(3294,plain,
! [SV1122: $i,SV594: $i,SV3: $i] :
( ( ! [SY4694: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SV594 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SY4694 @ ( tc_fun @ SV1122 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SY4694 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ ( tc_fun @ SV1122 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3295,plain,
! [SV1123: $i,SV595: $i,SV4: $i] :
( ( ! [SY4695: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ SV1123 @ ( tc_fun @ SY4695 @ tc_bool ) ) @ ( tc_fun @ SY4695 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ SV1123 @ ( tc_fun @ SY4695 @ tc_bool ) ) @ ( tc_fun @ SY4695 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3296,plain,
! [SV1124: $i,SV596: $i,SV5: $i] :
( ( ! [SY4696: $i,SY4697: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SY4696 ) @ SY4697 @ ( tc_fun @ SY4696 @ tc_bool ) )
| ! [SY4698: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY4698 @ ( c_COMBK @ SY4697 @ ( tc_fun @ SY4696 @ tc_bool ) @ SV1124 ) @ SV1124 @ SY4696 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SY4696 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3297,plain,
! [SV1125: $i,SV597: $i,SV6: $i] :
( ( ( c_Set_Oinsert @ SV6 @ ( c_Set_Oinsert @ SV597 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1125 @ tc_bool ) ) @ SV1125 ) @ SV1125 )
= ( c_Set_Oinsert @ SV597 @ ( c_Set_Oinsert @ SV6 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1125 @ tc_bool ) ) @ SV1125 ) @ SV1125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3298,plain,
! [SV1126: $i,SV598: $i,SV8: $i] :
( ( ! [SY4699: $i] :
( ( hAPP @ ( c_COMBK @ SV8 @ SV598 @ SV1126 ) @ SY4699 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3299,plain,
! [SV600: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true )
| ( ( ! [SY2178: $i,SY2179: $i] :
( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SY2178 @ SY2179 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2178 @ SY2179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(3300,plain,
! [SV1127: $i,SV601: $i,SV11: $i] :
( ( ! [SY4700: $i,SY4701: $i] :
( ( c_Relation_OImage @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV601 @ SV1127 @ ( tc_fun @ SY4700 @ tc_bool ) ) @ SY4700 @ SY4701 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV11 @ SV601 @ SY4700 @ SY4701 ) @ ( c_Relation_OImage @ SV11 @ SV1127 @ SY4700 @ SY4701 ) @ ( tc_fun @ SY4701 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3301,plain,
! [SV1128: $i,SV602: $i,SV12: $i] :
( ( ! [SY4702: $i,SY4703: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV12 @ SV602 @ ( tc_fun @ ( tc_prod @ SV1128 @ SY4702 ) @ tc_bool ) ) @ SY4703 @ SV1128 @ SY4702 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV12 @ SY4703 @ SV1128 @ SY4702 ) @ ( c_Relation_OImage @ SV602 @ SY4703 @ SV1128 @ SY4702 ) @ ( tc_fun @ SY4702 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3302,plain,
! [SV1129: $i,SV603: $i,SV13: $i] :
( ( ! [SY4704: $i,SY4705: $i,SY4706: $i,SY4707: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SY4704 @ SY4705 ) @ ( c_Relation_Orel__comp @ SY4706 @ SY4707 @ SV1129 @ SY4704 @ SY4705 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SY4705 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SY4707 @ ( tc_fun @ ( tc_prod @ SY4704 @ SY4705 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SY4706 @ ( tc_fun @ ( tc_prod @ SV1129 @ SY4704 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3303,plain,
! [SV14: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false )
| ( ( ! [SY2194: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2194 @ SY2194 @ SV14 )
= SY2194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(3304,plain,
! [SV1130: $i,SV605: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ ( c_Product__Type_OSigma @ SV605 @ ( c_COMBK @ SV605 @ ( tc_fun @ SV1130 @ tc_bool ) @ SV1130 ) @ SV1130 @ SV1130 ) @ ( tc_fun @ ( tc_prod @ SV1130 @ SV1130 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV605 @ SV16 @ SV1130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3305,plain,
! [SV607: $i,SV18: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV18 ) )
= $true )
| ( ( ! [SY3752: $i,SY3753: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SY3752 @ SV18 ) @ SY3753 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV607 @ SY3753 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3752 @ SY3753 @ SV18 ) @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(3306,plain,
! [SV608: $i,SV19: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV19 ) )
= $true )
| ( ( ! [SY3754: $i,SY3755: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3754 @ SY3755 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3754 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3755 @ SV19 ) @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(3307,plain,
! [SV1131: $i,SV609: $i,SV20: $i] :
( ( ! [SY4708: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV609 @ SV1131 @ ( tc_fun @ SY4708 @ tc_bool ) ) @ ( tc_fun @ SY4708 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV609 @ ( tc_fun @ SY4708 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV1131 @ ( tc_fun @ SY4708 @ tc_bool ) ) @ ( tc_fun @ SY4708 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3308,plain,
! [SV1132: $i,SV610: $i,SV21: $i] :
( ( ! [SY4709: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV610 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ SY4709 @ ( tc_fun @ SV1132 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV21 @ SY4709 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV610 @ SY4709 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( tc_fun @ SV1132 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3309,plain,
! [SV611: $i,SV22: $i] :
( ( ( SV22 = SV611 )
= $true )
| ( ( ! [SY3760: $i] :
~ ( c_in @ SV22 @ ( c_Set_Oinsert @ SV611 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3760 @ tc_bool ) ) @ SY3760 ) @ SY3760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(3310,plain,
! [SV1133: $i,SV612: $i,SV23: $i] :
( ( ! [SY4710: $i,SY4711: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV23 @ SV612 @ ( tc_fun @ SV1133 @ tc_bool ) ) @ SY4710 @ SV1133 @ SY4711 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV23 @ SY4710 @ SV1133 @ SY4711 ) @ ( c_Product__Type_OSigma @ SV612 @ SY4710 @ SV1133 @ SY4711 ) @ ( tc_fun @ ( tc_prod @ SV1133 @ SY4711 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3311,plain,
! [SV1134: $i,SV613: $i,SV24: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV24 @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3312,plain,
! [SV1135: $i,SV614: $i,SV25: $i] :
( ( ! [SY4712: $i] :
( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
| ! [SY4713: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SY4712 @ ( tc_fun @ SY4713 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY4713 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SY4712 @ ( tc_fun @ SY4713 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY4713 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SY4713 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY4712 @ SY4713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3313,plain,
! [SV1136: $i,SV615: $i,SV26: $i] :
( ( ! [SY4715: $i,SY4716: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SY4715 ) @ SY4715 @ SV1136 ) @ ( c_Product__Type_OSigma @ SY4716 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SY4715 ) @ SY4715 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SY4715 @ SV1136 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV26 @ SY4716 @ ( tc_fun @ SY4715 @ tc_bool ) )
| ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3314,plain,
! [SV1137: $i,SV616: $i,SV27: $i] :
( ( ( c_lessequals @ SV27 @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) )
| ! [SY4718: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4718 @ SV27 @ SV1137 ) @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3315,plain,
! [SV1138: $i,SV617: $i,SV28: $i] :
( ( ! [SY4719: $i] :
( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SV617 @ SV1138 @ SY4719 ) @ ( tc_fun @ SY4719 @ tc_bool ) )
| ~ ( c_lessequals @ SV28 @ SV1138 @ ( tc_fun @ SY4719 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3316,plain,
! [SV618: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true )
| ( ( ! [SY2236: $i,SY2237: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SY2236 @ SY2237 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2236 @ SY2237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(3317,plain,
! [SV1139: $i,SV619: $i,SV30: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV30 @ SV619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1139 @ SV619 ) @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV30 @ SV1139 @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) ) @ SV619 ) @ ( tc_fun @ ( tc_prod @ SV619 @ SV619 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3318,plain,
! [SV1140: $i,SV620: $i,SV31: $i] :
( ( ! [SY4720: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV31 @ SV620 @ SV1140 ) @ SY4720 @ ( tc_fun @ SV1140 @ tc_bool ) )
= ( c_Set_Oinsert @ SV31 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SY4720 @ ( tc_fun @ SV1140 @ tc_bool ) ) @ SV1140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3319,plain,
! [SV1141: $i,SV621: $i,SV32: $i] :
( ( ! [SY4721: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Set_Oinsert @ SV621 @ SV1141 @ SY4721 ) @ ( tc_fun @ SY4721 @ tc_bool ) )
= ( c_Set_Oinsert @ SV621 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV1141 @ ( tc_fun @ SY4721 @ tc_bool ) ) @ SY4721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3320,plain,
! [SV1142: $i,SV622: $i,SV33: $i] :
( ( ! [SY4722: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SV622 ) @ tc_bool ) ) @ SV1142 @ SV33 @ SV622 @ SY4722 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SY4722 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3321,plain,
! [SV1143: $i,SV623: $i,SV34: $i] :
( ( ! [SY4723: $i] :
( ( c_Relation_Orel__comp @ SV34 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV623 @ SV1143 ) @ tc_bool ) ) @ SY4723 @ SV623 @ SV1143 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4723 @ SV1143 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3322,plain,
! [SV37: $i] :
( ( ( class_Orderings_Obot @ SV37 )
= $false )
| ( ( ! [SY2254: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV37 ) @ SY2254 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3323,plain,
! [SV1144: $i,SV626: $i,SV38: $i] :
( ( ( c_Set_Oinsert @ SV38 @ SV626 @ SV1144 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3324,plain,
! [SV1145: $i,SV627: $i,SV39: $i] :
( ( ! [SY4724: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV39 @ SV627 @ SV1145 ) @ ( c_Set_Oinsert @ SV39 @ SY4724 @ SV1145 ) @ ( tc_fun @ SV1145 @ tc_bool ) )
= ( c_Set_Oinsert @ SV39 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV627 @ SY4724 @ ( tc_fun @ SV1145 @ tc_bool ) ) @ SV1145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3325,plain,
! [SV1146: $i,SV628: $i,SV40: $i] :
( ( ( c_Relation_OImage @ SV40 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV628 @ tc_bool ) ) @ SV628 @ SV1146 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1146 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3326,plain,
! [SV1147: $i,SV629: $i,SV41: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SV1147 @ SV1147 ) @ tc_bool ) ) @ SV1147 )
| ~ ( c_Relation_Osym @ SV629 @ SV1147 )
| ~ ( c_Relation_Osym @ SV41 @ SV1147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3327,plain,
! [SV1148: $i,SV630: $i,SV42: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV42 @ SV630 ) @ ( c_Transitive__Closure_Ortrancl @ SV1148 @ SV630 ) @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV42 @ SV1148 @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3328,plain,
! [SV1149: $i,SV631: $i,SV43: $i] :
( ( ! [SY4725: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV43 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SY4725 ) @ tc_bool ) ) @ SV1149 @ SY4725 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV43 @ SV1149 @ SY4725 ) @ ( c_Relation_ODomain @ SV631 @ SV1149 @ SY4725 ) @ ( tc_fun @ SV1149 @ tc_bool ) ) @ ( tc_fun @ SV1149 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3329,plain,
! [SV44: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV44 )
= $false )
| ( ( ! [SY2269: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2269 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= ( c_Orderings_Obot__class_Obot @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3330,plain,
! [SV45: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV45 )
= $false )
| ( ( ! [SY2270: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV45 ) @ SY2270 @ SV45 )
= ( c_Orderings_Obot__class_Obot @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(3331,plain,
! [SV1150: $i,SV634: $i,SV48: $i] :
( ( c_lessequals @ SV48 @ ( c_Set_Oinsert @ SV634 @ SV48 @ SV1150 ) @ ( tc_fun @ SV1150 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3332,plain,
! [SV1151: $i,SV635: $i,SV49: $i] :
( ( ! [SY4726: $i,SY4727: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV49 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1151 @ ( tc_fun @ SY4726 @ tc_bool ) ) @ SY4726 @ SY4727 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV49 @ SV635 @ SY4726 @ SY4727 ) @ ( c_Relation_OImage @ SV49 @ SV1151 @ SY4726 @ SY4727 ) @ ( tc_fun @ SY4727 @ tc_bool ) ) @ ( tc_fun @ SY4727 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3333,plain,
! [SV1152: $i,SV636: $i,SV50: $i] :
( ( ! [SY4728: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SV636 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ SY4728 @ ( tc_fun @ SV1152 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV636 @ SY4728 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ ( tc_fun @ SV1152 @ tc_bool ) ) )
| ( c_lessequals @ SY4728 @ SV50 @ ( tc_fun @ SV1152 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3334,plain,
! [SV1153: $i,SV637: $i,SV51: $i] :
( ( ! [SY4729: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SV637 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SY4729 @ ( tc_fun @ SV1153 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV637 @ SY4729 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ ( tc_fun @ SV1153 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4729 @ SV51 @ ( tc_fun @ SV1153 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3335,plain,
! [SV1154: $i,SV638: $i,SV52: $i] :
( ( ! [SY4730: $i,SY4731: $i,SY4732: $i,SY4733: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SY4730 @ SY4731 ) @ ( c_Product__Type_OSigma @ SY4732 @ ( c_COMBK @ SY4733 @ ( tc_fun @ SY4731 @ tc_bool ) @ SV1154 ) @ SV1154 @ SY4731 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SY4731 ) @ tc_bool ) )
| ! [SY4734: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY4734 @ ( c_COMBK @ SY4733 @ ( tc_fun @ SY4731 @ tc_bool ) @ SY4730 ) @ SY4730 @ SY4731 ) @ ( tc_fun @ ( tc_prod @ SY4730 @ SY4731 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SY4732 @ ( c_COMBK @ SY4734 @ ( tc_fun @ SY4730 @ tc_bool ) @ SV1154 ) @ SV1154 @ SY4730 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SY4730 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3336,plain,
! [SV1155: $i,SV639: $i,SV53: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV639 @ SV1155 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3337,plain,
! [SV640: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
= $true )
| ( ( ! [SY3811: $i] :
( ( hBOOL @ ( hAPP @ SY3811 @ SV640 ) )
| ! [SY3812: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3811 @ SV54 @ ( tc_fun @ SY3812 @ tc_bool ) ) @ SV640 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(3338,plain,
! [SV1156: $i,SV641: $i,SV55: $i] :
( ( ! [SY4735: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV641 @ ( tc_fun @ SV1156 @ tc_bool ) ) @ SY4735 ) )
| ~ ( hBOOL @ ( hAPP @ SV641 @ SY4735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3339,plain,
! [SV1157: $i,SV642: $i,SV56: $i] :
( ( ! [SY4736: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV642 @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SY4736 ) )
| ~ ( hBOOL @ ( hAPP @ SV56 @ SY4736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3340,plain,
! [SV1158: $i,SV643: $i,SV57: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SV1158 @ SV643 )
| ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3341,plain,
! [SV1159: $i,SV644: $i,SV58: $i] :
( ( ! [SY4737: $i,SY4738: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV644 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ ( c_COMBK @ SY4737 @ ( tc_fun @ SY4738 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY4738 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV58 @ ( c_COMBK @ SY4737 @ ( tc_fun @ SY4738 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY4738 ) @ ( c_Product__Type_OSigma @ SV644 @ ( c_COMBK @ SY4737 @ ( tc_fun @ SY4738 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY4738 ) @ ( tc_fun @ ( tc_prod @ SV1159 @ SY4738 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3342,plain,
! [SV1160: $i,SV645: $i,SV59: $i] :
( ( ! [SY4739: $i,SY4740: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SY4739 @ SY4740 ) @ SV1160 @ SY4740 )
| ~ ( c_Relation_Osingle__valued @ SV645 @ SY4739 @ SY4740 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SY4739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3343,plain,
! [SV1161: $i,SV646: $i,SV60: $i] :
( ( ! [SY4741: $i,SY4742: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4741 @ SY4742 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV646 @ SY4742 @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SY4741 @ SV1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3344,plain,
! [SV647: $i,SV61: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV61 ) )
= $true )
| ( ( ! [SY3827: $i,SY3828: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SY3827 @ SV61 ) @ SY3828 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3827 @ SY3828 @ SV61 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3345,plain,
! [SV648: $i,SV62: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV62 ) )
= $true )
| ( ( ! [SY3829: $i,SY3830: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ SY3830 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ SY3830 @ SV62 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3346,plain,
! [SV649: $i,SV63: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV63 ) )
= $true )
| ( ( ! [SY3831: $i,SY3832: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ SY3832 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ SY3832 @ SV63 ) @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3347,plain,
! [SV650: $i,SV64: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV64 ) )
= $true )
| ( ( ! [SY3833: $i,SY3834: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ SY3833 @ SV64 ) @ SY3834 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3833 @ SY3834 @ SV64 ) @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3348,plain,
! [SV1162: $i,SV651: $i,SV65: $i] :
( ( ! [SY4743: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ SV651 @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SY4743 @ ( tc_fun @ SV1162 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV651 @ SY4743 @ ( tc_fun @ SV1162 @ tc_bool ) ) @ ( tc_fun @ SV1162 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3349,plain,
! [SV1163: $i,SV652: $i,SV66: $i] :
( ( ! [SY4744: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ SV1163 @ ( tc_fun @ SY4744 @ tc_bool ) ) @ ( tc_fun @ SY4744 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ SV1163 @ ( tc_fun @ SY4744 @ tc_bool ) ) @ ( tc_fun @ SY4744 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3350,plain,
! [SV67: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV67 )
= $false )
| ( ( ! [SY2335: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2335 @ ( c_Orderings_Obot__class_Obot @ SV67 ) @ SV67 )
= SY2335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(3351,plain,
! [SV68: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV68 )
= $false )
| ( ( ! [SY2336: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV68 ) @ SY2336 @ SV68 )
= SY2336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(3352,plain,
! [SV1164: $i,SV655: $i,SV71: $i] :
( ( ! [SY4745: $i,SY4746: $i,SY4747: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY4745 @ SY4746 @ SY4747 ) @ ( tc_fun @ SY4747 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY4747 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SY4745 @ SV1164 @ SY4747 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV655 @ ( c_COMBK @ ( c_Set_Oinsert @ SY4745 @ SY4746 @ SY4747 ) @ ( tc_fun @ SY4747 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY4747 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ SY4746 @ ( tc_fun @ SY4747 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY4747 ) @ ( tc_fun @ ( tc_prod @ SV1164 @ SY4747 ) @ tc_bool ) ) @ ( tc_prod @ SV1164 @ SY4747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3353,plain,
! [SV656: $i,SV72: $i] :
( ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true )
| ( ( ! [SY3843: $i] :
( ~ ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SY3843 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY3843 @ SV656 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3354,plain,
! [SV657: $i,SV73: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV73 @ tc_bool ) ) @ SV657 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(3355,plain,
! [SV1165: $i,SV658: $i,SV74: $i] :
( ( ~ ( c_in @ SV74 @ SV658 @ SV1165 )
| ! [SY4748: $i] :
( ~ ( c_in @ SV74 @ SY4748 @ SV1165 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4748 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3356,plain,
! [SV659: $i,SV75: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV75 ) )
= $true )
| ( ( ! [SY3846: $i,SY3847: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3846 @ SY3847 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3846 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3847 @ SV75 ) @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(3357,plain,
! [SV76: $i] :
( ( ( class_Lattices_Olattice @ SV76 )
= $false )
| ( ( ! [SY2353: $i,SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2353 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2353 @ SY2354 @ SV76 ) @ SV76 )
= SY2353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3358,plain,
! [SV1166: $i,SV660: $i,SV77: $i] :
( ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
| ! [SY4749: $i] :
( ( ( c_Relation_Orel__comp @ SY4749 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4749 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3359,plain,
! [SV1167: $i,SV661: $i,SV78: $i] :
( ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
| ! [SY4750: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY4750 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4750 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3360,plain,
! [SV662: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true )
| ( ( ! [SY2362: $i,SY2363: $i] :
( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SY2362 @ SY2363 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2362 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(3361,plain,
! [SV663: $i,SV80: $i] :
( ( ( SV80 = SV663 )
= $true )
| ( ( ! [SY3854: $i] :
( ~ ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SY3854 @ tc_bool ) )
| ~ ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SY3854 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(3362,plain,
! [SV664: $i,SV81: $i] :
( ( ( SV81 = SV664 )
= $true )
| ( ( ! [SY3855: $i] :
( ~ ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SY3855 @ tc_bool ) )
| ~ ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SY3855 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(3363,plain,
! [SV82: $i] :
( ( ( class_Orderings_Oorder @ SV82 )
= $false )
| ( ( ! [SY2368: $i,SY2369: $i] :
( ( SY2368 = SY2369 )
| ~ ( c_lessequals @ SY2369 @ SY2368 @ SV82 )
| ~ ( c_lessequals @ SY2368 @ SY2369 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(3364,plain,
! [SV83: $i] :
( ( ( class_Orderings_Oorder @ SV83 )
= $false )
| ( ( ! [SY2370: $i,SY2371: $i] :
( ( SY2370 = SY2371 )
| ~ ( c_lessequals @ SY2371 @ SY2370 @ SV83 )
| ~ ( c_lessequals @ SY2370 @ SY2371 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3365,plain,
! [SV84: $i] :
( ( ( class_Orderings_Oorder @ SV84 )
= $false )
| ( ( ! [SY2372: $i,SY2373: $i] :
( ( SY2372 = SY2373 )
| ~ ( c_lessequals @ SY2372 @ SY2373 @ SV84 )
| ~ ( c_lessequals @ SY2373 @ SY2372 @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(3366,plain,
! [SV85: $i] :
( ( ( class_Lattices_Olattice @ SV85 )
= $false )
| ( ( ! [SY2374: $i,SY2375: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2374 @ SY2375 @ SV85 ) @ SV85 )
= SY2374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(3367,plain,
! [SV86: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false )
| ( ( ! [SY2376: $i,SY2377: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2376 @ SY2377 @ SV86 )
= SY2376 )
| ~ ( c_lessequals @ SY2377 @ SY2376 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(3368,plain,
! [SV87: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false )
| ( ( ! [SY2378: $i,SY2379: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2378 @ SY2379 @ SV87 )
!= SY2379 )
| ( c_lessequals @ SY2378 @ SY2379 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3369,plain,
! [SV88: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false )
| ( ( ! [SY2380: $i,SY2381: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2380 @ SY2381 @ SV88 )
= SY2381 )
| ~ ( c_lessequals @ SY2380 @ SY2381 @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3370,plain,
! [SV1168: $i,SV665: $i,SV89: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) )
= SV665 )
| ~ ( c_lessequals @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3371,plain,
! [SV1169: $i,SV666: $i,SV90: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV90 @ SV666 @ ( tc_fun @ SV1169 @ tc_bool ) )
= SV90 )
| ~ ( c_lessequals @ SV666 @ SV90 @ ( tc_fun @ SV1169 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3372,plain,
! [SV1170: $i,SV667: $i,SV91: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) )
!= SV667 )
| ( c_lessequals @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3373,plain,
! [SV1171: $i,SV668: $i,SV92: $i] :
( ( ! [SY4751: $i,SY4752: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4751 @ SY4752 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV668 @ SY4752 @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SY4751 @ SV1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3374,plain,
! [SV669: $i,SV93: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV93 ) )
= $true )
| ( ( ! [SY3862: $i,SY3863: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ SY3862 @ SV93 ) @ SY3863 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3862 @ SY3863 @ SV93 ) @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(3375,plain,
! [SV670: $i,SV94: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV94 ) )
= $true )
| ( ( ! [SY3864: $i,SY3865: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ SY3865 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ SY3865 @ SV94 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3376,plain,
! [SV671: $i,SV95: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV95 ) )
= $true )
| ( ( ! [SY3866: $i,SY3867: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ SY3867 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SY3867 @ SV95 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3377,plain,
! [SV672: $i,SV96: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV96 ) )
= $true )
| ( ( ! [SY3868: $i,SY3869: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SY3868 @ SV96 ) @ SY3869 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3868 @ SY3869 @ SV96 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(3378,plain,
! [SV1172: $i,SV673: $i,SV97: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) )
= SV97 )
| ~ ( c_lessequals @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3379,plain,
! [SV1173: $i,SV674: $i,SV98: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV674 @ ( tc_fun @ SV1173 @ tc_bool ) )
= SV674 )
| ~ ( c_lessequals @ SV674 @ SV98 @ ( tc_fun @ SV1173 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3380,plain,
! [SV99: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV99 )
= $false )
| ( ( ! [SY2408: $i,SY2409: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2408 @ SY2409 @ SV99 )
= SY2408 )
| ~ ( c_lessequals @ SY2408 @ SY2409 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3381,plain,
! [SV100: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV100 )
= $false )
| ( ( ! [SY2410: $i,SY2411: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2410 @ SY2411 @ SV100 )
!= SY2410 )
| ( c_lessequals @ SY2410 @ SY2411 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3382,plain,
! [SV101: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV101 )
= $false )
| ( ( ! [SY2412: $i,SY2413: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2412 @ SY2413 @ SV101 )
= SY2413 )
| ~ ( c_lessequals @ SY2413 @ SY2412 @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3383,plain,
! [SV1174: $i,SV675: $i,SV102: $i] :
( ( ! [SY4753: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SY4753 @ ( tc_fun @ SV1174 @ tc_bool ) )
| ~ ( c_lessequals @ SV675 @ SY4753 @ ( tc_fun @ SV1174 @ tc_bool ) )
| ~ ( c_lessequals @ SV102 @ SY4753 @ ( tc_fun @ SV1174 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3384,plain,
! [SV1175: $i,SV676: $i,SV103: $i] :
( ( c_lessequals @ SV103 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ SV103 @ ( tc_fun @ SV1175 @ tc_bool ) ) @ ( tc_fun @ SV1175 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3385,plain,
! [SV1176: $i,SV677: $i,SV104: $i] :
( ( c_lessequals @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV677 @ ( tc_fun @ SV1176 @ tc_bool ) ) @ ( tc_fun @ SV1176 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3386,plain,
! [SV1177: $i,SV678: $i,SV105: $i] :
( ( ! [SY4754: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SY4754 @ ( tc_fun @ SV1177 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SY4754 @ ( tc_fun @ SV1177 @ tc_bool ) )
| ~ ( c_lessequals @ SV105 @ SY4754 @ ( tc_fun @ SV1177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3387,plain,
! [SV679: $i,SV106: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV106 ) )
= $true )
| ( ( ! [SY3878: $i,SY3879: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SY3878 @ SV106 ) @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SY3878 @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SY3879 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(3388,plain,
! [SV107: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV107 )
= $false )
| ( ( ! [SY2427: $i,SY2428: $i] : ( c_lessequals @ SY2427 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2427 @ SY2428 @ SV107 ) @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2817]) ).
thf(3389,plain,
! [SV108: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV108 )
= $false )
| ( ( ! [SY2429: $i,SY2430: $i] : ( c_lessequals @ SY2429 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2430 @ SY2429 @ SV108 ) @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(3390,plain,
! [SV680: $i,SV109: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV109 ) )
= $true )
| ( ( ! [SY3880: $i,SY3881: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SY3880 @ SV109 ) @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SY3880 @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SY3881 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(3391,plain,
! [SV681: $i,SV110: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV110 ) )
= $true )
| ( ( ! [SY3882: $i,SY3883: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SY3882 @ SV110 ) @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SY3882 @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SY3883 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(3392,plain,
! [SV111: $i] :
( ( ( class_Lattices_Olattice @ SV111 )
= $false )
| ( ( ! [SY2437: $i,SY2438: $i] : ( c_lessequals @ SY2437 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2438 @ SY2437 @ SV111 ) @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3393,plain,
! [SV112: $i] :
( ( ( class_Lattices_Olattice @ SV112 )
= $false )
| ( ( ! [SY2439: $i,SY2440: $i] : ( c_lessequals @ SY2439 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2439 @ SY2440 @ SV112 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(3394,plain,
! [SV1178: $i,SV682: $i,SV113: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV113 @ SV682 @ ( tc_fun @ SV1178 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV682 @ SV113 @ ( tc_fun @ SV1178 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3395,plain,
! [SV114: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false )
| ( ( ! [SY2443: $i,SY2444: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2443 @ SY2444 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2444 @ SY2443 @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(3396,plain,
! [SV115: $i] :
( ( ( class_Lattices_Olattice @ SV115 )
= $false )
| ( ( ! [SY2445: $i,SY2446: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2445 @ SY2446 @ SV115 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2446 @ SY2445 @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3397,plain,
! [SV683: $i,SV116: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV116 @ SV683 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV116 @ SV683 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3398,plain,
! [SV684: $i,SV117: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV117 ) )
= $true )
| ( ( ! [SY3885: $i,SY3886: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3885 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3886 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3885 @ SY3886 @ SV117 ) @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(3399,plain,
! [SV1179: $i,SV685: $i,SV118: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) )
| ~ ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1179 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3400,plain,
! [SV1180: $i,SV686: $i,SV119: $i] :
( ( ( ( c_Set_Oinsert @ SV119 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 )
!= ( c_Set_Oinsert @ SV1180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 ) )
| ( SV119 = SV1180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3401,plain,
! [SV1181: $i,SV687: $i,SV120: $i] :
( ( ! [SY4755: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV120 @ SV687 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SY4755 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4755 @ SV120 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV687 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ SY4755 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4755 @ SV120 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3402,plain,
! [SV1182: $i,SV688: $i,SV122: $i] :
( ( ! [SY4756: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV688 @ SV1182 @ SV1182 ) @ SY4756 @ ( tc_prod @ SV1182 @ SV1182 ) ) @ SV1182 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV122 @ ( c_Set_Oinsert @ SV688 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1182 @ tc_bool ) ) @ SV1182 ) @ SV1182 ) @ ( c_Relation_OField @ SY4756 @ SV1182 ) @ ( tc_fun @ SV1182 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3403,plain,
! [SV1183: $i,SV689: $i,SV123: $i] :
( ( ( ( c_Set_Oinsert @ SV123 @ SV689 @ SV1183 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1183 @ tc_bool ) ) )
| ( c_in @ SV123 @ SV689 @ SV1183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3404,plain,
! [SV1184: $i,SV690: $i,SV125: $i] :
( ( ( c_in @ SV125 @ SV690 @ SV1184 )
| ! [SY4757: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SY4757 @ SV1184 ) @ SV690 @ ( tc_fun @ SV1184 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3405,plain,
! [SV1185: $i,SV691: $i,SV126: $i] :
( ( ! [SY4758: $i,SY4759: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV691 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SY4758 @ SV1185 @ SY4759 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV126 @ SY4758 @ SV1185 @ SY4759 ) @ ( c_Product__Type_OSigma @ SV691 @ SY4758 @ SV1185 @ SY4759 ) @ ( tc_fun @ ( tc_prod @ SV1185 @ SY4759 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3406,plain,
! [SV1186: $i,SV692: $i,SV127: $i] :
( ( ! [SY4760: $i] :
( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SV1186 @ SY4760 ) @ ( tc_fun @ SY4760 @ tc_bool ) )
| ~ ( c_lessequals @ SV127 @ SV1186 @ ( tc_fun @ SY4760 @ tc_bool ) )
| ( c_in @ SV692 @ SV127 @ SY4760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3407,plain,
! [SV1187: $i,SV693: $i,SV128: $i] :
( ( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SV1187 @ tc_bool ) )
| ! [SY4761: $i] :
( ( c_in @ SY4761 @ SV128 @ SV1187 )
| ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SY4761 @ SV693 @ SV1187 ) @ ( tc_fun @ SV1187 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3408,plain,
! [SV1188: $i,SV694: $i,SV129: $i] :
( ( ! [SY4762: $i] :
( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SV1188 @ SY4762 ) @ ( tc_fun @ SY4762 @ tc_bool ) )
| ~ ( c_lessequals @ SV129 @ SV1188 @ ( tc_fun @ SY4762 @ tc_bool ) )
| ( c_in @ SV694 @ SV129 @ SY4762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3409,plain,
! [SV1189: $i,SV695: $i,SV130: $i] :
( ( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SV1189 @ tc_bool ) )
| ! [SY4763: $i] :
( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SY4763 @ SV695 @ SV1189 ) @ ( tc_fun @ SV1189 @ tc_bool ) )
| ( c_in @ SY4763 @ SV130 @ SV1189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3410,plain,
! [SV1190: $i,SV696: $i,SV131: $i] :
( ( ! [SY4764: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ ( c_Set_Oinsert @ SV696 @ SV1190 @ SY4764 ) @ ( tc_fun @ SY4764 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV1190 @ ( tc_fun @ SY4764 @ tc_bool ) ) )
| ( c_in @ SV696 @ SV131 @ SY4764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3411,plain,
! [SV1191: $i,SV697: $i,SV132: $i] :
( ( ! [SY4765: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV132 @ SV697 @ SV1191 ) @ SY4765 @ ( tc_fun @ SV1191 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV697 @ SY4765 @ ( tc_fun @ SV1191 @ tc_bool ) ) )
| ( c_in @ SV132 @ SY4765 @ SV1191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3412,plain,
! [SV1192: $i,SV698: $i,SV133: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 @ SV698 @ ( tc_fun @ SV1192 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3413,plain,
! [SV1193: $i,SV699: $i,SV134: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ SV699 @ ( tc_fun @ SV1193 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) )
| ( SV134
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3414,plain,
! [SV135: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV135 )
= $false )
| ( ( ! [SY2492: $i] :
( ! [SY2493: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2492 @ SY2493 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) )
| ( SY2492
= ( c_Orderings_Obot__class_Obot @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3415,plain,
! [SV136: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV136 )
= $false )
| ( ( ! [SY2494: $i,SY2495: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2494 @ SY2495 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
| ( SY2495
= ( c_Orderings_Obot__class_Obot @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(3416,plain,
! [SV1194: $i,SV700: $i,SV137: $i] :
( ( ! [SY4766: $i,SY4767: $i,SY4768: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV700 @ ( tc_fun @ ( tc_prod @ SV1194 @ SY4766 ) @ tc_bool ) ) @ SY4767 @ SV1194 @ SY4766 @ SY4768 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SY4767 @ SV1194 @ SY4766 @ SY4768 ) @ ( c_Relation_Orel__comp @ SV700 @ SY4767 @ SV1194 @ SY4766 @ SY4768 ) @ ( tc_fun @ ( tc_prod @ SV1194 @ SY4768 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3417,plain,
! [SV1195: $i,SV701: $i,SV138: $i] :
( ( ! [SY4769: $i,SY4770: $i,SY4771: $i] :
( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV701 @ SV1195 @ ( tc_fun @ ( tc_prod @ SY4769 @ SY4770 ) @ tc_bool ) ) @ SY4771 @ SY4769 @ SY4770 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SV701 @ SY4771 @ SY4769 @ SY4770 ) @ ( c_Relation_Orel__comp @ SV138 @ SV1195 @ SY4771 @ SY4769 @ SY4770 ) @ ( tc_fun @ ( tc_prod @ SY4771 @ SY4770 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3418,plain,
! [SV1196: $i,SV702: $i,SV139: $i] :
( ( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV139 @ SV702 @ ( tc_fun @ ( tc_prod @ SV1196 @ SV1196 ) @ tc_bool ) ) @ SV1196 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV139 @ SV1196 ) @ ( c_Relation_OField @ SV702 @ SV1196 ) @ ( tc_fun @ SV1196 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3419,plain,
! [SV1197: $i,SV703: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) )
| ! [SY4772: $i] :
~ ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4772 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) ) @ ( tc_fun @ SV1197 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3420,plain,
! [SV1198: $i,SV704: $i,SV141: $i] :
( ( ( c_lessequals @ SV141 @ SV704 @ ( tc_fun @ SV1198 @ tc_bool ) )
| ! [SY4773: $i] :
~ ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV704 @ SY4773 @ ( tc_fun @ SV1198 @ tc_bool ) ) @ ( tc_fun @ SV1198 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3421,plain,
! [SV705: $i,SV142: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV142 ) )
= $true )
| ( ( ! [SY3926: $i] :
( ( c_lessequals @ SV705 @ SY3926 @ SV142 )
| ! [SY3927: $i] :
~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3926 @ SY3927 @ SV142 ) @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(3422,plain,
! [SV706: $i,SV143: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV143 ) )
= $true )
| ( ( ! [SY3928: $i] :
( ( c_lessequals @ SV706 @ SY3928 @ SV143 )
| ! [SY3929: $i] :
~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3929 @ SY3928 @ SV143 ) @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3423,plain,
! [SV707: $i,SV144: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV144 ) )
= $true )
| ( ( ! [SY3930: $i,SY3931: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SY3930 @ SV144 ) @ SY3931 @ SV144 )
| ~ ( c_lessequals @ SV707 @ SY3931 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(3424,plain,
! [SV708: $i,SV145: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV145 ) )
= $true )
| ( ( ! [SY3932: $i,SY3933: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SY3932 @ SV145 ) @ SY3933 @ SV145 )
| ~ ( c_lessequals @ SY3932 @ SY3933 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3425,plain,
! [SV709: $i,SV146: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV146 ) )
= $true )
| ( ( ! [SY3934: $i] :
( ( c_lessequals @ SV709 @ SY3934 @ SV146 )
| ! [SY3935: $i] :
~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3934 @ SY3935 @ SV146 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(3426,plain,
! [SV710: $i,SV147: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV147 ) )
= $true )
| ( ( ! [SY3936: $i] :
( ( c_lessequals @ SV710 @ SY3936 @ SV147 )
| ! [SY3937: $i] :
~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3937 @ SY3936 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(3427,plain,
! [SV1199: $i,SV711: $i,SV148: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV148 @ SV711 @ ( tc_fun @ SV1199 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SV148 @ ( tc_fun @ SV1199 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3428,plain,
! [SV149: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false )
| ( ( ! [SY2534: $i,SY2535: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2534 @ SY2535 @ SV149 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2535 @ SY2534 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3429,plain,
! [SV150: $i] :
( ( ( class_Lattices_Olattice @ SV150 )
= $false )
| ( ( ! [SY2536: $i,SY2537: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2536 @ SY2537 @ SV150 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2537 @ SY2536 @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3430,plain,
! [SV1200: $i,SV712: $i,SV151: $i] :
( ( ! [SY4774: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV712 @ ( tc_fun @ ( tc_prod @ SV1200 @ SY4774 ) @ tc_bool ) ) @ SV1200 @ SY4774 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV151 @ SV1200 @ SY4774 ) @ ( c_Relation_ODomain @ SV712 @ SV1200 @ SY4774 ) @ ( tc_fun @ SV1200 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3431,plain,
! [SV1201: $i,SV713: $i,SV152: $i] :
( ( ( c_Set_Oinsert @ SV152 @ SV713 @ SV1201 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV152 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1201 @ tc_bool ) ) @ SV1201 ) @ SV713 @ ( tc_fun @ SV1201 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3432,plain,
! [SV1202: $i,SV714: $i,SV153: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV153 @ tc_bool ) ) @ SV714 @ SV153 @ SV1202 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV153 @ SV1202 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3433,plain,
! [SV1203: $i,SV715: $i,SV154: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV154 @ SV715 ) @ ( c_Wellfounded_Oacc @ SV1203 @ SV715 ) @ ( tc_fun @ SV715 @ tc_bool ) )
| ~ ( c_lessequals @ SV1203 @ SV154 @ ( tc_fun @ ( tc_prod @ SV715 @ SV715 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3434,plain,
! [SV1204: $i,SV716: $i,SV155: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SV716 @ ( tc_fun @ SV1204 @ tc_bool ) ) @ ( tc_fun @ SV1204 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV155 @ SV716 @ ( tc_fun @ SV1204 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3435,plain,
! [SV156: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false )
| ( ( ! [SY2549: $i,SY2550: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) @ SV156 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(3436,plain,
! [SV157: $i] :
( ( ( class_Lattices_Olattice @ SV157 )
= $false )
| ( ( ! [SY2551: $i,SY2552: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) @ SV157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2551 @ SY2552 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(3437,plain,
! [SV1205: $i,SV717: $i,SV158: $i] :
( ( ( ( c_Relation_ODomain @ SV158 @ SV717 @ SV1205 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV717 @ tc_bool ) ) )
| ( SV158
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV717 @ SV1205 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3438,plain,
! [SV1206: $i,SV718: $i,SV159: $i] :
( ( ! [SY4775: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV718 @ ( tc_fun @ ( tc_prod @ SV1206 @ SY4775 ) @ tc_bool ) ) @ SV1206 @ SY4775 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV159 @ SV1206 @ SY4775 ) @ ( c_Relation_ORange @ SV718 @ SV1206 @ SY4775 ) @ ( tc_fun @ SY4775 @ tc_bool ) ) @ ( tc_fun @ SY4775 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3439,plain,
! [SV719: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true )
| ( ( ! [SY2559: $i,SY2560: $i] :
( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SY2559 @ SY2560 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2559 @ SY2560 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3440,plain,
! [SV1207: $i,SV720: $i,SV162: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV162 @ SV720 ) @ ( c_Transitive__Closure_Ortrancl @ SV1207 @ SV720 ) @ ( tc_fun @ ( tc_prod @ SV720 @ SV720 ) @ tc_bool ) ) @ SV720 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV162 @ SV1207 @ ( tc_fun @ ( tc_prod @ SV720 @ SV720 ) @ tc_bool ) ) @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3441,plain,
! [SV721: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV721 ) )
= $true )
| ( ( ! [SY3951: $i,SY3952: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3951 @ SV163 @ ( tc_fun @ SY3952 @ tc_bool ) ) @ SV721 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(3442,plain,
! [SV722: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ SV164 @ SV722 ) )
= $true )
| ( ( ! [SY3953: $i,SY3954: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SY3953 @ ( tc_fun @ SY3954 @ tc_bool ) ) @ SV722 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3443,plain,
! [SV1208: $i,SV723: $i,SV165: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1208 @ SV1208 ) @ tc_bool ) ) @ SV1208 )
| ~ ( c_Relation_Osym @ SV723 @ SV1208 )
| ~ ( c_Relation_Osym @ SV165 @ SV1208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3444,plain,
! [SV1209: $i,SV724: $i,SV166: $i] :
( ( ! [SY4776: $i,SY4777: $i,SY4778: $i] :
( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SY4776 @ SY4777 @ SY4778 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SY4776 @ SY4777 @ SY4778 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SY4776 @ SY4777 @ SY4778 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SY4776 @ SY4777 @ SY4778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3445,plain,
! [SV726: $i,SV168: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV168 @ SV726 )
= $true )
| ( ( ! [SY3960: $i,SY3961: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY3960 @ SY3961 @ SV726 @ SV726 ) @ SV168 @ ( tc_prod @ SV726 @ SV726 ) ) @ SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3446,plain,
! [SV1210: $i,SV727: $i,SV169: $i] :
( ( ~ ( class_HOL_Oord @ SV169 )
| ! [SY4779: $i] :
( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SY4779 @ SV1210 ) @ SV169 )
| ! [SY3964: $i] :
~ ( c_lessequals @ SV727 @ SY4779 @ ( tc_fun @ SY3964 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3447,plain,
! [SV1211: $i,SV728: $i,SV170: $i] :
( ( ! [SY4781: $i] :
( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SY4781 @ tc_bool ) ) @ SY4781 )
| ~ ( c_in @ SV170 @ SV1211 @ SY4781 )
| ~ ( c_in @ SV170 @ SV728 @ SY4781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3448,plain,
! [SV1212: $i,SV729: $i,SV171: $i] :
( ( ! [SY4782: $i] :
( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SY4782 @ tc_bool ) ) @ SY4782 )
| ~ ( c_in @ SV171 @ SV1212 @ SY4782 )
| ~ ( c_in @ SV171 @ SV729 @ SY4782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3449,plain,
! [SV1213: $i,SV730: $i,SV172: $i] :
( ( ( c_in @ SV172 @ SV730 @ SV1213 )
| ! [SY4783: $i] :
( ~ ( c_in @ SV172 @ SY4783 @ SV1213 )
| ~ ( c_lessequals @ SY4783 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3450,plain,
! [SV1214: $i,SV731: $i,SV173: $i] :
( ( ( c_in @ SV173 @ SV731 @ SV1214 )
| ! [SY4784: $i] :
( ~ ( c_lessequals @ SY4784 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) )
| ~ ( c_in @ SV173 @ SY4784 @ SV1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3451,plain,
! [SV1215: $i,SV732: $i,SV174: $i] :
( ( ( c_in @ SV174 @ SV732 @ SV1215 )
| ! [SY4785: $i] :
( ~ ( c_in @ SV174 @ SY4785 @ SV1215 )
| ~ ( c_lessequals @ SY4785 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3452,plain,
! [SV1216: $i,SV733: $i,SV175: $i] :
( ( ( c_in @ SV175 @ SV733 @ SV1216 )
| ! [SY4786: $i] :
( ~ ( c_in @ SV175 @ SY4786 @ SV1216 )
| ~ ( c_lessequals @ SY4786 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3453,plain,
! [SV1217: $i,SV734: $i,SV176: $i] :
( ( ! [SY4787: $i] :
( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV734 @ SV1217 @ ( tc_fun @ SY4787 @ tc_bool ) ) @ SY4787 )
| ~ ( c_in @ SV176 @ SV734 @ SY4787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3454,plain,
! [SV1218: $i,SV735: $i,SV177: $i] :
( ( ! [SY4788: $i] :
( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SV1218 @ ( tc_fun @ SY4788 @ tc_bool ) ) @ SY4788 )
| ~ ( c_in @ SV177 @ SV1218 @ SY4788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3455,plain,
! [SV736: $i,SV178: $i] :
( ( c_in @ SV178 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV736 @ tc_bool ) ) @ SV736 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3456,plain,
! [SV737: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ SV179 @ SV737 ) )
= $true )
| ( ( ! [SY3981: $i] :
~ ( c_in @ SV737 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3981 @ tc_bool ) ) @ SY3981 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3457,plain,
! [SV738: $i,SV180: $i] :
( ( c_in @ SV180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV738 @ tc_bool ) ) @ SV738 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(3458,plain,
! [SV739: $i,SV181: $i] :
( ( c_in @ SV181 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV739 @ tc_bool ) ) @ SV739 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(3459,plain,
! [SV1219: $i,SV740: $i,SV182: $i] :
( ( ( c_in @ SV182 @ SV740 @ SV1219 )
| ! [SY4789: $i] :
( ( c_in @ SV182 @ SY4789 @ SV1219 )
| ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4789 @ SV740 @ ( tc_fun @ SV1219 @ tc_bool ) ) @ SV1219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3460,plain,
! [SV1220: $i,SV741: $i,SV183: $i] :
( ( ( c_in @ SV183 @ SV741 @ SV1220 )
| ! [SY4790: $i] :
~ ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4790 @ SV741 @ ( tc_fun @ SV1220 @ tc_bool ) ) @ SV1220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3461,plain,
! [SV1221: $i,SV742: $i,SV184: $i] :
( ( ( c_in @ SV184 @ SV742 @ SV1221 )
| ! [SY4791: $i] :
~ ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV742 @ SY4791 @ ( tc_fun @ SV1221 @ tc_bool ) ) @ SV1221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3462,plain,
! [SV743: $i,SV185: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV185 @ SV743 ) ) )
= $true )
| ( ( ! [SY3988: $i] :
~ ( c_in @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3988 @ tc_bool ) ) @ SY3988 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(3463,plain,
! [SV1222: $i,SV744: $i,SV186: $i] :
( ( ! [SY4792: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SY4792 @ ( tc_fun @ ( tc_prod @ SV186 @ SV744 ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SV1222 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SY4792 ) @ ( tc_fun @ ( tc_prod @ SV744 @ SV186 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3464,plain,
! [SV745: $i,SV187: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV187 @ SV187 ) @ SV745 ) @ SV187 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV745 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3465,plain,
! [SV746: $i,SV188: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV188 @ SV746 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV746 @ SV746 ) @ SV188 ) @ SV746 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3466,plain,
! [SV1223: $i,SV748: $i,SV190: $i] :
( ( ! [SY4793: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1223 @ SY4793 @ ( tc_fun @ ( tc_prod @ SV190 @ SV748 ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SV1223 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SY4793 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV190 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3467,plain,
! [SV1224: $i,SV749: $i,SV191: $i] :
( ( ! [SY4794: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY4794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
| ~ ( c_in @ ( c_Pair @ SV191 @ SY4794 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
| ! [SY4795: $i] :
( ~ ( c_in @ SY4794 @ SY4795 @ SV749 )
| ~ ( c_in @ SV191 @ SY4795 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4795 @ SV1224 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3468,plain,
! [SV1225: $i,SV751: $i,SV194: $i] :
( ( ! [SY4796: $i,SY4797: $i] :
( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
!= ( c_Set_Oinsert @ SY4796 @ ( c_Set_Oinsert @ SY4797 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
| ( SV194 = SY4797 )
| ( SV194 = SY4796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3469,plain,
! [SV1226: $i,SV752: $i,SV195: $i] :
( ( ! [SY4798: $i] :
( ! [SY4799: $i] :
( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
!= ( c_Set_Oinsert @ SY4798 @ ( c_Set_Oinsert @ SY4799 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) )
| ( SV752 = SY4798 )
| ( SV195 = SY4798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3470,plain,
! [SV1227: $i,SV753: $i,SV196: $i] :
( ( ! [SY4800: $i,SY4801: $i] :
( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
!= ( c_Set_Oinsert @ SY4800 @ ( c_Set_Oinsert @ SY4801 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
| ( SV196 = SY4801 )
| ( SV753 = SY4801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3471,plain,
! [SV1228: $i,SV754: $i,SV197: $i] :
( ( ! [SY4802: $i,SY4803: $i] :
( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
!= ( c_Set_Oinsert @ SY4802 @ ( c_Set_Oinsert @ SY4803 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
| ( SV754 = SY4802 )
| ( SV754 = SY4803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3472,plain,
! [SV1229: $i,SV755: $i,SV198: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV198 @ SV755 ) @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV198 @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3473,plain,
! [SV1230: $i,SV756: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV199 @ SV756 ) @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3474,plain,
! [SV757: $i,SV200: $i] :
( ( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) @ ( tc_fun @ SV757 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2906]) ).
thf(3475,plain,
! [SV1231: $i,SV758: $i,SV202: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV758 @ SV1231 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3476,plain,
! [SV1232: $i,SV759: $i,SV204: $i] :
( ( ! [SY4804: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SV759 @ SV1232 ) @ SY4804 @ ( tc_fun @ SV1232 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV759 @ SY4804 @ ( tc_fun @ SV1232 @ tc_bool ) ) @ SV1232 ) )
| ~ ( c_in @ SV204 @ SY4804 @ SV1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3477,plain,
! [SV1233: $i,SV760: $i,SV205: $i] :
( ( ! [SY4805: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SV760 @ SV1233 @ SY4805 ) @ ( tc_fun @ SY4805 @ tc_bool ) )
= ( c_Set_Oinsert @ SV760 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV1233 @ ( tc_fun @ SY4805 @ tc_bool ) ) @ SY4805 ) )
| ~ ( c_in @ SV760 @ SV205 @ SY4805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3478,plain,
! [SV1234: $i,SV762: $i,SV207: $i] :
( ( ! [SY4806: $i,SY4807: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4806 @ SY4807 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV762 @ SY4807 @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SY4806 @ ( tc_fun @ SV1234 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3479,plain,
! [SV208: $i] :
( ( ( class_Lattices_Olattice @ SV208 )
= $false )
| ( ( ! [SY2672: $i,SY2673: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2672 @ SY2673 @ SV208 ) @ SY2672 @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3480,plain,
! [SV209: $i] :
( ( ( class_Lattices_Olattice @ SV209 )
= $false )
| ( ( ! [SY2674: $i,SY2675: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2674 @ SY2675 @ SV209 ) @ SY2675 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(3481,plain,
! [SV763: $i,SV210: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV210 ) )
= $true )
| ( ( ! [SY4018: $i,SY4019: $i] :
( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4018 @ SY4019 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4019 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4018 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3482,plain,
! [SV764: $i,SV211: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV211 ) )
= $true )
| ( ( ! [SY4020: $i,SY4021: $i] :
( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4020 @ SY4021 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4021 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4020 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3483,plain,
! [SV765: $i,SV212: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV212 ) )
= $true )
| ( ( ! [SY4022: $i,SY4023: $i] :
( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4022 @ SY4023 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4023 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4022 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3484,plain,
! [SV213: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV213 )
= $false )
| ( ( ! [SY2685: $i,SY2686: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2685 @ SY2686 @ SV213 ) @ SY2686 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(3485,plain,
! [SV214: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false )
| ( ( ! [SY2687: $i,SY2688: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2687 @ SY2688 @ SV214 ) @ SY2687 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3486,plain,
! [SV1235: $i,SV766: $i,SV215: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 @ SV766 @ ( tc_fun @ SV1235 @ tc_bool ) ) @ SV215 @ ( tc_fun @ SV1235 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3487,plain,
! [SV1236: $i,SV767: $i,SV216: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV216 @ SV767 @ ( tc_fun @ SV1236 @ tc_bool ) ) @ SV767 @ ( tc_fun @ SV1236 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3488,plain,
! [SV1237: $i,SV768: $i,SV217: $i] :
( ( ! [SY4808: $i] :
( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SY4808 @ tc_bool ) ) @ ( tc_fun @ SY4808 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SY4808 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SY4808 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3489,plain,
! [SV1238: $i,SV769: $i,SV218: $i] :
( ( ! [SY4809: $i] :
( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SY4809 @ tc_bool ) ) @ ( tc_fun @ SY4809 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SY4809 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SY4809 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3490,plain,
! [SV1239: $i,SV770: $i,SV219: $i] :
( ( ! [SY4810: $i,SY4811: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV770 @ ( tc_fun @ SV1239 @ tc_bool ) ) @ ( c_COMBK @ SY4810 @ ( tc_fun @ SY4811 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY4811 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV219 @ ( c_COMBK @ SY4810 @ ( tc_fun @ SY4811 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY4811 ) @ ( c_Product__Type_OSigma @ SV770 @ ( c_COMBK @ SY4810 @ ( tc_fun @ SY4811 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY4811 ) @ ( tc_fun @ ( tc_prod @ SV1239 @ SY4811 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3491,plain,
! [SV771: $i,SV220: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV220 ) )
= $true )
| ( ( ! [SY4033: $i,SY4034: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV771 @ SY4033 @ SV220 ) @ SY4034 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV771 @ SY4034 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4033 @ SY4034 @ SV220 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3492,plain,
! [SV772: $i,SV221: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV221 ) )
= $true )
| ( ( ! [SY4035: $i,SY4036: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4035 @ SY4036 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4035 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4036 @ SV221 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3493,plain,
! [SV1240: $i,SV773: $i,SV222: $i] :
( ( ! [SY4812: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV773 @ SV1240 @ ( tc_fun @ SY4812 @ tc_bool ) ) @ ( tc_fun @ SY4812 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV773 @ ( tc_fun @ SY4812 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV1240 @ ( tc_fun @ SY4812 @ tc_bool ) ) @ ( tc_fun @ SY4812 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3494,plain,
! [SV1241: $i,SV774: $i,SV223: $i] :
( ( ! [SY4813: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV223 @ SV774 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ SY4813 @ ( tc_fun @ SV1241 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV223 @ SY4813 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV774 @ SY4813 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ ( tc_fun @ SV1241 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3495,plain,
! [SV1242: $i,SV775: $i,SV224: $i] :
( ( ! [SY4814: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SY4814 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_lessequals @ SV775 @ SY4814 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_in @ SV224 @ SY4814 @ SV1242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3496,plain,
! [SV225: $i] :
( ( ( class_Lattices_Olattice @ SV225 )
= $false )
| ( ( ! [SY2718: $i,SY2719: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) @ SV225 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2718 @ SY2719 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3497,plain,
! [SV226: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false )
| ( ( ! [SY2720: $i,SY2721: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) @ SV226 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2720 @ SY2721 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3498,plain,
! [SV1243: $i,SV776: $i,SV227: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SV776 @ ( tc_fun @ SV1243 @ tc_bool ) ) @ ( tc_fun @ SV1243 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV227 @ SV776 @ ( tc_fun @ SV1243 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3499,plain,
! [SV1244: $i,SV777: $i,SV228: $i] :
( ( ( c_lessequals @ ( c_Relation_OField @ SV228 @ SV777 ) @ ( c_Relation_OField @ SV1244 @ SV777 ) @ ( tc_fun @ SV777 @ tc_bool ) )
| ~ ( c_lessequals @ SV228 @ SV1244 @ ( tc_fun @ ( tc_prod @ SV777 @ SV777 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3500,plain,
! [SV1245: $i,SV778: $i,SV229: $i] :
( ( ! [SY4815: $i,SY4816: $i] :
( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SV1245 @ ( tc_fun @ SY4815 @ tc_bool ) ) @ SY4815 @ SY4816 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SY4815 @ SY4816 ) @ ( c_Relation_OImage @ SV229 @ SV1245 @ SY4815 @ SY4816 ) @ ( tc_fun @ SY4816 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SY4815 @ SY4816 ) @ SV229 ) @ SY4816 @ SY4815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3501,plain,
! [SV1246: $i,SV779: $i,SV230: $i] :
( ( ! [SY4817: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV779 @ ( tc_fun @ ( tc_prod @ SV1246 @ SY4817 ) @ tc_bool ) ) @ SV1246 @ SY4817 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV230 @ SV1246 @ SY4817 ) @ ( c_Relation_ORange @ SV779 @ SV1246 @ SY4817 ) @ ( tc_fun @ SY4817 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3502,plain,
! [SV1247: $i,SV780: $i,SV231: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV231 @ SV780 @ ( tc_fun @ ( tc_prod @ SV1247 @ SV1247 ) @ tc_bool ) ) @ SV1247 )
| ~ ( c_Wellfounded_Owf @ SV231 @ SV1247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3503,plain,
! [SV1248: $i,SV781: $i,SV232: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV232 @ SV781 @ ( tc_fun @ ( tc_prod @ SV1248 @ SV1248 ) @ tc_bool ) ) @ SV1248 )
| ~ ( c_Wellfounded_Owf @ SV781 @ SV1248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3504,plain,
! [SV233: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV233 )
= $false )
| ( ( ! [SY2737: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2737 @ SY2737 @ SV233 )
= SY2737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3505,plain,
! [SV784: $i,SV236: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV236 ) )
= $true )
| ( ( ! [SY4052: $i] :
( ( c_lessequals @ SV784 @ SY4052 @ SV236 )
| ! [SY4053: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4053 @ SV784 @ SV236 ) @ SY4052 @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3506,plain,
! [SV785: $i,SV237: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV237 ) )
= $true )
| ( ( ! [SY4054: $i] :
( ( c_lessequals @ SV785 @ SY4054 @ SV237 )
| ! [SY4055: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SY4055 @ SV237 ) @ SY4054 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3507,plain,
! [SV786: $i,SV238: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV238 ) )
= $true )
| ( ( ! [SY4056: $i,SY4057: $i] :
( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4056 @ SY4057 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SV786 @ SY4057 @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(3508,plain,
! [SV787: $i,SV239: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV239 ) )
= $true )
| ( ( ! [SY4058: $i] :
( ! [SY4059: $i] : ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4058 @ SY4059 @ SV239 ) @ SV239 )
| ~ ( c_lessequals @ SV787 @ SY4058 @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3509,plain,
! [SV788: $i,SV240: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV240 ) )
= $true )
| ( ( ! [SY4060: $i] :
( ( c_lessequals @ SV788 @ SY4060 @ SV240 )
| ! [SY4061: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4061 @ SV788 @ SV240 ) @ SY4060 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(3510,plain,
! [SV789: $i,SV241: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV241 ) )
= $true )
| ( ( ! [SY4062: $i] :
( ( c_lessequals @ SV789 @ SY4062 @ SV241 )
| ! [SY4063: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SY4063 @ SV241 ) @ SY4062 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3511,plain,
! [SV1249: $i,SV790: $i,SV242: $i] :
( ( ( c_lessequals @ SV242 @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) )
| ! [SY4818: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SY4818 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3512,plain,
! [SV1250: $i,SV791: $i,SV243: $i] :
( ( ( c_lessequals @ SV243 @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) )
| ! [SY4819: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4819 @ SV243 @ ( tc_fun @ SV1250 @ tc_bool ) ) @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3513,plain,
! [SV792: $i,SV244: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV244 ) )
= $true )
| ( ( ! [SY4068: $i] :
( ( c_lessequals @ SV792 @ SY4068 @ SV244 )
| ! [SY4069: $i] :
( ~ ( c_lessequals @ SV792 @ SY4069 @ SV244 )
| ~ ( c_lessequals @ SY4069 @ SY4068 @ SV244 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3514,plain,
! [SV793: $i,SV245: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV245 ) )
= $true )
| ( ( ! [SY4070: $i] :
( ( c_lessequals @ SV793 @ SY4070 @ SV245 )
| ! [SY4071: $i] :
( ~ ( c_lessequals @ SY4071 @ SY4070 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SY4071 @ SV245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3515,plain,
! [SV1251: $i,SV796: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ! [SY4820: $i] :
( ~ ( c_lessequals @ SY4820 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY4820 @ ( tc_fun @ SV1251 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3516,plain,
! [SV797: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true )
| ( ( ! [SY4074: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4074 @ SV797 ) )
| ! [SY2777: $i] :
~ ( c_lessequals @ SY4074 @ SV249 @ ( tc_fun @ SY2777 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3517,plain,
! [SV798: $i,SV250: $i] :
( ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
= $true )
| ( ( ! [SY4076: $i] :
( ~ ( c_lessequals @ SV250 @ SY4076 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4076 @ SV798 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3518,plain,
! [SV251: $i] :
( ( ( class_Orderings_Oorder @ SV251 )
= $false )
| ( ( ! [SY2780: $i] : ( c_lessequals @ SY2780 @ SY2780 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3519,plain,
! [SV252: $i] :
( ( ( class_Orderings_Opreorder @ SV252 )
= $false )
| ( ( ! [SY2781: $i] : ( c_lessequals @ SY2781 @ SY2781 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3520,plain,
! [SV799: $i,SV253: $i] :
( ( ( c_Relation_Oantisym @ SV253 @ SV799 )
= $true )
| ( ( ! [SY4077: $i] :
( ~ ( c_Relation_Oantisym @ SY4077 @ SV799 )
| ~ ( c_lessequals @ SV253 @ SY4077 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3521,plain,
! [SV800: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true )
| ( ( ! [SY4078: $i] :
( ! [SY2786: $i] :
~ ( c_lessequals @ SY4078 @ SV254 @ ( tc_fun @ SY2786 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4078 @ SV800 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3522,plain,
! [SV801: $i,SV255: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
= $true )
| ( ( ! [SY4080: $i] :
( ~ ( c_lessequals @ SV255 @ SY4080 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4080 @ SV801 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3523,plain,
! [SV1252: $i,SV802: $i,SV256: $i] :
( ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
| ! [SY4821: $i] :
( ~ ( c_Relation_Osingle__valued @ SY4821 @ SV802 @ SV1252 )
| ~ ( c_lessequals @ SV256 @ SY4821 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3524,plain,
! [SV1253: $i,SV803: $i,SV257: $i] :
( ( ! [SY4822: $i,SY4823: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4822 @ SY4823 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV803 @ SY4823 @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SY4822 @ ( tc_fun @ SV1253 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3525,plain,
! [SV1254: $i,SV806: $i,SV260: $i] :
( ( ! [SY4824: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SV806 @ SV1254 ) @ ( c_Relation_ODomain @ SY4824 @ SV806 @ SV1254 ) @ ( tc_fun @ SV806 @ tc_bool ) )
| ~ ( c_lessequals @ SV260 @ SY4824 @ ( tc_fun @ ( tc_prod @ SV806 @ SV1254 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3526,plain,
! [SV1255: $i,SV807: $i,SV261: $i] :
( ( ( SV261
= ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) )
| ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) @ ( tc_fun @ SV1255 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3527,plain,
! [SV1256: $i,SV808: $i,SV262: $i] :
( ( ( c_Product__Type_OSigma @ SV262 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV808 @ tc_bool ) ) @ ( tc_fun @ SV808 @ tc_bool ) @ SV1256 ) @ SV1256 @ SV808 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1256 @ SV808 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3528,plain,
! [SV1257: $i,SV809: $i,SV263: $i] :
( ( ! [SY4825: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SY4825 ) )
| ~ ( hBOOL @ ( hAPP @ SV809 @ SY4825 ) )
| ~ ( hBOOL @ ( hAPP @ SV263 @ SY4825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3529,plain,
! [SV1258: $i,SV810: $i,SV264: $i] :
( ( ! [SY4826: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SV810 @ SV1258 ) @ ( c_Set_Oinsert @ SV264 @ SY4826 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_lessequals @ SV810 @ SY4826 @ ( tc_fun @ SV1258 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3530,plain,
! [SV1259: $i,SV811: $i,SV267: $i] :
( ( ( ( c_Relation_ORange @ SV267 @ SV811 @ SV1259 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) )
| ( SV267
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV811 @ SV1259 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3531,plain,
! [SV1260: $i,SV812: $i,SV268: $i] :
( ( ! [SY4827: $i,SY4828: $i,SY4829: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SY4827 ) @ ( c_Relation_OImage @ SY4828 @ SY4829 @ SV1260 @ SY4827 ) @ ( tc_fun @ SY4827 @ tc_bool ) )
| ~ ( c_lessequals @ SV812 @ SY4829 @ ( tc_fun @ SV1260 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SY4828 @ ( tc_fun @ ( tc_prod @ SV1260 @ SY4827 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3532,plain,
! [SV1261: $i,SV813: $i,SV269: $i] :
( ( ( c_lessequals @ SV269 @ ( c_Product__Type_OSigma @ SV813 @ ( c_COMBK @ SV813 @ ( tc_fun @ SV1261 @ tc_bool ) @ SV1261 ) @ SV1261 @ SV1261 ) @ ( tc_fun @ ( tc_prod @ SV1261 @ SV1261 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV813 @ SV269 @ SV1261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3533,plain,
! [SV270: $i] :
( ( ( class_Orderings_Olinorder @ SV270 )
= $false )
| ( ( ! [SY2820: $i,SY2821: $i] :
( ( c_lessequals @ SY2820 @ SY2821 @ SV270 )
| ( c_lessequals @ SY2821 @ SY2820 @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3534,plain,
! [SV1262: $i,SV814: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
| ! [SY4830: $i,SY4831: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SY4830 @ SY4831 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SY4830 @ SY4831 ) @ SY4831 @ SY4831 ) @ SY4830 @ ( tc_prod @ SY4831 @ SY4831 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SY4831 @ SY4831 ) @ ( c_Transitive__Closure_Ortrancl @ SY4830 @ SY4831 ) @ ( tc_prod @ SY4831 @ SY4831 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3535,plain,
! [SV1263: $i,SV815: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
| ! [SY4832: $i,SY4833: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SY4832 @ SY4833 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SY4832 @ SY4833 ) @ SY4833 @ SY4833 ) @ SY4832 @ ( tc_prod @ SY4833 @ SY4833 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
| ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SY4833 @ SY4833 ) @ ( c_Transitive__Closure_Ortrancl @ SY4832 @ SY4833 ) @ ( tc_prod @ SY4833 @ SY4833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3536,plain,
! [SV1264: $i,SV816: $i,SV273: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3537,plain,
! [SV1265: $i,SV817: $i,SV274: $i] :
( ( ! [SY4834: $i] :
( ( SV274 = SV817 )
| ! [SY4835: $i,SY4836: $i] :
( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SY4834 @ SY4835 ) @ SY4836 @ ( tc_prod @ SY4834 @ SY4835 ) )
| ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SY4834 @ SY4835 ) @ SY4836 @ ( tc_prod @ SY4834 @ SY4835 ) )
| ~ ( c_Relation_Osingle__valued @ SY4836 @ SY4834 @ SY4835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3538,plain,
! [SV1266: $i,SV818: $i,SV275: $i] :
( ( ! [SY4837: $i,SY4838: $i] :
( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SY4837 ) @ SY4837 @ SV1266 )
!= ( c_Product__Type_OSigma @ SY4838 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SY4837 ) @ SY4837 @ SV1266 ) )
| ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 )
| ( SV275 = SY4838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3539,plain,
! [SV1267: $i,SV819: $i,SV276: $i] :
( ( ! [SY4840: $i] :
( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV819 @ SV1267 @ ( tc_fun @ ( tc_prod @ SY4840 @ SY4840 ) @ tc_bool ) ) @ SY4840 ) @ ( tc_prod @ SY4840 @ SY4840 ) )
| ~ ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SV819 @ SY4840 ) @ ( tc_prod @ SY4840 @ SY4840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3540,plain,
! [SV1268: $i,SV820: $i,SV277: $i] :
( ( ! [SY4841: $i] :
( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1268 @ ( tc_fun @ ( tc_prod @ SY4841 @ SY4841 ) @ tc_bool ) ) @ SY4841 ) @ ( tc_prod @ SY4841 @ SY4841 ) )
| ~ ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SV1268 @ SY4841 ) @ ( tc_prod @ SY4841 @ SY4841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3541,plain,
! [SV1269: $i,SV821: $i,SV278: $i] :
( ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
| ! [SY4842: $i] :
( ~ ( c_lessequals @ SY4842 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) )
| ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SY4842 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3542,plain,
! [SV1270: $i,SV822: $i,SV279: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV279 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( c_Relation_Orel__comp @ SV1270 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV279 @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3543,plain,
! [SV1271: $i,SV823: $i,SV280: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV280 @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV280 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( c_Relation_Orel__comp @ SV823 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3544,plain,
! [SV824: $i,SV281: $i] :
( ( ( ( c_Relation_Orel__comp @ SV281 @ SV281 @ SV824 @ SV824 @ SV824 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV281 @ SV824 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3545,plain,
! [SV828: $i,SV286: $i] :
( ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV828 ) @ SV828 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV286 @ SV828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3546,plain,
! [SV1272: $i,SV831: $i,SV289: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV289 @ SV831 ) @ SV1272 @ SV831 @ SV831 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV289 @ SV1272 @ ( tc_fun @ SV831 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3547,plain,
! [SV832: $i,SV290: $i] :
( ( ( c_Relation_Oantisym @ SV290 @ SV832 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV290 @ ( c_Relation_OId @ SV832 ) @ ( tc_fun @ ( tc_prod @ SV832 @ SV832 ) @ tc_bool ) ) @ SV832 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3548,plain,
! [SV833: $i,SV291: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV291 @ ( c_Relation_OId @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) @ SV833 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV291 @ SV833 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3549,plain,
! [SV1273: $i,SV834: $i,SV292: $i] :
( ( ! [SY4843: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SY4843 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
| ! [SY4844: $i] :
( ~ ( c_in @ SY4843 @ SY4844 @ SV834 )
| ~ ( c_in @ SV292 @ SY4844 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4844 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SY4843 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3550,plain,
! [SV1274: $i,SV835: $i,SV293: $i] :
( ( ( c_in @ SV293 @ SV835 @ SV1274 )
| ! [SY4845: $i] :
( ( SV293 = SY4845 )
| ! [SY4846: $i] :
( ~ ( c_lessequals @ SY4846 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SY4845 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY4846 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3551,plain,
! [SV1275: $i,SV836: $i,SV294: $i] :
( ( ! [SY4847: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SY4847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV836 @ SY4847 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
| ! [SY4848: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4848 @ SV294 @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3552,plain,
! [SV837: $i,SV295: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SV837 ) @ ( c_Transitive__Closure_Ortrancl @ SV837 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY4133: $i] :
~ ( c_in @ ( c_Pair @ SY4133 @ SY4133 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SV837 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3553,plain,
! [SV1276: $i,SV838: $i,SV296: $i] :
( ( ! [SY4849: $i] :
( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
!= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SY4849 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
| ~ ( c_in @ SY4849 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SY4849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3554,plain,
! [SV297: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV297 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV297 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV297 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV297 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3555,plain,
! [SV1277: $i,SV298: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ SV298 ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ SV298 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ SV298 ) @ SV1277 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV298 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3556,plain,
! [SV1278: $i,SV839: $i,SV299: $i] :
( ( ! [SY4850: $i,SY4851: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SV1278 @ SY4850 @ SY4851 ) @ SV299 @ SY4850 )
| ~ ( c_in @ SV1278 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SY4850 @ SY4851 ) @ ( tc_prod @ SY4850 @ SY4851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3557,plain,
! [SV1279: $i,SV840: $i,SV300: $i] :
( ( ! [SY4852: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SV1279 @ SY4852 ) @ SV840 @ SY4852 @ SY4852 ) @ SV1279 @ ( tc_prod @ SY4852 @ SY4852 ) )
| ( SV300 = SV840 )
| ~ ( c_in @ ( c_Pair @ SV300 @ SV840 @ SY4852 @ SY4852 ) @ ( c_Transitive__Closure_Ortrancl @ SV1279 @ SY4852 ) @ ( tc_prod @ SY4852 @ SY4852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3558,plain,
! [SV1280: $i,SV841: $i,SV301: $i] :
( ( ! [SY4853: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SV1280 @ SY4853 ) @ SV1280 @ SY4853 @ SY4853 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY4853 ) @ ( tc_prod @ SY4853 @ SY4853 ) )
| ( SV841 = SV1280 )
| ~ ( c_in @ ( c_Pair @ SV841 @ SV1280 @ SY4853 @ SY4853 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY4853 ) @ ( tc_prod @ SY4853 @ SY4853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3559,plain,
! [SV1281: $i,SV842: $i,SV302: $i] :
( ( ! [SY4854: $i] :
( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SV1281 @ SY4854 ) @ SY4854 @ SY4854 ) @ SV842 @ ( tc_prod @ SY4854 @ SY4854 ) )
| ( SV302 = SV1281 )
| ~ ( c_in @ ( c_Pair @ SV302 @ SV1281 @ SY4854 @ SY4854 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SY4854 ) @ ( tc_prod @ SY4854 @ SY4854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3560,plain,
! [SV1282: $i,SV843: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
| ! [SY4855: $i,SY4856: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SY4855 @ SY4856 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SY4856 @ SY4856 ) @ ( c_Transitive__Closure_Ortrancl @ SY4855 @ SY4856 ) @ ( tc_prod @ SY4856 @ SY4856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3561,plain,
! [SV1283: $i,SV844: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
| ! [SY4857: $i,SY4858: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SY4857 @ SY4858 ) @ SV1283 @ SY4858 @ SY4858 ) @ ( c_Transitive__Closure_Ortrancl @ SY4857 @ SY4858 ) @ ( tc_prod @ SY4858 @ SY4858 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SY4858 @ SY4858 ) @ ( c_Transitive__Closure_Ortrancl @ SY4857 @ SY4858 ) @ ( tc_prod @ SY4858 @ SY4858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3562,plain,
! [SV1284: $i,SV845: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
| ! [SY4859: $i,SY4860: $i] :
( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SY4859 @ SY4860 ) @ SY4860 @ SY4860 ) @ ( c_Transitive__Closure_Ortrancl @ SY4859 @ SY4860 ) @ ( tc_prod @ SY4860 @ SY4860 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
| ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SY4860 @ SY4860 ) @ ( c_Transitive__Closure_Ortrancl @ SY4859 @ SY4860 ) @ ( tc_prod @ SY4860 @ SY4860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3563,plain,
! [SV1285: $i,SV846: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
| ! [SY4861: $i,SY4862: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SY4861 @ SY4862 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SY4862 @ SY4862 ) @ ( c_Transitive__Closure_Ortrancl @ SY4861 @ SY4862 ) @ ( tc_prod @ SY4862 @ SY4862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3564,plain,
! [SV1286: $i,SV847: $i,SV307: $i] :
( ( ! [SY4863: $i] :
( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SY4863 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SY4863 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ! [SY4864: $i] :
( ~ ( c_in @ ( c_Pair @ SY4864 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SY4863 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_in @ ( c_Pair @ SY4864 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SY4863 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SY4863 @ SV1286 @ SV1286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3565,plain,
! [SV1287: $i,SV848: $i,SV308: $i] :
( ( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SV848 @ SV1287 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SV848 = SV308 )
| ~ ( c_in @ ( c_Pair @ SV308 @ SV848 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3566,plain,
! [SV1288: $i,SV849: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
| ! [SY4865: $i,SY4866: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SY4865 @ SY4866 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
| ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SY4866 @ SY4866 ) @ ( c_Transitive__Closure_Ortrancl @ SY4865 @ SY4866 ) @ ( tc_prod @ SY4866 @ SY4866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3567,plain,
! [SV1289: $i,SV850: $i,SV310: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SV850 @ SV1289 ) @ SV850 @ t_a @ t_a ) @ SV1289 @ ( tc_prod @ t_a @ t_a ) )
| ( SV850 = SV310 )
| ~ ( c_in @ ( c_Pair @ SV310 @ SV850 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1289 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3568,plain,
! [SV1290: $i,SV851: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
| ! [SY4867: $i,SY4868: $i] :
( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SY4867 @ SY4868 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SY4868 @ SY4868 ) @ ( c_Transitive__Closure_Ortrancl @ SY4867 @ SY4868 ) @ ( tc_prod @ SY4868 @ SY4868 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3569,plain,
! [SV1291: $i,SV852: $i,SV312: $i] :
( ( ! [SY4869: $i] :
( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SV1291 @ SY4869 ) @ SY4869 @ SY4869 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SY4869 ) @ ( tc_prod @ SY4869 @ SY4869 ) )
| ( SV312 = SV852 )
| ~ ( c_in @ ( c_Pair @ SV312 @ SV852 @ SY4869 @ SY4869 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SY4869 ) @ ( tc_prod @ SY4869 @ SY4869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3570,plain,
! [SV1292: $i,SV853: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
| ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
| ! [SY4870: $i,SY4871: $i] :
( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SY4870 @ SY4871 ) @ SY4871 @ SY4871 ) @ SY4870 @ ( tc_prod @ SY4871 @ SY4871 ) )
| ~ ( c_Wellfounded_Owf @ SY4870 @ SY4871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3571,plain,
! [SV1293: $i,SV854: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
| ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
| ! [SY4872: $i,SY4873: $i] :
( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SY4872 @ SY4873 ) @ SY4873 @ SY4873 ) @ SY4872 @ ( tc_prod @ SY4873 @ SY4873 ) )
| ~ ( c_Wellfounded_Owf @ SY4872 @ SY4873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3572,plain,
! [SV1294: $i,SV855: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
| ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
| ! [SY4874: $i,SY4875: $i] :
( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SY4874 @ SY4875 ) @ SY4875 @ SY4875 ) @ SY4874 @ ( tc_prod @ SY4875 @ SY4875 ) )
| ~ ( c_Wellfounded_Owf @ SY4874 @ SY4875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3573,plain,
! [SV1295: $i,SV856: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
| ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
| ! [SY4876: $i,SY4877: $i] :
( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SY4876 @ SY4877 ) @ SY4877 @ SY4877 ) @ SY4876 @ ( tc_prod @ SY4877 @ SY4877 ) )
| ~ ( c_Wellfounded_Owf @ SY4876 @ SY4877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3574,plain,
! [SV1296: $i,SV857: $i,SV317: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV317 @ SV317 @ SV857 @ SV857 ) @ SV1296 @ ( tc_prod @ SV857 @ SV857 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ SV857 @ SV857 ) @ ( c_Transitive__Closure_Otrancl @ SV1296 @ SV857 ) @ ( tc_prod @ SV857 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3575,plain,
! [SV1297: $i,SV858: $i,SV318: $i] :
( ( ! [SY4878: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SV1297 @ SY4878 ) @ SV1297 @ SY4878 @ SY4878 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY4878 ) @ ( tc_prod @ SY4878 @ SY4878 ) )
| ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SY4878 @ SY4878 ) @ SV318 @ ( tc_prod @ SY4878 @ SY4878 ) )
| ~ ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SY4878 @ SY4878 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SY4878 ) @ ( tc_prod @ SY4878 @ SY4878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3576,plain,
! [SV1298: $i,SV859: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SV859 @ SV1298 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ SV1298 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3577,plain,
! [SV1299: $i,SV860: $i,SV320: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV320 @ SV320 @ SV860 @ SV860 ) @ ( c_Transitive__Closure_Otrancl @ SV1299 @ SV860 ) @ ( tc_prod @ SV860 @ SV860 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1299 @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3578,plain,
! [SV1300: $i,SV861: $i,SV321: $i] :
( ( ! [SY4879: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SV1300 @ SY4879 ) @ SV861 @ SY4879 @ SY4879 ) @ SV1300 @ ( tc_prod @ SY4879 @ SY4879 ) )
| ( c_in @ ( c_Pair @ SV321 @ SV861 @ SY4879 @ SY4879 ) @ SV1300 @ ( tc_prod @ SY4879 @ SY4879 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV861 @ SY4879 @ SY4879 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SY4879 ) @ ( tc_prod @ SY4879 @ SY4879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3579,plain,
! [SV1301: $i,SV862: $i,SV322: $i] :
( ( ! [SY4880: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SV1301 @ SY4880 ) @ SY4880 @ SY4880 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SY4880 ) @ ( tc_prod @ SY4880 @ SY4880 ) )
| ( c_in @ ( c_Pair @ SV322 @ SV862 @ SY4880 @ SY4880 ) @ SV1301 @ ( tc_prod @ SY4880 @ SY4880 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV862 @ SY4880 @ SY4880 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SY4880 ) @ ( tc_prod @ SY4880 @ SY4880 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3580,plain,
! [SV1302: $i,SV863: $i,SV323: $i] :
( ( ! [SY4881: $i] :
( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SV1302 @ SY4881 ) @ SY4881 @ SY4881 ) @ SV863 @ ( tc_prod @ SY4881 @ SY4881 ) )
| ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SY4881 @ SY4881 ) @ SV863 @ ( tc_prod @ SY4881 @ SY4881 ) )
| ~ ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SY4881 @ SY4881 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SY4881 ) @ ( tc_prod @ SY4881 @ SY4881 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3581,plain,
! [SV1303: $i,SV864: $i,SV324: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SV864 @ SV1303 ) @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3582,plain,
! [SV1304: $i,SV865: $i,SV325: $i] :
( ( ! [SY4882: $i] :
( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SY4882 @ ( tc_prod @ SV1304 @ SV1304 ) )
| ! [SY4883: $i] :
( ~ ( c_in @ SV865 @ SY4883 @ SV1304 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY4882 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SY4882 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4883 @ SY4882 @ SV1304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3583,plain,
! [SV1305: $i,SV866: $i,SV326: $i] :
( ( ! [SY4884: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SY4884 @ ( tc_prod @ SV1305 @ SV1305 ) )
| ! [SY4885: $i] :
~ ( c_in @ SY4885 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY4884 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SY4884 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
| ! [SY4886: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4886 @ SY4884 @ SV1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3584,plain,
! [SV1306: $i,SV867: $i,SV327: $i] :
( ( ! [SY4887: $i,SY4888: $i,SY4889: $i,SY4890: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SY4887 @ SY4888 @ SY4889 @ SY4890 ) @ SV867 @ SY4890 @ SY4889 ) @ SY4887 @ ( tc_prod @ SY4890 @ SY4889 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SY4888 @ SY4889 ) @ ( c_Relation_Orel__comp @ SV1306 @ SY4887 @ SY4888 @ SY4890 @ SY4889 ) @ ( tc_prod @ SY4888 @ SY4889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3585,plain,
! [SV1307: $i,SV868: $i,SV328: $i] :
( ( ! [SY4891: $i,SY4892: $i,SY4893: $i,SY4894: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SY4891 @ SY4892 @ SY4893 @ SY4894 ) @ SY4892 @ SY4894 ) @ SV1307 @ ( tc_prod @ SY4892 @ SY4894 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SY4892 @ SY4893 ) @ ( c_Relation_Orel__comp @ SV1307 @ SY4891 @ SY4892 @ SY4894 @ SY4893 ) @ ( tc_prod @ SY4892 @ SY4893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3586,plain,
! [SV1308: $i,SV869: $i,SV329: $i] :
( ( ! [SY4895: $i,SY4896: $i] :
( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SV869 @ SV1308 @ SY4895 @ SY4896 ) @ ( tc_fun @ SY4895 @ SY4896 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV869 @ SV1308 @ SV329 @ SY4895 @ SY4896 ) @ SV869 @ SY4895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3587,plain,
! [SV1309: $i,SV870: $i,SV330: $i] :
( ( ! [SY4897: $i,SY4898: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV870 @ SV1309 @ SY4897 @ SY4898 ) @ ( tc_fun @ SY4897 @ SY4898 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV870 @ SV1309 @ SV330 @ SY4897 @ SY4898 ) @ SV870 @ SY4897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3588,plain,
! [SV1310: $i,SV871: $i,SV331: $i] :
( ( ! [SY4899: $i,SY4900: $i] :
( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SV1310 @ SY4899 @ SY4900 ) @ ( tc_fun @ SY4899 @ SY4900 ) )
| ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SY4899 @ SY4900 ) ) @ ( hAPP @ SV1310 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SY4899 @ SY4900 ) ) @ SY4900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3589,plain,
! [SV1311: $i,SV872: $i,SV332: $i] :
( ( ! [SY4901: $i] :
( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SY4901 )
| ! [SY4902: $i,SY4903: $i] :
( ~ ( c_in @ SV872 @ SY4902 @ SY4903 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY4902 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SY4901 @ tc_bool ) @ SY4903 ) @ SY4903 @ SY4901 ) @ ( tc_fun @ SY4903 @ SY4901 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3590,plain,
! [SV1312: $i,SV873: $i,SV333: $i] :
( ( ! [SY4904: $i,SY4905: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SV1312 @ SY4904 @ SY4905 ) @ ( tc_fun @ SY4904 @ SY4905 ) )
| ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SY4904 @ SY4905 ) ) @ ( hAPP @ SV1312 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SY4904 @ SY4905 ) ) @ SY4905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3591,plain,
! [SV874: $i,SV334: $i] :
( ( ( SV334
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ SV874 @ SV874 ) )
= $true )
| ( ( ~ ( c_in @ SV334 @ ( c_Relation_OId @ SV874 ) @ ( tc_prod @ SV874 @ SV874 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3592,plain,
! [SV875: $i,SV335: $i] :
( ( ( c_Wellfounded_Owf @ SV335 @ SV875 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV335 @ SV875 ) @ ( c_Wellfounded_Oacc @ SV335 @ SV875 ) @ SV875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3593,plain,
! [SV876: $i,SV336: $i] :
( ( ( c_Wellfounded_Owf @ SV336 @ SV876 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV336 @ SV876 ) @ ( c_Wellfounded_Oacc @ SV336 @ SV876 ) @ SV876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3594,plain,
! [SV1313: $i,SV877: $i,SV337: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV337 @ SV877 @ SV1313 ) @ SV337 @ SV1313 )
| ~ ( c_in @ SV877 @ ( c_Relation_OId__on @ SV337 @ SV1313 ) @ ( tc_prod @ SV1313 @ SV1313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3595,plain,
! [SV1314: $i,SV878: $i,SV338: $i] :
( ( ( SV338
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ SV1314 @ SV1314 ) )
| ~ ( c_in @ SV338 @ ( c_Relation_OId__on @ SV878 @ SV1314 ) @ ( tc_prod @ SV1314 @ SV1314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3596,plain,
! [SV1315: $i,SV879: $i,SV339: $i] :
( ( ! [SY4906: $i,SY4907: $i,SY4908: $i] :
( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SV1315 @ SY4906 @ SY4907 )
= ( c_Recdef_Ocut @ SY4908 @ SV879 @ SV1315 @ SY4906 @ SY4907 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SY4908 @ SV879 @ SV1315 @ SY4906 @ SY4907 ) @ SV1315 @ SY4906 @ SY4906 ) @ SV879 @ ( tc_prod @ SY4906 @ SY4906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3597,plain,
! [SV1316: $i,SV343: $i] :
( ( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV343 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3598,plain,
! [SV1317: $i,SV344: $i] :
( ( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV344 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3599,plain,
! [SV345: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3046]) ).
thf(3600,plain,
! [SV346: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV346 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV346 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV346 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV346 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3601,plain,
! [SV884: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV884 @ SV884 ) @ SV348 ) @ SV348 @ SV884 @ SV884 @ SV884 ) @ ( tc_fun @ ( tc_prod @ SV884 @ SV884 ) @ tc_bool ) )
= $true )
| ( ( ! [SY4233: $i] :
~ ( c_Relation_Orefl__on @ SY4233 @ SV348 @ SV884 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3602,plain,
! [SV1318: $i,SV885: $i,SV349: $i] :
( ( ! [SY4909: $i] :
( ~ ( c_in @ ( c_Pair @ SV349 @ SV885 @ SV1318 @ SV1318 ) @ ( c_Transitive__Closure_Ortrancl @ SY4909 @ SV1318 ) @ ( tc_prod @ SV1318 @ SV1318 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SV1318 @ SV1318 ) @ SY4909 @ ( tc_prod @ SV1318 @ SV1318 ) ) @ SV1318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3603,plain,
! [SV1319: $i,SV886: $i,SV350: $i] :
( ( ! [SY4910: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SV1319 @ SV1319 ) @ SY4910 @ ( tc_prod @ SV1319 @ SV1319 ) ) @ SV1319 )
| ( c_in @ ( c_Pair @ SV886 @ SV350 @ SV1319 @ SV1319 ) @ ( c_Transitive__Closure_Ortrancl @ SY4910 @ SV1319 ) @ ( tc_prod @ SV1319 @ SV1319 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4910 @ SV1319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3604,plain,
! [SV1320: $i,SV887: $i,SV351: $i] :
( ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
| ! [SY4911: $i] :
( ~ ( c_in @ SV351 @ SY4911 @ SV1320 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4911 @ SV887 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3605,plain,
! [SV1321: $i,SV888: $i,SV352: $i] :
( ( ! [SY4912: $i,SY4913: $i] :
( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SV1321 @ SY4912 ) @ SY4913 @ ( tc_prod @ SV1321 @ SY4912 ) )
| ~ ( c_in @ SV888 @ ( c_Relation_OImage @ SY4913 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 @ SY4912 ) @ SY4912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3606,plain,
! [SV1322: $i,SV889: $i,SV353: $i] :
( ( ! [SY4914: $i,SY4915: $i] :
( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SV1322 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4914 @ tc_bool ) ) @ SY4914 ) @ SY4914 @ SY4915 ) @ SY4915 )
| ~ ( c_in @ ( c_Pair @ SV1322 @ SV353 @ SY4914 @ SY4915 ) @ SV889 @ ( tc_prod @ SY4914 @ SY4915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3607,plain,
! [SV1323: $i,SV890: $i,SV354: $i] :
( ( ! [SY4916: $i] :
( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SY4916 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
| ~ ( c_in @ ( c_Pair @ SV890 @ SY4916 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
| ! [SY4917: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4917 @ SV354 @ SV1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3608,plain,
! [SV1324: $i,SV891: $i,SV355: $i] :
( ( ! [SY4918: $i] :
( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SY4918 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
| ~ ( c_in @ ( c_Pair @ SV891 @ SY4918 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
| ! [SY4919: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4919 @ SV355 @ SV1324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3609,plain,
! [SV1325: $i,SV892: $i,SV356: $i] :
( ( ! [SY4920: $i] :
( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
!= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SY4920 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
| ( c_in @ ( c_Pair @ SV892 @ SY4920 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
| ! [SY4921: $i] :
( ~ ( c_in @ SY4920 @ SY4921 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4921 @ SV356 @ SV1325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3610,plain,
! [SV1326: $i,SV893: $i,SV357: $i] :
( ( ! [SY4922: $i] :
( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
!= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SY4922 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
| ! [SY4923: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY4923 @ SV357 @ SV1326 )
| ( c_in @ ( c_Pair @ SV893 @ SY4922 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SY4922 @ SY4923 @ SV1326 )
| ~ ( c_in @ SV893 @ SY4923 @ SV1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3611,plain,
! [SV1327: $i,SV894: $i,SV358: $i] :
( ( ! [SY4924: $i] :
( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SY4924 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
| ~ ( c_in @ ( c_Pair @ SV894 @ SY4924 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
| ! [SY4925: $i] :
( ~ ( c_in @ SY4924 @ SY4925 @ SV1327 )
| ~ ( c_in @ SV894 @ SY4925 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4925 @ SV358 @ SV1327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3612,plain,
! [SV1328: $i,SV895: $i,SV359: $i] :
( ( ! [SY4926: $i] :
( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
!= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SY4926 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
| ! [SY4927: $i] :
( ~ ( c_in @ SY4926 @ SY4927 @ SV1328 )
| ~ ( c_in @ SV895 @ SY4927 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4927 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SY4926 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3613,plain,
! [SV1329: $i,SV896: $i,SV360: $i] :
( ( ! [SY4928: $i] :
( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV896 @ SV360 @ SV1329 @ SY4928 ) @ SY4928 @ SY4928 ) @ SV896 @ ( tc_prod @ SY4928 @ SY4928 ) )
| ~ ( c_in @ ( c_Pair @ SV360 @ SV1329 @ SY4928 @ SY4928 ) @ ( c_Transitive__Closure_Otrancl @ SV896 @ SY4928 ) @ ( tc_prod @ SY4928 @ SY4928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3614,plain,
! [SV1330: $i,SV897: $i,SV361: $i] :
( ( ! [SY4929: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SV897 @ SV1330 @ SY4929 ) @ SV1330 @ SY4929 @ SY4929 ) @ SV361 @ ( tc_prod @ SY4929 @ SY4929 ) )
| ~ ( c_in @ ( c_Pair @ SV897 @ SV1330 @ SY4929 @ SY4929 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SY4929 ) @ ( tc_prod @ SY4929 @ SY4929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3615,plain,
! [SV898: $i,SV362: $i] :
( ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
= $true )
| ( ( ! [SY4268: $i,SY4269: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SY4268 @ SY4269 ) @ ( c_Wellfounded_Oacc @ SY4268 @ SY4269 ) @ SY4269 )
| ~ ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SY4268 @ SY4269 ) @ SY4269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3616,plain,
! [SV1331: $i,SV899: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV899 @ SV363 @ SV1331 ) @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3617,plain,
! [SV900: $i,SV364: $i] :
( ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
= $true )
| ( ( ! [SY4271: $i] :
( ~ ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SY4271 ) ) )
| ~ ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SY4271 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3618,plain,
! [SV901: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true )
| ( ( ! [SY4272: $i,SY4273: $i] :
( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SY4272 @ SY4273 ) ) )
| ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SY4272 @ SY4273 ) @ SY4273 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3619,plain,
! [SV1332: $i,SV902: $i,SV366: $i] :
( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV366 @ SV902 @ SV1332 ) @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 )
| ( c_in @ SV902 @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3620,plain,
! [SV903: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
= $true )
| ( ( ! [SY4275: $i,SY4276: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SY4275 @ SY4276 ) @ ( c_Wellfounded_Oacc @ SY4275 @ SY4276 ) @ SY4276 )
| ~ ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SY4275 @ SY4276 ) @ SY4276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3621,plain,
! [SV904: $i,SV368: $i] :
( ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
= $true )
| ( ( ! [SY4277: $i] :
( ~ ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SY4277 ) ) )
| ~ ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SY4277 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3622,plain,
! [SV905: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true )
| ( ( ! [SY4278: $i,SY4279: $i] :
( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SY4278 @ SY4279 ) ) )
| ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SY4278 @ SY4279 ) @ SY4279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3623,plain,
! [SV1333: $i,SV906: $i,SV370: $i] :
( ( ! [SY4930: $i,SY4931: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SV1333 @ SY4930 @ SY4931 ) @ SV370 @ SY4930 )
| ~ ( c_in @ SV906 @ ( c_Relation_OImage @ SV1333 @ SV370 @ SY4930 @ SY4931 ) @ SY4931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3624,plain,
! [SV1334: $i,SV907: $i,SV371: $i] :
( ( ! [SY4932: $i,SY4933: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SV1334 @ SY4932 @ SY4933 ) @ SV371 @ SY4932 )
| ~ ( c_in @ SV907 @ ( c_Relation_OImage @ SV1334 @ SV371 @ SY4932 @ SY4933 ) @ SY4933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3625,plain,
! [SV908: $i,SV372: $i] :
( ( ( c_Wellfounded_Owf @ SV372 @ SV908 )
= $true )
| ( ( ! [SY4286: $i,SY4287: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY4286 @ SY4287 @ SV908 @ SV908 ) @ SV372 @ ( tc_prod @ SV908 @ SV908 ) ) @ SV908 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3626,plain,
! [SV1335: $i,SV909: $i,SV373: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
| ! [SY4934: $i] :
~ ( c_in @ SY4934 @ SV373 @ SV1335 )
| ~ ( c_Wellfounded_Owf @ SV909 @ SV1335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3627,plain,
! [SV1336: $i,SV910: $i,SV374: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
| ! [SY4935: $i] :
~ ( c_in @ SY4935 @ SV374 @ SV1336 )
| ~ ( c_Wellfounded_Owf @ SV910 @ SV1336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3628,plain,
! [SV1337: $i,SV911: $i,SV375: $i] :
( ( ! [SY4936: $i,SY4937: $i,SY4938: $i,SY4939: $i,SY4940: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SY4936 ) @ SY4937 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SY4937 @ SY4938 @ SY4938 ) @ SY4939 @ ( tc_prod @ SY4938 @ SY4938 ) )
| ! [SY4298: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SY4936 @ SY4940 @ SY4940 ) @ SY4298 @ ( tc_prod @ SY4940 @ SY4940 ) )
| ! [SY3122: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY4298 @ SY4939 @ SV375 @ SY4940 @ SY4938 @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3629,plain,
! [SV912: $i,SV376: $i] :
( ( ( ( hAPP @ SV376 @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) @ SV912 ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_Odictator @ SV376 @ SV912 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3630,plain,
! [SV1338: $i,SV913: $i,SV377: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV377 @ SV913 @ SV1338 ) @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3631,plain,
! [SV1339: $i,SV914: $i,SV378: $i] :
( ( ! [SY4943: $i,SY4944: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV378 @ SV914 @ SV1339 @ SY4943 ) @ SY4944 @ ( tc_prod @ SV1339 @ SY4943 ) ) @ SV1339 @ SY4943 )
= ( c_Set_Oinsert @ SV378 @ ( c_Relation_ODomain @ SY4944 @ SV1339 @ SY4943 ) @ SV1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3632,plain,
! [SV915: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
= $true )
| ( ( ! [SY4304: $i] :
( ( SY4304 = SV915 )
| ! [SY4305: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY4304 @ SV379 @ SY4305 ) @ SV915 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3633,plain,
! [SV1340: $i,SV916: $i,SV380: $i] :
( ( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV380 @ SV916 @ SV1340 ) @ SV1340 )
= ( c_Set_Oinsert @ SV380 @ SV916 @ SV1340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3634,plain,
! [SV1341: $i,SV917: $i,SV381: $i] :
( ( ! [SY4945: $i] :
( ( c_Set_Oinsert @ SV381 @ ( c_Set_Oinsert @ SV917 @ SV1341 @ SY4945 ) @ SY4945 )
= ( c_Set_Oinsert @ SV917 @ ( c_Set_Oinsert @ SV381 @ SV1341 @ SY4945 ) @ SY4945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3635,plain,
! [SV1342: $i,SV918: $i,SV382: $i] :
( ( ! [SY4946: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SV918 @ SV1342 ) @ SY4946 ) )
| ~ ( hBOOL @ ( hAPP @ SV918 @ SY4946 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3636,plain,
! [SV1343: $i,SV919: $i,SV383: $i] :
( ( ! [SY4947: $i,SY4948: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV383 @ SV919 @ SV1343 @ SY4947 ) @ SY4948 @ ( tc_prod @ SV1343 @ SY4947 ) ) @ SV1343 @ SY4947 )
= ( c_Set_Oinsert @ SV919 @ ( c_Relation_ORange @ SY4948 @ SV1343 @ SY4947 ) @ SY4947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3637,plain,
! [SV1344: $i,SV920: $i,SV384: $i] :
( ( ! [SY4949: $i] :
( ( c_in @ SV384 @ ( c_Set_Oinsert @ SV920 @ SV1344 @ SY4949 ) @ SY4949 )
| ~ ( c_in @ SV384 @ SV1344 @ SY4949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3638,plain,
! [SV1345: $i,SV921: $i,SV385: $i] :
( ( ! [SY4950: $i] :
( ( c_in @ SV385 @ ( c_Set_Oinsert @ SV921 @ SV1345 @ SY4950 ) @ SY4950 )
| ~ ( c_in @ SV385 @ SV1345 @ SY4950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3639,plain,
! [SV1346: $i,SV922: $i,SV386: $i] :
( ( ( c_in @ SV386 @ SV922 @ SV1346 )
| ! [SY4951: $i] :
( ( SV386 = SY4951 )
| ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SY4951 @ SV922 @ SV1346 ) @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3640,plain,
! [SV1347: $i,SV923: $i,SV387: $i] :
( ( c_in @ SV387 @ ( c_Set_Oinsert @ SV387 @ SV923 @ SV1347 ) @ SV1347 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3641,plain,
! [SV1348: $i,SV924: $i,SV388: $i] :
( ( c_in @ SV388 @ ( c_Set_Oinsert @ SV388 @ SV924 @ SV1348 ) @ SV1348 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3642,plain,
! [SV1349: $i,SV925: $i,SV389: $i] :
( ( c_in @ SV389 @ ( c_Set_Oinsert @ SV389 @ SV925 @ SV1349 ) @ SV1349 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3643,plain,
! [SV1350: $i,SV926: $i,SV390: $i] :
( ( ! [SY4952: $i] :
( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
!= ( c_Set_Oinsert @ SV390 @ SY4952 @ SV1350 ) )
| ( c_in @ SV390 @ SY4952 @ SV1350 )
| ( SV926 = SY4952 )
| ( c_in @ SV390 @ SV926 @ SV1350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3644,plain,
! [SV1351: $i,SV927: $i,SV391: $i] :
( ( ( ( c_Set_Oinsert @ SV391 @ SV927 @ SV1351 )
= SV927 )
| ~ ( c_in @ SV391 @ SV927 @ SV1351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3645,plain,
! [SV1352: $i,SV928: $i,SV392: $i] :
( ( ! [SY4953: $i,SY4954: $i,SY4955: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SY4953 @ SY4954 )
| ! [SY4956: $i] :
( ~ ( c_in @ SV1352 @ SY4955 @ SY4956 )
| ! [SY4331: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY4331 @ SV392 @ SV928 @ SY4956 @ SY4953 @ SY4954 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4955 @ SY4331 @ SY4956 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3646,plain,
! [SV929: $i,SV395: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ SV395 @ SV929 )
= $true )
| ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV395 @ SV929 ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3096]) ).
thf(3647,plain,
! [SV930: $i,SV396: $i] :
( ( ( c_Nitpick_Orefl_H @ SV396 @ SV930 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ SV930 @ SV930 ) @ SV396 @ ( tc_prod @ SV930 @ SV930 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3648,plain,
! [SV1353: $i,SV931: $i,SV398: $i] :
( ( ~ ( c_in @ SV398 @ SV931 @ SV1353 )
| ! [SY4958: $i] :
( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SY4958 @ SV1353 ) @ SV1353 @ SV1353 ) @ SY4958 @ ( tc_prod @ SV1353 @ SV1353 ) )
| ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SY4958 @ SV1353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3649,plain,
! [SV1354: $i,SV932: $i,SV399: $i] :
( ( ~ ( c_in @ SV399 @ SV932 @ SV1354 )
| ! [SY4960: $i] :
( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SY4960 @ SV1354 ) @ SV1354 @ SV1354 ) @ SY4960 @ ( tc_prod @ SV1354 @ SV1354 ) )
| ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SY4960 @ SV1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3650,plain,
! [SV1355: $i,SV933: $i,SV400: $i] :
( ( ! [SY4962: $i,SY4963: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SV1355 @ SY4962 @ SY4963 ) @ SV933 @ SY4962 @ SY4963 ) @ SV1355 @ ( tc_prod @ SY4962 @ SY4963 ) )
| ~ ( c_in @ SV933 @ ( c_Relation_OImage @ SV1355 @ SV400 @ SY4962 @ SY4963 ) @ SY4963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3651,plain,
! [SV1356: $i,SV934: $i,SV401: $i] :
( ( ! [SY4964: $i,SY4965: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SV1356 @ SY4964 @ SY4965 ) @ SV934 @ SY4964 @ SY4965 ) @ SV1356 @ ( tc_prod @ SY4964 @ SY4965 ) )
| ~ ( c_in @ SV934 @ ( c_Relation_OImage @ SV1356 @ SV401 @ SY4964 @ SY4965 ) @ SY4965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3652,plain,
! [SV1357: $i,SV935: $i,SV402: $i] :
( ( ! [SY4966: $i] :
( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SV935 @ SV1357 @ SY4966 ) @ SV1357 @ SY4966 ) @ SV935 @ ( tc_prod @ SV1357 @ SY4966 ) )
| ~ ( c_in @ SV402 @ ( c_Relation_ODomain @ SV935 @ SV1357 @ SY4966 ) @ SV1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3653,plain,
! [SV1358: $i,SV936: $i,SV403: $i] :
( ( ! [SY4967: $i] :
( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SV936 @ SV1358 @ SY4967 ) @ SV1358 @ SY4967 ) @ SV936 @ ( tc_prod @ SV1358 @ SY4967 ) )
| ~ ( c_in @ SV403 @ ( c_Relation_ODomain @ SV936 @ SV1358 @ SY4967 ) @ SV1358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3654,plain,
! [SV937: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true )
| ( ( ! [SY4348: $i,SY4349: $i] :
( ( c_in @ SY4348 @ ( c_Wellfounded_Oacc @ SY4349 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4348 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SY4349 ) @ t_a @ t_a ) @ SY4349 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SY4349 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3655,plain,
! [SV938: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true )
| ( ( ! [SY4350: $i,SY4351: $i] :
( ( c_in @ SY4350 @ ( c_Wellfounded_Oacc @ SY4351 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4350 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SY4351 ) @ t_a @ t_a ) @ SY4351 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SY4351 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3656,plain,
! [SV1359: $i,SV939: $i,SV406: $i] :
( ( ( c_in @ SV406 @ ( c_Wellfounded_Oacc @ SV939 @ SV1359 ) @ SV1359 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV939 @ SV406 @ SV1359 ) @ SV406 @ SV1359 @ SV1359 ) @ SV939 @ ( tc_prod @ SV1359 @ SV1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3657,plain,
! [SV1360: $i,SV940: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
| ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
| ! [SY4968: $i,SY4969: $i] :
( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SY4968 @ SY4969 ) @ SY4969 @ SY4969 ) @ SY4968 @ ( tc_prod @ SY4969 @ SY4969 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SY4968 @ SY4969 ) @ SY4969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3658,plain,
! [SV941: $i,SV408: $i] :
( ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true )
| ( ( ! [SY4356: $i] :
( ( hBOOL @ ( hAPP @ SV408 @ SY4356 ) )
| ! [SY4357: $i] :
( ~ ( c_in @ ( c_Pair @ SY4356 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SY4357 ) @ t_a @ t_a ) @ SY4357 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SY4357 @ t_a ) @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3659,plain,
! [SV942: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true )
| ( ( ! [SY4358: $i] :
( ( hBOOL @ ( hAPP @ SV409 @ SY4358 ) )
| ! [SY4359: $i] :
( ~ ( c_in @ ( c_Pair @ SY4358 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SY4359 ) @ t_a @ t_a ) @ SY4359 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SY4359 @ t_a ) @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3660,plain,
! [SV1361: $i,SV943: $i,SV410: $i] :
( ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
| ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
| ! [SY4970: $i,SY4971: $i] :
( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SY4970 @ SY4971 ) @ SY4971 @ SY4971 ) @ SY4970 @ ( tc_prod @ SY4971 @ SY4971 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SY4970 @ SY4971 ) @ SY4971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3661,plain,
! [SV1362: $i,SV944: $i,SV411: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV411 @ SV944 @ SV1362 ) @ SV944 @ SV1362 @ SV1362 ) @ SV411 @ ( tc_prod @ SV1362 @ SV1362 ) )
| ( c_in @ SV944 @ ( c_Wellfounded_Oacc @ SV411 @ SV1362 ) @ SV1362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3662,plain,
! [SV1363: $i,SV945: $i,SV412: $i] :
( ( ! [SY4972: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SV1363 @ SV1363 ) @ SY4972 @ ( tc_prod @ SV1363 @ SV1363 ) ) @ SV1363 )
| ( c_in @ ( c_Pair @ SV945 @ SV412 @ SV1363 @ SV1363 ) @ ( c_Transitive__Closure_Ortrancl @ SY4972 @ SV1363 ) @ ( tc_prod @ SV1363 @ SV1363 ) )
| ~ ( c_Wellfounded_Owf @ SY4972 @ SV1363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3663,plain,
! [SV1364: $i,SV946: $i,SV413: $i] :
( ( ! [SY4973: $i] :
( ~ ( c_in @ ( c_Pair @ SV413 @ SV946 @ SV1364 @ SV1364 ) @ ( c_Transitive__Closure_Ortrancl @ SY4973 @ SV1364 ) @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SV1364 @ SV1364 ) @ SY4973 @ ( tc_prod @ SV1364 @ SV1364 ) ) @ SV1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3664,plain,
! [SV1365: $i,SV947: $i,SV414: $i] :
( ( ! [SY4974: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SV947 @ SV1365 @ SY4974 ) @ SV414 @ SY4974 @ SV1365 ) @ SV947 @ ( tc_prod @ SY4974 @ SV1365 ) )
| ~ ( c_in @ SV414 @ ( c_Relation_ORange @ SV947 @ SY4974 @ SV1365 ) @ SV1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3665,plain,
! [SV1366: $i,SV948: $i,SV415: $i] :
( ( ! [SY4975: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SV948 @ SV1366 @ SY4975 ) @ SV415 @ SY4975 @ SV1366 ) @ SV948 @ ( tc_prod @ SY4975 @ SV1366 ) )
| ~ ( c_in @ SV415 @ ( c_Relation_ORange @ SV948 @ SY4975 @ SV1366 ) @ SV1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3666,plain,
! [SV1367: $i,SV949: $i,SV416: $i] :
( ( ! [SY4976: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SV949 @ SV1367 @ SY4976 ) @ SV1367 @ SY4976 @ SY4976 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SY4976 ) @ ( tc_prod @ SY4976 @ SY4976 ) )
| ~ ( c_in @ ( c_Pair @ SV949 @ SV1367 @ SY4976 @ SY4976 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SY4976 ) @ ( tc_prod @ SY4976 @ SY4976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3667,plain,
! [SV1368: $i,SV950: $i,SV417: $i] :
( ( ! [SY4977: $i] :
( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV950 @ SV417 @ SV1368 @ SY4977 ) @ SY4977 @ SY4977 ) @ ( c_Transitive__Closure_Ortrancl @ SV950 @ SY4977 ) @ ( tc_prod @ SY4977 @ SY4977 ) )
| ~ ( c_in @ ( c_Pair @ SV417 @ SV1368 @ SY4977 @ SY4977 ) @ ( c_Transitive__Closure_Otrancl @ SV950 @ SY4977 ) @ ( tc_prod @ SY4977 @ SY4977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3668,plain,
! [SV1369: $i,SV951: $i,SV418: $i] :
( ( ! [SY4978: $i] :
( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SY4978 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
| ! [SY4979: $i] :
( ~ ( c_in @ ( c_Pair @ SY4979 @ SV951 @ SV1369 @ SV1369 ) @ SY4978 @ ( tc_prod @ SV1369 @ SV1369 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SY4979 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SY4978 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3669,plain,
! [SV1370: $i,SV952: $i,SV419: $i] :
( ( ! [SY4980: $i] :
( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SY4980 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ! [SY4981: $i] :
( ~ ( c_in @ ( c_Pair @ SY4981 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SY4980 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SY4981 @ SV1370 @ SV1370 ) @ SY4980 @ ( tc_prod @ SV1370 @ SV1370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3670,plain,
! [SV1371: $i,SV953: $i,SV420: $i] :
( ( ! [SY4982: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SY4982 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
| ! [SY4983: $i] :
( ~ ( c_in @ ( c_Pair @ SY4983 @ SV953 @ SV1371 @ SV1371 ) @ SY4982 @ ( tc_prod @ SV1371 @ SV1371 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SY4983 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SY4982 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3671,plain,
! [SV1372: $i,SV954: $i,SV421: $i] :
( ( ! [SY4984: $i,SY4985: $i,SY4986: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SY4984 @ SY4985 ) @ SY4986 )
= ( hAPP @ SV421 @ SY4986 ) )
| ~ ( c_in @ ( c_Pair @ SY4986 @ SV1372 @ SY4984 @ SY4984 ) @ SV954 @ ( tc_prod @ SY4984 @ SY4984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3672,plain,
! [SV1373: $i,SV955: $i,SV422: $i] :
( ( ! [SY4987: $i,SY4988: $i,SY4989: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SY4987 @ SY4988 ) @ SY4989 )
= ( hAPP @ SV422 @ SY4989 ) )
| ~ ( c_in @ ( c_Pair @ SY4989 @ SV1373 @ SY4987 @ SY4987 ) @ SV955 @ ( tc_prod @ SY4987 @ SY4987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3673,plain,
! [SV956: $i,SV423: $i] :
( ( ( SV423 = SV956 )
= $true )
| ( ( ! [SY4393: $i,SY4394: $i] :
( ~ ( c_in @ ( c_Pair @ SV423 @ SV956 @ SY4393 @ SY4393 ) @ ( c_Transitive__Closure_Ortrancl @ SY4394 @ SY4393 ) @ ( tc_prod @ SY4393 @ SY4393 ) )
| ( c_in @ SV423 @ ( c_Relation_ODomain @ SY4394 @ SY4393 @ SY4393 ) @ SY4393 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3674,plain,
! [SV1374: $i,SV957: $i,SV424: $i] :
( ( ( c_in @ SV424 @ ( c_Relation_ODomain @ SV957 @ SV1374 @ SV1374 ) @ SV1374 )
| ( c_in @ ( c_Pair @ SV424 @ SV424 @ SV1374 @ SV1374 ) @ ( c_Transitive__Closure_Ortrancl @ SV957 @ SV1374 ) @ ( tc_prod @ SV1374 @ SV1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3675,plain,
! [SV1375: $i,SV958: $i,SV425: $i] :
( ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
| ! [SY4990: $i] :
( ~ ( c_in @ ( c_Pair @ SV425 @ SY4990 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) )
| ~ ( c_in @ SY4990 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3676,plain,
! [SV1376: $i,SV959: $i,SV426: $i] :
( ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
| ! [SY4991: $i] :
( ~ ( c_in @ SY4991 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4991 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3677,plain,
! [SV960: $i,SV427: $i] :
( ( ( c_Relation_Osym @ SV427 @ SV960 )
= $true )
| ( ( ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV960 @ SV960 ) @ SV427 ) @ SV960 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3678,plain,
! [SV961: $i,SV428: $i] :
( ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV428 @ SV428 ) @ SV961 ) @ SV428 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV961 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3679,plain,
! [SV1377: $i,SV962: $i,SV429: $i] :
( ( ( c_Relation_Orefl__on @ SV429 @ SV962 @ SV1377 )
| ~ ( c_Relation_Orefl__on @ SV429 @ ( hAPP @ ( c_Relation_Oconverse @ SV1377 @ SV1377 ) @ SV962 ) @ SV1377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3680,plain,
! [SV1378: $i,SV963: $i,SV430: $i] :
( ( ( c_Relation_Orefl__on @ SV430 @ ( hAPP @ ( c_Relation_Oconverse @ SV963 @ SV963 ) @ SV1378 ) @ SV963 )
| ~ ( c_Relation_Orefl__on @ SV430 @ SV1378 @ SV963 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3681,plain,
! [SV964: $i,SV431: $i] :
( ( ( ( hAPP @ ( c_Relation_Oconverse @ SV431 @ SV431 ) @ SV964 )
= SV964 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV964 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3682,plain,
! [SV965: $i,SV432: $i] :
( ( ( ( hAPP @ ( c_Relation_Oconverse @ SV432 @ SV432 ) @ SV965 )
!= SV965 )
= $true )
| ( ( c_Relation_Osym @ SV965 @ SV432 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3683,plain,
! [SV1379: $i,SV966: $i,SV433: $i] :
( ( ! [SY4992: $i,SY4993: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SV966 ) @ ( c_Relation_Orel__comp @ SV1379 @ SY4992 @ SV433 @ SY4993 @ SV966 ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SY4993 @ SV966 ) @ SY4992 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SY4993 ) @ SV1379 ) @ SV966 @ SY4993 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3684,plain,
! [SV1380: $i,SV967: $i,SV435: $i] :
( ( ! [SY4994: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV435 @ SV435 ) @ ( c_Relation_Oinv__image @ SV967 @ SV1380 @ SY4994 @ SV435 ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ SY4994 @ SY4994 ) @ SV967 ) @ SV1380 @ SY4994 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3685,plain,
! [SV970: $i,SV438: $i] :
( ( ( c_Relation_Oantisym @ SV438 @ SV970 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV970 @ SV970 ) @ SV438 ) @ SV970 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3686,plain,
! [SV971: $i,SV439: $i] :
( ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV439 @ SV439 ) @ SV971 ) @ SV439 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV971 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3687,plain,
! [SV1381: $i,SV973: $i,SV441: $i] :
( ( ( c_Relation_Ototal__on @ SV441 @ SV973 @ SV1381 )
| ~ ( c_Relation_Ototal__on @ SV441 @ ( hAPP @ ( c_Relation_Oconverse @ SV1381 @ SV1381 ) @ SV973 ) @ SV1381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3688,plain,
! [SV1382: $i,SV974: $i,SV442: $i] :
( ( ( c_Relation_Ototal__on @ SV442 @ ( hAPP @ ( c_Relation_Oconverse @ SV974 @ SV974 ) @ SV1382 ) @ SV974 )
| ~ ( c_Relation_Ototal__on @ SV442 @ SV1382 @ SV974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3689,plain,
! [SV1383: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ SV443 @ ( c_Transitive__Closure_Ortrancl @ SV975 @ SV1383 ) @ ( tc_prod @ SV1383 @ SV1383 ) )
| ~ ( c_in @ SV443 @ SV975 @ ( tc_prod @ SV1383 @ SV1383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3690,plain,
! [SV1384: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ SV444 @ ( c_Transitive__Closure_Otrancl @ SV976 @ SV1384 ) @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_in @ SV444 @ SV976 @ ( tc_prod @ SV1384 @ SV1384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3691,plain,
! [SV1385: $i,SV977: $i,SV445: $i] :
( ( ! [SY4995: $i] :
( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SY4995 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ! [SY4996: $i] :
( ~ ( c_in @ ( c_Pair @ SY4996 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SY4995 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SY4996 @ SV1385 @ SV1385 ) @ SY4995 @ ( tc_prod @ SV1385 @ SV1385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3692,plain,
! [SV1386: $i,SV978: $i,SV446: $i] :
( ( ! [SY4997: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SY4997 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ! [SY4998: $i] :
( ~ ( c_in @ ( c_Pair @ SY4998 @ SV978 @ SV1386 @ SV1386 ) @ SY4997 @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY4998 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SY4997 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3693,plain,
! [SV1387: $i,SV979: $i,SV447: $i] :
( ( ! [SY4999: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Ortrancl @ SY4999 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SY4999 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ( SV447 = SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3694,plain,
! [SV1388: $i,SV980: $i,SV448: $i] :
( ( ! [SY5000: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Otrancl @ SY5000 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
| ( SV448 = SV980 )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Ortrancl @ SY5000 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3695,plain,
! [SV1389: $i,SV981: $i,SV449: $i] :
( ( ! [SY5001: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Otrancl @ SY5001 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
| ( SV449 = SV981 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Ortrancl @ SY5001 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3696,plain,
! [SV1390: $i,SV982: $i,SV450: $i] :
( ( ! [SY5002: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Ortrancl @ SY5002 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Otrancl @ SY5002 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3697,plain,
! [SV1391: $i,SV983: $i,SV451: $i] :
( ( ! [SY5003: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SY5003 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ! [SY5004: $i] :
( ~ ( c_in @ ( c_Pair @ SY5004 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SY5003 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SY5004 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SY5003 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3698,plain,
! [SV1392: $i,SV984: $i,SV452: $i] :
( ( ! [SY5005: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SY5005 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ! [SY5006: $i] :
( ~ ( c_in @ ( c_Pair @ SY5006 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SY5005 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SY5006 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SY5005 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3699,plain,
! [SV1393: $i,SV985: $i,SV453: $i] :
( ( ( c_in @ SV453 @ ( c_Wellfounded_Oacc @ SV985 @ SV1393 ) @ SV1393 )
| ~ ( c_Wellfounded_Owf @ SV985 @ SV1393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3700,plain,
! [SV986: $i,SV454: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV454 @ SV986 ) @ SV986 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV454 @ SV986 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3701,plain,
! [SV1394: $i,SV988: $i,SV457: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV457 ) @ SV988 @ SV457 @ SV457 @ SV1394 )
= SV988 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3702,plain,
! [SV1395: $i,SV989: $i,SV458: $i] :
( ( ( c_Relation_Orel__comp @ SV458 @ ( c_Relation_OId @ SV989 ) @ SV1395 @ SV989 @ SV989 )
= SV458 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3703,plain,
! [SV991: $i,SV460: $i] :
( ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ ( c_Transitive__Closure_Otrancl @ SV991 @ SV460 ) ) @ SV460 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ SV991 ) @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3704,plain,
! [SV992: $i,SV461: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV461 @ SV992 ) @ SV992 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV461 @ SV992 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3705,plain,
! [SV993: $i,SV462: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV462 @ SV462 @ SV993 @ SV993 @ SV993 ) @ SV993 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV462 @ SV993 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3706,plain,
! [SV994: $i,SV463: $i] :
( ( ( c_Wellfounded_Owf @ SV463 @ SV994 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV463 @ SV463 @ SV994 @ SV994 @ SV994 ) @ SV994 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3707,plain,
! [SV1396: $i,SV1000: $i,SV469: $i] :
( ( ! [SY5007: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SV1000 @ SV1396 @ SY5007 ) @ SY5007 )
| ~ ( c_Wellfounded_Owf @ SV469 @ SV1396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3708,plain,
! [SV1397: $i,SV1002: $i,SV471: $i] :
( ( ! [SY5008: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SV1002 @ SV1397 @ SY5008 ) @ SY5008 )
| ~ ( c_Relation_Osym @ SV471 @ SV1397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3709,plain,
! [SV1004: $i,SV473: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV473 @ SV1004 ) @ SV1004 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV473 @ SV1004 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3710,plain,
! [SV1398: $i,SV1005: $i,SV474: $i] :
( ( ! [SY5009: $i,SY5010: $i,SY5011: $i,SY5012: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SV1398 @ SY5009 @ SY5010 ) @ SY5011 @ SV1398 @ SY5010 @ SY5012 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SY5011 @ SY5009 @ SY5010 @ SY5012 ) @ SV1398 @ SY5009 @ SY5012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3711,plain,
! [SV1006: $i,SV475: $i] :
( ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV475 @ SV475 ) @ SV1006 ) @ SV1006 @ SV475 @ SV475 @ SV475 )
!= SV1006 )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV1006 @ SV475 @ SV475 ) @ SV1006 @ SV475 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3712,plain,
! [SV1399: $i,SV1007: $i,SV477: $i] :
( ( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ SV477 @ SV1007 ) @ SV1399 ) @ SV1007 @ SV477 )
= ( c_Relation_ODomain @ SV1399 @ SV477 @ SV1007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3713,plain,
! [SV1009: $i,SV479: $i] :
( ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV479 @ SV479 ) @ SV1009 ) @ SV1009 @ SV479 @ SV479 @ SV479 )
= SV1009 )
= $true )
| ( ( ! [SY4444: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4444 @ SV1009 @ SV479 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3714,plain,
! [SV1400: $i,SV1011: $i,SV481: $i] :
( ( ( c_Relation_Orefl__on @ SV481 @ SV1011 @ SV1400 )
| ~ ( c_Equiv__Relations_Oequiv @ SV481 @ SV1011 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3715,plain,
! [SV1012: $i,SV482: $i] :
( ( ( c_Relation_Osym @ SV482 @ SV1012 )
= $true )
| ( ( ! [SY4446: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4446 @ SV482 @ SV1012 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3180]) ).
thf(3716,plain,
! [SV1401: $i,SV1013: $i,SV483: $i] :
( ( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SV483 @ SV1013 ) @ SV1401 ) @ SV1013 @ SV483 )
= ( c_Relation_ORange @ SV1401 @ SV483 @ SV1013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3717,plain,
! [SV1402: $i,SV1016: $i,SV486: $i] :
( ( ( c_Relation_ORange @ SV486 @ SV1016 @ SV1402 )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ SV1016 @ SV1402 ) @ SV486 ) @ SV1402 @ SV1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3718,plain,
! [SV1403: $i,SV1019: $i,SV489: $i] :
( ( ! [SY5013: $i] :
( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SY5013 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ! [SY5014: $i] :
( ~ ( c_in @ ( c_Pair @ SY5014 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SY5013 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SY5014 @ SV1403 @ SV1403 ) @ SY5013 @ ( tc_prod @ SV1403 @ SV1403 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3719,plain,
! [SV1404: $i,SV1020: $i,SV490: $i] :
( ( ! [SY5015: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ ( c_Transitive__Closure_Otrancl @ SY5015 @ SV1404 ) @ ( tc_prod @ SV1404 @ SV1404 ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ SY5015 @ ( tc_prod @ SV1404 @ SV1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3720,plain,
! [SV1405: $i,SV1021: $i,SV491: $i] :
( ( ! [SY5016: $i] :
( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SY5016 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ! [SY5017: $i] :
( ~ ( c_in @ ( c_Pair @ SY5017 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SY5016 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SY5017 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SY5016 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3721,plain,
! [SV1406: $i,SV1022: $i,SV492: $i] :
( ( c_in @ ( c_Pair @ SV492 @ SV492 @ SV1022 @ SV1022 ) @ ( c_Transitive__Closure_Ortrancl @ SV1406 @ SV1022 ) @ ( tc_prod @ SV1022 @ SV1022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3722,plain,
! [SV1407: $i,SV1023: $i,SV493: $i] :
( ( c_in @ ( c_Pair @ SV493 @ SV493 @ SV1023 @ SV1023 ) @ ( c_Transitive__Closure_Ortrancl @ SV1407 @ SV1023 ) @ ( tc_prod @ SV1023 @ SV1023 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3723,plain,
! [SV1408: $i,SV1024: $i,SV494: $i] :
( ( ! [SY5018: $i] :
( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SY5018 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SY5018 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_Wellfounded_Owf @ SY5018 @ SV1408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3724,plain,
! [SV1025: $i,SV495: $i] :
( ( ( SV495 = SV1025 )
= $true )
| ( ( ! [SY4461: $i,SY4462: $i] :
( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SY4461 @ SY4461 ) @ SY4462 @ ( tc_prod @ SY4461 @ SY4461 ) )
| ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SY4461 @ SY4461 ) @ SY4462 @ ( tc_prod @ SY4461 @ SY4461 ) )
| ~ ( c_Relation_Oantisym @ SY4462 @ SY4461 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3725,plain,
! [SV1026: $i,SV496: $i] :
( ( ( SV496 = SV1026 )
= $true )
| ( ( ! [SY4463: $i,SY4464: $i] :
( ~ ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SY4463 @ SY4463 ) @ SY4464 @ ( tc_prod @ SY4463 @ SY4463 ) )
| ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SY4463 @ SY4463 ) @ SY4464 @ ( tc_prod @ SY4463 @ SY4463 ) )
| ~ ( c_Relation_Oantisym @ SY4464 @ SY4463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3726,plain,
! [SV1409: $i,SV1027: $i,SV497: $i] :
( ( ! [SY5019: $i] :
( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
| ! [SY5020: $i] :
( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SY5019 @ SY5019 ) @ SY5020 @ ( tc_prod @ SY5019 @ SY5019 ) )
| ! [SY3407: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5020 @ SV497 @ SY5019 @ SY3407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3727,plain,
! [SV1028: $i,SV498: $i] :
( ( ( SV498 = SV1028 )
= $true )
| ( ( ! [SY4469: $i,SY4470: $i] :
~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ SY4469 @ SY4469 ) @ ( c_Relation_OId__on @ SY4470 @ SY4469 ) @ ( tc_prod @ SY4469 @ SY4469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3728,plain,
! [SV1410: $i,SV1029: $i,SV499: $i] :
( ( ! [SY5022: $i,SY5023: $i,SY5024: $i] :
( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SY5022 @ SY5023 )
!= ( c_Recdef_Ocut @ SY5024 @ SV1029 @ SV1410 @ SY5022 @ SY5023 ) )
| ! [SY5025: $i] :
( ( ( hAPP @ SV499 @ SY5025 )
= ( hAPP @ SY5024 @ SY5025 ) )
| ~ ( c_in @ ( c_Pair @ SY5025 @ SV1410 @ SY5022 @ SY5022 ) @ SV1029 @ ( tc_prod @ SY5022 @ SY5022 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3729,plain,
! [SV1030: $i,SV500: $i] :
( ( ( SV500 = SV1030 )
= $true )
| ( ( ! [SY4476: $i] :
~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ SY4476 @ SY4476 ) @ ( c_Relation_OId @ SY4476 ) @ ( tc_prod @ SY4476 @ SY4476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3730,plain,
! [SV1411: $i,SV1031: $i,SV501: $i] :
( ( ( c_in @ ( c_Pair @ SV501 @ SV501 @ SV1031 @ SV1031 ) @ SV1411 @ ( tc_prod @ SV1031 @ SV1031 ) )
| ~ ( c_Nitpick_Orefl_H @ SV1411 @ SV1031 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3731,plain,
! [SV1412: $i,SV1032: $i,SV502: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV502 @ SV1032 @ SV1032 ) @ SV1412 @ ( tc_prod @ SV1032 @ SV1032 ) )
| ~ ( c_Wellfounded_Owf @ SV1412 @ SV1032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3732,plain,
! [SV1413: $i,SV1033: $i,SV503: $i] :
( ( ! [SY5026: $i,SY5027: $i,SY5028: $i] :
( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SY5026 @ SY5027 @ SY5028 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY5027 @ SV503 ) @ ( hAPP @ SY5027 @ SV1033 ) @ SY5028 @ SY5028 ) @ SY5026 @ ( tc_prod @ SY5028 @ SY5028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3733,plain,
! [SV1414: $i,SV1034: $i,SV504: $i] :
( ( ! [SY5029: $i,SY5030: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SY5029 @ SY5029 ) @ SY5030 @ ( tc_prod @ SY5029 @ SY5029 ) )
| ! [SY5031: $i] :
~ ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SY5031 @ SY5031 ) @ ( c_Relation_Oinv__image @ SY5030 @ SV504 @ SY5029 @ SY5031 ) @ ( tc_prod @ SY5031 @ SY5031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3734,plain,
! [SV1415: $i,SV1035: $i,SV505: $i] :
( ( ! [SY5032: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SY5032 @ ( tc_prod @ SV1415 @ SV1415 ) )
| ~ ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SY5032 @ ( tc_prod @ SV1415 @ SV1415 ) )
| ~ ( c_Relation_Osym @ SY5032 @ SV1415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3735,plain,
! [SV1416: $i,SV1036: $i,SV506: $i] :
( ( ! [SY5033: $i] :
( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SY5033 @ ( tc_prod @ SV1416 @ SV1416 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SY5033 @ ( tc_prod @ SV1416 @ SV1416 ) )
| ~ ( c_Relation_Osym @ SY5033 @ SV1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3736,plain,
! [SV1417: $i,SV1037: $i,SV507: $i] :
( ( ! [SY5034: $i,SY5035: $i,SY5036: $i,SY5037: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SY5034 ) @ ( c_Relation_Orel__comp @ SY5035 @ SY5036 @ SV1417 @ SY5037 @ SY5034 ) @ ( tc_prod @ SV1417 @ SY5034 ) )
| ! [SY5038: $i] :
( ~ ( c_in @ ( c_Pair @ SY5038 @ SV1037 @ SY5037 @ SY5034 ) @ SY5036 @ ( tc_prod @ SY5037 @ SY5034 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5038 @ SV1417 @ SY5037 ) @ SY5035 @ ( tc_prod @ SV1417 @ SY5037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3737,plain,
! [SV1418: $i,SV1038: $i,SV508: $i] :
( ( ! [SY5039: $i] :
( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SY5039 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
| ! [SY5040: $i] :
( ~ ( c_in @ ( c_Pair @ SY5040 @ SV1038 @ SV1418 @ SV1418 ) @ SY5039 @ ( tc_prod @ SV1418 @ SV1418 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SY5040 @ SV1418 @ SV1418 ) @ SY5039 @ ( tc_prod @ SV1418 @ SV1418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3738,plain,
! [SV1419: $i,SV1039: $i,SV509: $i] :
( ( ! [SY5041: $i] :
( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SY5041 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ! [SY5042: $i] :
( ~ ( c_in @ ( c_Pair @ SY5042 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SY5041 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SY5042 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SY5041 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3739,plain,
! [SV1420: $i,SV1042: $i,SV512: $i] :
( ( ! [SY5043: $i] :
( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SY5043 )
| ! [SY5044: $i,SY5045: $i] :
( ~ ( c_in @ SV1042 @ SY5044 @ SY5045 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SY5044 @ SV1420 @ SY5045 @ SY5043 ) @ ( tc_fun @ SY5045 @ SY5043 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3740,plain,
! [SV1421: $i,SV1043: $i,SV513: $i] :
( ( ! [SY5046: $i] :
( ~ ( c_in @ SV513 @ SV1043 @ SV1421 )
| ! [SY5047: $i,SY5048: $i] :
( ( c_in @ ( hAPP @ SY5046 @ SV513 ) @ ( hAPP @ SY5047 @ SV513 ) @ SY5048 )
| ~ ( c_in @ SY5046 @ ( c_FuncSet_OPi @ SV1043 @ SY5047 @ SV1421 @ SY5048 ) @ ( tc_fun @ SV1421 @ SY5048 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3741,plain,
! [SV1422: $i,SV1044: $i,SV514: $i] :
( ( ! [SY5049: $i] :
( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SY5049 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV514 = SV1044 )
| ( SV514 = SY5049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3742,plain,
! [SV1423: $i,SV1045: $i,SV515: $i] :
( ( ! [SY5050: $i] :
( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SY5050 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1045 = SY5050 )
| ( SV515 = SY5050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3743,plain,
! [SV1046: $i,SV516: $i] :
( ( c_in @ ( c_Pair @ SV516 @ SV516 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1046 @ SV516 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3744,plain,
! [SV1424: $i,SV1047: $i,SV517: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV517 @ SV1047 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1424 @ SV517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3745,plain,
! [SV1425: $i,SV1048: $i,SV518: $i] :
( ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1425 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5051: $i] :
( ( SV1048 = SY5051 )
| ~ ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1425 @ SY5051 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3746,plain,
! [SV1049: $i,SV519: $i] :
( ( ( SV519 = SV1049 )
= $true )
| ( ( ( SV1049 = SV519 )
| ! [SY4518: $i] : ( c_in @ ( c_Pair @ SV519 @ SV1049 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4518 @ SV519 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3747,plain,
! [SV1050: $i,SV520: $i] :
( ( c_in @ ( c_Pair @ SV520 @ SV520 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1050 @ SV520 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3748,plain,
! [SV1426: $i,SV1051: $i,SV521: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV521 @ SV1051 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1426 @ SV1051 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3749,plain,
! [SV1427: $i,SV1052: $i,SV522: $i] :
( ( ! [SY5052: $i] :
( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SY5052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV522 = SV1052 )
| ( SV1052 = SY5052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3750,plain,
! [SV1428: $i,SV1053: $i,SV523: $i] :
( ( ! [SY5053: $i] :
( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SY5053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV523 = SY5053 )
| ( SV1053 = SY5053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3751,plain,
! [SV1054: $i,SV524: $i] :
( ( ( SV524 = SV1054 )
= $true )
| ( ( ( SV524 = SV1054 )
| ! [SY4524: $i] : ( c_in @ ( c_Pair @ SV524 @ SV1054 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4524 @ SV1054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3752,plain,
! [SV1429: $i,SV1055: $i,SV525: $i] :
( ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1429 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5054: $i] :
( ( SV525 = SY5054 )
| ~ ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1429 @ SY5054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3753,plain,
! [SV1056: $i,SV526: $i] :
( ( ( SV526 = SV1056 )
= $true )
| ( ( c_in @ ( c_Pair @ SV526 @ SV1056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV526 @ SV1056 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3754,plain,
! [SV1430: $i,SV1057: $i,SV527: $i] :
( ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5055: $i] :
( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5055 @ ( v_sko__local__X3__1 @ SV1430 @ SY5055 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SY5055 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5055 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3755,plain,
! [SV1431: $i,SV1058: $i,SV528: $i] :
( ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5056: $i] :
( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5056 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SY5056 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5056 @ ( v_sko__local__X3__1 @ SY5056 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5056 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3756,plain,
! [SV1432: $i,SV1059: $i,SV529: $i] :
( ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5057: $i] :
( ~ ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5057 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5057 @ ( v_sko__local__X3__1 @ SV1432 @ SY5057 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SY5057 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5057 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3757,plain,
! [SV1433: $i,SV1060: $i,SV530: $i] :
( ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5058: $i] :
( ~ ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5058 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SY5058 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5058 @ ( v_sko__local__X3__1 @ SY5058 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5058 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3758,plain,
! [SV1434: $i,SV1061: $i,SV531: $i] :
( ( ! [SY5059: $i] :
( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SY5059 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5060: $i] :
( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SY5060 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5060 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SY5059 @ SY5060 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5059 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SY5059 @ SY5060 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5060 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5059 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3759,plain,
! [SV1435: $i,SV1062: $i,SV532: $i] :
( ( ! [SY5061: $i] :
( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SY5061 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5062: $i] :
( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SY5062 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5061 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5062 @ SY5061 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5062 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5062 @ SY5061 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5061 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5062 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3760,plain,
! [SV1436: $i,SV1063: $i,SV533: $i] :
( ( ! [SY5063: $i] :
( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SY5063 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5064: $i] :
( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SY5064 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5064 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SY5063 @ SY5064 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5063 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SY5063 @ SY5064 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5064 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5063 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3761,plain,
! [SV1437: $i,SV1064: $i,SV534: $i] :
( ( ! [SY5065: $i] :
( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SY5065 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5066: $i] :
( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SY5066 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5065 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5066 @ SY5065 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5066 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5066 @ SY5065 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5065 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5066 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3762,plain,
! [SV1438: $i,SV1065: $i,SV535: $i] :
( ( ! [SY5067: $i] :
( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SY5067 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5067 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SY5067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5067 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3763,plain,
! [SV1439: $i,SV1066: $i,SV536: $i] :
( ( ! [SY5068: $i] :
( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5069: $i,SY5070: $i] :
( ~ ( c_in @ ( c_Pair @ SY5068 @ SY5069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5070 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY5068 @ SY5069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5070 @ ( v_sko__local__X2__1 @ SV1439 @ SY5070 @ SV536 @ SY5068 @ SV1066 @ SY5069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SY5070 @ SV536 @ SY5068 @ SV1066 @ SY5069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5070 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SY5068 )
| ( SV536 = SY5069 )
| ( SY5068 = SY5069 )
| ( SV536 = SV1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3764,plain,
! [SV1440: $i,SV1067: $i,SV537: $i] :
( ( ! [SY5071: $i] :
( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5072: $i,SY5073: $i] :
( ~ ( c_in @ ( c_Pair @ SY5071 @ SY5072 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5073 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SY5073 @ SV1440 @ SY5071 @ SV537 @ SY5072 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY5071 @ SY5072 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5073 @ ( v_sko__local__X2__1 @ SY5073 @ SV1440 @ SY5071 @ SV537 @ SY5072 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5073 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5072 = SV537 )
| ( SY5071 = SV1067 )
| ( SV537 = SV1067 )
| ( SY5071 = SY5072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3765,plain,
! [SV1441: $i,SV1068: $i,SV538: $i] :
( ( ! [SY5074: $i] :
( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5075: $i,SY5076: $i] :
( ~ ( c_in @ ( c_Pair @ SY5074 @ SY5075 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5076 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY5074 @ SY5075 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5076 @ ( v_sko__local__X2__1 @ SV1441 @ SY5076 @ SV538 @ SY5074 @ SV1068 @ SY5075 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SY5076 @ SV538 @ SY5074 @ SV1068 @ SY5075 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5076 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SY5074 )
| ( SV538 = SY5075 )
| ( SY5074 = SY5075 )
| ( SV538 = SV1068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3766,plain,
! [SV1442: $i,SV1069: $i,SV539: $i] :
( ( ! [SY5077: $i] :
( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5078: $i,SY5079: $i] :
( ~ ( c_in @ ( c_Pair @ SY5077 @ SY5078 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5079 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SY5079 @ SV1442 @ SY5077 @ SV539 @ SY5078 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY5077 @ SY5078 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5079 @ ( v_sko__local__X2__1 @ SY5079 @ SV1442 @ SY5077 @ SV539 @ SY5078 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5079 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5078 = SV539 )
| ( SY5077 = SV1069 )
| ( SV539 = SV1069 )
| ( SY5077 = SY5078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3767,plain,
! [SV1443: $i,SV1070: $i,SV540: $i] :
( ( ! [SY5080: $i] :
( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5081: $i,SY5082: $i] :
( ~ ( c_in @ ( c_Pair @ SY5080 @ SY5081 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5082 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SY5082 @ SV1443 @ SY5080 @ SV540 @ SY5081 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY5080 @ SY5081 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5082 @ ( v_sko__local__X1__1 @ SY5082 @ SV1443 @ SY5080 @ SV540 @ SY5081 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5082 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5081 = SV540 )
| ( SY5080 = SV1070 )
| ( SV540 = SV1070 )
| ( SY5080 = SY5081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3768,plain,
! [SV1444: $i,SV1071: $i,SV541: $i] :
( ( ! [SY5083: $i] :
( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5084: $i,SY5085: $i] :
( ~ ( c_in @ ( c_Pair @ SY5083 @ SY5084 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5085 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SY5085 @ SV1444 @ SY5083 @ SV541 @ SY5084 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY5083 @ SY5084 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5085 @ ( v_sko__local__X1__1 @ SY5085 @ SV1444 @ SY5083 @ SV541 @ SY5084 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5085 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5084 = SV541 )
| ( SY5083 = SV1071 )
| ( SV541 = SV1071 )
| ( SY5083 = SY5084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3769,plain,
! [SV1445: $i,SV1072: $i,SV542: $i] :
( ( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SV1445 ) )
| ~ ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV542 @ SV1445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3770,plain,
! [SV1446: $i,SV1073: $i,SV543: $i] :
( ( ! [SY5086: $i,SY5087: $i,SY5088: $i] :
( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SY5086 ) @ ( c_Product__Type_OSigma @ SY5087 @ SY5088 @ SV1446 @ SY5086 ) @ ( tc_prod @ SV1446 @ SY5086 ) )
| ~ ( c_in @ SV1073 @ ( hAPP @ SY5088 @ SV543 ) @ SY5086 )
| ~ ( c_in @ SV543 @ SY5087 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3771,plain,
! [SV1447: $i,SV1074: $i,SV544: $i] :
( ( ! [SY5089: $i,SY5090: $i,SY5091: $i] :
( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SY5089 ) @ ( c_Product__Type_OSigma @ SY5090 @ SY5091 @ SV1447 @ SY5089 ) @ ( tc_prod @ SV1447 @ SY5089 ) )
| ~ ( c_in @ SV1074 @ ( hAPP @ SY5091 @ SV544 ) @ SY5089 )
| ~ ( c_in @ SV544 @ SY5090 @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3772,plain,
! [SV1448: $i,SV1075: $i,SV545: $i] :
( ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
| ! [SY5092: $i] :
( ~ ( c_in @ ( c_Pair @ SV545 @ SY5092 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SY5092 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3773,plain,
! [SV1449: $i,SV1076: $i,SV546: $i] :
( ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
| ! [SY5093: $i] :
( ~ ( c_in @ ( c_Pair @ SV546 @ SY5093 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) )
| ~ ( c_in @ SY5093 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3774,plain,
! [SV1450: $i,SV1077: $i,SV547: $i] :
( ( ! [SY5094: $i,SY5095: $i] :
( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SY5094 @ SY5095 ) @ SY5095 )
| ! [SY5096: $i] :
( ~ ( c_in @ ( c_Pair @ SY5096 @ SV547 @ SY5094 @ SY5095 ) @ SV1077 @ ( tc_prod @ SY5094 @ SY5095 ) )
| ~ ( c_in @ SY5096 @ SV1450 @ SY5094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3775,plain,
! [SV1451: $i,SV1078: $i,SV548: $i] :
( ( ! [SY5097: $i,SY5098: $i] :
( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SY5097 @ SY5098 ) @ SY5098 )
| ! [SY5099: $i] :
( ~ ( c_in @ ( c_Pair @ SY5099 @ SV548 @ SY5097 @ SY5098 ) @ SV1078 @ ( tc_prod @ SY5097 @ SY5098 ) )
| ~ ( c_in @ SY5099 @ SV1451 @ SY5097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3776,plain,
! [SV1452: $i,SV1079: $i,SV549: $i] :
( ( ( c_in @ SV549 @ SV1079 @ SV1452 )
| ! [SY5100: $i] :
~ ( c_in @ ( c_Pair @ SV549 @ SY5100 @ SV1452 @ SV1452 ) @ ( c_Relation_OId__on @ SV1079 @ SV1452 ) @ ( tc_prod @ SV1452 @ SV1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3777,plain,
! [SV1453: $i,SV1080: $i,SV550: $i] :
( ( ( c_in @ ( c_Pair @ SV550 @ SV550 @ SV1080 @ SV1080 ) @ ( c_Relation_OId__on @ SV1453 @ SV1080 ) @ ( tc_prod @ SV1080 @ SV1080 ) )
| ~ ( c_in @ SV550 @ SV1453 @ SV1080 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3778,plain,
! [SV1454: $i,SV1081: $i,SV551: $i] :
( ( ( c_in @ SV551 @ SV1081 @ SV1454 )
| ! [SY5101: $i,SY5102: $i] :
( ~ ( c_in @ ( c_Pair @ SY5101 @ SV551 @ SV1454 @ SV1454 ) @ SY5102 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SY5102 @ SV1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3779,plain,
! [SV1455: $i,SV1082: $i,SV552: $i] :
( ( ( c_in @ SV552 @ SV1082 @ SV1455 )
| ! [SY5103: $i,SY5104: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY5103 @ SV1455 @ SV1455 ) @ SY5104 @ ( tc_prod @ SV1455 @ SV1455 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SY5104 @ SV1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3780,plain,
! [SV1456: $i,SV1083: $i,SV553: $i] :
( ( ! [SY5105: $i] :
( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SV1456 @ SY5105 ) @ SY5105 )
| ! [SY5106: $i] :
~ ( c_in @ ( c_Pair @ SY5106 @ SV553 @ SV1456 @ SY5105 ) @ SV1083 @ ( tc_prod @ SV1456 @ SY5105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3781,plain,
! [SV1457: $i,SV1084: $i,SV554: $i] :
( ( ! [SY5107: $i] :
( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SV1457 @ SY5107 ) @ SY5107 )
| ! [SY5108: $i] :
~ ( c_in @ ( c_Pair @ SY5108 @ SV554 @ SV1457 @ SY5107 ) @ SV1084 @ ( tc_prod @ SV1457 @ SY5107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3782,plain,
! [SV1458: $i,SV1085: $i,SV555: $i] :
( ( ! [SY5109: $i] :
( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SV1458 @ SY5109 ) @ SV1458 )
| ! [SY5110: $i] :
~ ( c_in @ ( c_Pair @ SV555 @ SY5110 @ SV1458 @ SY5109 ) @ SV1085 @ ( tc_prod @ SV1458 @ SY5109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3783,plain,
! [SV1459: $i,SV1086: $i,SV556: $i] :
( ( ! [SY5111: $i] :
( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SV1459 @ SY5111 ) @ SV1459 )
| ! [SY5112: $i] :
~ ( c_in @ ( c_Pair @ SV556 @ SY5112 @ SV1459 @ SY5111 ) @ SV1086 @ ( tc_prod @ SV1459 @ SY5111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3784,plain,
! [SV1460: $i,SV1087: $i,SV557: $i] :
( ( ! [SY5113: $i] :
( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SY5113 )
| ! [SY5114: $i,SY5115: $i] :
~ ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SY5114 @ SY5113 ) @ ( c_Product__Type_OSigma @ SY5115 @ SV1087 @ SY5114 @ SY5113 ) @ ( tc_prod @ SY5114 @ SY5113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3785,plain,
! [SV1461: $i,SV1088: $i,SV558: $i] :
( ( ! [SY5116: $i] :
( ( c_in @ SV558 @ SV1088 @ SV1461 )
| ! [SY5117: $i,SY5118: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SY5116 @ SV1461 @ SY5117 ) @ ( c_Product__Type_OSigma @ SV1088 @ SY5118 @ SV1461 @ SY5117 ) @ ( tc_prod @ SV1461 @ SY5117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3786,plain,
! [SV1462: $i,SV1089: $i,SV559: $i] :
( ( ! [SY5119: $i] :
( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SY5119 @ ( tc_prod @ SV1462 @ SV1462 ) )
| ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SY5119 @ ( tc_prod @ SV1462 @ SV1462 ) )
| ( SV1089 = SV559 )
| ! [SY5120: $i] :
( ~ ( c_in @ SV559 @ SY5120 @ SV1462 )
| ~ ( c_in @ SV1089 @ SY5120 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SY5120 @ SY5119 @ SV1462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(3787,plain,
! [SV1463: $i,SV1090: $i,SV560: $i] :
( ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
| ! [SY5121: $i] :
( ~ ( c_in @ SV560 @ SY5121 @ SV1090 )
| ~ ( c_Relation_Orefl__on @ SY5121 @ SV1463 @ SV1090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(3788,plain,
! [SV1464: $i,SV1091: $i,SV561: $i] :
( ( ( c_in @ SV561 @ SV1091 @ SV1464 )
| ! [SY5122: $i,SY5123: $i] :
( ~ ( c_in @ ( c_Pair @ SY5122 @ SV561 @ SV1464 @ SV1464 ) @ SY5123 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1091 @ SY5123 @ SV1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3789,plain,
! [SV1465: $i,SV1092: $i,SV562: $i] :
( ( ( c_in @ SV562 @ SV1092 @ SV1465 )
| ! [SY5124: $i,SY5125: $i] :
( ~ ( c_in @ ( c_Pair @ SV562 @ SY5124 @ SV1465 @ SV1465 ) @ SY5125 @ ( tc_prod @ SV1465 @ SV1465 ) )
| ~ ( c_Relation_Orefl__on @ SV1092 @ SY5125 @ SV1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(3790,plain,
! [SV1466: $i,SV1093: $i,SV563: $i] :
( ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
| ! [SY5126: $i] :
( ~ ( c_in @ SV563 @ SY5126 @ SV1093 )
| ~ ( c_Relation_Orefl__on @ SY5126 @ SV1466 @ SV1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(3791,plain,
! [SV1467: $i,SV1094: $i,SV564: $i] :
( ( ! [SY5127: $i] :
( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ SY5127 ) @ SV1467 ) @ ( tc_prod @ SV1467 @ SV1467 ) )
| ~ ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ SY5127 @ SV1467 ) ) @ ( tc_prod @ SV1467 @ SV1467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3792,plain,
! [SV1468: $i,SV1095: $i,SV565: $i] :
( ( ! [SY5128: $i] :
( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ SY5128 @ SV1468 ) ) @ ( tc_prod @ SV1468 @ SV1468 ) )
| ~ ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ SY5128 ) @ SV1468 ) @ ( tc_prod @ SV1468 @ SV1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3793,plain,
! [SV1469: $i,SV1096: $i,SV566: $i] :
( ( ! [SY5129: $i] :
( ( c_in @ ( c_Pair @ SV566 @ SV1096 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SY5129 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
| ~ ( c_in @ ( c_Pair @ SV1096 @ SV566 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1469 @ SV1469 ) @ SY5129 ) @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3794,plain,
! [SV1470: $i,SV1097: $i,SV567: $i] :
( ( ! [SY5130: $i] :
( ( c_in @ ( c_Pair @ SV567 @ SV1097 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1470 @ SV1470 ) @ SY5130 ) @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
| ~ ( c_in @ ( c_Pair @ SV1097 @ SV567 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SY5130 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3795,plain,
! [SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5131: $i,SY5132: $i,SY5133: $i,SY5134: $i,SY5135: $i,SY5136: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SY5131 @ ( hAPP @ SY5132 @ SY5133 ) ) )
| ! [SY5137: $i,SY5138: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SY5134 @ SY5135 @ SY5136 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SY5131 @ SY5132 @ SY5137 @ SY5135 @ SY5138 ) @ SY5133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3796,plain,
! [SV1472: $i,SV1099: $i,SV569: $i] :
( ( ! [SY5139: $i,SY5140: $i,SY5141: $i,SY5142: $i] :
( ! [SY5143: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SY5139 @ SY5140 )
!= ( c_Fun_Ocomp @ SY5141 @ SY5142 @ SY5143 @ SY5139 @ SY5140 ) )
| ! [SY4659: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY4659 ) )
= ( hAPP @ SY5141 @ ( hAPP @ SY5142 @ SY4659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3797,plain,
! [SV1473: $i,SV1100: $i,SV570: $i] :
( ( ! [SY5145: $i,SY5146: $i,SY5147: $i] :
( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SY5145 )
!= ( c_Pair @ SY5146 @ SY5147 @ SV1473 @ SY5145 ) )
| ( SV1100 = SY5147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3798,plain,
! [SV1474: $i,SV1101: $i,SV571: $i] :
( ( ! [SY5148: $i,SY5149: $i] :
( ! [SY5150: $i] :
( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SY5148 )
!= ( c_Pair @ SY5149 @ SY5150 @ SV1474 @ SY5148 ) )
| ( SV571 = SY5149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3799,plain,
! [SV1475: $i,SV1102: $i,SV572: $i] :
( ( ! [SY5151: $i,SY5152: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SV1475 @ SY5151 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY5151 @ SV1475 ) @ SY5152 ) @ ( tc_prod @ SV1475 @ SY5151 ) )
| ~ ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SY5151 @ SV1475 ) @ SY5152 @ ( tc_prod @ SY5151 @ SV1475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3800,plain,
! [SV1476: $i,SV1103: $i,SV573: $i] :
( ( ! [SY5153: $i,SY5154: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SV1476 @ SY5153 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY5153 @ SV1476 ) @ SY5154 ) @ ( tc_prod @ SV1476 @ SY5153 ) )
| ~ ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SY5153 @ SV1476 ) @ SY5154 @ ( tc_prod @ SY5153 @ SV1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3801,plain,
! [SV1477: $i,SV1104: $i,SV574: $i] :
( ( ! [SY5155: $i,SY5156: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SV1477 @ SY5155 ) @ SY5156 @ ( tc_prod @ SV1477 @ SY5155 ) )
| ~ ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SY5155 @ SV1477 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1477 @ SY5155 ) @ SY5156 ) @ ( tc_prod @ SY5155 @ SV1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3802,plain,
! [SV1478: $i,SV1105: $i,SV575: $i] :
( ( ! [SY5157: $i,SY5158: $i,SY5159: $i,SY5160: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SV1478 @ SY5157 @ SY5158 @ SY5159 ) @ SY5158 @ SY5160 @ SY5159 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SY5158 @ SY5160 @ SY5157 ) @ SV1478 @ SY5157 @ SY5160 @ SY5159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3803,plain,
! [SV576: $i] :
( ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV576 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ SV576 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3804,plain,
! [SV577: $i] :
( ( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ SV577 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ SV577 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3805,plain,
! [SV1479: $i,SV1106: $i,SV578: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV578 @ SV1106 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1106 @ SV578 ) @ SV1479 ) )
= SV1479 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3806,plain,
! [SV1480: $i,SV1107: $i,SV579: $i] :
( ( ! [SY5161: $i,SY5162: $i,SY5163: $i] :
( ( hAPP @ SV579 @ ( hAPP @ SV1107 @ SV1480 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SV1107 @ SY5161 @ SY5162 @ SY5163 ) @ SV1480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3807,plain,
! [SV1481: $i,SV1108: $i,SV580: $i] :
( ( ! [SY5164: $i,SY5165: $i,SY5166: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SV1108 @ SV1481 @ SY5164 @ SY5165 ) @ SY5166 )
= ( hAPP @ SV580 @ ( hAPP @ SV1108 @ SY5166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3808,plain,
! [SV1109: $i,SV581: $i] :
( ( ( ! [SY4691: $i] : ( c_in @ SV581 @ SV1109 @ SY4691 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1109 @ SV581 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3279]) ).
thf(3809,plain,
! [SV1110: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ SV582 @ SV1110 ) )
= $true )
| ( ( ! [SY4692: $i] :
~ ( c_in @ SV1110 @ SV582 @ SY4692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3810,plain,
! [SV1111: $i,SV583: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV583 @ SV1111 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3811,plain,
! [SV1112: $i,SV584: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV584 @ SV1112 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3812,plain,
! [SV1113: $i,SV585: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV585 @ SV1113 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV1113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3813,plain,
! [SV1114: $i,SV586: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV586 @ SV1114 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV1114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3814,plain,
! [SV1115: $i,SV587: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV587 @ SV1115 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3815,plain,
! [SV1116: $i,SV588: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV588 @ SV1116 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3816,plain,
! [SV1117: $i,SV589: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV589 @ SV1117 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3817,plain,
! [SV1118: $i,SV590: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV590 @ SV1118 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3818,plain,
! [SV1119: $i,SV591: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV591 @ SV1119 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV1119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3819,plain,
! [SV1121: $i,SV593: $i] :
( ( ( SV593 = SV1121 )
= $true )
| ( ( ! [SY4693: $i] :
~ ( c_fequal @ SV593 @ SV1121 @ SY4693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3820,plain,
! [SV1482: $i,SV1122: $i,SV594: $i,SV3: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SV594 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SV1482 @ ( tc_fun @ SV1122 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SV1482 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ ( tc_fun @ SV1122 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3821,plain,
! [SV1483: $i,SV1123: $i,SV595: $i,SV4: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ SV1123 @ ( tc_fun @ SV1483 @ tc_bool ) ) @ ( tc_fun @ SV1483 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV4 @ SV1123 @ ( tc_fun @ SV1483 @ tc_bool ) ) @ ( tc_fun @ SV1483 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(3822,plain,
! [SV1484: $i,SV1124: $i,SV596: $i,SV5: $i] :
( ( ! [SY5167: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SV1484 ) @ SY5167 @ ( tc_fun @ SV1484 @ tc_bool ) )
| ! [SY5168: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY5168 @ ( c_COMBK @ SY5167 @ ( tc_fun @ SV1484 @ tc_bool ) @ SV1124 ) @ SV1124 @ SV1484 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SV1484 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3823,plain,
! [SV1485: $i,SV1126: $i,SV598: $i,SV8: $i] :
( ( ( hAPP @ ( c_COMBK @ SV8 @ SV598 @ SV1126 ) @ SV1485 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3824,plain,
! [SV600: $i,SV1486: $i,SV10: $i] :
( ( ( ! [SY5169: $i] :
( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SV1486 @ SY5169 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1486 @ SY5169 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3825,plain,
! [SV1487: $i,SV1127: $i,SV601: $i,SV11: $i] :
( ( ! [SY5170: $i] :
( ( c_Relation_OImage @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV601 @ SV1127 @ ( tc_fun @ SV1487 @ tc_bool ) ) @ SV1487 @ SY5170 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV11 @ SV601 @ SV1487 @ SY5170 ) @ ( c_Relation_OImage @ SV11 @ SV1127 @ SV1487 @ SY5170 ) @ ( tc_fun @ SY5170 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3826,plain,
! [SV1488: $i,SV1128: $i,SV602: $i,SV12: $i] :
( ( ! [SY5171: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV12 @ SV602 @ ( tc_fun @ ( tc_prod @ SV1128 @ SV1488 ) @ tc_bool ) ) @ SY5171 @ SV1128 @ SV1488 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV12 @ SY5171 @ SV1128 @ SV1488 ) @ ( c_Relation_OImage @ SV602 @ SY5171 @ SV1128 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3827,plain,
! [SV1489: $i,SV1129: $i,SV603: $i,SV13: $i] :
( ( ! [SY5172: $i,SY5173: $i,SY5174: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SY5172 ) @ ( c_Relation_Orel__comp @ SY5173 @ SY5174 @ SV1129 @ SV1489 @ SY5172 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SY5172 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SY5174 @ ( tc_fun @ ( tc_prod @ SV1489 @ SY5172 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SY5173 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3828,plain,
! [SV14: $i,SV1490: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1490 @ SV1490 @ SV14 )
= SV1490 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3829,plain,
! [SV1130: $i,SV605: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ ( c_Product__Type_OSigma @ SV605 @ ( c_COMBK @ SV605 @ ( tc_fun @ SV1130 @ tc_bool ) @ SV1130 ) @ SV1130 @ SV1130 ) @ ( tc_fun @ ( tc_prod @ SV1130 @ SV1130 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV605 @ SV16 @ SV1130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3830,plain,
! [SV607: $i,SV18: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV18 )
= $false )
| ( ( ! [SY3752: $i,SY3753: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SY3752 @ SV18 ) @ SY3753 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV607 @ SY3753 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3752 @ SY3753 @ SV18 ) @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3831,plain,
! [SV608: $i,SV19: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV19 )
= $false )
| ( ( ! [SY3754: $i,SY3755: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3754 @ SY3755 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3754 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY3755 @ SV19 ) @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3832,plain,
! [SV1491: $i,SV1131: $i,SV609: $i,SV20: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV609 @ SV1131 @ ( tc_fun @ SV1491 @ tc_bool ) ) @ ( tc_fun @ SV1491 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV609 @ ( tc_fun @ SV1491 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV1131 @ ( tc_fun @ SV1491 @ tc_bool ) ) @ ( tc_fun @ SV1491 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3833,plain,
! [SV1492: $i,SV1132: $i,SV610: $i,SV21: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV610 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ SV1492 @ ( tc_fun @ SV1132 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV21 @ SV1492 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV610 @ SV1492 @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3834,plain,
! [SV1493: $i,SV611: $i,SV22: $i] :
( ( ( ~ ( c_in @ SV22 @ ( c_Set_Oinsert @ SV611 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1493 @ tc_bool ) ) @ SV1493 ) @ SV1493 ) )
= $true )
| ( ( SV22 = SV611 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3835,plain,
! [SV1494: $i,SV1133: $i,SV612: $i,SV23: $i] :
( ( ! [SY5175: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV23 @ SV612 @ ( tc_fun @ SV1133 @ tc_bool ) ) @ SV1494 @ SV1133 @ SY5175 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV23 @ SV1494 @ SV1133 @ SY5175 ) @ ( c_Product__Type_OSigma @ SV612 @ SV1494 @ SV1133 @ SY5175 ) @ ( tc_fun @ ( tc_prod @ SV1133 @ SY5175 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3836,plain,
! [SV1134: $i,SV613: $i,SV24: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV24 @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3837,plain,
! [SV1495: $i,SV1135: $i,SV614: $i,SV25: $i] :
( ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
| ! [SY5176: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SY5176 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY5176 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SY5176 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY5176 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SY5176 ) @ tc_bool ) )
| ! [SY5177: $i] :
~ ( c_in @ SY5177 @ SV1495 @ SY5176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3838,plain,
! [SV1496: $i,SV1136: $i,SV615: $i,SV26: $i] :
( ( ! [SY5178: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SY5178 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV26 @ SY5178 @ ( tc_fun @ SV1496 @ tc_bool ) )
| ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3839,plain,
! [SV1137: $i,SV616: $i,SV27: $i] :
( ( ( c_lessequals @ SV27 @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) )
= $true )
| ( ( ! [SY4718: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4718 @ SV27 @ SV1137 ) @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3840,plain,
! [SV1497: $i,SV1138: $i,SV617: $i,SV28: $i] :
( ( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SV617 @ SV1138 @ SV1497 ) @ ( tc_fun @ SV1497 @ tc_bool ) )
| ~ ( c_lessequals @ SV28 @ SV1138 @ ( tc_fun @ SV1497 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3841,plain,
! [SV618: $i,SV1498: $i,SV29: $i] :
( ( ( ! [SY5180: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SV1498 @ SY5180 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1498 @ SY5180 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3842,plain,
! [SV1499: $i,SV1140: $i,SV620: $i,SV31: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV31 @ SV620 @ SV1140 ) @ SV1499 @ ( tc_fun @ SV1140 @ tc_bool ) )
= ( c_Set_Oinsert @ SV31 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SV1499 @ ( tc_fun @ SV1140 @ tc_bool ) ) @ SV1140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3843,plain,
! [SV1500: $i,SV1141: $i,SV621: $i,SV32: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Set_Oinsert @ SV621 @ SV1141 @ SV1500 ) @ ( tc_fun @ SV1500 @ tc_bool ) )
= ( c_Set_Oinsert @ SV621 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV1141 @ ( tc_fun @ SV1500 @ tc_bool ) ) @ SV1500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3844,plain,
! [SV1501: $i,SV1142: $i,SV622: $i,SV33: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SV622 ) @ tc_bool ) ) @ SV1142 @ SV33 @ SV622 @ SV1501 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV33 @ SV1501 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3845,plain,
! [SV1502: $i,SV1143: $i,SV623: $i,SV34: $i] :
( ( ( c_Relation_Orel__comp @ SV34 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV623 @ SV1143 ) @ tc_bool ) ) @ SV1502 @ SV623 @ SV1143 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1502 @ SV1143 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3846,plain,
! [SV1503: $i,SV37: $i] :
( ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV37 ) @ SV1503 @ SV37 )
= $true )
| ( ( class_Orderings_Obot @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3847,plain,
! [SV1144: $i,SV626: $i,SV38: $i] :
( ( ( c_Set_Oinsert @ SV38 @ SV626 @ SV1144 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3848,plain,
! [SV1504: $i,SV1145: $i,SV627: $i,SV39: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV39 @ SV627 @ SV1145 ) @ ( c_Set_Oinsert @ SV39 @ SV1504 @ SV1145 ) @ ( tc_fun @ SV1145 @ tc_bool ) )
= ( c_Set_Oinsert @ SV39 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV627 @ SV1504 @ ( tc_fun @ SV1145 @ tc_bool ) ) @ SV1145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3849,plain,
! [SV1147: $i,SV629: $i,SV41: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SV1147 @ SV1147 ) @ tc_bool ) ) @ SV1147 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV629 @ SV1147 )
| ~ ( c_Relation_Osym @ SV41 @ SV1147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(3850,plain,
! [SV1148: $i,SV630: $i,SV42: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV42 @ SV630 ) @ ( c_Transitive__Closure_Ortrancl @ SV1148 @ SV630 ) @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV42 @ SV1148 @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3851,plain,
! [SV1505: $i,SV1149: $i,SV631: $i,SV43: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV43 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1505 ) @ tc_bool ) ) @ SV1149 @ SV1505 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV43 @ SV1149 @ SV1505 ) @ ( c_Relation_ODomain @ SV631 @ SV1149 @ SV1505 ) @ ( tc_fun @ SV1149 @ tc_bool ) ) @ ( tc_fun @ SV1149 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(3852,plain,
! [SV44: $i,SV1506: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1506 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= ( c_Orderings_Obot__class_Obot @ SV44 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3853,plain,
! [SV1507: $i,SV45: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV45 ) @ SV1507 @ SV45 )
= ( c_Orderings_Obot__class_Obot @ SV45 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3854,plain,
! [SV1508: $i,SV1151: $i,SV635: $i,SV49: $i] :
( ( ! [SY5181: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV49 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1151 @ ( tc_fun @ SV1508 @ tc_bool ) ) @ SV1508 @ SY5181 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV49 @ SV635 @ SV1508 @ SY5181 ) @ ( c_Relation_OImage @ SV49 @ SV1151 @ SV1508 @ SY5181 ) @ ( tc_fun @ SY5181 @ tc_bool ) ) @ ( tc_fun @ SY5181 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3855,plain,
! [SV1509: $i,SV1152: $i,SV636: $i,SV50: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SV636 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV636 @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ ( tc_fun @ SV1152 @ tc_bool ) ) )
| ( c_lessequals @ SV1509 @ SV50 @ ( tc_fun @ SV1152 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3333]) ).
thf(3856,plain,
! [SV1510: $i,SV1153: $i,SV637: $i,SV51: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SV637 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV637 @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ ( tc_fun @ SV1153 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1510 @ SV51 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3857,plain,
! [SV1511: $i,SV1154: $i,SV638: $i,SV52: $i] :
( ( ! [SY5182: $i,SY5183: $i,SY5184: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SY5182 ) @ ( c_Product__Type_OSigma @ SY5183 @ ( c_COMBK @ SY5184 @ ( tc_fun @ SY5182 @ tc_bool ) @ SV1154 ) @ SV1154 @ SY5182 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SY5182 ) @ tc_bool ) )
| ! [SY5185: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY5185 @ ( c_COMBK @ SY5184 @ ( tc_fun @ SY5182 @ tc_bool ) @ SV1511 ) @ SV1511 @ SY5182 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SY5182 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SY5183 @ ( c_COMBK @ SY5185 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3858,plain,
! [SV1155: $i,SV639: $i,SV53: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV639 @ SV1155 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3859,plain,
! [SV54: $i,SV640: $i,SV1512: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1512 @ SV640 ) )
| ! [SY5186: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1512 @ SV54 @ ( tc_fun @ SY5186 @ tc_bool ) ) @ SV640 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3860,plain,
! [SV1513: $i,SV1156: $i,SV641: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV641 @ ( tc_fun @ SV1156 @ tc_bool ) ) @ SV1513 ) )
| ~ ( hBOOL @ ( hAPP @ SV641 @ SV1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3861,plain,
! [SV1514: $i,SV1157: $i,SV642: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV642 @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV1514 ) )
| ~ ( hBOOL @ ( hAPP @ SV56 @ SV1514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(3862,plain,
! [SV1158: $i,SV643: $i,SV57: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1158 @ SV643 )
| ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3863,plain,
! [SV1515: $i,SV1159: $i,SV644: $i,SV58: $i] :
( ( ! [SY5187: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV644 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ ( c_COMBK @ SV1515 @ ( tc_fun @ SY5187 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY5187 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV58 @ ( c_COMBK @ SV1515 @ ( tc_fun @ SY5187 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY5187 ) @ ( c_Product__Type_OSigma @ SV644 @ ( c_COMBK @ SV1515 @ ( tc_fun @ SY5187 @ tc_bool ) @ SV1159 ) @ SV1159 @ SY5187 ) @ ( tc_fun @ ( tc_prod @ SV1159 @ SY5187 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(3864,plain,
! [SV1516: $i,SV1160: $i,SV645: $i,SV59: $i] :
( ( ! [SY5188: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SY5188 ) @ SV1160 @ SY5188 )
| ~ ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SY5188 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3865,plain,
! [SV1517: $i,SV1161: $i,SV646: $i,SV60: $i] :
( ( ! [SY5189: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SY5189 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV646 @ SY5189 @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3866,plain,
! [SV647: $i,SV61: $i] :
( ( ( class_Lattices_Olattice @ SV61 )
= $false )
| ( ( ! [SY3827: $i,SY3828: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SY3827 @ SV61 ) @ SY3828 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3827 @ SY3828 @ SV61 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3867,plain,
! [SV648: $i,SV62: $i] :
( ( ( class_Lattices_Olattice @ SV62 )
= $false )
| ( ( ! [SY3829: $i,SY3830: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ SY3830 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3829 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ SY3830 @ SV62 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3868,plain,
! [SV649: $i,SV63: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV63 )
= $false )
| ( ( ! [SY3831: $i,SY3832: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ SY3832 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3831 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ SY3832 @ SV63 ) @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3869,plain,
! [SV650: $i,SV64: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false )
| ( ( ! [SY3833: $i,SY3834: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ SY3833 @ SV64 ) @ SY3834 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3833 @ SY3834 @ SV64 ) @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3870,plain,
! [SV1518: $i,SV1162: $i,SV651: $i,SV65: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ SV651 @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1518 @ ( tc_fun @ SV1162 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV65 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV651 @ SV1518 @ ( tc_fun @ SV1162 @ tc_bool ) ) @ ( tc_fun @ SV1162 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3871,plain,
! [SV1519: $i,SV1163: $i,SV652: $i,SV66: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ SV1163 @ ( tc_fun @ SV1519 @ tc_bool ) ) @ ( tc_fun @ SV1519 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV652 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV66 @ SV1163 @ ( tc_fun @ SV1519 @ tc_bool ) ) @ ( tc_fun @ SV1519 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3872,plain,
! [SV67: $i,SV1520: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1520 @ ( c_Orderings_Obot__class_Obot @ SV67 ) @ SV67 )
= SV1520 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3873,plain,
! [SV1521: $i,SV68: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV68 ) @ SV1521 @ SV68 )
= SV1521 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3874,plain,
! [SV1522: $i,SV1164: $i,SV655: $i,SV71: $i] :
( ( ! [SY5190: $i,SY5191: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SY5190 @ SY5191 ) @ ( tc_fun @ SY5191 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5191 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SV1522 @ SV1164 @ SY5191 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV655 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SY5190 @ SY5191 ) @ ( tc_fun @ SY5191 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5191 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ SY5190 @ ( tc_fun @ SY5191 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5191 ) @ ( tc_fun @ ( tc_prod @ SV1164 @ SY5191 ) @ tc_bool ) ) @ ( tc_prod @ SV1164 @ SY5191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3875,plain,
! [SV656: $i,SV1523: $i,SV72: $i] :
( ( ( ~ ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SV1523 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1523 @ SV656 ) )
= $true )
| ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3876,plain,
! [SV1165: $i,SV658: $i,SV74: $i] :
( ( ( ~ ( c_in @ SV74 @ SV658 @ SV1165 ) )
= $true )
| ( ( ! [SY4748: $i] :
( ~ ( c_in @ SV74 @ SY4748 @ SV1165 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4748 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3877,plain,
! [SV659: $i,SV75: $i] :
( ( ( class_Lattices_Olattice @ SV75 )
= $false )
| ( ( ! [SY3846: $i,SY3847: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3846 @ SY3847 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3846 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY3847 @ SV75 ) @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3878,plain,
! [SV76: $i,SV1524: $i] :
( ( ( ! [SY5192: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1524 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1524 @ SY5192 @ SV76 ) @ SV76 )
= SV1524 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3879,plain,
! [SV1166: $i,SV660: $i,SV77: $i] :
( ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY4749: $i] :
( ( ( c_Relation_Orel__comp @ SY4749 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4749 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3880,plain,
! [SV1167: $i,SV661: $i,SV78: $i] :
( ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY4750: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY4750 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4750 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3881,plain,
! [SV662: $i,SV1525: $i,SV79: $i] :
( ( ( ! [SY5193: $i] :
( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SV1525 @ SY5193 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1525 @ SY5193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3882,plain,
! [SV1526: $i,SV80: $i,SV663: $i] :
( ( ( ~ ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SV1526 @ tc_bool ) )
| ~ ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SV1526 @ tc_bool ) ) )
= $true )
| ( ( SV80 = SV663 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3883,plain,
! [SV1527: $i,SV81: $i,SV664: $i] :
( ( ( ~ ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SV1527 @ tc_bool ) )
| ~ ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SV1527 @ tc_bool ) ) )
= $true )
| ( ( SV81 = SV664 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3884,plain,
! [SV82: $i,SV1528: $i] :
( ( ( ! [SY5194: $i] :
( ( SV1528 = SY5194 )
| ~ ( c_lessequals @ SY5194 @ SV1528 @ SV82 )
| ~ ( c_lessequals @ SV1528 @ SY5194 @ SV82 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3885,plain,
! [SV83: $i,SV1529: $i] :
( ( ( ! [SY5195: $i] :
( ( SV1529 = SY5195 )
| ~ ( c_lessequals @ SY5195 @ SV1529 @ SV83 )
| ~ ( c_lessequals @ SV1529 @ SY5195 @ SV83 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3886,plain,
! [SV84: $i,SV1530: $i] :
( ( ( ! [SY5196: $i] :
( ( SV1530 = SY5196 )
| ~ ( c_lessequals @ SV1530 @ SY5196 @ SV84 )
| ~ ( c_lessequals @ SY5196 @ SV1530 @ SV84 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3887,plain,
! [SV85: $i,SV1531: $i] :
( ( ( ! [SY5197: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1531 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1531 @ SY5197 @ SV85 ) @ SV85 )
= SV1531 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3888,plain,
! [SV86: $i,SV1532: $i] :
( ( ( ! [SY5198: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1532 @ SY5198 @ SV86 )
= SV1532 )
| ~ ( c_lessequals @ SY5198 @ SV1532 @ SV86 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3889,plain,
! [SV87: $i,SV1533: $i] :
( ( ( ! [SY5199: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1533 @ SY5199 @ SV87 )
!= SY5199 )
| ( c_lessequals @ SV1533 @ SY5199 @ SV87 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3890,plain,
! [SV88: $i,SV1534: $i] :
( ( ( ! [SY5200: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1534 @ SY5200 @ SV88 )
= SY5200 )
| ~ ( c_lessequals @ SV1534 @ SY5200 @ SV88 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3891,plain,
! [SV1168: $i,SV665: $i,SV89: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) )
= SV665 )
= $true )
| ( ( ~ ( c_lessequals @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3370]) ).
thf(3892,plain,
! [SV1169: $i,SV666: $i,SV90: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV90 @ SV666 @ ( tc_fun @ SV1169 @ tc_bool ) )
= SV90 )
= $true )
| ( ( ~ ( c_lessequals @ SV666 @ SV90 @ ( tc_fun @ SV1169 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3371]) ).
thf(3893,plain,
! [SV1170: $i,SV667: $i,SV91: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) )
!= SV667 )
= $true )
| ( ( c_lessequals @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3894,plain,
! [SV1535: $i,SV1171: $i,SV668: $i,SV92: $i] :
( ( ! [SY5201: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SY5201 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV668 @ SY5201 @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3895,plain,
! [SV669: $i,SV93: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV93 )
= $false )
| ( ( ! [SY3862: $i,SY3863: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ SY3862 @ SV93 ) @ SY3863 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3862 @ SY3863 @ SV93 ) @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3374]) ).
thf(3896,plain,
! [SV670: $i,SV94: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV94 )
= $false )
| ( ( ! [SY3864: $i,SY3865: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ SY3865 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ SY3865 @ SV94 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3375]) ).
thf(3897,plain,
! [SV671: $i,SV95: $i] :
( ( ( class_Lattices_Olattice @ SV95 )
= $false )
| ( ( ! [SY3866: $i,SY3867: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ SY3867 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3866 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SY3867 @ SV95 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3898,plain,
! [SV672: $i,SV96: $i] :
( ( ( class_Lattices_Olattice @ SV96 )
= $false )
| ( ( ! [SY3868: $i,SY3869: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SY3868 @ SV96 ) @ SY3869 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3868 @ SY3869 @ SV96 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3899,plain,
! [SV1172: $i,SV673: $i,SV97: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) )
= SV97 )
= $true )
| ( ( ~ ( c_lessequals @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3900,plain,
! [SV1173: $i,SV674: $i,SV98: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV674 @ ( tc_fun @ SV1173 @ tc_bool ) )
= SV674 )
= $true )
| ( ( ~ ( c_lessequals @ SV674 @ SV98 @ ( tc_fun @ SV1173 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3901,plain,
! [SV99: $i,SV1536: $i] :
( ( ( ! [SY5202: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1536 @ SY5202 @ SV99 )
= SV1536 )
| ~ ( c_lessequals @ SV1536 @ SY5202 @ SV99 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3902,plain,
! [SV100: $i,SV1537: $i] :
( ( ( ! [SY5203: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1537 @ SY5203 @ SV100 )
!= SV1537 )
| ( c_lessequals @ SV1537 @ SY5203 @ SV100 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3903,plain,
! [SV101: $i,SV1538: $i] :
( ( ( ! [SY5204: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1538 @ SY5204 @ SV101 )
= SY5204 )
| ~ ( c_lessequals @ SY5204 @ SV1538 @ SV101 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3904,plain,
! [SV1539: $i,SV1174: $i,SV675: $i,SV102: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
| ~ ( c_lessequals @ SV675 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
| ~ ( c_lessequals @ SV102 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3905,plain,
! [SV1540: $i,SV1177: $i,SV678: $i,SV105: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
| ~ ( c_lessequals @ SV105 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3906,plain,
! [SV679: $i,SV106: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false )
| ( ( ! [SY3878: $i,SY3879: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SY3878 @ SV106 ) @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SY3878 @ SY3879 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SY3879 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3907,plain,
! [SV107: $i,SV1541: $i] :
( ( ( ! [SY5205: $i] : ( c_lessequals @ SV1541 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1541 @ SY5205 @ SV107 ) @ SV107 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3908,plain,
! [SV108: $i,SV1542: $i] :
( ( ( ! [SY5206: $i] : ( c_lessequals @ SV1542 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5206 @ SV1542 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3909,plain,
! [SV680: $i,SV109: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false )
| ( ( ! [SY3880: $i,SY3881: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SY3880 @ SV109 ) @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SY3880 @ SY3881 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SY3881 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3910,plain,
! [SV681: $i,SV110: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false )
| ( ( ! [SY3882: $i,SY3883: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SY3882 @ SV110 ) @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SY3882 @ SY3883 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SY3883 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3911,plain,
! [SV111: $i,SV1543: $i] :
( ( ( ! [SY5207: $i] : ( c_lessequals @ SV1543 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5207 @ SV1543 @ SV111 ) @ SV111 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3912,plain,
! [SV112: $i,SV1544: $i] :
( ( ( ! [SY5208: $i] : ( c_lessequals @ SV1544 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1544 @ SY5208 @ SV112 ) @ SV112 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(3913,plain,
! [SV114: $i,SV1545: $i] :
( ( ( ! [SY5209: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1545 @ SY5209 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5209 @ SV1545 @ SV114 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3914,plain,
! [SV115: $i,SV1546: $i] :
( ( ( ! [SY5210: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1546 @ SY5210 @ SV115 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5210 @ SV1546 @ SV115 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(3915,plain,
! [SV683: $i,SV116: $i] :
( ( ( c_Wellfounded_Owf @ SV116 @ SV683 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV116 @ SV683 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3916,plain,
! [SV684: $i,SV117: $i] :
( ( ( class_Lattices_Olattice @ SV117 )
= $false )
| ( ( ! [SY3885: $i,SY3886: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3885 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY3886 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3885 @ SY3886 @ SV117 ) @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3917,plain,
! [SV1179: $i,SV685: $i,SV118: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1179 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3918,plain,
! [SV1180: $i,SV686: $i,SV119: $i] :
( ( ( ( c_Set_Oinsert @ SV119 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 )
!= ( c_Set_Oinsert @ SV1180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 ) )
= $true )
| ( ( SV119 = SV1180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3919,plain,
! [SV1547: $i,SV1181: $i,SV687: $i,SV120: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV120 @ SV687 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SV1547 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1547 @ SV120 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV687 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ SV1547 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1547 @ SV120 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ ( tc_fun @ SV1181 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3920,plain,
! [SV1548: $i,SV1182: $i,SV688: $i,SV122: $i] :
( ( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV688 @ SV1182 @ SV1182 ) @ SV1548 @ ( tc_prod @ SV1182 @ SV1182 ) ) @ SV1182 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV122 @ ( c_Set_Oinsert @ SV688 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1182 @ tc_bool ) ) @ SV1182 ) @ SV1182 ) @ ( c_Relation_OField @ SV1548 @ SV1182 ) @ ( tc_fun @ SV1182 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3921,plain,
! [SV1183: $i,SV689: $i,SV123: $i] :
( ( ( ( c_Set_Oinsert @ SV123 @ SV689 @ SV1183 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV123 @ SV689 @ SV1183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3922,plain,
! [SV1184: $i,SV690: $i,SV125: $i] :
( ( ( c_in @ SV125 @ SV690 @ SV1184 )
= $true )
| ( ( ! [SY4757: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SY4757 @ SV1184 ) @ SV690 @ ( tc_fun @ SV1184 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3404]) ).
thf(3923,plain,
! [SV1549: $i,SV1185: $i,SV691: $i,SV126: $i] :
( ( ! [SY5211: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV691 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SV1549 @ SV1185 @ SY5211 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV126 @ SV1549 @ SV1185 @ SY5211 ) @ ( c_Product__Type_OSigma @ SV691 @ SV1549 @ SV1185 @ SY5211 ) @ ( tc_fun @ ( tc_prod @ SV1185 @ SY5211 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3924,plain,
! [SV1550: $i,SV1186: $i,SV692: $i,SV127: $i] :
( ( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SV1186 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
| ~ ( c_lessequals @ SV127 @ SV1186 @ ( tc_fun @ SV1550 @ tc_bool ) )
| ( c_in @ SV692 @ SV127 @ SV1550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3925,plain,
! [SV1187: $i,SV693: $i,SV128: $i] :
( ( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SV1187 @ tc_bool ) )
= $true )
| ( ( ! [SY4761: $i] :
( ( c_in @ SY4761 @ SV128 @ SV1187 )
| ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SY4761 @ SV693 @ SV1187 ) @ ( tc_fun @ SV1187 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3407]) ).
thf(3926,plain,
! [SV1551: $i,SV1188: $i,SV694: $i,SV129: $i] :
( ( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SV1188 @ SV1551 ) @ ( tc_fun @ SV1551 @ tc_bool ) )
| ~ ( c_lessequals @ SV129 @ SV1188 @ ( tc_fun @ SV1551 @ tc_bool ) )
| ( c_in @ SV694 @ SV129 @ SV1551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3927,plain,
! [SV1189: $i,SV695: $i,SV130: $i] :
( ( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SV1189 @ tc_bool ) )
= $true )
| ( ( ! [SY4763: $i] :
( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SY4763 @ SV695 @ SV1189 ) @ ( tc_fun @ SV1189 @ tc_bool ) )
| ( c_in @ SY4763 @ SV130 @ SV1189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3928,plain,
! [SV1552: $i,SV1190: $i,SV696: $i,SV131: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ ( c_Set_Oinsert @ SV696 @ SV1190 @ SV1552 ) @ ( tc_fun @ SV1552 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV1190 @ ( tc_fun @ SV1552 @ tc_bool ) ) )
| ( c_in @ SV696 @ SV131 @ SV1552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3929,plain,
! [SV1553: $i,SV1191: $i,SV697: $i,SV132: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV132 @ SV697 @ SV1191 ) @ SV1553 @ ( tc_fun @ SV1191 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV697 @ SV1553 @ ( tc_fun @ SV1191 @ tc_bool ) ) )
| ( c_in @ SV132 @ SV1553 @ SV1191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3930,plain,
! [SV1192: $i,SV698: $i,SV133: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 @ SV698 @ ( tc_fun @ SV1192 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) )
= $true )
| ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3412]) ).
thf(3931,plain,
! [SV1193: $i,SV699: $i,SV134: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ SV699 @ ( tc_fun @ SV1193 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) )
= $true )
| ( ( SV134
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3413]) ).
thf(3932,plain,
! [SV135: $i,SV1554: $i] :
( ( ( ! [SY5212: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1554 @ SY5212 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) )
| ( SV1554
= ( c_Orderings_Obot__class_Obot @ SV135 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(3933,plain,
! [SV136: $i,SV1555: $i] :
( ( ( ! [SY5213: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1555 @ SY5213 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
| ( SY5213
= ( c_Orderings_Obot__class_Obot @ SV136 ) ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3934,plain,
! [SV1556: $i,SV1194: $i,SV700: $i,SV137: $i] :
( ( ! [SY5214: $i,SY5215: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV700 @ ( tc_fun @ ( tc_prod @ SV1194 @ SV1556 ) @ tc_bool ) ) @ SY5214 @ SV1194 @ SV1556 @ SY5215 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SY5214 @ SV1194 @ SV1556 @ SY5215 ) @ ( c_Relation_Orel__comp @ SV700 @ SY5214 @ SV1194 @ SV1556 @ SY5215 ) @ ( tc_fun @ ( tc_prod @ SV1194 @ SY5215 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3935,plain,
! [SV1557: $i,SV1195: $i,SV701: $i,SV138: $i] :
( ( ! [SY5216: $i,SY5217: $i] :
( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV701 @ SV1195 @ ( tc_fun @ ( tc_prod @ SV1557 @ SY5216 ) @ tc_bool ) ) @ SY5217 @ SV1557 @ SY5216 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SV701 @ SY5217 @ SV1557 @ SY5216 ) @ ( c_Relation_Orel__comp @ SV138 @ SV1195 @ SY5217 @ SV1557 @ SY5216 ) @ ( tc_fun @ ( tc_prod @ SY5217 @ SY5216 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3936,plain,
! [SV1197: $i,SV703: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) )
= $true )
| ( ( ! [SY4772: $i] :
~ ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4772 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) ) @ ( tc_fun @ SV1197 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3419]) ).
thf(3937,plain,
! [SV1198: $i,SV704: $i,SV141: $i] :
( ( ( c_lessequals @ SV141 @ SV704 @ ( tc_fun @ SV1198 @ tc_bool ) )
= $true )
| ( ( ! [SY4773: $i] :
~ ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV704 @ SY4773 @ ( tc_fun @ SV1198 @ tc_bool ) ) @ ( tc_fun @ SV1198 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(3938,plain,
! [SV705: $i,SV142: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV142 )
= $false )
| ( ( ! [SY3926: $i] :
( ( c_lessequals @ SV705 @ SY3926 @ SV142 )
| ! [SY3927: $i] :
~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3926 @ SY3927 @ SV142 ) @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3939,plain,
! [SV706: $i,SV143: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false )
| ( ( ! [SY3928: $i] :
( ( c_lessequals @ SV706 @ SY3928 @ SV143 )
| ! [SY3929: $i] :
~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3929 @ SY3928 @ SV143 ) @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3940,plain,
! [SV707: $i,SV144: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false )
| ( ( ! [SY3930: $i,SY3931: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SY3930 @ SV144 ) @ SY3931 @ SV144 )
| ~ ( c_lessequals @ SV707 @ SY3931 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3941,plain,
! [SV708: $i,SV145: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV145 )
= $false )
| ( ( ! [SY3932: $i,SY3933: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SY3932 @ SV145 ) @ SY3933 @ SV145 )
| ~ ( c_lessequals @ SY3932 @ SY3933 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3942,plain,
! [SV709: $i,SV146: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV146 )
= $false )
| ( ( ! [SY3934: $i] :
( ( c_lessequals @ SV709 @ SY3934 @ SV146 )
| ! [SY3935: $i] :
~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3934 @ SY3935 @ SV146 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3943,plain,
! [SV710: $i,SV147: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV147 )
= $false )
| ( ( ! [SY3936: $i] :
( ( c_lessequals @ SV710 @ SY3936 @ SV147 )
| ! [SY3937: $i] :
~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3937 @ SY3936 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3944,plain,
! [SV149: $i,SV1558: $i] :
( ( ( ! [SY5218: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1558 @ SY5218 @ SV149 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5218 @ SV1558 @ SV149 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3945,plain,
! [SV150: $i,SV1559: $i] :
( ( ( ! [SY5219: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1559 @ SY5219 @ SV150 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5219 @ SV1559 @ SV150 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3946,plain,
! [SV1560: $i,SV1200: $i,SV712: $i,SV151: $i] :
( ( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV712 @ ( tc_fun @ ( tc_prod @ SV1200 @ SV1560 ) @ tc_bool ) ) @ SV1200 @ SV1560 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV151 @ SV1200 @ SV1560 ) @ ( c_Relation_ODomain @ SV712 @ SV1200 @ SV1560 ) @ ( tc_fun @ SV1200 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3947,plain,
! [SV1203: $i,SV715: $i,SV154: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV154 @ SV715 ) @ ( c_Wellfounded_Oacc @ SV1203 @ SV715 ) @ ( tc_fun @ SV715 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1203 @ SV154 @ ( tc_fun @ ( tc_prod @ SV715 @ SV715 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3433]) ).
thf(3948,plain,
! [SV156: $i,SV1561: $i] :
( ( ( ! [SY5220: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ SY5220 @ SV156 ) @ SV156 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ SY5220 @ SV156 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3949,plain,
! [SV157: $i,SV1562: $i] :
( ( ( ! [SY5221: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ SY5221 @ SV157 ) @ SV157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ SY5221 @ SV157 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(3950,plain,
! [SV1205: $i,SV717: $i,SV158: $i] :
( ( ( ( c_Relation_ODomain @ SV158 @ SV717 @ SV1205 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV717 @ tc_bool ) ) )
= $true )
| ( ( SV158
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV717 @ SV1205 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(3951,plain,
! [SV1563: $i,SV1206: $i,SV718: $i,SV159: $i] :
( ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV718 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1563 ) @ tc_bool ) ) @ SV1206 @ SV1563 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV159 @ SV1206 @ SV1563 ) @ ( c_Relation_ORange @ SV718 @ SV1206 @ SV1563 ) @ ( tc_fun @ SV1563 @ tc_bool ) ) @ ( tc_fun @ SV1563 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(3952,plain,
! [SV719: $i,SV1564: $i,SV160: $i] :
( ( ( ! [SY5222: $i] :
( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SV1564 @ SY5222 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1564 @ SY5222 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(3953,plain,
! [SV721: $i,SV163: $i,SV1565: $i] :
( ( ( ! [SY5223: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1565 @ SV163 @ ( tc_fun @ SY5223 @ tc_bool ) ) @ SV721 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV721 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3954,plain,
! [SV722: $i,SV1566: $i,SV164: $i] :
( ( ( ! [SY5224: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SV1566 @ ( tc_fun @ SY5224 @ tc_bool ) ) @ SV722 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV164 @ SV722 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(3955,plain,
! [SV1208: $i,SV723: $i,SV165: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1208 @ SV1208 ) @ tc_bool ) ) @ SV1208 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV723 @ SV1208 )
| ~ ( c_Relation_Osym @ SV165 @ SV1208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3443]) ).
thf(3956,plain,
! [SV1567: $i,SV1209: $i,SV724: $i,SV166: $i] :
( ( ! [SY5225: $i,SY5226: $i] :
( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SY5225 @ SY5226 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SY5225 @ SY5226 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SV1567 @ SY5225 @ SY5226 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SV1567 @ SY5225 @ SY5226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(3957,plain,
! [SV168: $i,SV726: $i,SV1568: $i] :
( ( ( ! [SY5227: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1568 @ SY5227 @ SV726 @ SV726 ) @ SV168 @ ( tc_prod @ SV726 @ SV726 ) ) @ SV726 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV168 @ SV726 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3958,plain,
! [SV1210: $i,SV727: $i,SV169: $i] :
( ( ( ~ ( class_HOL_Oord @ SV169 ) )
= $true )
| ( ( ! [SY4779: $i] :
( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SY4779 @ SV1210 ) @ SV169 )
| ! [SY3964: $i] :
~ ( c_lessequals @ SV727 @ SY4779 @ ( tc_fun @ SY3964 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3959,plain,
! [SV1569: $i,SV1211: $i,SV728: $i,SV170: $i] :
( ( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV1569 )
| ~ ( c_in @ SV170 @ SV1211 @ SV1569 )
| ~ ( c_in @ SV170 @ SV728 @ SV1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(3960,plain,
! [SV1570: $i,SV1212: $i,SV729: $i,SV171: $i] :
( ( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
| ~ ( c_in @ SV171 @ SV1212 @ SV1570 )
| ~ ( c_in @ SV171 @ SV729 @ SV1570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(3961,plain,
! [SV1213: $i,SV730: $i,SV172: $i] :
( ( ( c_in @ SV172 @ SV730 @ SV1213 )
= $true )
| ( ( ! [SY4783: $i] :
( ~ ( c_in @ SV172 @ SY4783 @ SV1213 )
| ~ ( c_lessequals @ SY4783 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3962,plain,
! [SV1214: $i,SV731: $i,SV173: $i] :
( ( ( c_in @ SV173 @ SV731 @ SV1214 )
= $true )
| ( ( ! [SY4784: $i] :
( ~ ( c_lessequals @ SY4784 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) )
| ~ ( c_in @ SV173 @ SY4784 @ SV1214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3963,plain,
! [SV1215: $i,SV732: $i,SV174: $i] :
( ( ( c_in @ SV174 @ SV732 @ SV1215 )
= $true )
| ( ( ! [SY4785: $i] :
( ~ ( c_in @ SV174 @ SY4785 @ SV1215 )
| ~ ( c_lessequals @ SY4785 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3451]) ).
thf(3964,plain,
! [SV1216: $i,SV733: $i,SV175: $i] :
( ( ( c_in @ SV175 @ SV733 @ SV1216 )
= $true )
| ( ( ! [SY4786: $i] :
( ~ ( c_in @ SV175 @ SY4786 @ SV1216 )
| ~ ( c_lessequals @ SY4786 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3452]) ).
thf(3965,plain,
! [SV1571: $i,SV1217: $i,SV734: $i,SV176: $i] :
( ( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV734 @ SV1217 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
| ~ ( c_in @ SV176 @ SV734 @ SV1571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3966,plain,
! [SV1572: $i,SV1218: $i,SV735: $i,SV177: $i] :
( ( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SV1218 @ ( tc_fun @ SV1572 @ tc_bool ) ) @ SV1572 )
| ~ ( c_in @ SV177 @ SV1218 @ SV1572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3967,plain,
! [SV179: $i,SV1573: $i,SV737: $i] :
( ( ( ~ ( c_in @ SV737 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1573 @ tc_bool ) ) @ SV1573 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV179 @ SV737 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3968,plain,
! [SV1219: $i,SV740: $i,SV182: $i] :
( ( ( c_in @ SV182 @ SV740 @ SV1219 )
= $true )
| ( ( ! [SY4789: $i] :
( ( c_in @ SV182 @ SY4789 @ SV1219 )
| ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4789 @ SV740 @ ( tc_fun @ SV1219 @ tc_bool ) ) @ SV1219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3969,plain,
! [SV1220: $i,SV741: $i,SV183: $i] :
( ( ( c_in @ SV183 @ SV741 @ SV1220 )
= $true )
| ( ( ! [SY4790: $i] :
~ ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4790 @ SV741 @ ( tc_fun @ SV1220 @ tc_bool ) ) @ SV1220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3460]) ).
thf(3970,plain,
! [SV1221: $i,SV742: $i,SV184: $i] :
( ( ( c_in @ SV184 @ SV742 @ SV1221 )
= $true )
| ( ( ! [SY4791: $i] :
~ ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV742 @ SY4791 @ ( tc_fun @ SV1221 @ tc_bool ) ) @ SV1221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(3971,plain,
! [SV743: $i,SV185: $i] :
( ( ( hBOOL @ ( hAPP @ SV185 @ SV743 ) )
= $false )
| ( ( ! [SY3988: $i] :
~ ( c_in @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3988 @ tc_bool ) ) @ SY3988 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3972,plain,
! [SV1574: $i,SV1222: $i,SV744: $i,SV186: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SV1574 @ ( tc_fun @ ( tc_prod @ SV186 @ SV744 ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SV1222 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV186 @ SV744 ) @ SV1574 ) @ ( tc_fun @ ( tc_prod @ SV744 @ SV186 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3973,plain,
! [SV187: $i,SV745: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV745 @ SV187 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV187 @ SV187 ) @ SV745 ) @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3974,plain,
! [SV188: $i,SV746: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ SV746 @ SV746 ) @ SV188 ) @ SV746 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV188 @ SV746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3975,plain,
! [SV1575: $i,SV1223: $i,SV748: $i,SV190: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1223 @ SV1575 @ ( tc_fun @ ( tc_prod @ SV190 @ SV748 ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SV1223 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV190 @ SV748 ) @ SV1575 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV190 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(3976,plain,
! [SV1576: $i,SV1224: $i,SV749: $i,SV191: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
| ~ ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
| ! [SY5228: $i] :
( ~ ( c_in @ SV1576 @ SY5228 @ SV749 )
| ~ ( c_in @ SV191 @ SY5228 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5228 @ SV1224 @ SV749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3977,plain,
! [SV1577: $i,SV1225: $i,SV751: $i,SV194: $i] :
( ( ! [SY5229: $i] :
( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
!= ( c_Set_Oinsert @ SV1577 @ ( c_Set_Oinsert @ SY5229 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
| ( SV194 = SY5229 )
| ( SV194 = SV1577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3978,plain,
! [SV1578: $i,SV1226: $i,SV752: $i,SV195: $i] :
( ( ! [SY5230: $i] :
( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
!= ( c_Set_Oinsert @ SV1578 @ ( c_Set_Oinsert @ SY5230 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) )
| ( SV752 = SV1578 )
| ( SV195 = SV1578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3979,plain,
! [SV1579: $i,SV1227: $i,SV753: $i,SV196: $i] :
( ( ! [SY5231: $i] :
( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
!= ( c_Set_Oinsert @ SV1579 @ ( c_Set_Oinsert @ SY5231 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
| ( SV196 = SY5231 )
| ( SV753 = SY5231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(3980,plain,
! [SV1580: $i,SV1228: $i,SV754: $i,SV197: $i] :
( ( ! [SY5232: $i] :
( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
!= ( c_Set_Oinsert @ SV1580 @ ( c_Set_Oinsert @ SY5232 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
| ( SV754 = SV1580 )
| ( SV754 = SY5232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(3981,plain,
! [SV1229: $i,SV755: $i,SV198: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV198 @ SV755 ) @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV198 @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3472]) ).
thf(3982,plain,
! [SV1230: $i,SV756: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV199 @ SV756 ) @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV199 @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3983,plain,
! [SV757: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) @ ( tc_fun @ SV757 @ tc_bool ) )
= $false )
| ( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3984,plain,
! [SV1231: $i,SV758: $i,SV202: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_bool ) )
= ( c_Set_Oinsert @ SV758 @ SV1231 @ SV202 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3985,plain,
! [SV1581: $i,SV1232: $i,SV759: $i,SV204: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SV759 @ SV1232 ) @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV759 @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) ) @ SV1232 ) )
| ~ ( c_in @ SV204 @ SV1581 @ SV1232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(3986,plain,
! [SV1582: $i,SV1233: $i,SV760: $i,SV205: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SV760 @ SV1233 @ SV1582 ) @ ( tc_fun @ SV1582 @ tc_bool ) )
= ( c_Set_Oinsert @ SV760 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV1233 @ ( tc_fun @ SV1582 @ tc_bool ) ) @ SV1582 ) )
| ~ ( c_in @ SV760 @ SV205 @ SV1582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(3987,plain,
! [SV1583: $i,SV1234: $i,SV762: $i,SV207: $i] :
( ( ! [SY5233: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SY5233 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV762 @ SY5233 @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3988,plain,
! [SV208: $i,SV1584: $i] :
( ( ( ! [SY5234: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1584 @ SY5234 @ SV208 ) @ SV1584 @ SV208 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3989,plain,
! [SV209: $i,SV1585: $i] :
( ( ( ! [SY5235: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1585 @ SY5235 @ SV209 ) @ SY5235 @ SV209 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(3990,plain,
! [SV763: $i,SV210: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false )
| ( ( ! [SY4018: $i,SY4019: $i] :
( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4018 @ SY4019 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4019 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY4018 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3991,plain,
! [SV764: $i,SV211: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false )
| ( ( ! [SY4020: $i,SY4021: $i] :
( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4020 @ SY4021 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4021 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY4020 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3992,plain,
! [SV765: $i,SV212: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false )
| ( ( ! [SY4022: $i,SY4023: $i] :
( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4022 @ SY4023 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4023 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY4022 @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3993,plain,
! [SV213: $i,SV1586: $i] :
( ( ( ! [SY5236: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1586 @ SY5236 @ SV213 ) @ SY5236 @ SV213 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3994,plain,
! [SV214: $i,SV1587: $i] :
( ( ( ! [SY5237: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1587 @ SY5237 @ SV214 ) @ SV1587 @ SV214 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(3995,plain,
! [SV1588: $i,SV1237: $i,SV768: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ ( tc_fun @ SV1588 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SV1588 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(3996,plain,
! [SV1589: $i,SV1238: $i,SV769: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ ( tc_fun @ SV1589 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SV1589 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3997,plain,
! [SV1590: $i,SV1239: $i,SV770: $i,SV219: $i] :
( ( ! [SY5238: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV770 @ ( tc_fun @ SV1239 @ tc_bool ) ) @ ( c_COMBK @ SV1590 @ ( tc_fun @ SY5238 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY5238 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV219 @ ( c_COMBK @ SV1590 @ ( tc_fun @ SY5238 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY5238 ) @ ( c_Product__Type_OSigma @ SV770 @ ( c_COMBK @ SV1590 @ ( tc_fun @ SY5238 @ tc_bool ) @ SV1239 ) @ SV1239 @ SY5238 ) @ ( tc_fun @ ( tc_prod @ SV1239 @ SY5238 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3998,plain,
! [SV771: $i,SV220: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV220 )
= $false )
| ( ( ! [SY4033: $i,SY4034: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV771 @ SY4033 @ SV220 ) @ SY4034 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV771 @ SY4034 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4033 @ SY4034 @ SV220 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3999,plain,
! [SV772: $i,SV221: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV221 )
= $false )
| ( ( ! [SY4035: $i,SY4036: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4035 @ SY4036 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4035 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY4036 @ SV221 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(4000,plain,
! [SV1591: $i,SV1240: $i,SV773: $i,SV222: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV773 @ SV1240 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ ( tc_fun @ SV1591 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV773 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV1240 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ ( tc_fun @ SV1591 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4001,plain,
! [SV1592: $i,SV1241: $i,SV774: $i,SV223: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV223 @ SV774 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ SV1592 @ ( tc_fun @ SV1241 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV223 @ SV1592 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV774 @ SV1592 @ ( tc_fun @ SV1241 @ tc_bool ) ) @ ( tc_fun @ SV1241 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4002,plain,
! [SV1593: $i,SV1242: $i,SV775: $i,SV224: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_lessequals @ SV775 @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_in @ SV224 @ SV1593 @ SV1242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4003,plain,
! [SV225: $i,SV1594: $i] :
( ( ( ! [SY5239: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ SY5239 @ SV225 ) @ SV225 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ SY5239 @ SV225 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4004,plain,
! [SV226: $i,SV1595: $i] :
( ( ( ! [SY5240: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ SY5240 @ SV226 ) @ SV226 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ SY5240 @ SV226 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4005,plain,
! [SV1244: $i,SV777: $i,SV228: $i] :
( ( ( c_lessequals @ ( c_Relation_OField @ SV228 @ SV777 ) @ ( c_Relation_OField @ SV1244 @ SV777 ) @ ( tc_fun @ SV777 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV228 @ SV1244 @ ( tc_fun @ ( tc_prod @ SV777 @ SV777 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(4006,plain,
! [SV1596: $i,SV1245: $i,SV778: $i,SV229: $i] :
( ( ! [SY5241: $i] :
( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SV1245 @ ( tc_fun @ SV1596 @ tc_bool ) ) @ SV1596 @ SY5241 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SV1596 @ SY5241 ) @ ( c_Relation_OImage @ SV229 @ SV1245 @ SV1596 @ SY5241 ) @ ( tc_fun @ SY5241 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SV1596 @ SY5241 ) @ SV229 ) @ SY5241 @ SV1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4007,plain,
! [SV1597: $i,SV1246: $i,SV779: $i,SV230: $i] :
( ( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV779 @ ( tc_fun @ ( tc_prod @ SV1246 @ SV1597 ) @ tc_bool ) ) @ SV1246 @ SV1597 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV230 @ SV1246 @ SV1597 ) @ ( c_Relation_ORange @ SV779 @ SV1246 @ SV1597 ) @ ( tc_fun @ SV1597 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4008,plain,
! [SV1247: $i,SV780: $i,SV231: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV231 @ SV780 @ ( tc_fun @ ( tc_prod @ SV1247 @ SV1247 ) @ tc_bool ) ) @ SV1247 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV231 @ SV1247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(4009,plain,
! [SV1248: $i,SV781: $i,SV232: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV232 @ SV781 @ ( tc_fun @ ( tc_prod @ SV1248 @ SV1248 ) @ tc_bool ) ) @ SV1248 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV781 @ SV1248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(4010,plain,
! [SV233: $i,SV1598: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1598 @ SV1598 @ SV233 )
= SV1598 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV233 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4011,plain,
! [SV784: $i,SV236: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV236 )
= $false )
| ( ( ! [SY4052: $i] :
( ( c_lessequals @ SV784 @ SY4052 @ SV236 )
| ! [SY4053: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4053 @ SV784 @ SV236 ) @ SY4052 @ SV236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(4012,plain,
! [SV785: $i,SV237: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV237 )
= $false )
| ( ( ! [SY4054: $i] :
( ( c_lessequals @ SV785 @ SY4054 @ SV237 )
| ! [SY4055: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SY4055 @ SV237 ) @ SY4054 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(4013,plain,
! [SV786: $i,SV238: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV238 )
= $false )
| ( ( ! [SY4056: $i,SY4057: $i] :
( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4056 @ SY4057 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SV786 @ SY4057 @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(4014,plain,
! [SV787: $i,SV239: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV239 )
= $false )
| ( ( ! [SY4058: $i] :
( ! [SY4059: $i] : ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4058 @ SY4059 @ SV239 ) @ SV239 )
| ~ ( c_lessequals @ SV787 @ SY4058 @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(4015,plain,
! [SV788: $i,SV240: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV240 )
= $false )
| ( ( ! [SY4060: $i] :
( ( c_lessequals @ SV788 @ SY4060 @ SV240 )
| ! [SY4061: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4061 @ SV788 @ SV240 ) @ SY4060 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3509]) ).
thf(4016,plain,
! [SV789: $i,SV241: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV241 )
= $false )
| ( ( ! [SY4062: $i] :
( ( c_lessequals @ SV789 @ SY4062 @ SV241 )
| ! [SY4063: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SY4063 @ SV241 ) @ SY4062 @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(4017,plain,
! [SV1249: $i,SV790: $i,SV242: $i] :
( ( ( c_lessequals @ SV242 @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) )
= $true )
| ( ( ! [SY4818: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SY4818 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(4018,plain,
! [SV1250: $i,SV791: $i,SV243: $i] :
( ( ( c_lessequals @ SV243 @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $true )
| ( ( ! [SY4819: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4819 @ SV243 @ ( tc_fun @ SV1250 @ tc_bool ) ) @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(4019,plain,
! [SV792: $i,SV244: $i] :
( ( ( class_Orderings_Oorder @ SV244 )
= $false )
| ( ( ! [SY4068: $i] :
( ( c_lessequals @ SV792 @ SY4068 @ SV244 )
| ! [SY4069: $i] :
( ~ ( c_lessequals @ SV792 @ SY4069 @ SV244 )
| ~ ( c_lessequals @ SY4069 @ SY4068 @ SV244 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(4020,plain,
! [SV793: $i,SV245: $i] :
( ( ( class_Orderings_Opreorder @ SV245 )
= $false )
| ( ( ! [SY4070: $i] :
( ( c_lessequals @ SV793 @ SY4070 @ SV245 )
| ! [SY4071: $i] :
( ~ ( c_lessequals @ SY4071 @ SY4070 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SY4071 @ SV245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(4021,plain,
! [SV1251: $i,SV796: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $true )
| ( ( ! [SY4820: $i] :
( ~ ( c_lessequals @ SY4820 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY4820 @ ( tc_fun @ SV1251 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(4022,plain,
! [SV249: $i,SV797: $i,SV1599: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1599 @ SV797 ) )
| ! [SY5242: $i] :
~ ( c_lessequals @ SV1599 @ SV249 @ ( tc_fun @ SY5242 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4023,plain,
! [SV798: $i,SV1600: $i,SV250: $i] :
( ( ( ~ ( c_lessequals @ SV250 @ SV1600 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1600 @ SV798 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4024,plain,
! [SV251: $i,SV1601: $i] :
( ( ( c_lessequals @ SV1601 @ SV1601 @ SV251 )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4025,plain,
! [SV252: $i,SV1602: $i] :
( ( ( c_lessequals @ SV1602 @ SV1602 @ SV252 )
= $true )
| ( ( class_Orderings_Opreorder @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4026,plain,
! [SV253: $i,SV799: $i,SV1603: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1603 @ SV799 )
| ~ ( c_lessequals @ SV253 @ SV1603 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV253 @ SV799 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4027,plain,
! [SV800: $i,SV254: $i,SV1604: $i] :
( ( ( ! [SY5243: $i] :
~ ( c_lessequals @ SV1604 @ SV254 @ ( tc_fun @ SY5243 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1604 @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4028,plain,
! [SV801: $i,SV1605: $i,SV255: $i] :
( ( ( ~ ( c_lessequals @ SV255 @ SV1605 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1605 @ SV801 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4029,plain,
! [SV1252: $i,SV802: $i,SV256: $i] :
( ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
= $true )
| ( ( ! [SY4821: $i] :
( ~ ( c_Relation_Osingle__valued @ SY4821 @ SV802 @ SV1252 )
| ~ ( c_lessequals @ SV256 @ SY4821 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3523]) ).
thf(4030,plain,
! [SV1606: $i,SV1253: $i,SV803: $i,SV257: $i] :
( ( ! [SY5244: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SY5244 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV803 @ SY5244 @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4031,plain,
! [SV1607: $i,SV1254: $i,SV806: $i,SV260: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SV806 @ SV1254 ) @ ( c_Relation_ODomain @ SV1607 @ SV806 @ SV1254 ) @ ( tc_fun @ SV806 @ tc_bool ) )
| ~ ( c_lessequals @ SV260 @ SV1607 @ ( tc_fun @ ( tc_prod @ SV806 @ SV1254 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4032,plain,
! [SV1255: $i,SV807: $i,SV261: $i] :
( ( ( SV261
= ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) )
= $true )
| ( ( ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) @ ( tc_fun @ SV1255 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(4033,plain,
! [SV1608: $i,SV1257: $i,SV809: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1608 ) )
| ~ ( hBOOL @ ( hAPP @ SV809 @ SV1608 ) )
| ~ ( hBOOL @ ( hAPP @ SV263 @ SV1608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4034,plain,
! [SV1609: $i,SV1258: $i,SV810: $i,SV264: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SV810 @ SV1258 ) @ ( c_Set_Oinsert @ SV264 @ SV1609 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_lessequals @ SV810 @ SV1609 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4035,plain,
! [SV1259: $i,SV811: $i,SV267: $i] :
( ( ( ( c_Relation_ORange @ SV267 @ SV811 @ SV1259 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) )
= $true )
| ( ( SV267
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV811 @ SV1259 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(4036,plain,
! [SV1610: $i,SV1260: $i,SV812: $i,SV268: $i] :
( ( ! [SY5245: $i,SY5246: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SY5245 @ SY5246 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
| ~ ( c_lessequals @ SV812 @ SY5246 @ ( tc_fun @ SV1260 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SY5245 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4037,plain,
! [SV1261: $i,SV813: $i,SV269: $i] :
( ( ( c_lessequals @ SV269 @ ( c_Product__Type_OSigma @ SV813 @ ( c_COMBK @ SV813 @ ( tc_fun @ SV1261 @ tc_bool ) @ SV1261 ) @ SV1261 @ SV1261 ) @ ( tc_fun @ ( tc_prod @ SV1261 @ SV1261 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV813 @ SV269 @ SV1261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(4038,plain,
! [SV270: $i,SV1611: $i] :
( ( ( ! [SY5247: $i] :
( ( c_lessequals @ SV1611 @ SY5247 @ SV270 )
| ( c_lessequals @ SY5247 @ SV1611 @ SV270 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4039,plain,
! [SV1262: $i,SV814: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true )
| ( ( ! [SY4830: $i,SY4831: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SY4830 @ SY4831 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SY4830 @ SY4831 ) @ SY4831 @ SY4831 ) @ SY4830 @ ( tc_prod @ SY4831 @ SY4831 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SY4831 @ SY4831 ) @ ( c_Transitive__Closure_Ortrancl @ SY4830 @ SY4831 ) @ ( tc_prod @ SY4831 @ SY4831 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(4040,plain,
! [SV1263: $i,SV815: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true )
| ( ( ! [SY4832: $i,SY4833: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SY4832 @ SY4833 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SY4832 @ SY4833 ) @ SY4833 @ SY4833 ) @ SY4832 @ ( tc_prod @ SY4833 @ SY4833 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
| ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SY4833 @ SY4833 ) @ ( c_Transitive__Closure_Ortrancl @ SY4832 @ SY4833 ) @ ( tc_prod @ SY4833 @ SY4833 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(4041,plain,
! [SV1264: $i,SV816: $i,SV273: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(4042,plain,
! [SV1612: $i,SV1265: $i,SV817: $i,SV274: $i] :
( ( ( SV274 = SV817 )
| ! [SY5248: $i,SY5249: $i] :
( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SY5248 ) @ SY5249 @ ( tc_prod @ SV1612 @ SY5248 ) )
| ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SY5248 ) @ SY5249 @ ( tc_prod @ SV1612 @ SY5248 ) )
| ~ ( c_Relation_Osingle__valued @ SY5249 @ SV1612 @ SY5248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4043,plain,
! [SV1613: $i,SV1266: $i,SV818: $i,SV275: $i] :
( ( ! [SY5250: $i] :
( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
!= ( c_Product__Type_OSigma @ SY5250 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
| ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 )
| ( SV275 = SY5250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4044,plain,
! [SV1614: $i,SV1267: $i,SV819: $i,SV276: $i] :
( ( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV819 @ SV1267 @ ( tc_fun @ ( tc_prod @ SV1614 @ SV1614 ) @ tc_bool ) ) @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
| ~ ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SV819 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4045,plain,
! [SV1615: $i,SV1268: $i,SV820: $i,SV277: $i] :
( ( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1268 @ ( tc_fun @ ( tc_prod @ SV1615 @ SV1615 ) @ tc_bool ) ) @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ~ ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SV1268 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4046,plain,
! [SV1269: $i,SV821: $i,SV278: $i] :
( ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $true )
| ( ( ! [SY4842: $i] :
( ~ ( c_lessequals @ SY4842 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) )
| ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SY4842 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(4047,plain,
! [SV1270: $i,SV822: $i,SV279: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV279 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( c_Relation_Orel__comp @ SV1270 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV279 @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(4048,plain,
! [SV1271: $i,SV823: $i,SV280: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV280 @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV280 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( c_Relation_Orel__comp @ SV823 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(4049,plain,
! [SV824: $i,SV281: $i] :
( ( ( ( c_Relation_Orel__comp @ SV281 @ SV281 @ SV824 @ SV824 @ SV824 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV281 @ SV824 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(4050,plain,
! [SV828: $i,SV286: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV286 @ SV828 )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV828 ) @ SV828 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(4051,plain,
! [SV832: $i,SV290: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV290 @ ( c_Relation_OId @ SV832 ) @ ( tc_fun @ ( tc_prod @ SV832 @ SV832 ) @ tc_bool ) ) @ SV832 )
= $false )
| ( ( c_Relation_Oantisym @ SV290 @ SV832 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(4052,plain,
! [SV833: $i,SV291: $i] :
( ( ( c_Relation_Oantisym @ SV291 @ SV833 )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV291 @ ( c_Relation_OId @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) @ SV833 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(4053,plain,
! [SV1616: $i,SV1273: $i,SV834: $i,SV292: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
| ! [SY5252: $i] :
( ~ ( c_in @ SV1616 @ SY5252 @ SV834 )
| ~ ( c_in @ SV292 @ SY5252 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5252 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4054,plain,
! [SV1274: $i,SV835: $i,SV293: $i] :
( ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true )
| ( ( ! [SY4845: $i] :
( ( SV293 = SY4845 )
| ! [SY4846: $i] :
( ~ ( c_lessequals @ SY4846 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SY4845 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY4846 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(4055,plain,
! [SV1617: $i,SV1275: $i,SV836: $i,SV294: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
| ! [SY4848: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4848 @ SV294 @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4056,plain,
! [SV837: $i,SV295: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SV837 ) @ ( c_Transitive__Closure_Ortrancl @ SV837 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY4133: $i] :
~ ( c_in @ ( c_Pair @ SY4133 @ SY4133 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SV837 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(4057,plain,
! [SV1618: $i,SV1276: $i,SV838: $i,SV296: $i] :
( ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
!= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
| ~ ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4058,plain,
! [SV1619: $i,SV1278: $i,SV839: $i,SV299: $i] :
( ( ! [SY5254: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SV1278 @ SV1619 @ SY5254 ) @ SV299 @ SV1619 )
| ~ ( c_in @ SV1278 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SV1619 @ SY5254 ) @ ( tc_prod @ SV1619 @ SY5254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4059,plain,
! [SV1620: $i,SV1279: $i,SV840: $i,SV300: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SV1279 @ SV1620 ) @ SV840 @ SV1620 @ SV1620 ) @ SV1279 @ ( tc_prod @ SV1620 @ SV1620 ) )
| ( SV300 = SV840 )
| ~ ( c_in @ ( c_Pair @ SV300 @ SV840 @ SV1620 @ SV1620 ) @ ( c_Transitive__Closure_Ortrancl @ SV1279 @ SV1620 ) @ ( tc_prod @ SV1620 @ SV1620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4060,plain,
! [SV1621: $i,SV1280: $i,SV841: $i,SV301: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SV1280 @ SV1621 ) @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) )
| ( SV841 = SV1280 )
| ~ ( c_in @ ( c_Pair @ SV841 @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4061,plain,
! [SV1622: $i,SV1281: $i,SV842: $i,SV302: $i] :
( ( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SV1281 @ SV1622 ) @ SV1622 @ SV1622 ) @ SV842 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ( SV302 = SV1281 )
| ~ ( c_in @ ( c_Pair @ SV302 @ SV1281 @ SV1622 @ SV1622 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SV1622 ) @ ( tc_prod @ SV1622 @ SV1622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4062,plain,
! [SV1282: $i,SV843: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true )
| ( ( ! [SY4855: $i,SY4856: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SY4855 @ SY4856 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SY4856 @ SY4856 ) @ ( c_Transitive__Closure_Ortrancl @ SY4855 @ SY4856 ) @ ( tc_prod @ SY4856 @ SY4856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(4063,plain,
! [SV1283: $i,SV844: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true )
| ( ( ! [SY4857: $i,SY4858: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SY4857 @ SY4858 ) @ SV1283 @ SY4858 @ SY4858 ) @ ( c_Transitive__Closure_Ortrancl @ SY4857 @ SY4858 ) @ ( tc_prod @ SY4858 @ SY4858 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SY4858 @ SY4858 ) @ ( c_Transitive__Closure_Ortrancl @ SY4857 @ SY4858 ) @ ( tc_prod @ SY4858 @ SY4858 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(4064,plain,
! [SV1284: $i,SV845: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true )
| ( ( ! [SY4859: $i,SY4860: $i] :
( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SY4859 @ SY4860 ) @ SY4860 @ SY4860 ) @ ( c_Transitive__Closure_Ortrancl @ SY4859 @ SY4860 ) @ ( tc_prod @ SY4860 @ SY4860 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
| ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SY4860 @ SY4860 ) @ ( c_Transitive__Closure_Ortrancl @ SY4859 @ SY4860 ) @ ( tc_prod @ SY4860 @ SY4860 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3562]) ).
thf(4065,plain,
! [SV1285: $i,SV846: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true )
| ( ( ! [SY4861: $i,SY4862: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SY4861 @ SY4862 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SY4862 @ SY4862 ) @ ( c_Transitive__Closure_Ortrancl @ SY4861 @ SY4862 ) @ ( tc_prod @ SY4862 @ SY4862 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3563]) ).
thf(4066,plain,
! [SV1623: $i,SV1286: $i,SV847: $i,SV307: $i] :
( ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ! [SY5255: $i] :
( ~ ( c_in @ ( c_Pair @ SY5255 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_in @ ( c_Pair @ SY5255 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4067,plain,
! [SV1287: $i,SV848: $i,SV308: $i] :
( ( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SV848 @ SV1287 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV848 = SV308 )
| ~ ( c_in @ ( c_Pair @ SV308 @ SV848 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(4068,plain,
! [SV1288: $i,SV849: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true )
| ( ( ! [SY4865: $i,SY4866: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SY4865 @ SY4866 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
| ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SY4866 @ SY4866 ) @ ( c_Transitive__Closure_Ortrancl @ SY4865 @ SY4866 ) @ ( tc_prod @ SY4866 @ SY4866 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(4069,plain,
! [SV1289: $i,SV850: $i,SV310: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SV850 @ SV1289 ) @ SV850 @ t_a @ t_a ) @ SV1289 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV850 = SV310 )
| ~ ( c_in @ ( c_Pair @ SV310 @ SV850 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1289 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(4070,plain,
! [SV1290: $i,SV851: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true )
| ( ( ! [SY4867: $i,SY4868: $i] :
( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SY4867 @ SY4868 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SY4868 @ SY4868 ) @ ( c_Transitive__Closure_Ortrancl @ SY4867 @ SY4868 ) @ ( tc_prod @ SY4868 @ SY4868 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(4071,plain,
! [SV1624: $i,SV1291: $i,SV852: $i,SV312: $i] :
( ( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SV1291 @ SV1624 ) @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) )
| ( SV312 = SV852 )
| ~ ( c_in @ ( c_Pair @ SV312 @ SV852 @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4072,plain,
! [SV1292: $i,SV853: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
| ! [SY4870: $i,SY4871: $i] :
( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SY4870 @ SY4871 ) @ SY4871 @ SY4871 ) @ SY4870 @ ( tc_prod @ SY4871 @ SY4871 ) )
| ~ ( c_Wellfounded_Owf @ SY4870 @ SY4871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(4073,plain,
! [SV1293: $i,SV854: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
| ! [SY4872: $i,SY4873: $i] :
( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SY4872 @ SY4873 ) @ SY4873 @ SY4873 ) @ SY4872 @ ( tc_prod @ SY4873 @ SY4873 ) )
| ~ ( c_Wellfounded_Owf @ SY4872 @ SY4873 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(4074,plain,
! [SV1294: $i,SV855: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
| ! [SY4874: $i,SY4875: $i] :
( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SY4874 @ SY4875 ) @ SY4875 @ SY4875 ) @ SY4874 @ ( tc_prod @ SY4875 @ SY4875 ) )
| ~ ( c_Wellfounded_Owf @ SY4874 @ SY4875 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(4075,plain,
! [SV1295: $i,SV856: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
| ! [SY4876: $i,SY4877: $i] :
( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SY4876 @ SY4877 ) @ SY4877 @ SY4877 ) @ SY4876 @ ( tc_prod @ SY4877 @ SY4877 ) )
| ~ ( c_Wellfounded_Owf @ SY4876 @ SY4877 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(4076,plain,
! [SV1296: $i,SV857: $i,SV317: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV317 @ SV317 @ SV857 @ SV857 ) @ SV1296 @ ( tc_prod @ SV857 @ SV857 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ SV857 @ SV857 ) @ ( c_Transitive__Closure_Otrancl @ SV1296 @ SV857 ) @ ( tc_prod @ SV857 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3574]) ).
thf(4077,plain,
! [SV1625: $i,SV1297: $i,SV858: $i,SV318: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SV1297 @ SV1625 ) @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) )
| ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ SV318 @ ( tc_prod @ SV1625 @ SV1625 ) )
| ~ ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4078,plain,
! [SV1298: $i,SV859: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SV859 @ SV1298 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ SV1298 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3576]) ).
thf(4079,plain,
! [SV1299: $i,SV860: $i,SV320: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV320 @ SV320 @ SV860 @ SV860 ) @ ( c_Transitive__Closure_Otrancl @ SV1299 @ SV860 ) @ ( tc_prod @ SV860 @ SV860 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1299 @ SV860 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3577]) ).
thf(4080,plain,
! [SV1626: $i,SV1300: $i,SV861: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SV1300 @ SV1626 ) @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
| ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV1626 ) @ ( tc_prod @ SV1626 @ SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4081,plain,
! [SV1627: $i,SV1301: $i,SV862: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SV1301 @ SV1627 ) @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
| ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ SV1301 @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4082,plain,
! [SV1628: $i,SV1302: $i,SV863: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SV1302 @ SV1628 ) @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
| ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
| ~ ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SV1628 ) @ ( tc_prod @ SV1628 @ SV1628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(4083,plain,
! [SV1303: $i,SV864: $i,SV324: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SV864 @ SV1303 ) @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(4084,plain,
! [SV1629: $i,SV1304: $i,SV865: $i,SV325: $i] :
( ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
| ! [SY5256: $i] :
( ~ ( c_in @ SV865 @ SY5256 @ SV1304 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY5256 @ SV1629 @ SV1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4085,plain,
! [SV1630: $i,SV1305: $i,SV866: $i,SV326: $i] :
( ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
| ! [SY5257: $i] :
~ ( c_in @ SY5257 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
| ! [SY5258: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5258 @ SV1630 @ SV1305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(4086,plain,
! [SV1631: $i,SV1306: $i,SV867: $i,SV327: $i] :
( ( ! [SY5259: $i,SY5260: $i,SY5261: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SY5259 @ SY5260 @ SY5261 ) @ SV867 @ SY5261 @ SY5260 ) @ SV1631 @ ( tc_prod @ SY5261 @ SY5260 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SY5259 @ SY5260 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SY5259 @ SY5261 @ SY5260 ) @ ( tc_prod @ SY5259 @ SY5260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4087,plain,
! [SV1632: $i,SV1307: $i,SV868: $i,SV328: $i] :
( ( ! [SY5262: $i,SY5263: $i,SY5264: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SY5262 @ SY5263 @ SY5264 ) @ SY5262 @ SY5264 ) @ SV1307 @ ( tc_prod @ SY5262 @ SY5264 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SY5262 @ SY5263 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SY5262 @ SY5264 @ SY5263 ) @ ( tc_prod @ SY5262 @ SY5263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4088,plain,
! [SV1633: $i,SV1308: $i,SV869: $i,SV329: $i] :
( ( ! [SY5265: $i] :
( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SV869 @ SV1308 @ SV1633 @ SY5265 ) @ ( tc_fun @ SV1633 @ SY5265 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV869 @ SV1308 @ SV329 @ SV1633 @ SY5265 ) @ SV869 @ SV1633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(4089,plain,
! [SV1634: $i,SV1309: $i,SV870: $i,SV330: $i] :
( ( ! [SY5266: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV870 @ SV1309 @ SV1634 @ SY5266 ) @ ( tc_fun @ SV1634 @ SY5266 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV870 @ SV1309 @ SV330 @ SV1634 @ SY5266 ) @ SV870 @ SV1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4090,plain,
! [SV1635: $i,SV1310: $i,SV871: $i,SV331: $i] :
( ( ! [SY5267: $i] :
( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SV1310 @ SV1635 @ SY5267 ) @ ( tc_fun @ SV1635 @ SY5267 ) )
| ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SY5267 ) ) @ ( hAPP @ SV1310 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SY5267 ) ) @ SY5267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(4091,plain,
! [SV1636: $i,SV1311: $i,SV872: $i,SV332: $i] :
( ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
| ! [SY5268: $i,SY5269: $i] :
( ~ ( c_in @ SV872 @ SY5268 @ SY5269 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY5268 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SY5269 ) @ SY5269 @ SV1636 ) @ ( tc_fun @ SY5269 @ SV1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4092,plain,
! [SV1637: $i,SV1312: $i,SV873: $i,SV333: $i] :
( ( ! [SY5270: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SV1312 @ SV1637 @ SY5270 ) @ ( tc_fun @ SV1637 @ SY5270 ) )
| ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SY5270 ) ) @ ( hAPP @ SV1312 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SY5270 ) ) @ SY5270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4093,plain,
! [SV874: $i,SV334: $i] :
( ( ( c_in @ SV334 @ ( c_Relation_OId @ SV874 ) @ ( tc_prod @ SV874 @ SV874 ) )
= $false )
| ( ( SV334
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV334 @ SV874 ) @ SV874 @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(4094,plain,
! [SV875: $i,SV335: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV335 @ SV875 ) @ ( c_Wellfounded_Oacc @ SV335 @ SV875 ) @ SV875 )
= $false )
| ( ( c_Wellfounded_Owf @ SV335 @ SV875 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(4095,plain,
! [SV876: $i,SV336: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV336 @ SV876 ) @ ( c_Wellfounded_Oacc @ SV336 @ SV876 ) @ SV876 )
= $false )
| ( ( c_Wellfounded_Owf @ SV336 @ SV876 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(4096,plain,
! [SV1313: $i,SV877: $i,SV337: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV337 @ SV877 @ SV1313 ) @ SV337 @ SV1313 )
= $true )
| ( ( ~ ( c_in @ SV877 @ ( c_Relation_OId__on @ SV337 @ SV1313 ) @ ( tc_prod @ SV1313 @ SV1313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4097,plain,
! [SV1314: $i,SV878: $i,SV338: $i] :
( ( ( SV338
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ SV1314 @ SV1314 ) )
= $true )
| ( ( ~ ( c_in @ SV338 @ ( c_Relation_OId__on @ SV878 @ SV1314 ) @ ( tc_prod @ SV1314 @ SV1314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4098,plain,
! [SV1638: $i,SV1315: $i,SV879: $i,SV339: $i] :
( ( ! [SY5271: $i,SY5272: $i] :
( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SV1315 @ SV1638 @ SY5271 )
= ( c_Recdef_Ocut @ SY5272 @ SV879 @ SV1315 @ SV1638 @ SY5271 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SY5272 @ SV879 @ SV1315 @ SV1638 @ SY5271 ) @ SV1315 @ SV1638 @ SV1638 ) @ SV879 @ ( tc_prod @ SV1638 @ SV1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4099,plain,
! [SV1316: $i,SV343: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4100,plain,
! [SV1317: $i,SV344: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4101,plain,
! [SV345: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(4102,plain,
! [SV884: $i,SV348: $i,SV1639: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1639 @ SV348 @ SV884 ) )
= $true )
| ( ( c_lessequals @ SV348 @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV884 @ SV884 ) @ SV348 ) @ SV348 @ SV884 @ SV884 @ SV884 ) @ ( tc_fun @ ( tc_prod @ SV884 @ SV884 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4103,plain,
! [SV1640: $i,SV1318: $i,SV885: $i,SV349: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV349 @ SV885 @ SV1318 @ SV1318 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1318 ) @ ( tc_prod @ SV1318 @ SV1318 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SV1318 @ SV1318 ) @ SV1640 @ ( tc_prod @ SV1318 @ SV1318 ) ) @ SV1318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4104,plain,
! [SV1641: $i,SV1319: $i,SV886: $i,SV350: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SV1319 @ SV1319 ) @ SV1641 @ ( tc_prod @ SV1319 @ SV1319 ) ) @ SV1319 )
| ( c_in @ ( c_Pair @ SV886 @ SV350 @ SV1319 @ SV1319 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1319 ) @ ( tc_prod @ SV1319 @ SV1319 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1641 @ SV1319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4105,plain,
! [SV1320: $i,SV887: $i,SV351: $i] :
( ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
= $true )
| ( ( ! [SY4911: $i] :
( ~ ( c_in @ SV351 @ SY4911 @ SV1320 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4911 @ SV887 @ SV1320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(4106,plain,
! [SV1642: $i,SV1321: $i,SV888: $i,SV352: $i] :
( ( ! [SY5273: $i] :
( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SV1321 @ SV1642 ) @ SY5273 @ ( tc_prod @ SV1321 @ SV1642 ) )
| ~ ( c_in @ SV888 @ ( c_Relation_OImage @ SY5273 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 @ SV1642 ) @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4107,plain,
! [SV1643: $i,SV1322: $i,SV889: $i,SV353: $i] :
( ( ! [SY5274: $i] :
( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SV1322 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1643 @ tc_bool ) ) @ SV1643 ) @ SV1643 @ SY5274 ) @ SY5274 )
| ~ ( c_in @ ( c_Pair @ SV1322 @ SV353 @ SV1643 @ SY5274 ) @ SV889 @ ( tc_prod @ SV1643 @ SY5274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4108,plain,
! [SV1644: $i,SV1323: $i,SV890: $i,SV354: $i] :
( ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
| ~ ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
| ! [SY4917: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4917 @ SV354 @ SV1323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4109,plain,
! [SV1645: $i,SV1324: $i,SV891: $i,SV355: $i] :
( ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
| ~ ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
| ! [SY4919: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4919 @ SV355 @ SV1324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4110,plain,
! [SV1646: $i,SV1325: $i,SV892: $i,SV356: $i] :
( ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
!= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
| ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
| ! [SY5277: $i] :
( ~ ( c_in @ SV1646 @ SY5277 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5277 @ SV356 @ SV1325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4111,plain,
! [SV1647: $i,SV1326: $i,SV893: $i,SV357: $i] :
( ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
!= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
| ! [SY5278: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5278 @ SV357 @ SV1326 )
| ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SY5278 @ SV1326 )
| ~ ( c_in @ SV893 @ SY5278 @ SV1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4112,plain,
! [SV1648: $i,SV1327: $i,SV894: $i,SV358: $i] :
( ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
| ~ ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
| ! [SY5279: $i] :
( ~ ( c_in @ SV1648 @ SY5279 @ SV1327 )
| ~ ( c_in @ SV894 @ SY5279 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5279 @ SV358 @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4113,plain,
! [SV1649: $i,SV1328: $i,SV895: $i,SV359: $i] :
( ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
!= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
| ! [SY5280: $i] :
( ~ ( c_in @ SV1649 @ SY5280 @ SV1328 )
| ~ ( c_in @ SV895 @ SY5280 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5280 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4114,plain,
! [SV1650: $i,SV1329: $i,SV896: $i,SV360: $i] :
( ( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV896 @ SV360 @ SV1329 @ SV1650 ) @ SV1650 @ SV1650 ) @ SV896 @ ( tc_prod @ SV1650 @ SV1650 ) )
| ~ ( c_in @ ( c_Pair @ SV360 @ SV1329 @ SV1650 @ SV1650 ) @ ( c_Transitive__Closure_Otrancl @ SV896 @ SV1650 ) @ ( tc_prod @ SV1650 @ SV1650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4115,plain,
! [SV1651: $i,SV1330: $i,SV897: $i,SV361: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SV897 @ SV1330 @ SV1651 ) @ SV1330 @ SV1651 @ SV1651 ) @ SV361 @ ( tc_prod @ SV1651 @ SV1651 ) )
| ~ ( c_in @ ( c_Pair @ SV897 @ SV1330 @ SV1651 @ SV1651 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SV1651 ) @ ( tc_prod @ SV1651 @ SV1651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4116,plain,
! [SV898: $i,SV1652: $i,SV362: $i] :
( ( ( ! [SY5281: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SV1652 @ SY5281 ) @ ( c_Wellfounded_Oacc @ SV1652 @ SY5281 ) @ SY5281 )
| ~ ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SV1652 @ SY5281 ) @ SY5281 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4117,plain,
! [SV1331: $i,SV899: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV899 @ SV363 @ SV1331 ) @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(4118,plain,
! [SV900: $i,SV1653: $i,SV364: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SV1653 ) ) )
| ~ ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SV1653 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4119,plain,
! [SV901: $i,SV1654: $i,SV365: $i] :
( ( ( ! [SY5282: $i] :
( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SV1654 @ SY5282 ) ) )
| ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SV1654 @ SY5282 ) @ SY5282 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4120,plain,
! [SV1332: $i,SV902: $i,SV366: $i] :
( ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV366 @ SV902 @ SV1332 ) @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 ) )
= $true )
| ( ( c_in @ SV902 @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(4121,plain,
! [SV903: $i,SV1655: $i,SV367: $i] :
( ( ( ! [SY5283: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SV1655 @ SY5283 ) @ ( c_Wellfounded_Oacc @ SV1655 @ SY5283 ) @ SY5283 )
| ~ ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SV1655 @ SY5283 ) @ SY5283 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4122,plain,
! [SV904: $i,SV1656: $i,SV368: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SV1656 ) ) )
| ~ ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SV1656 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4123,plain,
! [SV905: $i,SV1657: $i,SV369: $i] :
( ( ( ! [SY5284: $i] :
( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SV1657 @ SY5284 ) ) )
| ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SV1657 @ SY5284 ) @ SY5284 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4124,plain,
! [SV1658: $i,SV1333: $i,SV906: $i,SV370: $i] :
( ( ! [SY5285: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SV1333 @ SV1658 @ SY5285 ) @ SV370 @ SV1658 )
| ~ ( c_in @ SV906 @ ( c_Relation_OImage @ SV1333 @ SV370 @ SV1658 @ SY5285 ) @ SY5285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4125,plain,
! [SV1659: $i,SV1334: $i,SV907: $i,SV371: $i] :
( ( ! [SY5286: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SV1334 @ SV1659 @ SY5286 ) @ SV371 @ SV1659 )
| ~ ( c_in @ SV907 @ ( c_Relation_OImage @ SV1334 @ SV371 @ SV1659 @ SY5286 ) @ SY5286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4126,plain,
! [SV372: $i,SV908: $i,SV1660: $i] :
( ( ( ! [SY5287: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1660 @ SY5287 @ SV908 @ SV908 ) @ SV372 @ ( tc_prod @ SV908 @ SV908 ) ) @ SV908 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV372 @ SV908 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4127,plain,
! [SV1335: $i,SV909: $i,SV373: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
= $true )
| ( ( ! [SY4934: $i] :
~ ( c_in @ SY4934 @ SV373 @ SV1335 )
| ~ ( c_Wellfounded_Owf @ SV909 @ SV1335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(4128,plain,
! [SV1336: $i,SV910: $i,SV374: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
= $true )
| ( ( ! [SY4935: $i] :
~ ( c_in @ SY4935 @ SV374 @ SV1336 )
| ~ ( c_Wellfounded_Owf @ SV910 @ SV1336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(4129,plain,
! [SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ! [SY5288: $i,SY5289: $i,SY5290: $i,SY5291: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SY5288 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SY5288 @ SY5289 @ SY5289 ) @ SY5290 @ ( tc_prod @ SY5289 @ SY5289 ) )
| ! [SY5292: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SY5291 @ SY5291 ) @ SY5292 @ ( tc_prod @ SY5291 @ SY5291 ) )
| ! [SY3122: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5292 @ SY5290 @ SV375 @ SY5291 @ SY5289 @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4130,plain,
! [SV912: $i,SV376: $i] :
( ( ( ( hAPP @ SV376 @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) )
= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ SV376 @ SV912 ) @ SV912 ) )
= $false )
| ( ( c_Arrow__Order__Mirabelle_Odictator @ SV376 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(4131,plain,
! [SV1662: $i,SV1339: $i,SV914: $i,SV378: $i] :
( ( ! [SY5294: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV378 @ SV914 @ SV1339 @ SV1662 ) @ SY5294 @ ( tc_prod @ SV1339 @ SV1662 ) ) @ SV1339 @ SV1662 )
= ( c_Set_Oinsert @ SV378 @ ( c_Relation_ODomain @ SY5294 @ SV1339 @ SV1662 ) @ SV1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4132,plain,
! [SV379: $i,SV915: $i,SV1663: $i] :
( ( ( ( SV1663 = SV915 )
| ! [SY5295: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1663 @ SV379 @ SY5295 ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4133,plain,
! [SV1664: $i,SV1341: $i,SV917: $i,SV381: $i] :
( ( ( c_Set_Oinsert @ SV381 @ ( c_Set_Oinsert @ SV917 @ SV1341 @ SV1664 ) @ SV1664 )
= ( c_Set_Oinsert @ SV917 @ ( c_Set_Oinsert @ SV381 @ SV1341 @ SV1664 ) @ SV1664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4134,plain,
! [SV1665: $i,SV1342: $i,SV918: $i,SV382: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SV918 @ SV1342 ) @ SV1665 ) )
| ~ ( hBOOL @ ( hAPP @ SV918 @ SV1665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(4135,plain,
! [SV1666: $i,SV1343: $i,SV919: $i,SV383: $i] :
( ( ! [SY5296: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV383 @ SV919 @ SV1343 @ SV1666 ) @ SY5296 @ ( tc_prod @ SV1343 @ SV1666 ) ) @ SV1343 @ SV1666 )
= ( c_Set_Oinsert @ SV919 @ ( c_Relation_ORange @ SY5296 @ SV1343 @ SV1666 ) @ SV1666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(4136,plain,
! [SV1667: $i,SV1344: $i,SV920: $i,SV384: $i] :
( ( ( c_in @ SV384 @ ( c_Set_Oinsert @ SV920 @ SV1344 @ SV1667 ) @ SV1667 )
| ~ ( c_in @ SV384 @ SV1344 @ SV1667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4137,plain,
! [SV1668: $i,SV1345: $i,SV921: $i,SV385: $i] :
( ( ( c_in @ SV385 @ ( c_Set_Oinsert @ SV921 @ SV1345 @ SV1668 ) @ SV1668 )
| ~ ( c_in @ SV385 @ SV1345 @ SV1668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4138,plain,
! [SV1346: $i,SV922: $i,SV386: $i] :
( ( ( c_in @ SV386 @ SV922 @ SV1346 )
= $true )
| ( ( ! [SY4951: $i] :
( ( SV386 = SY4951 )
| ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SY4951 @ SV922 @ SV1346 ) @ SV1346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(4139,plain,
! [SV1669: $i,SV1350: $i,SV926: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
!= ( c_Set_Oinsert @ SV390 @ SV1669 @ SV1350 ) )
| ( c_in @ SV390 @ SV1669 @ SV1350 )
| ( SV926 = SV1669 )
| ( c_in @ SV390 @ SV926 @ SV1350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4140,plain,
! [SV1351: $i,SV927: $i,SV391: $i] :
( ( ( ( c_Set_Oinsert @ SV391 @ SV927 @ SV1351 )
= SV927 )
= $true )
| ( ( ~ ( c_in @ SV391 @ SV927 @ SV1351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(4141,plain,
! [SV1670: $i,SV1352: $i,SV928: $i,SV392: $i] :
( ( ! [SY5297: $i,SY5298: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SY5297 )
| ! [SY5299: $i] :
( ~ ( c_in @ SV1352 @ SY5298 @ SY5299 )
| ! [SY5300: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5300 @ SV392 @ SV928 @ SY5299 @ SV1670 @ SY5297 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5298 @ SY5300 @ SY5299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4142,plain,
! [SV930: $i,SV396: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV396 @ SV930 ) @ SV930 @ SV930 ) @ SV396 @ ( tc_prod @ SV930 @ SV930 ) )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV396 @ SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3647]) ).
thf(4143,plain,
! [SV1353: $i,SV931: $i,SV398: $i] :
( ( ( ~ ( c_in @ SV398 @ SV931 @ SV1353 ) )
= $true )
| ( ( ! [SY4958: $i] :
( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SY4958 @ SV1353 ) @ SV1353 @ SV1353 ) @ SY4958 @ ( tc_prod @ SV1353 @ SV1353 ) )
| ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SY4958 @ SV1353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4144,plain,
! [SV1354: $i,SV932: $i,SV399: $i] :
( ( ( ~ ( c_in @ SV399 @ SV932 @ SV1354 ) )
= $true )
| ( ( ! [SY4960: $i] :
( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SY4960 @ SV1354 ) @ SV1354 @ SV1354 ) @ SY4960 @ ( tc_prod @ SV1354 @ SV1354 ) )
| ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SY4960 @ SV1354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4145,plain,
! [SV1671: $i,SV1355: $i,SV933: $i,SV400: $i] :
( ( ! [SY5301: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SV1355 @ SV1671 @ SY5301 ) @ SV933 @ SV1671 @ SY5301 ) @ SV1355 @ ( tc_prod @ SV1671 @ SY5301 ) )
| ~ ( c_in @ SV933 @ ( c_Relation_OImage @ SV1355 @ SV400 @ SV1671 @ SY5301 ) @ SY5301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(4146,plain,
! [SV1672: $i,SV1356: $i,SV934: $i,SV401: $i] :
( ( ! [SY5302: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SV1356 @ SV1672 @ SY5302 ) @ SV934 @ SV1672 @ SY5302 ) @ SV1356 @ ( tc_prod @ SV1672 @ SY5302 ) )
| ~ ( c_in @ SV934 @ ( c_Relation_OImage @ SV1356 @ SV401 @ SV1672 @ SY5302 ) @ SY5302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(4147,plain,
! [SV1673: $i,SV1357: $i,SV935: $i,SV402: $i] :
( ( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SV935 @ SV1357 @ SV1673 ) @ SV1357 @ SV1673 ) @ SV935 @ ( tc_prod @ SV1357 @ SV1673 ) )
| ~ ( c_in @ SV402 @ ( c_Relation_ODomain @ SV935 @ SV1357 @ SV1673 ) @ SV1357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4148,plain,
! [SV1674: $i,SV1358: $i,SV936: $i,SV403: $i] :
( ( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SV936 @ SV1358 @ SV1674 ) @ SV1358 @ SV1674 ) @ SV936 @ ( tc_prod @ SV1358 @ SV1674 ) )
| ~ ( c_in @ SV403 @ ( c_Relation_ODomain @ SV936 @ SV1358 @ SV1674 ) @ SV1358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4149,plain,
! [SV937: $i,SV404: $i,SV1675: $i] :
( ( ( ! [SY5303: $i] :
( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SY5303 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SY5303 ) @ t_a @ t_a ) @ SY5303 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SY5303 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4150,plain,
! [SV938: $i,SV405: $i,SV1676: $i] :
( ( ( ! [SY5304: $i] :
( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SY5304 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SY5304 ) @ t_a @ t_a ) @ SY5304 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SY5304 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4151,plain,
! [SV1359: $i,SV939: $i,SV406: $i] :
( ( ( c_in @ SV406 @ ( c_Wellfounded_Oacc @ SV939 @ SV1359 ) @ SV1359 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV939 @ SV406 @ SV1359 ) @ SV406 @ SV1359 @ SV1359 ) @ SV939 @ ( tc_prod @ SV1359 @ SV1359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(4152,plain,
! [SV1360: $i,SV940: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
| ! [SY4968: $i,SY4969: $i] :
( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SY4968 @ SY4969 ) @ SY4969 @ SY4969 ) @ SY4968 @ ( tc_prod @ SY4969 @ SY4969 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SY4968 @ SY4969 ) @ SY4969 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(4153,plain,
! [SV941: $i,SV1677: $i,SV408: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
| ! [SY5305: $i] :
( ~ ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SY5305 ) @ t_a @ t_a ) @ SY5305 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SY5305 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4154,plain,
! [SV942: $i,SV1678: $i,SV409: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
| ! [SY5306: $i] :
( ~ ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SY5306 ) @ t_a @ t_a ) @ SY5306 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SY5306 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4155,plain,
! [SV1361: $i,SV943: $i,SV410: $i] :
( ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
| ! [SY4970: $i,SY4971: $i] :
( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SY4970 @ SY4971 ) @ SY4971 @ SY4971 ) @ SY4970 @ ( tc_prod @ SY4971 @ SY4971 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SY4970 @ SY4971 ) @ SY4971 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(4156,plain,
! [SV1362: $i,SV944: $i,SV411: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV411 @ SV944 @ SV1362 ) @ SV944 @ SV1362 @ SV1362 ) @ SV411 @ ( tc_prod @ SV1362 @ SV1362 ) )
= $true )
| ( ( c_in @ SV944 @ ( c_Wellfounded_Oacc @ SV411 @ SV1362 ) @ SV1362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(4157,plain,
! [SV1679: $i,SV1363: $i,SV945: $i,SV412: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SV1363 @ SV1363 ) @ SV1679 @ ( tc_prod @ SV1363 @ SV1363 ) ) @ SV1363 )
| ( c_in @ ( c_Pair @ SV945 @ SV412 @ SV1363 @ SV1363 ) @ ( c_Transitive__Closure_Ortrancl @ SV1679 @ SV1363 ) @ ( tc_prod @ SV1363 @ SV1363 ) )
| ~ ( c_Wellfounded_Owf @ SV1679 @ SV1363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4158,plain,
! [SV1680: $i,SV1364: $i,SV946: $i,SV413: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV413 @ SV946 @ SV1364 @ SV1364 ) @ ( c_Transitive__Closure_Ortrancl @ SV1680 @ SV1364 ) @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SV1364 @ SV1364 ) @ SV1680 @ ( tc_prod @ SV1364 @ SV1364 ) ) @ SV1364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(4159,plain,
! [SV1681: $i,SV1365: $i,SV947: $i,SV414: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SV947 @ SV1365 @ SV1681 ) @ SV414 @ SV1681 @ SV1365 ) @ SV947 @ ( tc_prod @ SV1681 @ SV1365 ) )
| ~ ( c_in @ SV414 @ ( c_Relation_ORange @ SV947 @ SV1681 @ SV1365 ) @ SV1365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4160,plain,
! [SV1682: $i,SV1366: $i,SV948: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SV948 @ SV1366 @ SV1682 ) @ SV415 @ SV1682 @ SV1366 ) @ SV948 @ ( tc_prod @ SV1682 @ SV1366 ) )
| ~ ( c_in @ SV415 @ ( c_Relation_ORange @ SV948 @ SV1682 @ SV1366 ) @ SV1366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(4161,plain,
! [SV1683: $i,SV1367: $i,SV949: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SV949 @ SV1367 @ SV1683 ) @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) )
| ~ ( c_in @ ( c_Pair @ SV949 @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(4162,plain,
! [SV1684: $i,SV1368: $i,SV950: $i,SV417: $i] :
( ( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV950 @ SV417 @ SV1368 @ SV1684 ) @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Ortrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) )
| ~ ( c_in @ ( c_Pair @ SV417 @ SV1368 @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Otrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4163,plain,
! [SV1685: $i,SV1369: $i,SV951: $i,SV418: $i] :
( ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
| ! [SY5307: $i] :
( ~ ( c_in @ ( c_Pair @ SY5307 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SY5307 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(4164,plain,
! [SV1686: $i,SV1370: $i,SV952: $i,SV419: $i] :
( ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ! [SY5308: $i] :
( ~ ( c_in @ ( c_Pair @ SY5308 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SY5308 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(4165,plain,
! [SV1687: $i,SV1371: $i,SV953: $i,SV420: $i] :
( ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
| ! [SY5309: $i] :
( ~ ( c_in @ ( c_Pair @ SY5309 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SY5309 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4166,plain,
! [SV1688: $i,SV1372: $i,SV954: $i,SV421: $i] :
( ( ! [SY5310: $i,SY5311: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SV1688 @ SY5310 ) @ SY5311 )
= ( hAPP @ SV421 @ SY5311 ) )
| ~ ( c_in @ ( c_Pair @ SY5311 @ SV1372 @ SV1688 @ SV1688 ) @ SV954 @ ( tc_prod @ SV1688 @ SV1688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4167,plain,
! [SV1689: $i,SV1373: $i,SV955: $i,SV422: $i] :
( ( ! [SY5312: $i,SY5313: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SV1689 @ SY5312 ) @ SY5313 )
= ( hAPP @ SV422 @ SY5313 ) )
| ~ ( c_in @ ( c_Pair @ SY5313 @ SV1373 @ SV1689 @ SV1689 ) @ SV955 @ ( tc_prod @ SV1689 @ SV1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4168,plain,
! [SV1690: $i,SV956: $i,SV423: $i] :
( ( ( ! [SY5314: $i] :
( ~ ( c_in @ ( c_Pair @ SV423 @ SV956 @ SV1690 @ SV1690 ) @ ( c_Transitive__Closure_Ortrancl @ SY5314 @ SV1690 ) @ ( tc_prod @ SV1690 @ SV1690 ) )
| ( c_in @ SV423 @ ( c_Relation_ODomain @ SY5314 @ SV1690 @ SV1690 ) @ SV1690 ) ) )
= $true )
| ( ( SV423 = SV956 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4169,plain,
! [SV1374: $i,SV957: $i,SV424: $i] :
( ( ( c_in @ SV424 @ ( c_Relation_ODomain @ SV957 @ SV1374 @ SV1374 ) @ SV1374 )
= $true )
| ( ( c_in @ ( c_Pair @ SV424 @ SV424 @ SV1374 @ SV1374 ) @ ( c_Transitive__Closure_Ortrancl @ SV957 @ SV1374 ) @ ( tc_prod @ SV1374 @ SV1374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3674]) ).
thf(4170,plain,
! [SV1375: $i,SV958: $i,SV425: $i] :
( ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $true )
| ( ( ! [SY4990: $i] :
( ~ ( c_in @ ( c_Pair @ SV425 @ SY4990 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) )
| ~ ( c_in @ SY4990 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(4171,plain,
! [SV1376: $i,SV959: $i,SV426: $i] :
( ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $true )
| ( ( ! [SY4991: $i] :
( ~ ( c_in @ SY4991 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4991 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(4172,plain,
! [SV427: $i,SV960: $i] :
( ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV960 @ SV960 ) @ SV427 ) @ SV960 )
= $false )
| ( ( c_Relation_Osym @ SV427 @ SV960 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(4173,plain,
! [SV428: $i,SV961: $i] :
( ( ( c_Relation_Osym @ SV961 @ SV428 )
= $false )
| ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ SV428 @ SV428 ) @ SV961 ) @ SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(4174,plain,
! [SV1377: $i,SV962: $i,SV429: $i] :
( ( ( c_Relation_Orefl__on @ SV429 @ SV962 @ SV1377 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV429 @ ( hAPP @ ( c_Relation_Oconverse @ SV1377 @ SV1377 ) @ SV962 ) @ SV1377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(4175,plain,
! [SV1378: $i,SV963: $i,SV430: $i] :
( ( ( c_Relation_Orefl__on @ SV430 @ ( hAPP @ ( c_Relation_Oconverse @ SV963 @ SV963 ) @ SV1378 ) @ SV963 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV430 @ SV1378 @ SV963 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(4176,plain,
! [SV431: $i,SV964: $i] :
( ( ( c_Relation_Osym @ SV964 @ SV431 )
= $false )
| ( ( ( hAPP @ ( c_Relation_Oconverse @ SV431 @ SV431 ) @ SV964 )
= SV964 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(4177,plain,
! [SV965: $i,SV432: $i] :
( ( ( ( hAPP @ ( c_Relation_Oconverse @ SV432 @ SV432 ) @ SV965 )
= SV965 )
= $false )
| ( ( c_Relation_Osym @ SV965 @ SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(4178,plain,
! [SV1691: $i,SV1379: $i,SV966: $i,SV433: $i] :
( ( ! [SY5315: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SV966 ) @ ( c_Relation_Orel__comp @ SV1379 @ SV1691 @ SV433 @ SY5315 @ SV966 ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SY5315 @ SV966 ) @ SV1691 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SY5315 ) @ SV1379 ) @ SV966 @ SY5315 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4179,plain,
! [SV1692: $i,SV1380: $i,SV967: $i,SV435: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV435 @ SV435 ) @ ( c_Relation_Oinv__image @ SV967 @ SV1380 @ SV1692 @ SV435 ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ SV1692 @ SV1692 ) @ SV967 ) @ SV1380 @ SV1692 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(4180,plain,
! [SV438: $i,SV970: $i] :
( ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV970 @ SV970 ) @ SV438 ) @ SV970 )
= $false )
| ( ( c_Relation_Oantisym @ SV438 @ SV970 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(4181,plain,
! [SV439: $i,SV971: $i] :
( ( ( c_Relation_Oantisym @ SV971 @ SV439 )
= $false )
| ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ SV439 @ SV439 ) @ SV971 ) @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(4182,plain,
! [SV1381: $i,SV973: $i,SV441: $i] :
( ( ( c_Relation_Ototal__on @ SV441 @ SV973 @ SV1381 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV441 @ ( hAPP @ ( c_Relation_Oconverse @ SV1381 @ SV1381 ) @ SV973 ) @ SV1381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(4183,plain,
! [SV1382: $i,SV974: $i,SV442: $i] :
( ( ( c_Relation_Ototal__on @ SV442 @ ( hAPP @ ( c_Relation_Oconverse @ SV974 @ SV974 ) @ SV1382 ) @ SV974 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV442 @ SV1382 @ SV974 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(4184,plain,
! [SV1383: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ SV443 @ ( c_Transitive__Closure_Ortrancl @ SV975 @ SV1383 ) @ ( tc_prod @ SV1383 @ SV1383 ) )
= $true )
| ( ( ~ ( c_in @ SV443 @ SV975 @ ( tc_prod @ SV1383 @ SV1383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(4185,plain,
! [SV1384: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ SV444 @ ( c_Transitive__Closure_Otrancl @ SV976 @ SV1384 ) @ ( tc_prod @ SV1384 @ SV1384 ) )
= $true )
| ( ( ~ ( c_in @ SV444 @ SV976 @ ( tc_prod @ SV1384 @ SV1384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(4186,plain,
! [SV1693: $i,SV1385: $i,SV977: $i,SV445: $i] :
( ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ! [SY5316: $i] :
( ~ ( c_in @ ( c_Pair @ SY5316 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SY5316 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4187,plain,
! [SV1694: $i,SV1386: $i,SV978: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ! [SY5317: $i] :
( ~ ( c_in @ ( c_Pair @ SY5317 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY5317 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4188,plain,
! [SV1695: $i,SV1387: $i,SV979: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Ortrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ( SV447 = SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4189,plain,
! [SV1696: $i,SV1388: $i,SV980: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Otrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
| ( SV448 = SV980 )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Ortrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(4190,plain,
! [SV1697: $i,SV1389: $i,SV981: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Otrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
| ( SV449 = SV981 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Ortrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(4191,plain,
! [SV1698: $i,SV1390: $i,SV982: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Ortrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Otrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4192,plain,
! [SV1699: $i,SV1391: $i,SV983: $i,SV451: $i] :
( ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ! [SY5318: $i] :
( ~ ( c_in @ ( c_Pair @ SY5318 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SY5318 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4193,plain,
! [SV1700: $i,SV1392: $i,SV984: $i,SV452: $i] :
( ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ! [SY5319: $i] :
( ~ ( c_in @ ( c_Pair @ SY5319 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SY5319 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4194,plain,
! [SV1393: $i,SV985: $i,SV453: $i] :
( ( ( c_in @ SV453 @ ( c_Wellfounded_Oacc @ SV985 @ SV1393 ) @ SV1393 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV985 @ SV1393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(4195,plain,
! [SV986: $i,SV454: $i] :
( ( ( c_Relation_Osym @ SV454 @ SV986 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV454 @ SV986 ) @ SV986 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(4196,plain,
! [SV991: $i,SV460: $i] :
( ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ SV991 ) @ SV460 )
= $false )
| ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ SV460 @ SV460 ) @ ( c_Transitive__Closure_Otrancl @ SV991 @ SV460 ) ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(4197,plain,
! [SV992: $i,SV461: $i] :
( ( ( c_Relation_Osym @ SV461 @ SV992 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV461 @ SV992 ) @ SV992 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(4198,plain,
! [SV993: $i,SV462: $i] :
( ( ( c_Wellfounded_Owf @ SV462 @ SV993 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV462 @ SV462 @ SV993 @ SV993 @ SV993 ) @ SV993 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(4199,plain,
! [SV994: $i,SV463: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV463 @ SV463 @ SV994 @ SV994 @ SV994 ) @ SV994 )
= $false )
| ( ( c_Wellfounded_Owf @ SV463 @ SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(4200,plain,
! [SV1396: $i,SV1000: $i,SV469: $i] :
( ( ( ! [SY5007: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SV1000 @ SV1396 @ SY5007 ) @ SY5007 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV469 @ SV1396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(4201,plain,
! [SV1397: $i,SV1002: $i,SV471: $i] :
( ( ( ! [SY5008: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SV1002 @ SV1397 @ SY5008 ) @ SY5008 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV471 @ SV1397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3708]) ).
thf(4202,plain,
! [SV1004: $i,SV473: $i] :
( ( ( c_Wellfounded_Owf @ SV473 @ SV1004 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV473 @ SV1004 ) @ SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(4203,plain,
! [SV1701: $i,SV1398: $i,SV1005: $i,SV474: $i] :
( ( ! [SY5320: $i,SY5321: $i,SY5322: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SV1398 @ SV1701 @ SY5320 ) @ SY5321 @ SV1398 @ SY5320 @ SY5322 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SY5321 @ SV1701 @ SY5320 @ SY5322 ) @ SV1398 @ SV1701 @ SY5322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4204,plain,
! [SV1006: $i,SV475: $i] :
( ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV475 @ SV475 ) @ SV1006 ) @ SV1006 @ SV475 @ SV475 @ SV475 )
= SV1006 )
= $false )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV1006 @ SV475 @ SV475 ) @ SV1006 @ SV475 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(4205,plain,
! [SV479: $i,SV1009: $i,SV1702: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1702 @ SV1009 @ SV479 ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV479 @ SV479 ) @ SV1009 ) @ SV1009 @ SV479 @ SV479 @ SV479 )
= SV1009 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4206,plain,
! [SV1400: $i,SV1011: $i,SV481: $i] :
( ( ( c_Relation_Orefl__on @ SV481 @ SV1011 @ SV1400 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV481 @ SV1011 @ SV1400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(4207,plain,
! [SV1012: $i,SV482: $i,SV1703: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1703 @ SV482 @ SV1012 ) )
= $true )
| ( ( c_Relation_Osym @ SV482 @ SV1012 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4208,plain,
! [SV1704: $i,SV1403: $i,SV1019: $i,SV489: $i] :
( ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ! [SY5323: $i] :
( ~ ( c_in @ ( c_Pair @ SY5323 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SY5323 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4209,plain,
! [SV1705: $i,SV1404: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ ( c_Transitive__Closure_Otrancl @ SV1705 @ SV1404 ) @ ( tc_prod @ SV1404 @ SV1404 ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ SV1705 @ ( tc_prod @ SV1404 @ SV1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3719]) ).
thf(4210,plain,
! [SV1706: $i,SV1405: $i,SV1021: $i,SV491: $i] :
( ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ! [SY5324: $i] :
( ~ ( c_in @ ( c_Pair @ SY5324 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SY5324 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4211,plain,
! [SV1707: $i,SV1408: $i,SV1024: $i,SV494: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_Wellfounded_Owf @ SV1707 @ SV1408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(4212,plain,
! [SV1708: $i,SV495: $i,SV1025: $i] :
( ( ( ! [SY5325: $i] :
( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SY5325 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SY5325 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_Relation_Oantisym @ SY5325 @ SV1708 ) ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4213,plain,
! [SV1709: $i,SV496: $i,SV1026: $i] :
( ( ( ! [SY5326: $i] :
( ~ ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SY5326 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SY5326 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_Relation_Oantisym @ SY5326 @ SV1709 ) ) )
= $true )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(4214,plain,
! [SV1710: $i,SV1409: $i,SV1027: $i,SV497: $i] :
( ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
| ! [SY5327: $i] :
( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SY5327 @ ( tc_prod @ SV1710 @ SV1710 ) )
| ! [SY5328: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5327 @ SV497 @ SV1710 @ SY5328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(4215,plain,
! [SV1711: $i,SV1028: $i,SV498: $i] :
( ( ( ! [SY5329: $i] :
~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ SV1711 @ SV1711 ) @ ( c_Relation_OId__on @ SY5329 @ SV1711 ) @ ( tc_prod @ SV1711 @ SV1711 ) ) )
= $true )
| ( ( SV498 = SV1028 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(4216,plain,
! [SV1712: $i,SV1410: $i,SV1029: $i,SV499: $i] :
( ( ! [SY5330: $i,SY5331: $i] :
( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SY5330 )
!= ( c_Recdef_Ocut @ SY5331 @ SV1029 @ SV1410 @ SV1712 @ SY5330 ) )
| ! [SY5332: $i] :
( ( ( hAPP @ SV499 @ SY5332 )
= ( hAPP @ SY5331 @ SY5332 ) )
| ~ ( c_in @ ( c_Pair @ SY5332 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(4217,plain,
! [SV1713: $i,SV1030: $i,SV500: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ SV1713 @ SV1713 ) @ ( c_Relation_OId @ SV1713 ) @ ( tc_prod @ SV1713 @ SV1713 ) ) )
= $true )
| ( ( SV500 = SV1030 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(4218,plain,
! [SV1411: $i,SV1031: $i,SV501: $i] :
( ( ( c_in @ ( c_Pair @ SV501 @ SV501 @ SV1031 @ SV1031 ) @ SV1411 @ ( tc_prod @ SV1031 @ SV1031 ) )
= $true )
| ( ( ~ ( c_Nitpick_Orefl_H @ SV1411 @ SV1031 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(4219,plain,
! [SV1412: $i,SV1032: $i,SV502: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV502 @ SV1032 @ SV1032 ) @ SV1412 @ ( tc_prod @ SV1032 @ SV1032 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1412 @ SV1032 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4220,plain,
! [SV1714: $i,SV1413: $i,SV1033: $i,SV503: $i] :
( ( ! [SY5333: $i,SY5334: $i] :
( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SV1714 @ SY5333 @ SY5334 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY5333 @ SV503 ) @ ( hAPP @ SY5333 @ SV1033 ) @ SY5334 @ SY5334 ) @ SV1714 @ ( tc_prod @ SY5334 @ SY5334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4221,plain,
! [SV1715: $i,SV1414: $i,SV1034: $i,SV504: $i] :
( ( ! [SY5335: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SV1715 @ SV1715 ) @ SY5335 @ ( tc_prod @ SV1715 @ SV1715 ) )
| ! [SY5336: $i] :
~ ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SY5336 @ SY5336 ) @ ( c_Relation_Oinv__image @ SY5335 @ SV504 @ SV1715 @ SY5336 ) @ ( tc_prod @ SY5336 @ SY5336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(4222,plain,
! [SV1716: $i,SV1415: $i,SV1035: $i,SV505: $i] :
( ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
| ~ ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
| ~ ( c_Relation_Osym @ SV1716 @ SV1415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4223,plain,
! [SV1717: $i,SV1416: $i,SV1036: $i,SV506: $i] :
( ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
| ~ ( c_Relation_Osym @ SV1717 @ SV1416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4224,plain,
! [SV1718: $i,SV1417: $i,SV1037: $i,SV507: $i] :
( ( ! [SY5337: $i,SY5338: $i,SY5339: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SY5337 @ SY5338 @ SV1417 @ SY5339 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
| ! [SY5340: $i] :
( ~ ( c_in @ ( c_Pair @ SY5340 @ SV1037 @ SY5339 @ SV1718 ) @ SY5338 @ ( tc_prod @ SY5339 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5340 @ SV1417 @ SY5339 ) @ SY5337 @ ( tc_prod @ SV1417 @ SY5339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4225,plain,
! [SV1719: $i,SV1418: $i,SV1038: $i,SV508: $i] :
( ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
| ! [SY5341: $i] :
( ~ ( c_in @ ( c_Pair @ SY5341 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SY5341 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4226,plain,
! [SV1720: $i,SV1419: $i,SV1039: $i,SV509: $i] :
( ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ! [SY5342: $i] :
( ~ ( c_in @ ( c_Pair @ SY5342 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SY5342 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4227,plain,
! [SV1721: $i,SV1420: $i,SV1042: $i,SV512: $i] :
( ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
| ! [SY5343: $i,SY5344: $i] :
( ~ ( c_in @ SV1042 @ SY5343 @ SY5344 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SY5343 @ SV1420 @ SY5344 @ SV1721 ) @ ( tc_fun @ SY5344 @ SV1721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3739]) ).
thf(4228,plain,
! [SV1722: $i,SV1421: $i,SV1043: $i,SV513: $i] :
( ( ~ ( c_in @ SV513 @ SV1043 @ SV1421 )
| ! [SY5345: $i,SY5346: $i] :
( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SY5345 @ SV513 ) @ SY5346 )
| ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SY5345 @ SV1421 @ SY5346 ) @ ( tc_fun @ SV1421 @ SY5346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3740]) ).
thf(4229,plain,
! [SV1723: $i,SV1422: $i,SV1044: $i,SV514: $i] :
( ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SV1723 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV514 = SV1044 )
| ( SV514 = SV1723 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(4230,plain,
! [SV1724: $i,SV1423: $i,SV1045: $i,SV515: $i] :
( ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SV1724 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1045 = SV1724 )
| ( SV515 = SV1724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(4231,plain,
! [SV1424: $i,SV1047: $i,SV517: $i] :
( ( c_in @ ( c_Pair @ SV517 @ SV1047 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1424 @ SV517 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(4232,plain,
! [SV1425: $i,SV1048: $i,SV518: $i] :
( ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1425 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5051: $i] :
( ( SV1048 = SY5051 )
| ~ ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1425 @ SY5051 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(4233,plain,
! [SV519: $i,SV1049: $i] :
( ( ( SV1049 = SV519 )
= $true )
| ( ( ! [SY4518: $i] : ( c_in @ ( c_Pair @ SV519 @ SV1049 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4518 @ SV519 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV519 = SV1049 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(4234,plain,
! [SV1426: $i,SV1051: $i,SV521: $i] :
( ( c_in @ ( c_Pair @ SV521 @ SV1051 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1426 @ SV1051 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(4235,plain,
! [SV1725: $i,SV1427: $i,SV1052: $i,SV522: $i] :
( ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SV1725 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV522 = SV1052 )
| ( SV1052 = SV1725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(4236,plain,
! [SV1726: $i,SV1428: $i,SV1053: $i,SV523: $i] :
( ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SV1726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV523 = SV1726 )
| ( SV1053 = SV1726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(4237,plain,
! [SV1054: $i,SV524: $i] :
( ( ( SV524 = SV1054 )
= $true )
| ( ( ! [SY4524: $i] : ( c_in @ ( c_Pair @ SV524 @ SV1054 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4524 @ SV1054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV524 = SV1054 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3751]) ).
thf(4238,plain,
! [SV1429: $i,SV1055: $i,SV525: $i] :
( ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1429 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5054: $i] :
( ( SV525 = SY5054 )
| ~ ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1429 @ SY5054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(4239,plain,
! [SV1430: $i,SV1057: $i,SV527: $i] :
( ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5055: $i] :
( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5055 @ ( v_sko__local__X3__1 @ SV1430 @ SY5055 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SY5055 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5055 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(4240,plain,
! [SV1431: $i,SV1058: $i,SV528: $i] :
( ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5056: $i] :
( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5056 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SY5056 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5056 @ ( v_sko__local__X3__1 @ SY5056 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5056 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(4241,plain,
! [SV1432: $i,SV1059: $i,SV529: $i] :
( ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5057: $i] :
( ~ ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5057 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5057 @ ( v_sko__local__X3__1 @ SV1432 @ SY5057 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SY5057 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5057 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(4242,plain,
! [SV1433: $i,SV1060: $i,SV530: $i] :
( ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5058: $i] :
( ~ ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5058 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SY5058 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5058 @ ( v_sko__local__X3__1 @ SY5058 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5058 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(4243,plain,
! [SV1727: $i,SV1434: $i,SV1061: $i,SV531: $i] :
( ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5347: $i] :
( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SY5347 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5347 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SY5347 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SY5347 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5347 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(4244,plain,
! [SV1728: $i,SV1435: $i,SV1062: $i,SV532: $i] :
( ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5348: $i] :
( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SY5348 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5348 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5348 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5348 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5348 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(4245,plain,
! [SV1729: $i,SV1436: $i,SV1063: $i,SV533: $i] :
( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5349: $i] :
( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SY5349 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5349 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SY5349 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SY5349 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5349 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(4246,plain,
! [SV1730: $i,SV1437: $i,SV1064: $i,SV534: $i] :
( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5350: $i] :
( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SY5350 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5350 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5350 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5350 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5350 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(4247,plain,
! [SV1731: $i,SV1438: $i,SV1065: $i,SV535: $i] :
( ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4248,plain,
! [SV1732: $i,SV1439: $i,SV1066: $i,SV536: $i] :
( ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5351: $i,SY5352: $i] :
( ~ ( c_in @ ( c_Pair @ SV1732 @ SY5351 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5352 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1732 @ SY5351 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5352 @ ( v_sko__local__X2__1 @ SV1439 @ SY5352 @ SV536 @ SV1732 @ SV1066 @ SY5351 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SY5352 @ SV536 @ SV1732 @ SV1066 @ SY5351 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5352 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SY5351 )
| ( SV1732 = SY5351 )
| ( SV536 = SV1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(4249,plain,
! [SV1733: $i,SV1440: $i,SV1067: $i,SV537: $i] :
( ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5353: $i,SY5354: $i] :
( ~ ( c_in @ ( c_Pair @ SV1733 @ SY5353 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5354 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SY5354 @ SV1440 @ SV1733 @ SV537 @ SY5353 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SY5353 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5354 @ ( v_sko__local__X2__1 @ SY5354 @ SV1440 @ SV1733 @ SV537 @ SY5353 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5354 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5353 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SY5353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(4250,plain,
! [SV1734: $i,SV1441: $i,SV1068: $i,SV538: $i] :
( ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5355: $i,SY5356: $i] :
( ~ ( c_in @ ( c_Pair @ SV1734 @ SY5355 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5356 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1734 @ SY5355 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5356 @ ( v_sko__local__X2__1 @ SV1441 @ SY5356 @ SV538 @ SV1734 @ SV1068 @ SY5355 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SY5356 @ SV538 @ SV1734 @ SV1068 @ SY5355 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5356 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SY5355 )
| ( SV1734 = SY5355 )
| ( SV538 = SV1068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(4251,plain,
! [SV1735: $i,SV1442: $i,SV1069: $i,SV539: $i] :
( ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5357: $i,SY5358: $i] :
( ~ ( c_in @ ( c_Pair @ SV1735 @ SY5357 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5358 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SY5358 @ SV1442 @ SV1735 @ SV539 @ SY5357 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SY5357 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5358 @ ( v_sko__local__X2__1 @ SY5358 @ SV1442 @ SV1735 @ SV539 @ SY5357 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5358 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5357 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SY5357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(4252,plain,
! [SV1736: $i,SV1443: $i,SV1070: $i,SV540: $i] :
( ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5359: $i,SY5360: $i] :
( ~ ( c_in @ ( c_Pair @ SV1736 @ SY5359 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5360 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SY5360 @ SV1443 @ SV1736 @ SV540 @ SY5359 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SY5359 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5360 @ ( v_sko__local__X1__1 @ SY5360 @ SV1443 @ SV1736 @ SV540 @ SY5359 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5360 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5359 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SY5359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(4253,plain,
! [SV1737: $i,SV1444: $i,SV1071: $i,SV541: $i] :
( ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5361: $i,SY5362: $i] :
( ~ ( c_in @ ( c_Pair @ SV1737 @ SY5361 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5362 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SY5362 @ SV1444 @ SV1737 @ SV541 @ SY5361 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SY5361 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5362 @ ( v_sko__local__X1__1 @ SY5362 @ SV1444 @ SV1737 @ SV541 @ SY5361 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5362 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5361 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SY5361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(4254,plain,
! [SV1445: $i,SV1072: $i,SV542: $i] :
( ( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SV1445 ) )
= $true )
| ( ( ~ ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV542 @ SV1445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3769]) ).
thf(4255,plain,
! [SV1738: $i,SV1446: $i,SV1073: $i,SV543: $i] :
( ( ! [SY5363: $i,SY5364: $i] :
( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SY5363 @ SY5364 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
| ~ ( c_in @ SV1073 @ ( hAPP @ SY5364 @ SV543 ) @ SV1738 )
| ~ ( c_in @ SV543 @ SY5363 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(4256,plain,
! [SV1739: $i,SV1447: $i,SV1074: $i,SV544: $i] :
( ( ! [SY5365: $i,SY5366: $i] :
( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SY5365 @ SY5366 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
| ~ ( c_in @ SV1074 @ ( hAPP @ SY5366 @ SV544 ) @ SV1739 )
| ~ ( c_in @ SV544 @ SY5365 @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3771]) ).
thf(4257,plain,
! [SV1448: $i,SV1075: $i,SV545: $i] :
( ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $true )
| ( ( ! [SY5092: $i] :
( ~ ( c_in @ ( c_Pair @ SV545 @ SY5092 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SY5092 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(4258,plain,
! [SV1449: $i,SV1076: $i,SV546: $i] :
( ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $true )
| ( ( ! [SY5093: $i] :
( ~ ( c_in @ ( c_Pair @ SV546 @ SY5093 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) )
| ~ ( c_in @ SY5093 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(4259,plain,
! [SV1740: $i,SV1450: $i,SV1077: $i,SV547: $i] :
( ( ! [SY5367: $i] :
( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SY5367 ) @ SY5367 )
| ! [SY5368: $i] :
( ~ ( c_in @ ( c_Pair @ SY5368 @ SV547 @ SV1740 @ SY5367 ) @ SV1077 @ ( tc_prod @ SV1740 @ SY5367 ) )
| ~ ( c_in @ SY5368 @ SV1450 @ SV1740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4260,plain,
! [SV1741: $i,SV1451: $i,SV1078: $i,SV548: $i] :
( ( ! [SY5369: $i] :
( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SY5369 ) @ SY5369 )
| ! [SY5370: $i] :
( ~ ( c_in @ ( c_Pair @ SY5370 @ SV548 @ SV1741 @ SY5369 ) @ SV1078 @ ( tc_prod @ SV1741 @ SY5369 ) )
| ~ ( c_in @ SY5370 @ SV1451 @ SV1741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(4261,plain,
! [SV1452: $i,SV1079: $i,SV549: $i] :
( ( ( c_in @ SV549 @ SV1079 @ SV1452 )
= $true )
| ( ( ! [SY5100: $i] :
~ ( c_in @ ( c_Pair @ SV549 @ SY5100 @ SV1452 @ SV1452 ) @ ( c_Relation_OId__on @ SV1079 @ SV1452 ) @ ( tc_prod @ SV1452 @ SV1452 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3776]) ).
thf(4262,plain,
! [SV1453: $i,SV1080: $i,SV550: $i] :
( ( ( c_in @ ( c_Pair @ SV550 @ SV550 @ SV1080 @ SV1080 ) @ ( c_Relation_OId__on @ SV1453 @ SV1080 ) @ ( tc_prod @ SV1080 @ SV1080 ) )
= $true )
| ( ( ~ ( c_in @ SV550 @ SV1453 @ SV1080 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(4263,plain,
! [SV1454: $i,SV1081: $i,SV551: $i] :
( ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true )
| ( ( ! [SY5101: $i,SY5102: $i] :
( ~ ( c_in @ ( c_Pair @ SY5101 @ SV551 @ SV1454 @ SV1454 ) @ SY5102 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SY5102 @ SV1454 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(4264,plain,
! [SV1455: $i,SV1082: $i,SV552: $i] :
( ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true )
| ( ( ! [SY5103: $i,SY5104: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY5103 @ SV1455 @ SV1455 ) @ SY5104 @ ( tc_prod @ SV1455 @ SV1455 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SY5104 @ SV1455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(4265,plain,
! [SV1742: $i,SV1456: $i,SV1083: $i,SV553: $i] :
( ( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SV1456 @ SV1742 ) @ SV1742 )
| ! [SY5371: $i] :
~ ( c_in @ ( c_Pair @ SY5371 @ SV553 @ SV1456 @ SV1742 ) @ SV1083 @ ( tc_prod @ SV1456 @ SV1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(4266,plain,
! [SV1743: $i,SV1457: $i,SV1084: $i,SV554: $i] :
( ( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SV1457 @ SV1743 ) @ SV1743 )
| ! [SY5372: $i] :
~ ( c_in @ ( c_Pair @ SY5372 @ SV554 @ SV1457 @ SV1743 ) @ SV1084 @ ( tc_prod @ SV1457 @ SV1743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4267,plain,
! [SV1744: $i,SV1458: $i,SV1085: $i,SV555: $i] :
( ( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SV1458 @ SV1744 ) @ SV1458 )
| ! [SY5373: $i] :
~ ( c_in @ ( c_Pair @ SV555 @ SY5373 @ SV1458 @ SV1744 ) @ SV1085 @ ( tc_prod @ SV1458 @ SV1744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4268,plain,
! [SV1745: $i,SV1459: $i,SV1086: $i,SV556: $i] :
( ( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SV1459 @ SV1745 ) @ SV1459 )
| ! [SY5374: $i] :
~ ( c_in @ ( c_Pair @ SV556 @ SY5374 @ SV1459 @ SV1745 ) @ SV1086 @ ( tc_prod @ SV1459 @ SV1745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(4269,plain,
! [SV1746: $i,SV1460: $i,SV1087: $i,SV557: $i] :
( ( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SV1746 )
| ! [SY5375: $i,SY5376: $i] :
~ ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SY5375 @ SV1746 ) @ ( c_Product__Type_OSigma @ SY5376 @ SV1087 @ SY5375 @ SV1746 ) @ ( tc_prod @ SY5375 @ SV1746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(4270,plain,
! [SV1747: $i,SV1461: $i,SV1088: $i,SV558: $i] :
( ( ( c_in @ SV558 @ SV1088 @ SV1461 )
| ! [SY5377: $i,SY5378: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SV1747 @ SV1461 @ SY5377 ) @ ( c_Product__Type_OSigma @ SV1088 @ SY5378 @ SV1461 @ SY5377 ) @ ( tc_prod @ SV1461 @ SY5377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4271,plain,
! [SV1748: $i,SV1462: $i,SV1089: $i,SV559: $i] :
( ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
| ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
| ( SV1089 = SV559 )
| ! [SY5379: $i] :
( ~ ( c_in @ SV559 @ SY5379 @ SV1462 )
| ~ ( c_in @ SV1089 @ SY5379 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SY5379 @ SV1748 @ SV1462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(4272,plain,
! [SV1463: $i,SV1090: $i,SV560: $i] :
( ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
= $true )
| ( ( ! [SY5121: $i] :
( ~ ( c_in @ SV560 @ SY5121 @ SV1090 )
| ~ ( c_Relation_Orefl__on @ SY5121 @ SV1463 @ SV1090 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(4273,plain,
! [SV1464: $i,SV1091: $i,SV561: $i] :
( ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true )
| ( ( ! [SY5122: $i,SY5123: $i] :
( ~ ( c_in @ ( c_Pair @ SY5122 @ SV561 @ SV1464 @ SV1464 ) @ SY5123 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1091 @ SY5123 @ SV1464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(4274,plain,
! [SV1465: $i,SV1092: $i,SV562: $i] :
( ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true )
| ( ( ! [SY5124: $i,SY5125: $i] :
( ~ ( c_in @ ( c_Pair @ SV562 @ SY5124 @ SV1465 @ SV1465 ) @ SY5125 @ ( tc_prod @ SV1465 @ SV1465 ) )
| ~ ( c_Relation_Orefl__on @ SV1092 @ SY5125 @ SV1465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3789]) ).
thf(4275,plain,
! [SV1466: $i,SV1093: $i,SV563: $i] :
( ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
= $true )
| ( ( ! [SY5126: $i] :
( ~ ( c_in @ SV563 @ SY5126 @ SV1093 )
| ~ ( c_Relation_Orefl__on @ SY5126 @ SV1466 @ SV1093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(4276,plain,
! [SV1749: $i,SV1467: $i,SV1094: $i,SV564: $i] :
( ( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ SV1749 ) @ SV1467 ) @ ( tc_prod @ SV1467 @ SV1467 ) )
| ~ ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ SV1749 @ SV1467 ) ) @ ( tc_prod @ SV1467 @ SV1467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4277,plain,
! [SV1750: $i,SV1468: $i,SV1095: $i,SV565: $i] :
( ( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ SV1750 @ SV1468 ) ) @ ( tc_prod @ SV1468 @ SV1468 ) )
| ~ ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ SV1750 ) @ SV1468 ) @ ( tc_prod @ SV1468 @ SV1468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(4278,plain,
! [SV1751: $i,SV1469: $i,SV1096: $i,SV566: $i] :
( ( ( c_in @ ( c_Pair @ SV566 @ SV1096 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1751 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
| ~ ( c_in @ ( c_Pair @ SV1096 @ SV566 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1469 @ SV1469 ) @ SV1751 ) @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(4279,plain,
! [SV1752: $i,SV1470: $i,SV1097: $i,SV567: $i] :
( ( ( c_in @ ( c_Pair @ SV567 @ SV1097 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1470 @ SV1470 ) @ SV1752 ) @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
| ~ ( c_in @ ( c_Pair @ SV1097 @ SV567 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1752 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(4280,plain,
! [SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5380: $i,SY5381: $i,SY5382: $i,SY5383: $i,SY5384: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SY5380 @ SY5381 ) ) )
| ! [SY5385: $i,SY5386: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SY5382 @ SY5383 @ SY5384 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SY5380 @ SY5385 @ SY5383 @ SY5386 ) @ SY5381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4281,plain,
! [SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ! [SY5387: $i,SY5388: $i,SY5389: $i] :
( ! [SY5390: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SY5387 )
!= ( c_Fun_Ocomp @ SY5388 @ SY5389 @ SY5390 @ SV1754 @ SY5387 ) )
| ! [SY4659: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY4659 ) )
= ( hAPP @ SY5388 @ ( hAPP @ SY5389 @ SY4659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4282,plain,
! [SV1755: $i,SV1473: $i,SV1100: $i,SV570: $i] :
( ( ! [SY5392: $i,SY5393: $i] :
( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SV1755 )
!= ( c_Pair @ SY5392 @ SY5393 @ SV1473 @ SV1755 ) )
| ( SV1100 = SY5393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(4283,plain,
! [SV1756: $i,SV1474: $i,SV1101: $i,SV571: $i] :
( ( ! [SY5394: $i] :
( ! [SY5395: $i] :
( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SV1756 )
!= ( c_Pair @ SY5394 @ SY5395 @ SV1474 @ SV1756 ) )
| ( SV571 = SY5394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(4284,plain,
! [SV1757: $i,SV1475: $i,SV1102: $i,SV572: $i] :
( ( ! [SY5396: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SV1475 @ SV1757 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1757 @ SV1475 ) @ SY5396 ) @ ( tc_prod @ SV1475 @ SV1757 ) )
| ~ ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SV1757 @ SV1475 ) @ SY5396 @ ( tc_prod @ SV1757 @ SV1475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(4285,plain,
! [SV1758: $i,SV1476: $i,SV1103: $i,SV573: $i] :
( ( ! [SY5397: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SV1476 @ SV1758 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1758 @ SV1476 ) @ SY5397 ) @ ( tc_prod @ SV1476 @ SV1758 ) )
| ~ ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SV1758 @ SV1476 ) @ SY5397 @ ( tc_prod @ SV1758 @ SV1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(4286,plain,
! [SV1759: $i,SV1477: $i,SV1104: $i,SV574: $i] :
( ( ! [SY5398: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SV1477 @ SV1759 ) @ SY5398 @ ( tc_prod @ SV1477 @ SV1759 ) )
| ~ ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SV1759 @ SV1477 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1477 @ SV1759 ) @ SY5398 ) @ ( tc_prod @ SV1759 @ SV1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(4287,plain,
! [SV1760: $i,SV1478: $i,SV1105: $i,SV575: $i] :
( ( ! [SY5399: $i,SY5400: $i,SY5401: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SV1478 @ SV1760 @ SY5399 @ SY5400 ) @ SY5399 @ SY5401 @ SY5400 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SY5399 @ SY5401 @ SV1760 ) @ SV1478 @ SV1760 @ SY5401 @ SY5400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(4288,plain,
! [SV1761: $i,SV1480: $i,SV1107: $i,SV579: $i] :
( ( ! [SY5402: $i,SY5403: $i] :
( ( hAPP @ SV579 @ ( hAPP @ SV1107 @ SV1480 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SV1107 @ SV1761 @ SY5402 @ SY5403 ) @ SV1480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4289,plain,
! [SV1762: $i,SV1481: $i,SV1108: $i,SV580: $i] :
( ( ! [SY5404: $i,SY5405: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SV1108 @ SV1481 @ SV1762 @ SY5404 ) @ SY5405 )
= ( hAPP @ SV580 @ ( hAPP @ SV1108 @ SY5405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4290,plain,
! [SV1763: $i,SV1109: $i,SV581: $i] :
( ( ( c_in @ SV581 @ SV1109 @ SV1763 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1109 @ SV581 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4291,plain,
! [SV1764: $i,SV582: $i,SV1110: $i] :
( ( ( ~ ( c_in @ SV1110 @ SV582 @ SV1764 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV582 @ SV1110 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(4292,plain,
! [SV583: $i,SV1111: $i] :
( ( ( class_Lattices_Olattice @ SV1111 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV583 @ SV1111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(4293,plain,
! [SV584: $i,SV1112: $i] :
( ( ( class_Lattices_Olattice @ SV1112 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV584 @ SV1112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(4294,plain,
! [SV585: $i,SV1113: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV1113 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV585 @ SV1113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(4295,plain,
! [SV586: $i,SV1114: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV1114 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV586 @ SV1114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(4296,plain,
! [SV587: $i,SV1115: $i] :
( ( ( class_Orderings_Opreorder @ SV1115 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV587 @ SV1115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(4297,plain,
! [SV588: $i,SV1116: $i] :
( ( ( class_Lattices_Olattice @ SV1116 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV588 @ SV1116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(4298,plain,
! [SV589: $i,SV1117: $i] :
( ( ( class_Orderings_Oorder @ SV1117 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV589 @ SV1117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(4299,plain,
! [SV590: $i,SV1118: $i] :
( ( ( class_Orderings_Obot @ SV1118 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV590 @ SV1118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3817]) ).
thf(4300,plain,
! [SV591: $i,SV1119: $i] :
( ( ( class_HOL_Oord @ SV1119 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV591 @ SV1119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(4301,plain,
! [SV1765: $i,SV1121: $i,SV593: $i] :
( ( ( ~ ( c_fequal @ SV593 @ SV1121 @ SV1765 ) )
= $true )
| ( ( SV593 = SV1121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(4302,plain,
! [SV1766: $i,SV1484: $i,SV1124: $i,SV596: $i,SV5: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SV1484 ) @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) )
| ! [SY5406: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY5406 @ ( c_COMBK @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) @ SV1124 ) @ SV1124 @ SV1484 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SV1484 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(4303,plain,
! [SV600: $i,SV1767: $i,SV1486: $i,SV10: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SV1486 @ SV1767 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1486 @ SV1767 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4304,plain,
! [SV1768: $i,SV1487: $i,SV1127: $i,SV601: $i,SV11: $i] :
( ( ( c_Relation_OImage @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV601 @ SV1127 @ ( tc_fun @ SV1487 @ tc_bool ) ) @ SV1487 @ SV1768 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV11 @ SV601 @ SV1487 @ SV1768 ) @ ( c_Relation_OImage @ SV11 @ SV1127 @ SV1487 @ SV1768 ) @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(4305,plain,
! [SV1769: $i,SV1488: $i,SV1128: $i,SV602: $i,SV12: $i] :
( ( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV12 @ SV602 @ ( tc_fun @ ( tc_prod @ SV1128 @ SV1488 ) @ tc_bool ) ) @ SV1769 @ SV1128 @ SV1488 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV12 @ SV1769 @ SV1128 @ SV1488 ) @ ( c_Relation_OImage @ SV602 @ SV1769 @ SV1128 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4306,plain,
! [SV1770: $i,SV1489: $i,SV1129: $i,SV603: $i,SV13: $i] :
( ( ! [SY5407: $i,SY5408: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SY5407 @ SY5408 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SY5408 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SY5407 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4307,plain,
! [SV1130: $i,SV16: $i,SV605: $i] :
( ( ( c_Relation_Orefl__on @ SV605 @ SV16 @ SV1130 )
= $false )
| ( ( c_lessequals @ SV16 @ ( c_Product__Type_OSigma @ SV605 @ ( c_COMBK @ SV605 @ ( tc_fun @ SV1130 @ tc_bool ) @ SV1130 ) @ SV1130 @ SV1130 ) @ ( tc_fun @ ( tc_prod @ SV1130 @ SV1130 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(4308,plain,
! [SV18: $i,SV1771: $i,SV607: $i] :
( ( ( ! [SY5409: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1771 @ SV18 ) @ SY5409 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV607 @ SY5409 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1771 @ SY5409 @ SV18 ) @ SV18 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4309,plain,
! [SV19: $i,SV1772: $i,SV608: $i] :
( ( ( ! [SY5410: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1772 @ SY5410 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SV1772 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SY5410 @ SV19 ) @ SV19 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4310,plain,
! [SV1493: $i,SV611: $i,SV22: $i] :
( ( ( c_in @ SV22 @ ( c_Set_Oinsert @ SV611 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1493 @ tc_bool ) ) @ SV1493 ) @ SV1493 )
= $false )
| ( ( SV22 = SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4311,plain,
! [SV1773: $i,SV1494: $i,SV1133: $i,SV612: $i,SV23: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV23 @ SV612 @ ( tc_fun @ SV1133 @ tc_bool ) ) @ SV1494 @ SV1133 @ SV1773 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV23 @ SV1494 @ SV1133 @ SV1773 ) @ ( c_Product__Type_OSigma @ SV612 @ SV1494 @ SV1133 @ SV1773 ) @ ( tc_fun @ ( tc_prod @ SV1133 @ SV1773 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4312,plain,
! [SV1134: $i,SV613: $i,SV24: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV24 @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4313,plain,
! [SV1495: $i,SV1135: $i,SV614: $i,SV25: $i] :
( ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true )
| ( ( ! [SY5176: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SY5176 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY5176 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SY5176 @ tc_bool ) @ SV1135 ) @ SV1135 @ SY5176 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SY5176 ) @ tc_bool ) )
| ! [SY5177: $i] :
~ ( c_in @ SY5177 @ SV1495 @ SY5176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4314,plain,
! [SV1774: $i,SV1496: $i,SV1136: $i,SV615: $i,SV26: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) )
| ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4315,plain,
! [SV616: $i,SV1137: $i,SV27: $i,SV1775: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1775 @ SV27 @ SV1137 ) @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV27 @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4316,plain,
! [SV1497: $i,SV1138: $i,SV617: $i,SV28: $i] :
( ( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SV617 @ SV1138 @ SV1497 ) @ ( tc_fun @ SV1497 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV28 @ SV1138 @ ( tc_fun @ SV1497 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4317,plain,
! [SV618: $i,SV1776: $i,SV1498: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SV1498 @ SV1776 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1498 @ SV1776 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4318,plain,
! [SV41: $i,SV1147: $i,SV629: $i] :
( ( ( ~ ( c_Relation_Osym @ SV629 @ SV1147 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV41 @ SV1147 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SV1147 @ SV1147 ) @ tc_bool ) ) @ SV1147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(4319,plain,
! [SV630: $i,SV1148: $i,SV42: $i] :
( ( ( c_lessequals @ SV42 @ SV1148 @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV42 @ SV630 ) @ ( c_Transitive__Closure_Ortrancl @ SV1148 @ SV630 ) @ ( tc_fun @ ( tc_prod @ SV630 @ SV630 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(4320,plain,
! [SV1777: $i,SV1508: $i,SV1151: $i,SV635: $i,SV49: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV49 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1151 @ ( tc_fun @ SV1508 @ tc_bool ) ) @ SV1508 @ SV1777 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV49 @ SV635 @ SV1508 @ SV1777 ) @ ( c_Relation_OImage @ SV49 @ SV1151 @ SV1508 @ SV1777 ) @ ( tc_fun @ SV1777 @ tc_bool ) ) @ ( tc_fun @ SV1777 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4321,plain,
! [SV1509: $i,SV1152: $i,SV636: $i,SV50: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SV636 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV636 @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ ( tc_fun @ SV1152 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1509 @ SV50 @ ( tc_fun @ SV1152 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4322,plain,
! [SV1510: $i,SV1153: $i,SV637: $i,SV51: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SV637 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV637 @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1510 @ SV51 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3856]) ).
thf(4323,plain,
! [SV1778: $i,SV1511: $i,SV1154: $i,SV638: $i,SV52: $i] :
( ( ! [SY5412: $i,SY5413: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SY5412 @ ( c_COMBK @ SY5413 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
| ! [SY5414: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY5414 @ ( c_COMBK @ SY5413 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SY5412 @ ( c_COMBK @ SY5414 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4324,plain,
! [SV1155: $i,SV639: $i,SV53: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV639 @ SV1155 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4325,plain,
! [SV54: $i,SV640: $i,SV1512: $i] :
( ( ( hBOOL @ ( hAPP @ SV1512 @ SV640 ) )
= $true )
| ( ( ! [SY5186: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1512 @ SV54 @ ( tc_fun @ SY5186 @ tc_bool ) ) @ SV640 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4326,plain,
! [SV1513: $i,SV1156: $i,SV641: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV641 @ ( tc_fun @ SV1156 @ tc_bool ) ) @ SV1513 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV641 @ SV1513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4327,plain,
! [SV1514: $i,SV1157: $i,SV642: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV642 @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV1514 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV56 @ SV1514 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4328,plain,
! [SV1158: $i,SV643: $i,SV57: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1158 @ SV643 )
| ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4329,plain,
! [SV1779: $i,SV1515: $i,SV1159: $i,SV644: $i,SV58: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV644 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ ( c_COMBK @ SV1515 @ ( tc_fun @ SV1779 @ tc_bool ) @ SV1159 ) @ SV1159 @ SV1779 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV58 @ ( c_COMBK @ SV1515 @ ( tc_fun @ SV1779 @ tc_bool ) @ SV1159 ) @ SV1159 @ SV1779 ) @ ( c_Product__Type_OSigma @ SV644 @ ( c_COMBK @ SV1515 @ ( tc_fun @ SV1779 @ tc_bool ) @ SV1159 ) @ SV1159 @ SV1779 ) @ ( tc_fun @ ( tc_prod @ SV1159 @ SV1779 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4330,plain,
! [SV1780: $i,SV1516: $i,SV1160: $i,SV645: $i,SV59: $i] :
( ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SV1780 ) @ SV1160 @ SV1780 )
| ~ ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SV1780 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4331,plain,
! [SV1781: $i,SV1517: $i,SV1161: $i,SV646: $i,SV60: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SV1781 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV646 @ SV1781 @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4332,plain,
! [SV61: $i,SV1782: $i,SV647: $i] :
( ( ( ! [SY5415: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SV1782 @ SV61 ) @ SY5415 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1782 @ SY5415 @ SV61 ) @ SV61 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4333,plain,
! [SV62: $i,SV1783: $i,SV648: $i] :
( ( ( ! [SY5416: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1783 @ SY5416 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1783 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ SY5416 @ SV62 ) @ SV62 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4334,plain,
! [SV63: $i,SV1784: $i,SV649: $i] :
( ( ( ! [SY5417: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1784 @ SY5417 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1784 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ SY5417 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4335,plain,
! [SV64: $i,SV1785: $i,SV650: $i] :
( ( ( ! [SY5418: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ SV1785 @ SV64 ) @ SY5418 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SY5418 @ SV64 ) @ SV64 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4336,plain,
! [SV1786: $i,SV1522: $i,SV1164: $i,SV655: $i,SV71: $i] :
( ( ! [SY5419: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SV1786 @ SY5419 ) @ ( tc_fun @ SY5419 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5419 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SV1522 @ SV1164 @ SY5419 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV655 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SV1786 @ SY5419 ) @ ( tc_fun @ SY5419 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5419 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ SV1786 @ ( tc_fun @ SY5419 @ tc_bool ) @ SV1164 ) @ SV1164 @ SY5419 ) @ ( tc_fun @ ( tc_prod @ SV1164 @ SY5419 ) @ tc_bool ) ) @ ( tc_prod @ SV1164 @ SY5419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4337,plain,
! [SV656: $i,SV1523: $i,SV72: $i] :
( ( ( ~ ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SV1523 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1523 @ SV656 ) )
= $true )
| ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4338,plain,
! [SV1165: $i,SV658: $i,SV74: $i] :
( ( ( c_in @ SV74 @ SV658 @ SV1165 )
= $false )
| ( ( ! [SY4748: $i] :
( ~ ( c_in @ SV74 @ SY4748 @ SV1165 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4748 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4339,plain,
! [SV75: $i,SV1787: $i,SV659: $i] :
( ( ( ! [SY5420: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1787 @ SY5420 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SV1787 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SY5420 @ SV75 ) @ SV75 ) @ SV75 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4340,plain,
! [SV76: $i,SV1788: $i,SV1524: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1524 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1524 @ SV1788 @ SV76 ) @ SV76 )
= SV1524 )
= $true )
| ( ( class_Lattices_Olattice @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4341,plain,
! [SV1166: $i,SV660: $i,SV77: $i] :
( ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY4749: $i] :
( ( ( c_Relation_Orel__comp @ SY4749 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4749 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(4342,plain,
! [SV1167: $i,SV661: $i,SV78: $i] :
( ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY4750: $i] :
( ( ( c_Relation_Orel__comp @ SV78 @ SY4750 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4750 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(4343,plain,
! [SV662: $i,SV1789: $i,SV1525: $i,SV79: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SV1525 @ SV1789 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1525 @ SV1789 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3881]) ).
thf(4344,plain,
! [SV1526: $i,SV80: $i,SV663: $i] :
( ( ( ~ ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SV1526 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SV1526 @ tc_bool ) ) )
= $true )
| ( ( SV80 = SV663 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4345,plain,
! [SV1527: $i,SV81: $i,SV664: $i] :
( ( ( ~ ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SV1527 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SV1527 @ tc_bool ) ) )
= $true )
| ( ( SV81 = SV664 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4346,plain,
! [SV82: $i,SV1790: $i,SV1528: $i] :
( ( ( ( SV1528 = SV1790 )
| ~ ( c_lessequals @ SV1790 @ SV1528 @ SV82 )
| ~ ( c_lessequals @ SV1528 @ SV1790 @ SV82 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4347,plain,
! [SV83: $i,SV1791: $i,SV1529: $i] :
( ( ( ( SV1529 = SV1791 )
| ~ ( c_lessequals @ SV1791 @ SV1529 @ SV83 )
| ~ ( c_lessequals @ SV1529 @ SV1791 @ SV83 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4348,plain,
! [SV84: $i,SV1792: $i,SV1530: $i] :
( ( ( ( SV1530 = SV1792 )
| ~ ( c_lessequals @ SV1530 @ SV1792 @ SV84 )
| ~ ( c_lessequals @ SV1792 @ SV1530 @ SV84 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4349,plain,
! [SV85: $i,SV1793: $i,SV1531: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1531 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1531 @ SV1793 @ SV85 ) @ SV85 )
= SV1531 )
= $true )
| ( ( class_Lattices_Olattice @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(4350,plain,
! [SV86: $i,SV1794: $i,SV1532: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1532 @ SV1794 @ SV86 )
= SV1532 )
| ~ ( c_lessequals @ SV1794 @ SV1532 @ SV86 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4351,plain,
! [SV87: $i,SV1795: $i,SV1533: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1533 @ SV1795 @ SV87 )
!= SV1795 )
| ( c_lessequals @ SV1533 @ SV1795 @ SV87 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4352,plain,
! [SV88: $i,SV1796: $i,SV1534: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1534 @ SV1796 @ SV88 )
= SV1796 )
| ~ ( c_lessequals @ SV1534 @ SV1796 @ SV88 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(4353,plain,
! [SV1168: $i,SV665: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV89 @ SV665 @ ( tc_fun @ SV1168 @ tc_bool ) )
= SV665 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(4354,plain,
! [SV1169: $i,SV90: $i,SV666: $i] :
( ( ( c_lessequals @ SV666 @ SV90 @ ( tc_fun @ SV1169 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV90 @ SV666 @ ( tc_fun @ SV1169 @ tc_bool ) )
= SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4355,plain,
! [SV1170: $i,SV667: $i,SV91: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) )
= SV667 )
= $false )
| ( ( c_lessequals @ SV91 @ SV667 @ ( tc_fun @ SV1170 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(4356,plain,
! [SV1797: $i,SV1535: $i,SV1171: $i,SV668: $i,SV92: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SV1797 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV668 @ SV1797 @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4357,plain,
! [SV93: $i,SV1798: $i,SV669: $i] :
( ( ( ! [SY5421: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ SV1798 @ SV93 ) @ SY5421 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1798 @ SY5421 @ SV93 ) @ SV93 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4358,plain,
! [SV94: $i,SV1799: $i,SV670: $i] :
( ( ( ! [SY5422: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1799 @ SY5422 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1799 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ SY5422 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4359,plain,
! [SV95: $i,SV1800: $i,SV671: $i] :
( ( ( ! [SY5423: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1800 @ SY5423 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1800 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SY5423 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4360,plain,
! [SV96: $i,SV1801: $i,SV672: $i] :
( ( ( ! [SY5424: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SV1801 @ SV96 ) @ SY5424 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1801 @ SY5424 @ SV96 ) @ SV96 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4361,plain,
! [SV1172: $i,SV673: $i,SV97: $i] :
( ( ( c_lessequals @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV97 @ SV673 @ ( tc_fun @ SV1172 @ tc_bool ) )
= SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(4362,plain,
! [SV1173: $i,SV98: $i,SV674: $i] :
( ( ( c_lessequals @ SV674 @ SV98 @ ( tc_fun @ SV1173 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV674 @ ( tc_fun @ SV1173 @ tc_bool ) )
= SV674 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4363,plain,
! [SV99: $i,SV1802: $i,SV1536: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1536 @ SV1802 @ SV99 )
= SV1536 )
| ~ ( c_lessequals @ SV1536 @ SV1802 @ SV99 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4364,plain,
! [SV100: $i,SV1803: $i,SV1537: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1537 @ SV1803 @ SV100 )
!= SV1537 )
| ( c_lessequals @ SV1537 @ SV1803 @ SV100 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4365,plain,
! [SV101: $i,SV1804: $i,SV1538: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1538 @ SV1804 @ SV101 )
= SV1804 )
| ~ ( c_lessequals @ SV1804 @ SV1538 @ SV101 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4366,plain,
! [SV1539: $i,SV1174: $i,SV675: $i,SV102: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV675 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
| ~ ( c_lessequals @ SV102 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4367,plain,
! [SV1540: $i,SV1177: $i,SV678: $i,SV105: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV678 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
| ~ ( c_lessequals @ SV105 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4368,plain,
! [SV106: $i,SV1805: $i,SV679: $i] :
( ( ( ! [SY5425: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SY5425 @ SV106 )
| ~ ( c_lessequals @ SV1805 @ SY5425 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SY5425 @ SV106 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3906]) ).
thf(4369,plain,
! [SV107: $i,SV1806: $i,SV1541: $i] :
( ( ( c_lessequals @ SV1541 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1541 @ SV1806 @ SV107 ) @ SV107 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3907]) ).
thf(4370,plain,
! [SV108: $i,SV1807: $i,SV1542: $i] :
( ( ( c_lessequals @ SV1542 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1807 @ SV1542 @ SV108 ) @ SV108 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(4371,plain,
! [SV109: $i,SV1808: $i,SV680: $i] :
( ( ( ! [SY5426: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SY5426 @ SV109 )
| ~ ( c_lessequals @ SV1808 @ SY5426 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SY5426 @ SV109 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4372,plain,
! [SV110: $i,SV1809: $i,SV681: $i] :
( ( ( ! [SY5427: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SY5427 @ SV110 )
| ~ ( c_lessequals @ SV1809 @ SY5427 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SY5427 @ SV110 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4373,plain,
! [SV111: $i,SV1810: $i,SV1543: $i] :
( ( ( c_lessequals @ SV1543 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1810 @ SV1543 @ SV111 ) @ SV111 )
= $true )
| ( ( class_Lattices_Olattice @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4374,plain,
! [SV112: $i,SV1811: $i,SV1544: $i] :
( ( ( c_lessequals @ SV1544 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1544 @ SV1811 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Lattices_Olattice @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4375,plain,
! [SV114: $i,SV1812: $i,SV1545: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1545 @ SV1812 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1812 @ SV1545 @ SV114 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4376,plain,
! [SV115: $i,SV1813: $i,SV1546: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1546 @ SV1813 @ SV115 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1813 @ SV1546 @ SV115 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4377,plain,
! [SV117: $i,SV1814: $i,SV684: $i] :
( ( ( ! [SY5428: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SV1814 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SY5428 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1814 @ SY5428 @ SV117 ) @ SV117 ) @ SV117 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4378,plain,
! [SV685: $i,SV1179: $i,SV118: $i] :
( ( ( ~ ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1179 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3917]) ).
thf(4379,plain,
! [SV1180: $i,SV686: $i,SV119: $i] :
( ( ( ( c_Set_Oinsert @ SV119 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 )
= ( c_Set_Oinsert @ SV1180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV686 @ tc_bool ) ) @ SV686 ) )
= $false )
| ( ( SV119 = SV1180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(4380,plain,
! [SV1183: $i,SV689: $i,SV123: $i] :
( ( ( ( c_Set_Oinsert @ SV123 @ SV689 @ SV1183 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV123 @ SV689 @ SV1183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(4381,plain,
! [SV690: $i,SV1184: $i,SV1815: $i,SV125: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SV1815 @ SV1184 ) @ SV690 @ ( tc_fun @ SV1184 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV125 @ SV690 @ SV1184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4382,plain,
! [SV1816: $i,SV1549: $i,SV1185: $i,SV691: $i,SV126: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV691 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SV1549 @ SV1185 @ SV1816 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV126 @ SV1549 @ SV1185 @ SV1816 ) @ ( c_Product__Type_OSigma @ SV691 @ SV1549 @ SV1185 @ SV1816 ) @ ( tc_fun @ ( tc_prod @ SV1185 @ SV1816 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4383,plain,
! [SV1550: $i,SV1186: $i,SV692: $i,SV127: $i] :
( ( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SV1186 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV127 @ SV1186 @ ( tc_fun @ SV1550 @ tc_bool ) )
| ( c_in @ SV692 @ SV127 @ SV1550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4384,plain,
! [SV693: $i,SV1187: $i,SV128: $i,SV1817: $i] :
( ( ( ( c_in @ SV1817 @ SV128 @ SV1187 )
| ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SV1817 @ SV693 @ SV1187 ) @ ( tc_fun @ SV1187 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SV1187 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4385,plain,
! [SV1551: $i,SV1188: $i,SV694: $i,SV129: $i] :
( ( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SV1188 @ SV1551 ) @ ( tc_fun @ SV1551 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV129 @ SV1188 @ ( tc_fun @ SV1551 @ tc_bool ) )
| ( c_in @ SV694 @ SV129 @ SV1551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4386,plain,
! [SV1189: $i,SV695: $i,SV1818: $i,SV130: $i] :
( ( ( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SV1818 @ SV695 @ SV1189 ) @ ( tc_fun @ SV1189 @ tc_bool ) )
| ( c_in @ SV1818 @ SV130 @ SV1189 ) )
= $true )
| ( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SV1189 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4387,plain,
! [SV1552: $i,SV1190: $i,SV696: $i,SV131: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ ( c_Set_Oinsert @ SV696 @ SV1190 @ SV1552 ) @ ( tc_fun @ SV1552 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV1190 @ ( tc_fun @ SV1552 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV696 @ SV131 @ SV1552 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4388,plain,
! [SV1553: $i,SV1191: $i,SV697: $i,SV132: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV132 @ SV697 @ SV1191 ) @ SV1553 @ ( tc_fun @ SV1191 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV697 @ SV1553 @ ( tc_fun @ SV1191 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV132 @ SV1553 @ SV1191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4389,plain,
! [SV1192: $i,SV698: $i,SV133: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 @ SV698 @ ( tc_fun @ SV1192 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) )
= $false )
| ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1192 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3930]) ).
thf(4390,plain,
! [SV1193: $i,SV699: $i,SV134: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ SV699 @ ( tc_fun @ SV1193 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) )
= $false )
| ( ( SV134
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4391,plain,
! [SV135: $i,SV1554: $i] :
( ( ( ! [SY5212: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1554 @ SY5212 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) ) )
= $true )
| ( ( SV1554
= ( c_Orderings_Obot__class_Obot @ SV135 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3932]) ).
thf(4392,plain,
! [SV136: $i,SV1819: $i,SV1555: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1555 @ SV1819 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
| ( SV1819
= ( c_Orderings_Obot__class_Obot @ SV136 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4393,plain,
! [SV1820: $i,SV1556: $i,SV1194: $i,SV700: $i,SV137: $i] :
( ( ! [SY5429: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV700 @ ( tc_fun @ ( tc_prod @ SV1194 @ SV1556 ) @ tc_bool ) ) @ SV1820 @ SV1194 @ SV1556 @ SY5429 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SV1820 @ SV1194 @ SV1556 @ SY5429 ) @ ( c_Relation_Orel__comp @ SV700 @ SV1820 @ SV1194 @ SV1556 @ SY5429 ) @ ( tc_fun @ ( tc_prod @ SV1194 @ SY5429 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(4394,plain,
! [SV1821: $i,SV1557: $i,SV1195: $i,SV701: $i,SV138: $i] :
( ( ! [SY5430: $i] :
( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV701 @ SV1195 @ ( tc_fun @ ( tc_prod @ SV1557 @ SV1821 ) @ tc_bool ) ) @ SY5430 @ SV1557 @ SV1821 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SV701 @ SY5430 @ SV1557 @ SV1821 ) @ ( c_Relation_Orel__comp @ SV138 @ SV1195 @ SY5430 @ SV1557 @ SV1821 ) @ ( tc_fun @ ( tc_prod @ SY5430 @ SV1821 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4395,plain,
! [SV1197: $i,SV703: $i,SV1822: $i,SV140: $i] :
( ( ( ~ ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1822 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) ) @ ( tc_fun @ SV1197 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV140 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4396,plain,
! [SV1198: $i,SV1823: $i,SV704: $i,SV141: $i] :
( ( ( ~ ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV704 @ SV1823 @ ( tc_fun @ SV1198 @ tc_bool ) ) @ ( tc_fun @ SV1198 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV141 @ SV704 @ ( tc_fun @ SV1198 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4397,plain,
! [SV142: $i,SV1824: $i,SV705: $i] :
( ( ( ( c_lessequals @ SV705 @ SV1824 @ SV142 )
| ! [SY5431: $i] :
~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1824 @ SY5431 @ SV142 ) @ SV142 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4398,plain,
! [SV143: $i,SV1825: $i,SV706: $i] :
( ( ( ( c_lessequals @ SV706 @ SV1825 @ SV143 )
| ! [SY5432: $i] :
~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5432 @ SV1825 @ SV143 ) @ SV143 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4399,plain,
! [SV144: $i,SV1826: $i,SV707: $i] :
( ( ( ! [SY5433: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SV1826 @ SV144 ) @ SY5433 @ SV144 )
| ~ ( c_lessequals @ SV707 @ SY5433 @ SV144 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4400,plain,
! [SV145: $i,SV1827: $i,SV708: $i] :
( ( ( ! [SY5434: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SV1827 @ SV145 ) @ SY5434 @ SV145 )
| ~ ( c_lessequals @ SV1827 @ SY5434 @ SV145 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4401,plain,
! [SV146: $i,SV1828: $i,SV709: $i] :
( ( ( ( c_lessequals @ SV709 @ SV1828 @ SV146 )
| ! [SY5435: $i] :
~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1828 @ SY5435 @ SV146 ) @ SV146 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4402,plain,
! [SV147: $i,SV1829: $i,SV710: $i] :
( ( ( ( c_lessequals @ SV710 @ SV1829 @ SV147 )
| ! [SY5436: $i] :
~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5436 @ SV1829 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4403,plain,
! [SV149: $i,SV1830: $i,SV1558: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1558 @ SV1830 @ SV149 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1830 @ SV1558 @ SV149 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4404,plain,
! [SV150: $i,SV1831: $i,SV1559: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1559 @ SV1831 @ SV150 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1831 @ SV1559 @ SV150 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4405,plain,
! [SV715: $i,SV154: $i,SV1203: $i] :
( ( ( c_lessequals @ SV1203 @ SV154 @ ( tc_fun @ ( tc_prod @ SV715 @ SV715 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV154 @ SV715 ) @ ( c_Wellfounded_Oacc @ SV1203 @ SV715 ) @ ( tc_fun @ SV715 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(4406,plain,
! [SV156: $i,SV1832: $i,SV1561: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ SV1832 @ SV156 ) @ SV156 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1561 @ SV1832 @ SV156 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3948]) ).
thf(4407,plain,
! [SV157: $i,SV1833: $i,SV1562: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ SV1833 @ SV157 ) @ SV157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1562 @ SV1833 @ SV157 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4408,plain,
! [SV1205: $i,SV717: $i,SV158: $i] :
( ( ( ( c_Relation_ODomain @ SV158 @ SV717 @ SV1205 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV717 @ tc_bool ) ) )
= $false )
| ( ( SV158
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV717 @ SV1205 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4409,plain,
! [SV719: $i,SV1834: $i,SV1564: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SV1564 @ SV1834 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1564 @ SV1834 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4410,plain,
! [SV721: $i,SV1835: $i,SV163: $i,SV1565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1565 @ SV163 @ ( tc_fun @ SV1835 @ tc_bool ) ) @ SV721 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV721 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4411,plain,
! [SV722: $i,SV1836: $i,SV1566: $i,SV164: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SV1566 @ ( tc_fun @ SV1836 @ tc_bool ) ) @ SV722 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV164 @ SV722 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4412,plain,
! [SV165: $i,SV1208: $i,SV723: $i] :
( ( ( ~ ( c_Relation_Osym @ SV723 @ SV1208 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV165 @ SV1208 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1208 @ SV1208 ) @ tc_bool ) ) @ SV1208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3955]) ).
thf(4413,plain,
! [SV1837: $i,SV1567: $i,SV1209: $i,SV724: $i,SV166: $i] :
( ( ! [SY5437: $i] :
( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SY5437 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SY5437 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SV1567 @ SV1837 @ SY5437 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SY5437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4414,plain,
! [SV168: $i,SV726: $i,SV1838: $i,SV1568: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1568 @ SV1838 @ SV726 @ SV726 ) @ SV168 @ ( tc_prod @ SV726 @ SV726 ) ) @ SV726 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV168 @ SV726 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4415,plain,
! [SV1210: $i,SV727: $i,SV169: $i] :
( ( ( class_HOL_Oord @ SV169 )
= $false )
| ( ( ! [SY4779: $i] :
( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SY4779 @ SV1210 ) @ SV169 )
| ! [SY3964: $i] :
~ ( c_lessequals @ SV727 @ SY4779 @ ( tc_fun @ SY3964 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4416,plain,
! [SV1569: $i,SV1211: $i,SV728: $i,SV170: $i] :
( ( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV1569 )
= $true )
| ( ( ~ ( c_in @ SV170 @ SV1211 @ SV1569 )
| ~ ( c_in @ SV170 @ SV728 @ SV1569 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4417,plain,
! [SV1570: $i,SV1212: $i,SV729: $i,SV171: $i] :
( ( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true )
| ( ( ~ ( c_in @ SV171 @ SV1212 @ SV1570 )
| ~ ( c_in @ SV171 @ SV729 @ SV1570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4418,plain,
! [SV730: $i,SV1213: $i,SV1839: $i,SV172: $i] :
( ( ( ~ ( c_in @ SV172 @ SV1839 @ SV1213 )
| ~ ( c_lessequals @ SV1839 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV172 @ SV730 @ SV1213 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3961]) ).
thf(4419,plain,
! [SV173: $i,SV1214: $i,SV731: $i,SV1840: $i] :
( ( ( ~ ( c_lessequals @ SV1840 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) )
| ~ ( c_in @ SV173 @ SV1840 @ SV1214 ) )
= $true )
| ( ( c_in @ SV173 @ SV731 @ SV1214 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4420,plain,
! [SV732: $i,SV1215: $i,SV1841: $i,SV174: $i] :
( ( ( ~ ( c_in @ SV174 @ SV1841 @ SV1215 )
| ~ ( c_lessequals @ SV1841 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV174 @ SV732 @ SV1215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4421,plain,
! [SV733: $i,SV1216: $i,SV1842: $i,SV175: $i] :
( ( ( ~ ( c_in @ SV175 @ SV1842 @ SV1216 )
| ~ ( c_lessequals @ SV1842 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV175 @ SV733 @ SV1216 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4422,plain,
! [SV1571: $i,SV1217: $i,SV734: $i,SV176: $i] :
( ( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV734 @ SV1217 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true )
| ( ( ~ ( c_in @ SV176 @ SV734 @ SV1571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3965]) ).
thf(4423,plain,
! [SV1572: $i,SV1218: $i,SV735: $i,SV177: $i] :
( ( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SV1218 @ ( tc_fun @ SV1572 @ tc_bool ) ) @ SV1572 )
= $true )
| ( ( ~ ( c_in @ SV177 @ SV1218 @ SV1572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4424,plain,
! [SV179: $i,SV1573: $i,SV737: $i] :
( ( ( c_in @ SV737 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1573 @ tc_bool ) ) @ SV1573 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV179 @ SV737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4425,plain,
! [SV740: $i,SV1219: $i,SV1843: $i,SV182: $i] :
( ( ( ( c_in @ SV182 @ SV1843 @ SV1219 )
| ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1843 @ SV740 @ ( tc_fun @ SV1219 @ tc_bool ) ) @ SV1219 ) )
= $true )
| ( ( c_in @ SV182 @ SV740 @ SV1219 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3968]) ).
thf(4426,plain,
! [SV1220: $i,SV741: $i,SV1844: $i,SV183: $i] :
( ( ( ~ ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1844 @ SV741 @ ( tc_fun @ SV1220 @ tc_bool ) ) @ SV1220 ) )
= $true )
| ( ( c_in @ SV183 @ SV741 @ SV1220 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3969]) ).
thf(4427,plain,
! [SV1221: $i,SV1845: $i,SV742: $i,SV184: $i] :
( ( ( ~ ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV742 @ SV1845 @ ( tc_fun @ SV1221 @ tc_bool ) ) @ SV1221 ) )
= $true )
| ( ( c_in @ SV184 @ SV742 @ SV1221 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3970]) ).
thf(4428,plain,
! [SV185: $i,SV1846: $i,SV743: $i] :
( ( ( ~ ( c_in @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1846 @ tc_bool ) ) @ SV1846 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV743 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4429,plain,
! [SV1576: $i,SV1224: $i,SV749: $i,SV191: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
| ! [SY5228: $i] :
( ~ ( c_in @ SV1576 @ SY5228 @ SV749 )
| ~ ( c_in @ SV191 @ SY5228 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5228 @ SV1224 @ SV749 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3976]) ).
thf(4430,plain,
! [SV1847: $i,SV1577: $i,SV1225: $i,SV751: $i,SV194: $i] :
( ( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
!= ( c_Set_Oinsert @ SV1577 @ ( c_Set_Oinsert @ SV1847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
| ( SV194 = SV1847 )
| ( SV194 = SV1577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4431,plain,
! [SV1578: $i,SV1226: $i,SV752: $i,SV195: $i] :
( ( ( ! [SY5230: $i] :
( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
!= ( c_Set_Oinsert @ SV1578 @ ( c_Set_Oinsert @ SY5230 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) ) )
= $true )
| ( ( ( SV752 = SV1578 )
| ( SV195 = SV1578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4432,plain,
! [SV1848: $i,SV1579: $i,SV1227: $i,SV753: $i,SV196: $i] :
( ( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
!= ( c_Set_Oinsert @ SV1579 @ ( c_Set_Oinsert @ SV1848 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
| ( SV196 = SV1848 )
| ( SV753 = SV1848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4433,plain,
! [SV1849: $i,SV1580: $i,SV1228: $i,SV754: $i,SV197: $i] :
( ( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
!= ( c_Set_Oinsert @ SV1580 @ ( c_Set_Oinsert @ SV1849 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
| ( SV754 = SV1580 )
| ( SV754 = SV1849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4434,plain,
! [SV755: $i,SV1229: $i,SV198: $i] :
( ( ( c_lessequals @ SV198 @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV198 @ SV755 ) @ ( c_Product__Type_OSigma @ SV1229 @ ( c_COMBK @ SV1229 @ ( tc_fun @ SV755 @ tc_bool ) @ SV755 ) @ SV755 @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4435,plain,
! [SV756: $i,SV1230: $i,SV199: $i] :
( ( ( c_lessequals @ SV199 @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV199 @ SV756 ) @ ( c_Transitive__Closure_Ortrancl @ SV1230 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4436,plain,
! [SV1581: $i,SV1232: $i,SV759: $i,SV204: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SV759 @ SV1232 ) @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV759 @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) ) @ SV1232 ) )
= $true )
| ( ( ~ ( c_in @ SV204 @ SV1581 @ SV1232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4437,plain,
! [SV1582: $i,SV1233: $i,SV760: $i,SV205: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SV760 @ SV1233 @ SV1582 ) @ ( tc_fun @ SV1582 @ tc_bool ) )
= ( c_Set_Oinsert @ SV760 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV1233 @ ( tc_fun @ SV1582 @ tc_bool ) ) @ SV1582 ) )
= $true )
| ( ( ~ ( c_in @ SV760 @ SV205 @ SV1582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3986]) ).
thf(4438,plain,
! [SV1850: $i,SV1583: $i,SV1234: $i,SV762: $i,SV207: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV762 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4439,plain,
! [SV208: $i,SV1851: $i,SV1584: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1584 @ SV1851 @ SV208 ) @ SV1584 @ SV208 )
= $true )
| ( ( class_Lattices_Olattice @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4440,plain,
! [SV209: $i,SV1852: $i,SV1585: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1585 @ SV1852 @ SV209 ) @ SV1852 @ SV209 )
= $true )
| ( ( class_Lattices_Olattice @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4441,plain,
! [SV210: $i,SV1853: $i,SV763: $i] :
( ( ( ! [SY5438: $i] :
( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SY5438 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SV763 @ SY5438 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SV1853 @ SV210 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(4442,plain,
! [SV211: $i,SV1854: $i,SV764: $i] :
( ( ( ! [SY5439: $i] :
( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SY5439 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV764 @ SY5439 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SV1854 @ SV211 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4443,plain,
! [SV212: $i,SV1855: $i,SV765: $i] :
( ( ( ! [SY5440: $i] :
( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SY5440 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SV765 @ SY5440 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SV1855 @ SV212 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3992]) ).
thf(4444,plain,
! [SV213: $i,SV1856: $i,SV1586: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1586 @ SV1856 @ SV213 ) @ SV1856 @ SV213 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4445,plain,
! [SV214: $i,SV1857: $i,SV1587: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1587 @ SV1857 @ SV214 ) @ SV1587 @ SV214 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4446,plain,
! [SV1588: $i,SV1237: $i,SV768: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ ( tc_fun @ SV1588 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) )
| ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SV1588 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4447,plain,
! [SV1589: $i,SV1238: $i,SV769: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ ( tc_fun @ SV1589 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) )
| ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SV1589 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4448,plain,
! [SV1858: $i,SV1590: $i,SV1239: $i,SV770: $i,SV219: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV770 @ ( tc_fun @ SV1239 @ tc_bool ) ) @ ( c_COMBK @ SV1590 @ ( tc_fun @ SV1858 @ tc_bool ) @ SV1239 ) @ SV1239 @ SV1858 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV219 @ ( c_COMBK @ SV1590 @ ( tc_fun @ SV1858 @ tc_bool ) @ SV1239 ) @ SV1239 @ SV1858 ) @ ( c_Product__Type_OSigma @ SV770 @ ( c_COMBK @ SV1590 @ ( tc_fun @ SV1858 @ tc_bool ) @ SV1239 ) @ SV1239 @ SV1858 ) @ ( tc_fun @ ( tc_prod @ SV1239 @ SV1858 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4449,plain,
! [SV220: $i,SV1859: $i,SV771: $i] :
( ( ( ! [SY5441: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV771 @ SV1859 @ SV220 ) @ SY5441 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV771 @ SY5441 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SY5441 @ SV220 ) @ SV220 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4450,plain,
! [SV221: $i,SV1860: $i,SV772: $i] :
( ( ( ! [SY5442: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1860 @ SY5442 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SV1860 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SY5442 @ SV221 ) @ SV221 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4451,plain,
! [SV1593: $i,SV1242: $i,SV775: $i,SV224: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV775 @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_in @ SV224 @ SV1593 @ SV1242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4452,plain,
! [SV225: $i,SV1861: $i,SV1594: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ SV1861 @ SV225 ) @ SV225 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1594 @ SV1861 @ SV225 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4453,plain,
! [SV226: $i,SV1862: $i,SV1595: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ SV1862 @ SV226 ) @ SV226 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1595 @ SV1862 @ SV226 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4454,plain,
! [SV777: $i,SV1244: $i,SV228: $i] :
( ( ( c_lessequals @ SV228 @ SV1244 @ ( tc_fun @ ( tc_prod @ SV777 @ SV777 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OField @ SV228 @ SV777 ) @ ( c_Relation_OField @ SV1244 @ SV777 ) @ ( tc_fun @ SV777 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4455,plain,
! [SV1863: $i,SV1596: $i,SV1245: $i,SV778: $i,SV229: $i] :
( ( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SV1245 @ ( tc_fun @ SV1596 @ tc_bool ) ) @ SV1596 @ SV1863 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SV1596 @ SV1863 ) @ ( c_Relation_OImage @ SV229 @ SV1245 @ SV1596 @ SV1863 ) @ ( tc_fun @ SV1863 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SV1596 @ SV1863 ) @ SV229 ) @ SV1863 @ SV1596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4456,plain,
! [SV780: $i,SV1247: $i,SV231: $i] :
( ( ( c_Wellfounded_Owf @ SV231 @ SV1247 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV231 @ SV780 @ ( tc_fun @ ( tc_prod @ SV1247 @ SV1247 ) @ tc_bool ) ) @ SV1247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4457,plain,
! [SV232: $i,SV1248: $i,SV781: $i] :
( ( ( c_Wellfounded_Owf @ SV781 @ SV1248 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV232 @ SV781 @ ( tc_fun @ ( tc_prod @ SV1248 @ SV1248 ) @ tc_bool ) ) @ SV1248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4009]) ).
thf(4458,plain,
! [SV236: $i,SV1864: $i,SV784: $i] :
( ( ( ( c_lessequals @ SV784 @ SV1864 @ SV236 )
| ! [SY5443: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5443 @ SV784 @ SV236 ) @ SV1864 @ SV236 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4459,plain,
! [SV237: $i,SV1865: $i,SV785: $i] :
( ( ( ( c_lessequals @ SV785 @ SV1865 @ SV237 )
| ! [SY5444: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SY5444 @ SV237 ) @ SV1865 @ SV237 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4460,plain,
! [SV238: $i,SV1866: $i,SV786: $i] :
( ( ( ! [SY5445: $i] :
( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1866 @ SY5445 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SV786 @ SY5445 @ SV238 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4461,plain,
! [SV239: $i,SV1867: $i,SV787: $i] :
( ( ( ! [SY5446: $i] : ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1867 @ SY5446 @ SV239 ) @ SV239 )
| ~ ( c_lessequals @ SV787 @ SV1867 @ SV239 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4462,plain,
! [SV240: $i,SV1868: $i,SV788: $i] :
( ( ( ( c_lessequals @ SV788 @ SV1868 @ SV240 )
| ! [SY5447: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5447 @ SV788 @ SV240 ) @ SV1868 @ SV240 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV240 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4463,plain,
! [SV241: $i,SV1869: $i,SV789: $i] :
( ( ( ( c_lessequals @ SV789 @ SV1869 @ SV241 )
| ! [SY5448: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SY5448 @ SV241 ) @ SV1869 @ SV241 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4464,plain,
! [SV790: $i,SV1249: $i,SV1870: $i,SV242: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SV1870 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV242 @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4465,plain,
! [SV791: $i,SV1250: $i,SV243: $i,SV1871: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1871 @ SV243 @ ( tc_fun @ SV1250 @ tc_bool ) ) @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV243 @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4466,plain,
! [SV244: $i,SV1872: $i,SV792: $i] :
( ( ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
| ! [SY5449: $i] :
( ~ ( c_lessequals @ SV792 @ SY5449 @ SV244 )
| ~ ( c_lessequals @ SY5449 @ SV1872 @ SV244 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4019]) ).
thf(4467,plain,
! [SV245: $i,SV1873: $i,SV793: $i] :
( ( ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
| ! [SY5450: $i] :
( ~ ( c_lessequals @ SY5450 @ SV1873 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SY5450 @ SV245 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4468,plain,
! [SV248: $i,SV1251: $i,SV796: $i,SV1874: $i] :
( ( ( ~ ( c_lessequals @ SV1874 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV1874 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4469,plain,
! [SV249: $i,SV797: $i,SV1599: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1599 @ SV797 ) ) )
= $true )
| ( ( ! [SY5242: $i] :
~ ( c_lessequals @ SV1599 @ SV249 @ ( tc_fun @ SY5242 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4022]) ).
thf(4470,plain,
! [SV798: $i,SV1600: $i,SV250: $i] :
( ( ( ~ ( c_lessequals @ SV250 @ SV1600 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1600 @ SV798 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4471,plain,
! [SV253: $i,SV799: $i,SV1603: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1603 @ SV799 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV253 @ SV1603 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV253 @ SV799 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4472,plain,
! [SV800: $i,SV254: $i,SV1604: $i] :
( ( ( ! [SY5243: $i] :
~ ( c_lessequals @ SV1604 @ SV254 @ ( tc_fun @ SY5243 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1604 @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4473,plain,
! [SV801: $i,SV1605: $i,SV255: $i] :
( ( ( ~ ( c_lessequals @ SV255 @ SV1605 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1605 @ SV801 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4474,plain,
! [SV256: $i,SV1252: $i,SV802: $i,SV1875: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1875 @ SV802 @ SV1252 )
| ~ ( c_lessequals @ SV256 @ SV1875 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4029]) ).
thf(4475,plain,
! [SV1876: $i,SV1606: $i,SV1253: $i,SV803: $i,SV257: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV803 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4476,plain,
! [SV1607: $i,SV1254: $i,SV806: $i,SV260: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SV806 @ SV1254 ) @ ( c_Relation_ODomain @ SV1607 @ SV806 @ SV1254 ) @ ( tc_fun @ SV806 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV260 @ SV1607 @ ( tc_fun @ ( tc_prod @ SV806 @ SV1254 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4477,plain,
! [SV807: $i,SV1255: $i,SV261: $i] :
( ( ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) @ ( tc_fun @ SV1255 @ tc_bool ) ) )
= $true )
| ( ( SV261
= ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4478,plain,
! [SV1608: $i,SV1257: $i,SV809: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1608 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV809 @ SV1608 ) )
| ~ ( hBOOL @ ( hAPP @ SV263 @ SV1608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4033]) ).
thf(4479,plain,
! [SV1609: $i,SV1258: $i,SV810: $i,SV264: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SV810 @ SV1258 ) @ ( c_Set_Oinsert @ SV264 @ SV1609 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV810 @ SV1609 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4034]) ).
thf(4480,plain,
! [SV1259: $i,SV811: $i,SV267: $i] :
( ( ( ( c_Relation_ORange @ SV267 @ SV811 @ SV1259 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) )
= $false )
| ( ( SV267
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV811 @ SV1259 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4481,plain,
! [SV1877: $i,SV1610: $i,SV1260: $i,SV812: $i,SV268: $i] :
( ( ! [SY5451: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SY5451 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
| ~ ( c_lessequals @ SV812 @ SY5451 @ ( tc_fun @ SV1260 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4482,plain,
! [SV1261: $i,SV269: $i,SV813: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV813 @ SV269 @ SV1261 )
= $false )
| ( ( c_lessequals @ SV269 @ ( c_Product__Type_OSigma @ SV813 @ ( c_COMBK @ SV813 @ ( tc_fun @ SV1261 @ tc_bool ) @ SV1261 ) @ SV1261 @ SV1261 ) @ ( tc_fun @ ( tc_prod @ SV1261 @ SV1261 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4483,plain,
! [SV270: $i,SV1878: $i,SV1611: $i] :
( ( ( ( c_lessequals @ SV1611 @ SV1878 @ SV270 )
| ( c_lessequals @ SV1878 @ SV1611 @ SV270 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4038]) ).
thf(4484,plain,
! [SV814: $i,SV1879: $i,SV1262: $i,SV271: $i] :
( ( ( ! [SY5452: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SY5452 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SY5452 ) @ SY5452 @ SY5452 ) @ SV1879 @ ( tc_prod @ SY5452 @ SY5452 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SY5452 @ SY5452 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SY5452 ) @ ( tc_prod @ SY5452 @ SY5452 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4485,plain,
! [SV815: $i,SV1880: $i,SV1263: $i,SV272: $i] :
( ( ( ! [SY5453: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SY5453 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SY5453 ) @ SY5453 @ SY5453 ) @ SV1880 @ ( tc_prod @ SY5453 @ SY5453 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
| ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SY5453 @ SY5453 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SY5453 ) @ ( tc_prod @ SY5453 @ SY5453 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4486,plain,
! [SV1264: $i,SV816: $i,SV273: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4487,plain,
! [SV1612: $i,SV1265: $i,SV817: $i,SV274: $i] :
( ( ( SV274 = SV817 )
= $true )
| ( ( ! [SY5248: $i,SY5249: $i] :
( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SY5248 ) @ SY5249 @ ( tc_prod @ SV1612 @ SY5248 ) )
| ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SY5248 ) @ SY5249 @ ( tc_prod @ SV1612 @ SY5248 ) )
| ~ ( c_Relation_Osingle__valued @ SY5249 @ SV1612 @ SY5248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4042]) ).
thf(4488,plain,
! [SV1881: $i,SV1613: $i,SV1266: $i,SV818: $i,SV275: $i] :
( ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
!= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
| ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 )
| ( SV275 = SV1881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4489,plain,
! [SV1614: $i,SV1267: $i,SV819: $i,SV276: $i] :
( ( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV819 @ SV1267 @ ( tc_fun @ ( tc_prod @ SV1614 @ SV1614 ) @ tc_bool ) ) @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true )
| ( ( ~ ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SV819 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4044]) ).
thf(4490,plain,
! [SV1615: $i,SV1268: $i,SV820: $i,SV277: $i] :
( ( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1268 @ ( tc_fun @ ( tc_prod @ SV1615 @ SV1615 ) @ tc_bool ) ) @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true )
| ( ( ~ ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SV1268 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4045]) ).
thf(4491,plain,
! [SV278: $i,SV1269: $i,SV821: $i,SV1882: $i] :
( ( ( ~ ( c_lessequals @ SV1882 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) )
| ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV1882 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) ) )
= $true )
| ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(4492,plain,
! [SV822: $i,SV1270: $i,SV279: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV279 @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV279 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( c_Relation_Orel__comp @ SV1270 @ SV279 @ SV822 @ SV822 @ SV822 ) @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV1270 @ ( tc_fun @ ( tc_prod @ SV822 @ SV822 ) @ tc_bool ) ) @ SV822 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4493,plain,
! [SV823: $i,SV1271: $i,SV280: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV280 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( c_Relation_Orel__comp @ SV823 @ SV280 @ SV1271 @ SV1271 @ SV1271 ) @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV280 @ SV823 @ ( tc_fun @ ( tc_prod @ SV1271 @ SV1271 ) @ tc_bool ) ) @ SV1271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4494,plain,
! [SV1616: $i,SV1273: $i,SV834: $i,SV292: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $true )
| ( ( ! [SY5252: $i] :
( ~ ( c_in @ SV1616 @ SY5252 @ SV834 )
| ~ ( c_in @ SV292 @ SY5252 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5252 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4053]) ).
thf(4495,plain,
! [SV1274: $i,SV835: $i,SV1883: $i,SV293: $i] :
( ( ( ( SV293 = SV1883 )
| ! [SY5455: $i] :
( ~ ( c_lessequals @ SY5455 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY5455 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) ) )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4496,plain,
! [SV1617: $i,SV1275: $i,SV836: $i,SV294: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
| ! [SY4848: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4848 @ SV294 @ SV1275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4497,plain,
! [SV837: $i,SV295: $i,SV1884: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1884 @ SV1884 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SV837 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SV837 ) @ ( c_Transitive__Closure_Ortrancl @ SV837 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4056]) ).
thf(4498,plain,
! [SV1618: $i,SV1276: $i,SV838: $i,SV296: $i] :
( ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
!= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $true )
| ( ( ~ ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4499,plain,
! [SV1885: $i,SV1619: $i,SV1278: $i,SV839: $i,SV299: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SV1278 @ SV1619 @ SV1885 ) @ SV299 @ SV1619 )
| ~ ( c_in @ SV1278 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SV1619 @ SV1885 ) @ ( tc_prod @ SV1619 @ SV1885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4500,plain,
! [SV1620: $i,SV1279: $i,SV840: $i,SV300: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SV1279 @ SV1620 ) @ SV840 @ SV1620 @ SV1620 ) @ SV1279 @ ( tc_prod @ SV1620 @ SV1620 ) )
= $true )
| ( ( ( SV300 = SV840 )
| ~ ( c_in @ ( c_Pair @ SV300 @ SV840 @ SV1620 @ SV1620 ) @ ( c_Transitive__Closure_Ortrancl @ SV1279 @ SV1620 ) @ ( tc_prod @ SV1620 @ SV1620 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4501,plain,
! [SV1621: $i,SV1280: $i,SV841: $i,SV301: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SV1280 @ SV1621 ) @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) )
= $true )
| ( ( ( SV841 = SV1280 )
| ~ ( c_in @ ( c_Pair @ SV841 @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4502,plain,
! [SV1622: $i,SV1281: $i,SV842: $i,SV302: $i] :
( ( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SV1281 @ SV1622 ) @ SV1622 @ SV1622 ) @ SV842 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $true )
| ( ( ( SV302 = SV1281 )
| ~ ( c_in @ ( c_Pair @ SV302 @ SV1281 @ SV1622 @ SV1622 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SV1622 ) @ ( tc_prod @ SV1622 @ SV1622 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4503,plain,
! [SV843: $i,SV1886: $i,SV1282: $i,SV303: $i] :
( ( ( ! [SY5456: $i] :
( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SY5456 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SY5456 @ SY5456 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SY5456 ) @ ( tc_prod @ SY5456 @ SY5456 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4504,plain,
! [SV844: $i,SV1887: $i,SV1283: $i,SV304: $i] :
( ( ( ! [SY5457: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SY5457 ) @ SV1283 @ SY5457 @ SY5457 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SY5457 ) @ ( tc_prod @ SY5457 @ SY5457 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SY5457 @ SY5457 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SY5457 ) @ ( tc_prod @ SY5457 @ SY5457 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4505,plain,
! [SV845: $i,SV1888: $i,SV305: $i,SV1284: $i] :
( ( ( ! [SY5458: $i] :
( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SY5458 ) @ SY5458 @ SY5458 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SY5458 ) @ ( tc_prod @ SY5458 @ SY5458 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
| ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SY5458 @ SY5458 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SY5458 ) @ ( tc_prod @ SY5458 @ SY5458 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4506,plain,
! [SV846: $i,SV1889: $i,SV1285: $i,SV306: $i] :
( ( ( ! [SY5459: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SY5459 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SY5459 @ SY5459 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SY5459 ) @ ( tc_prod @ SY5459 @ SY5459 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4507,plain,
! [SV1623: $i,SV1286: $i,SV847: $i,SV307: $i] :
( ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ! [SY5255: $i] :
( ~ ( c_in @ ( c_Pair @ SY5255 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_in @ ( c_Pair @ SY5255 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4508,plain,
! [SV1287: $i,SV308: $i,SV848: $i] :
( ( ( SV848 = SV308 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV308 @ SV848 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SV848 @ SV1287 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4509,plain,
! [SV849: $i,SV1890: $i,SV1288: $i,SV309: $i] :
( ( ( ! [SY5460: $i] :
( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SY5460 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
| ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SY5460 @ SY5460 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SY5460 ) @ ( tc_prod @ SY5460 @ SY5460 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4510,plain,
! [SV1289: $i,SV310: $i,SV850: $i] :
( ( ( SV850 = SV310 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV310 @ SV850 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1289 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SV850 @ SV1289 ) @ SV850 @ t_a @ t_a ) @ SV1289 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4511,plain,
! [SV851: $i,SV1891: $i,SV1290: $i,SV311: $i] :
( ( ( ! [SY5461: $i] :
( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SY5461 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SY5461 @ SY5461 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SY5461 ) @ ( tc_prod @ SY5461 @ SY5461 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4512,plain,
! [SV1624: $i,SV1291: $i,SV852: $i,SV312: $i] :
( ( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SV1291 @ SV1624 ) @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) )
= $true )
| ( ( ( SV312 = SV852 )
| ~ ( c_in @ ( c_Pair @ SV312 @ SV852 @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4071]) ).
thf(4513,plain,
! [SV853: $i,SV1292: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( ! [SY4870: $i,SY4871: $i] :
( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SY4870 @ SY4871 ) @ SY4871 @ SY4871 ) @ SY4870 @ ( tc_prod @ SY4871 @ SY4871 ) )
| ~ ( c_Wellfounded_Owf @ SY4870 @ SY4871 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4514,plain,
! [SV854: $i,SV1293: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( ! [SY4872: $i,SY4873: $i] :
( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SY4872 @ SY4873 ) @ SY4873 @ SY4873 ) @ SY4872 @ ( tc_prod @ SY4873 @ SY4873 ) )
| ~ ( c_Wellfounded_Owf @ SY4872 @ SY4873 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4515,plain,
! [SV855: $i,SV1294: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( ! [SY4874: $i,SY4875: $i] :
( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SY4874 @ SY4875 ) @ SY4875 @ SY4875 ) @ SY4874 @ ( tc_prod @ SY4875 @ SY4875 ) )
| ~ ( c_Wellfounded_Owf @ SY4874 @ SY4875 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4516,plain,
! [SV856: $i,SV1295: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( ! [SY4876: $i,SY4877: $i] :
( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SY4876 @ SY4877 ) @ SY4877 @ SY4877 ) @ SY4876 @ ( tc_prod @ SY4877 @ SY4877 ) )
| ~ ( c_Wellfounded_Owf @ SY4876 @ SY4877 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4075]) ).
thf(4517,plain,
! [SV1296: $i,SV857: $i,SV317: $i] :
( ( ( c_in @ ( c_Pair @ SV317 @ SV317 @ SV857 @ SV857 ) @ SV1296 @ ( tc_prod @ SV857 @ SV857 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1296 @ SV857 ) @ SV857 @ SV857 ) @ ( c_Transitive__Closure_Otrancl @ SV1296 @ SV857 ) @ ( tc_prod @ SV857 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4518,plain,
! [SV1625: $i,SV1297: $i,SV858: $i,SV318: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SV1297 @ SV1625 ) @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ SV318 @ ( tc_prod @ SV1625 @ SV1625 ) )
| ~ ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4519,plain,
! [SV1298: $i,SV859: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ SV1298 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SV859 @ SV1298 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4078]) ).
thf(4520,plain,
! [SV1299: $i,SV860: $i,SV320: $i] :
( ( ( c_in @ ( c_Pair @ SV320 @ SV320 @ SV860 @ SV860 ) @ ( c_Transitive__Closure_Otrancl @ SV1299 @ SV860 ) @ ( tc_prod @ SV860 @ SV860 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1299 @ SV860 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4521,plain,
! [SV1626: $i,SV1300: $i,SV861: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SV1300 @ SV1626 ) @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV1626 ) @ ( tc_prod @ SV1626 @ SV1626 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4080]) ).
thf(4522,plain,
! [SV1627: $i,SV1301: $i,SV862: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SV1301 @ SV1627 ) @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ SV1301 @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4081]) ).
thf(4523,plain,
! [SV1628: $i,SV1302: $i,SV863: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SV1302 @ SV1628 ) @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
| ~ ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SV1628 ) @ ( tc_prod @ SV1628 @ SV1628 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4082]) ).
thf(4524,plain,
! [SV1303: $i,SV864: $i,SV324: $i] :
( ( ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SV864 @ SV1303 ) @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4083]) ).
thf(4525,plain,
! [SV1629: $i,SV1304: $i,SV865: $i,SV325: $i] :
( ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true )
| ( ( ! [SY5256: $i] :
( ~ ( c_in @ SV865 @ SY5256 @ SV1304 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY5256 @ SV1629 @ SV1304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4526,plain,
! [SV1630: $i,SV1305: $i,SV866: $i,SV326: $i] :
( ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true )
| ( ( ! [SY5257: $i] :
~ ( c_in @ SY5257 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
| ! [SY5258: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5258 @ SV1630 @ SV1305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4527,plain,
! [SV1892: $i,SV1631: $i,SV1306: $i,SV867: $i,SV327: $i] :
( ( ! [SY5462: $i,SY5463: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SV1892 @ SY5462 @ SY5463 ) @ SV867 @ SY5463 @ SY5462 ) @ SV1631 @ ( tc_prod @ SY5463 @ SY5462 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SV1892 @ SY5462 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SV1892 @ SY5463 @ SY5462 ) @ ( tc_prod @ SV1892 @ SY5462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4086]) ).
thf(4528,plain,
! [SV1893: $i,SV1632: $i,SV1307: $i,SV868: $i,SV328: $i] :
( ( ! [SY5464: $i,SY5465: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SV1893 @ SY5464 @ SY5465 ) @ SV1893 @ SY5465 ) @ SV1307 @ ( tc_prod @ SV1893 @ SY5465 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SV1893 @ SY5464 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SV1893 @ SY5465 @ SY5464 ) @ ( tc_prod @ SV1893 @ SY5464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4529,plain,
! [SV1894: $i,SV1633: $i,SV1308: $i,SV869: $i,SV329: $i] :
( ( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SV869 @ SV1308 @ SV1633 @ SV1894 ) @ ( tc_fun @ SV1633 @ SV1894 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV869 @ SV1308 @ SV329 @ SV1633 @ SV1894 ) @ SV869 @ SV1633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4530,plain,
! [SV1895: $i,SV1634: $i,SV1309: $i,SV870: $i,SV330: $i] :
( ( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV870 @ SV1309 @ SV1634 @ SV1895 ) @ ( tc_fun @ SV1634 @ SV1895 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV870 @ SV1309 @ SV330 @ SV1634 @ SV1895 ) @ SV870 @ SV1634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4531,plain,
! [SV1896: $i,SV1635: $i,SV1310: $i,SV871: $i,SV331: $i] :
( ( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SV1310 @ SV1635 @ SV1896 ) @ ( tc_fun @ SV1635 @ SV1896 ) )
| ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ ( hAPP @ SV1310 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ SV1896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4090]) ).
thf(4532,plain,
! [SV1636: $i,SV1311: $i,SV872: $i,SV332: $i] :
( ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true )
| ( ( ! [SY5268: $i,SY5269: $i] :
( ~ ( c_in @ SV872 @ SY5268 @ SY5269 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY5268 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SY5269 ) @ SY5269 @ SV1636 ) @ ( tc_fun @ SY5269 @ SV1636 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4533,plain,
! [SV1897: $i,SV1637: $i,SV1312: $i,SV873: $i,SV333: $i] :
( ( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SV1312 @ SV1637 @ SV1897 ) @ ( tc_fun @ SV1637 @ SV1897 ) )
| ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ ( hAPP @ SV1312 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ SV1897 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4534,plain,
! [SV1313: $i,SV337: $i,SV877: $i] :
( ( ( c_in @ SV877 @ ( c_Relation_OId__on @ SV337 @ SV1313 ) @ ( tc_prod @ SV1313 @ SV1313 ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV337 @ SV877 @ SV1313 ) @ SV337 @ SV1313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4535,plain,
! [SV1314: $i,SV878: $i,SV338: $i] :
( ( ( c_in @ SV338 @ ( c_Relation_OId__on @ SV878 @ SV1314 ) @ ( tc_prod @ SV1314 @ SV1314 ) )
= $false )
| ( ( SV338
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV878 @ SV338 @ SV1314 ) @ SV1314 @ SV1314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4536,plain,
! [SV1898: $i,SV1638: $i,SV1315: $i,SV879: $i,SV339: $i] :
( ( ! [SY5466: $i] :
( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SV1315 @ SV1638 @ SV1898 )
= ( c_Recdef_Ocut @ SY5466 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SY5466 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) @ SV1315 @ SV1638 @ SV1638 ) @ SV879 @ ( tc_prod @ SV1638 @ SV1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4537,plain,
! [SV1316: $i,SV343: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV343 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV343 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV343 ) @ SV1316 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4099]) ).
thf(4538,plain,
! [SV1317: $i,SV344: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV344 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV344 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV344 ) @ SV1317 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4539,plain,
! [SV345: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ SV345 ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ SV345 ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV345 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ SV345 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_Arrow__Order__Mirabelle_OIIA @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4540,plain,
! [SV884: $i,SV348: $i,SV1639: $i] :
( ( ( c_Relation_Orefl__on @ SV1639 @ SV348 @ SV884 )
= $false )
| ( ( c_lessequals @ SV348 @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV884 @ SV884 ) @ SV348 ) @ SV348 @ SV884 @ SV884 @ SV884 ) @ ( tc_fun @ ( tc_prod @ SV884 @ SV884 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4541,plain,
! [SV1640: $i,SV1318: $i,SV885: $i,SV349: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV349 @ SV885 @ SV1318 @ SV1318 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1318 ) @ ( tc_prod @ SV1318 @ SV1318 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SV1318 @ SV1318 ) @ SV1640 @ ( tc_prod @ SV1318 @ SV1318 ) ) @ SV1318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4542,plain,
! [SV1641: $i,SV1319: $i,SV886: $i,SV350: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SV1319 @ SV1319 ) @ SV1641 @ ( tc_prod @ SV1319 @ SV1319 ) ) @ SV1319 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV886 @ SV350 @ SV1319 @ SV1319 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1319 ) @ ( tc_prod @ SV1319 @ SV1319 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1641 @ SV1319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4543,plain,
! [SV887: $i,SV1320: $i,SV1899: $i,SV351: $i] :
( ( ( ~ ( c_in @ SV351 @ SV1899 @ SV1320 )
| ~ ( c_Equiv__Relations_Oequiv @ SV1899 @ SV887 @ SV1320 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4544,plain,
! [SV1900: $i,SV1642: $i,SV1321: $i,SV888: $i,SV352: $i] :
( ( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SV1321 @ SV1642 ) @ SV1900 @ ( tc_prod @ SV1321 @ SV1642 ) )
| ~ ( c_in @ SV888 @ ( c_Relation_OImage @ SV1900 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 @ SV1642 ) @ SV1642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4545,plain,
! [SV1901: $i,SV1643: $i,SV1322: $i,SV889: $i,SV353: $i] :
( ( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SV1322 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1643 @ tc_bool ) ) @ SV1643 ) @ SV1643 @ SV1901 ) @ SV1901 )
| ~ ( c_in @ ( c_Pair @ SV1322 @ SV353 @ SV1643 @ SV1901 ) @ SV889 @ ( tc_prod @ SV1643 @ SV1901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(4546,plain,
! [SV1644: $i,SV1323: $i,SV890: $i,SV354: $i] :
( ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
| ! [SY4917: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4917 @ SV354 @ SV1323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4547,plain,
! [SV1645: $i,SV1324: $i,SV891: $i,SV355: $i] :
( ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
| ! [SY4919: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4919 @ SV355 @ SV1324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4109]) ).
thf(4548,plain,
! [SV1646: $i,SV1325: $i,SV892: $i,SV356: $i] :
( ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
!= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
| ! [SY5277: $i] :
( ~ ( c_in @ SV1646 @ SY5277 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5277 @ SV356 @ SV1325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4549,plain,
! [SV1647: $i,SV1326: $i,SV893: $i,SV357: $i] :
( ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
!= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $true )
| ( ( ! [SY5278: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5278 @ SV357 @ SV1326 )
| ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SY5278 @ SV1326 )
| ~ ( c_in @ SV893 @ SY5278 @ SV1326 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4550,plain,
! [SV1648: $i,SV1327: $i,SV894: $i,SV358: $i] :
( ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
| ! [SY5279: $i] :
( ~ ( c_in @ SV1648 @ SY5279 @ SV1327 )
| ~ ( c_in @ SV894 @ SY5279 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5279 @ SV358 @ SV1327 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4551,plain,
! [SV1649: $i,SV1328: $i,SV895: $i,SV359: $i] :
( ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
!= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $true )
| ( ( ! [SY5280: $i] :
( ~ ( c_in @ SV1649 @ SY5280 @ SV1328 )
| ~ ( c_in @ SV895 @ SY5280 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5280 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4552,plain,
! [SV1650: $i,SV1329: $i,SV896: $i,SV360: $i] :
( ( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV896 @ SV360 @ SV1329 @ SV1650 ) @ SV1650 @ SV1650 ) @ SV896 @ ( tc_prod @ SV1650 @ SV1650 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV360 @ SV1329 @ SV1650 @ SV1650 ) @ ( c_Transitive__Closure_Otrancl @ SV896 @ SV1650 ) @ ( tc_prod @ SV1650 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4553,plain,
! [SV1651: $i,SV1330: $i,SV897: $i,SV361: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SV897 @ SV1330 @ SV1651 ) @ SV1330 @ SV1651 @ SV1651 ) @ SV361 @ ( tc_prod @ SV1651 @ SV1651 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV897 @ SV1330 @ SV1651 @ SV1651 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SV1651 ) @ ( tc_prod @ SV1651 @ SV1651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4554,plain,
! [SV898: $i,SV1902: $i,SV1652: $i,SV362: $i] :
( ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SV1652 @ SV1902 ) @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 )
| ~ ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4555,plain,
! [SV1331: $i,SV363: $i,SV899: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV899 @ SV363 @ SV1331 ) @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 )
= $false )
| ( ( c_in @ SV363 @ ( c_Wellfounded_Oacc @ SV899 @ SV1331 ) @ SV1331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4117]) ).
thf(4556,plain,
! [SV900: $i,SV1653: $i,SV364: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SV1653 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SV1653 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4557,plain,
! [SV901: $i,SV1903: $i,SV1654: $i,SV365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SV1654 @ SV1903 ) ) )
| ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SV1654 @ SV1903 ) @ SV1903 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4558,plain,
! [SV1332: $i,SV902: $i,SV366: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV366 @ SV902 @ SV1332 ) @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 )
= $false )
| ( ( c_in @ SV902 @ ( c_Wellfounded_Oacc @ SV366 @ SV1332 ) @ SV1332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4120]) ).
thf(4559,plain,
! [SV903: $i,SV1904: $i,SV1655: $i,SV367: $i] :
( ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SV1655 @ SV1904 ) @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 )
| ~ ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4560,plain,
! [SV904: $i,SV1656: $i,SV368: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SV1656 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SV1656 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4561,plain,
! [SV905: $i,SV1905: $i,SV1657: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SV1657 @ SV1905 ) ) )
| ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SV1657 @ SV1905 ) @ SV1905 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(4562,plain,
! [SV1906: $i,SV1658: $i,SV1333: $i,SV906: $i,SV370: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SV1333 @ SV1658 @ SV1906 ) @ SV370 @ SV1658 )
| ~ ( c_in @ SV906 @ ( c_Relation_OImage @ SV1333 @ SV370 @ SV1658 @ SV1906 ) @ SV1906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4563,plain,
! [SV1907: $i,SV1659: $i,SV1334: $i,SV907: $i,SV371: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SV1334 @ SV1659 @ SV1907 ) @ SV371 @ SV1659 )
| ~ ( c_in @ SV907 @ ( c_Relation_OImage @ SV1334 @ SV371 @ SV1659 @ SV1907 ) @ SV1907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4564,plain,
! [SV372: $i,SV908: $i,SV1908: $i,SV1660: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1660 @ SV1908 @ SV908 @ SV908 ) @ SV372 @ ( tc_prod @ SV908 @ SV908 ) ) @ SV908 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV372 @ SV908 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4565,plain,
! [SV909: $i,SV1335: $i,SV373: $i] :
( ( ( ! [SY4934: $i] :
~ ( c_in @ SY4934 @ SV373 @ SV1335 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV909 @ SV1335 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4566,plain,
! [SV910: $i,SV1336: $i,SV374: $i] :
( ( ( ! [SY4935: $i] :
~ ( c_in @ SY4935 @ SV374 @ SV1336 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV910 @ SV1336 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4567,plain,
! [SV1909: $i,SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ! [SY5467: $i,SY5468: $i,SY5469: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SY5467 @ SY5467 ) @ SY5468 @ ( tc_prod @ SY5467 @ SY5467 ) )
| ! [SY5292: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SY5469 @ SY5469 ) @ SY5292 @ ( tc_prod @ SY5469 @ SY5469 ) )
| ! [SY3122: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5292 @ SY5468 @ SV375 @ SY5469 @ SY5467 @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4568,plain,
! [SV1910: $i,SV1662: $i,SV1339: $i,SV914: $i,SV378: $i] :
( ( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV378 @ SV914 @ SV1339 @ SV1662 ) @ SV1910 @ ( tc_prod @ SV1339 @ SV1662 ) ) @ SV1339 @ SV1662 )
= ( c_Set_Oinsert @ SV378 @ ( c_Relation_ODomain @ SV1910 @ SV1339 @ SV1662 ) @ SV1339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4569,plain,
! [SV379: $i,SV915: $i,SV1663: $i] :
( ( ( SV1663 = SV915 )
= $true )
| ( ( ! [SY5295: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1663 @ SV379 @ SY5295 ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4132]) ).
thf(4570,plain,
! [SV1665: $i,SV1342: $i,SV918: $i,SV382: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SV918 @ SV1342 ) @ SV1665 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV918 @ SV1665 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4571,plain,
! [SV1911: $i,SV1666: $i,SV1343: $i,SV919: $i,SV383: $i] :
( ( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV383 @ SV919 @ SV1343 @ SV1666 ) @ SV1911 @ ( tc_prod @ SV1343 @ SV1666 ) ) @ SV1343 @ SV1666 )
= ( c_Set_Oinsert @ SV919 @ ( c_Relation_ORange @ SV1911 @ SV1343 @ SV1666 ) @ SV1666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4572,plain,
! [SV1667: $i,SV1344: $i,SV920: $i,SV384: $i] :
( ( ( c_in @ SV384 @ ( c_Set_Oinsert @ SV920 @ SV1344 @ SV1667 ) @ SV1667 )
= $true )
| ( ( ~ ( c_in @ SV384 @ SV1344 @ SV1667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4573,plain,
! [SV1668: $i,SV1345: $i,SV921: $i,SV385: $i] :
( ( ( c_in @ SV385 @ ( c_Set_Oinsert @ SV921 @ SV1345 @ SV1668 ) @ SV1668 )
= $true )
| ( ( ~ ( c_in @ SV385 @ SV1345 @ SV1668 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4137]) ).
thf(4574,plain,
! [SV1346: $i,SV922: $i,SV1912: $i,SV386: $i] :
( ( ( ( SV386 = SV1912 )
| ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SV1912 @ SV922 @ SV1346 ) @ SV1346 ) )
= $true )
| ( ( c_in @ SV386 @ SV922 @ SV1346 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4575,plain,
! [SV1669: $i,SV1350: $i,SV926: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
!= ( c_Set_Oinsert @ SV390 @ SV1669 @ SV1350 ) )
= $true )
| ( ( ( c_in @ SV390 @ SV1669 @ SV1350 )
| ( SV926 = SV1669 )
| ( c_in @ SV390 @ SV926 @ SV1350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4576,plain,
! [SV1351: $i,SV927: $i,SV391: $i] :
( ( ( c_in @ SV391 @ SV927 @ SV1351 )
= $false )
| ( ( ( c_Set_Oinsert @ SV391 @ SV927 @ SV1351 )
= SV927 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4577,plain,
! [SV1913: $i,SV1670: $i,SV1352: $i,SV928: $i,SV392: $i] :
( ( ! [SY5472: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
| ! [SY5473: $i] :
( ~ ( c_in @ SV1352 @ SY5472 @ SY5473 )
| ! [SY5474: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5474 @ SV392 @ SV928 @ SY5473 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5472 @ SY5474 @ SY5473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4578,plain,
! [SV1353: $i,SV931: $i,SV398: $i] :
( ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false )
| ( ( ! [SY4958: $i] :
( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SY4958 @ SV1353 ) @ SV1353 @ SV1353 ) @ SY4958 @ ( tc_prod @ SV1353 @ SV1353 ) )
| ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SY4958 @ SV1353 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4579,plain,
! [SV1354: $i,SV932: $i,SV399: $i] :
( ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false )
| ( ( ! [SY4960: $i] :
( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SY4960 @ SV1354 ) @ SV1354 @ SV1354 ) @ SY4960 @ ( tc_prod @ SV1354 @ SV1354 ) )
| ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SY4960 @ SV1354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4580,plain,
! [SV1914: $i,SV1671: $i,SV1355: $i,SV933: $i,SV400: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SV1355 @ SV1671 @ SV1914 ) @ SV933 @ SV1671 @ SV1914 ) @ SV1355 @ ( tc_prod @ SV1671 @ SV1914 ) )
| ~ ( c_in @ SV933 @ ( c_Relation_OImage @ SV1355 @ SV400 @ SV1671 @ SV1914 ) @ SV1914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(4581,plain,
! [SV1915: $i,SV1672: $i,SV1356: $i,SV934: $i,SV401: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SV1356 @ SV1672 @ SV1915 ) @ SV934 @ SV1672 @ SV1915 ) @ SV1356 @ ( tc_prod @ SV1672 @ SV1915 ) )
| ~ ( c_in @ SV934 @ ( c_Relation_OImage @ SV1356 @ SV401 @ SV1672 @ SV1915 ) @ SV1915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4582,plain,
! [SV1673: $i,SV1357: $i,SV935: $i,SV402: $i] :
( ( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SV935 @ SV1357 @ SV1673 ) @ SV1357 @ SV1673 ) @ SV935 @ ( tc_prod @ SV1357 @ SV1673 ) )
= $true )
| ( ( ~ ( c_in @ SV402 @ ( c_Relation_ODomain @ SV935 @ SV1357 @ SV1673 ) @ SV1357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4147]) ).
thf(4583,plain,
! [SV1674: $i,SV1358: $i,SV936: $i,SV403: $i] :
( ( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SV936 @ SV1358 @ SV1674 ) @ SV1358 @ SV1674 ) @ SV936 @ ( tc_prod @ SV1358 @ SV1674 ) )
= $true )
| ( ( ~ ( c_in @ SV403 @ ( c_Relation_ODomain @ SV936 @ SV1358 @ SV1674 ) @ SV1358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4148]) ).
thf(4584,plain,
! [SV937: $i,SV404: $i,SV1916: $i,SV1675: $i] :
( ( ( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SV1916 ) @ t_a @ t_a ) @ SV1916 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(4585,plain,
! [SV938: $i,SV405: $i,SV1917: $i,SV1676: $i] :
( ( ( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SV1917 ) @ t_a @ t_a ) @ SV1917 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(4586,plain,
! [SV940: $i,SV1360: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( ! [SY4968: $i,SY4969: $i] :
( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SY4968 @ SY4969 ) @ SY4969 @ SY4969 ) @ SY4968 @ ( tc_prod @ SY4969 @ SY4969 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SY4968 @ SY4969 ) @ SY4969 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4152]) ).
thf(4587,plain,
! [SV941: $i,SV1677: $i,SV408: $i] :
( ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
= $true )
| ( ( ! [SY5305: $i] :
( ~ ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SY5305 ) @ t_a @ t_a ) @ SY5305 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SY5305 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4588,plain,
! [SV942: $i,SV1678: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
= $true )
| ( ( ! [SY5306: $i] :
( ~ ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SY5306 ) @ t_a @ t_a ) @ SY5306 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SY5306 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4589,plain,
! [SV943: $i,SV1361: $i,SV410: $i] :
( ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( ! [SY4970: $i,SY4971: $i] :
( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SY4970 @ SY4971 ) @ SY4971 @ SY4971 ) @ SY4970 @ ( tc_prod @ SY4971 @ SY4971 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SY4970 @ SY4971 ) @ SY4971 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4590,plain,
! [SV1679: $i,SV1363: $i,SV945: $i,SV412: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SV1363 @ SV1363 ) @ SV1679 @ ( tc_prod @ SV1363 @ SV1363 ) ) @ SV1363 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV945 @ SV412 @ SV1363 @ SV1363 ) @ ( c_Transitive__Closure_Ortrancl @ SV1679 @ SV1363 ) @ ( tc_prod @ SV1363 @ SV1363 ) )
| ~ ( c_Wellfounded_Owf @ SV1679 @ SV1363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4157]) ).
thf(4591,plain,
! [SV1680: $i,SV1364: $i,SV946: $i,SV413: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV413 @ SV946 @ SV1364 @ SV1364 ) @ ( c_Transitive__Closure_Ortrancl @ SV1680 @ SV1364 ) @ ( tc_prod @ SV1364 @ SV1364 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SV1364 @ SV1364 ) @ SV1680 @ ( tc_prod @ SV1364 @ SV1364 ) ) @ SV1364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4592,plain,
! [SV1681: $i,SV1365: $i,SV947: $i,SV414: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SV947 @ SV1365 @ SV1681 ) @ SV414 @ SV1681 @ SV1365 ) @ SV947 @ ( tc_prod @ SV1681 @ SV1365 ) )
= $true )
| ( ( ~ ( c_in @ SV414 @ ( c_Relation_ORange @ SV947 @ SV1681 @ SV1365 ) @ SV1365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4593,plain,
! [SV1682: $i,SV1366: $i,SV948: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SV948 @ SV1366 @ SV1682 ) @ SV415 @ SV1682 @ SV1366 ) @ SV948 @ ( tc_prod @ SV1682 @ SV1366 ) )
= $true )
| ( ( ~ ( c_in @ SV415 @ ( c_Relation_ORange @ SV948 @ SV1682 @ SV1366 ) @ SV1366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4160]) ).
thf(4594,plain,
! [SV1683: $i,SV1367: $i,SV949: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SV949 @ SV1367 @ SV1683 ) @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV949 @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4595,plain,
! [SV1684: $i,SV1368: $i,SV950: $i,SV417: $i] :
( ( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV950 @ SV417 @ SV1368 @ SV1684 ) @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Ortrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV417 @ SV1368 @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Otrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4596,plain,
! [SV1685: $i,SV1369: $i,SV951: $i,SV418: $i] :
( ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $true )
| ( ( ! [SY5307: $i] :
( ~ ( c_in @ ( c_Pair @ SY5307 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SY5307 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4163]) ).
thf(4597,plain,
! [SV1686: $i,SV1370: $i,SV952: $i,SV419: $i] :
( ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $true )
| ( ( ! [SY5308: $i] :
( ~ ( c_in @ ( c_Pair @ SY5308 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SY5308 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4598,plain,
! [SV1687: $i,SV1371: $i,SV953: $i,SV420: $i] :
( ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true )
| ( ( ! [SY5309: $i] :
( ~ ( c_in @ ( c_Pair @ SY5309 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SY5309 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4165]) ).
thf(4599,plain,
! [SV1918: $i,SV1688: $i,SV1372: $i,SV954: $i,SV421: $i] :
( ( ! [SY5475: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SV1688 @ SV1918 ) @ SY5475 )
= ( hAPP @ SV421 @ SY5475 ) )
| ~ ( c_in @ ( c_Pair @ SY5475 @ SV1372 @ SV1688 @ SV1688 ) @ SV954 @ ( tc_prod @ SV1688 @ SV1688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4166]) ).
thf(4600,plain,
! [SV1919: $i,SV1689: $i,SV1373: $i,SV955: $i,SV422: $i] :
( ( ! [SY5476: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SV1689 @ SV1919 ) @ SY5476 )
= ( hAPP @ SV422 @ SY5476 ) )
| ~ ( c_in @ ( c_Pair @ SY5476 @ SV1373 @ SV1689 @ SV1689 ) @ SV955 @ ( tc_prod @ SV1689 @ SV1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4601,plain,
! [SV1920: $i,SV1690: $i,SV956: $i,SV423: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV423 @ SV956 @ SV1690 @ SV1690 ) @ ( c_Transitive__Closure_Ortrancl @ SV1920 @ SV1690 ) @ ( tc_prod @ SV1690 @ SV1690 ) )
| ( c_in @ SV423 @ ( c_Relation_ODomain @ SV1920 @ SV1690 @ SV1690 ) @ SV1690 ) )
= $true )
| ( ( SV423 = SV956 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4602,plain,
! [SV958: $i,SV1375: $i,SV1921: $i,SV425: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV425 @ SV1921 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) )
| ~ ( c_in @ SV1921 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 ) )
= $true )
| ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4603,plain,
! [SV426: $i,SV1376: $i,SV959: $i,SV1922: $i] :
( ( ( ~ ( c_in @ SV1922 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
| ~ ( c_in @ ( c_Pair @ SV426 @ SV1922 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) )
= $true )
| ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4604,plain,
! [SV962: $i,SV1377: $i,SV429: $i] :
( ( ( c_Relation_Orefl__on @ SV429 @ ( hAPP @ ( c_Relation_Oconverse @ SV1377 @ SV1377 ) @ SV962 ) @ SV1377 )
= $false )
| ( ( c_Relation_Orefl__on @ SV429 @ SV962 @ SV1377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4605,plain,
! [SV963: $i,SV1378: $i,SV430: $i] :
( ( ( c_Relation_Orefl__on @ SV430 @ SV1378 @ SV963 )
= $false )
| ( ( c_Relation_Orefl__on @ SV430 @ ( hAPP @ ( c_Relation_Oconverse @ SV963 @ SV963 ) @ SV1378 ) @ SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4606,plain,
! [SV1923: $i,SV1691: $i,SV1379: $i,SV966: $i,SV433: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SV966 ) @ ( c_Relation_Orel__comp @ SV1379 @ SV1691 @ SV433 @ SV1923 @ SV966 ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV1923 @ SV966 ) @ SV1691 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV433 @ SV1923 ) @ SV1379 ) @ SV966 @ SV1923 @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4607,plain,
! [SV973: $i,SV1381: $i,SV441: $i] :
( ( ( c_Relation_Ototal__on @ SV441 @ ( hAPP @ ( c_Relation_Oconverse @ SV1381 @ SV1381 ) @ SV973 ) @ SV1381 )
= $false )
| ( ( c_Relation_Ototal__on @ SV441 @ SV973 @ SV1381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4182]) ).
thf(4608,plain,
! [SV974: $i,SV1382: $i,SV442: $i] :
( ( ( c_Relation_Ototal__on @ SV442 @ SV1382 @ SV974 )
= $false )
| ( ( c_Relation_Ototal__on @ SV442 @ ( hAPP @ ( c_Relation_Oconverse @ SV974 @ SV974 ) @ SV1382 ) @ SV974 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4609,plain,
! [SV1383: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ SV443 @ SV975 @ ( tc_prod @ SV1383 @ SV1383 ) )
= $false )
| ( ( c_in @ SV443 @ ( c_Transitive__Closure_Ortrancl @ SV975 @ SV1383 ) @ ( tc_prod @ SV1383 @ SV1383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4610,plain,
! [SV1384: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ SV444 @ SV976 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false )
| ( ( c_in @ SV444 @ ( c_Transitive__Closure_Otrancl @ SV976 @ SV1384 ) @ ( tc_prod @ SV1384 @ SV1384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4611,plain,
! [SV1693: $i,SV1385: $i,SV977: $i,SV445: $i] :
( ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true )
| ( ( ! [SY5316: $i] :
( ~ ( c_in @ ( c_Pair @ SY5316 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SY5316 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4612,plain,
! [SV1694: $i,SV1386: $i,SV978: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true )
| ( ( ! [SY5317: $i] :
( ~ ( c_in @ ( c_Pair @ SY5317 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY5317 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4613,plain,
! [SV1695: $i,SV1387: $i,SV979: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Ortrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ( SV447 = SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4614,plain,
! [SV1696: $i,SV1388: $i,SV980: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Otrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
= $true )
| ( ( ( SV448 = SV980 )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Ortrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4189]) ).
thf(4615,plain,
! [SV1697: $i,SV1389: $i,SV981: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Otrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
= $true )
| ( ( ( SV449 = SV981 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Ortrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4190]) ).
thf(4616,plain,
! [SV1698: $i,SV1390: $i,SV982: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Ortrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Otrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4617,plain,
! [SV1699: $i,SV1391: $i,SV983: $i,SV451: $i] :
( ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $true )
| ( ( ! [SY5318: $i] :
( ~ ( c_in @ ( c_Pair @ SY5318 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SY5318 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4192]) ).
thf(4618,plain,
! [SV1700: $i,SV1392: $i,SV984: $i,SV452: $i] :
( ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $true )
| ( ( ! [SY5319: $i] :
( ~ ( c_in @ ( c_Pair @ SY5319 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SY5319 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4193]) ).
thf(4619,plain,
! [SV453: $i,SV1393: $i,SV985: $i] :
( ( ( c_Wellfounded_Owf @ SV985 @ SV1393 )
= $false )
| ( ( c_in @ SV453 @ ( c_Wellfounded_Oacc @ SV985 @ SV1393 ) @ SV1393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4620,plain,
! [SV1924: $i,SV1396: $i,SV1000: $i,SV469: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SV1000 @ SV1396 @ SV1924 ) @ SV1924 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV469 @ SV1396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4621,plain,
! [SV1925: $i,SV1397: $i,SV1002: $i,SV471: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SV1002 @ SV1397 @ SV1925 ) @ SV1925 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV471 @ SV1397 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(4622,plain,
! [SV1926: $i,SV1701: $i,SV1398: $i,SV1005: $i,SV474: $i] :
( ( ! [SY5477: $i,SY5478: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SV1398 @ SV1701 @ SV1926 ) @ SY5477 @ SV1398 @ SV1926 @ SY5478 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SY5477 @ SV1701 @ SV1926 @ SY5478 ) @ SV1398 @ SV1701 @ SY5478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4623,plain,
! [SV479: $i,SV1009: $i,SV1702: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1702 @ SV1009 @ SV479 )
= $false )
| ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ SV479 @ SV479 ) @ SV1009 ) @ SV1009 @ SV479 @ SV479 @ SV479 )
= SV1009 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4624,plain,
! [SV1400: $i,SV1011: $i,SV481: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV481 @ SV1011 @ SV1400 )
= $false )
| ( ( c_Relation_Orefl__on @ SV481 @ SV1011 @ SV1400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4625,plain,
! [SV1012: $i,SV482: $i,SV1703: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1703 @ SV482 @ SV1012 )
= $false )
| ( ( c_Relation_Osym @ SV482 @ SV1012 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4626,plain,
! [SV1704: $i,SV1403: $i,SV1019: $i,SV489: $i] :
( ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $true )
| ( ( ! [SY5323: $i] :
( ~ ( c_in @ ( c_Pair @ SY5323 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SY5323 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4627,plain,
! [SV1705: $i,SV1404: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ ( c_Transitive__Closure_Otrancl @ SV1705 @ SV1404 ) @ ( tc_prod @ SV1404 @ SV1404 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ SV1705 @ ( tc_prod @ SV1404 @ SV1404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4628,plain,
! [SV1706: $i,SV1405: $i,SV1021: $i,SV491: $i] :
( ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $true )
| ( ( ! [SY5324: $i] :
( ~ ( c_in @ ( c_Pair @ SY5324 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SY5324 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4629,plain,
! [SV1707: $i,SV1408: $i,SV1024: $i,SV494: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_Wellfounded_Owf @ SV1707 @ SV1408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4630,plain,
! [SV1927: $i,SV1708: $i,SV495: $i,SV1025: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_Relation_Oantisym @ SV1927 @ SV1708 ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4631,plain,
! [SV1928: $i,SV1709: $i,SV496: $i,SV1026: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_Relation_Oantisym @ SV1928 @ SV1709 ) )
= $true )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4632,plain,
! [SV1710: $i,SV1409: $i,SV1027: $i,SV497: $i] :
( ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true )
| ( ( ! [SY5327: $i] :
( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SY5327 @ ( tc_prod @ SV1710 @ SV1710 ) )
| ! [SY5328: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5327 @ SV497 @ SV1710 @ SY5328 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4214]) ).
thf(4633,plain,
! [SV1929: $i,SV1711: $i,SV1028: $i,SV498: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ SV1711 @ SV1711 ) @ ( c_Relation_OId__on @ SV1929 @ SV1711 ) @ ( tc_prod @ SV1711 @ SV1711 ) ) )
= $true )
| ( ( SV498 = SV1028 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4215]) ).
thf(4634,plain,
! [SV1930: $i,SV1712: $i,SV1410: $i,SV1029: $i,SV499: $i] :
( ( ! [SY5479: $i] :
( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
!= ( c_Recdef_Ocut @ SY5479 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
| ! [SY5332: $i] :
( ( ( hAPP @ SV499 @ SY5332 )
= ( hAPP @ SY5479 @ SY5332 ) )
| ~ ( c_in @ ( c_Pair @ SY5332 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(4635,plain,
! [SV1713: $i,SV1030: $i,SV500: $i] :
( ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ SV1713 @ SV1713 ) @ ( c_Relation_OId @ SV1713 ) @ ( tc_prod @ SV1713 @ SV1713 ) )
= $false )
| ( ( SV500 = SV1030 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4636,plain,
! [SV501: $i,SV1031: $i,SV1411: $i] :
( ( ( c_Nitpick_Orefl_H @ SV1411 @ SV1031 )
= $false )
| ( ( c_in @ ( c_Pair @ SV501 @ SV501 @ SV1031 @ SV1031 ) @ SV1411 @ ( tc_prod @ SV1031 @ SV1031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4637,plain,
! [SV1412: $i,SV1032: $i,SV502: $i] :
( ( ( c_in @ ( c_Pair @ SV502 @ SV502 @ SV1032 @ SV1032 ) @ SV1412 @ ( tc_prod @ SV1032 @ SV1032 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1412 @ SV1032 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4638,plain,
! [SV1931: $i,SV1714: $i,SV1413: $i,SV1033: $i,SV503: $i] :
( ( ! [SY5481: $i] :
( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SV1714 @ SV1931 @ SY5481 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1931 @ SV503 ) @ ( hAPP @ SV1931 @ SV1033 ) @ SY5481 @ SY5481 ) @ SV1714 @ ( tc_prod @ SY5481 @ SY5481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(4639,plain,
! [SV1932: $i,SV1715: $i,SV1414: $i,SV1034: $i,SV504: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SV1715 @ SV1715 ) @ SV1932 @ ( tc_prod @ SV1715 @ SV1715 ) )
| ! [SY5482: $i] :
~ ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SY5482 @ SY5482 ) @ ( c_Relation_Oinv__image @ SV1932 @ SV504 @ SV1715 @ SY5482 ) @ ( tc_prod @ SY5482 @ SY5482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4221]) ).
thf(4640,plain,
! [SV1716: $i,SV1415: $i,SV1035: $i,SV505: $i] :
( ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
| ~ ( c_Relation_Osym @ SV1716 @ SV1415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(4641,plain,
! [SV1717: $i,SV1416: $i,SV1036: $i,SV506: $i] :
( ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
| ~ ( c_Relation_Osym @ SV1717 @ SV1416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4642,plain,
! [SV1933: $i,SV1718: $i,SV1417: $i,SV1037: $i,SV507: $i] :
( ( ! [SY5483: $i,SY5484: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SY5483 @ SV1417 @ SY5484 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
| ! [SY5485: $i] :
( ~ ( c_in @ ( c_Pair @ SY5485 @ SV1037 @ SY5484 @ SV1718 ) @ SY5483 @ ( tc_prod @ SY5484 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5485 @ SV1417 @ SY5484 ) @ SV1933 @ ( tc_prod @ SV1417 @ SY5484 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4224]) ).
thf(4643,plain,
! [SV1719: $i,SV1418: $i,SV1038: $i,SV508: $i] :
( ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
= $true )
| ( ( ! [SY5341: $i] :
( ~ ( c_in @ ( c_Pair @ SY5341 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SY5341 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4644,plain,
! [SV1720: $i,SV1419: $i,SV1039: $i,SV509: $i] :
( ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $true )
| ( ( ! [SY5342: $i] :
( ~ ( c_in @ ( c_Pair @ SY5342 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SY5342 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4645,plain,
! [SV1721: $i,SV1420: $i,SV1042: $i,SV512: $i] :
( ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true )
| ( ( ! [SY5343: $i,SY5344: $i] :
( ~ ( c_in @ SV1042 @ SY5343 @ SY5344 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SY5343 @ SV1420 @ SY5344 @ SV1721 ) @ ( tc_fun @ SY5344 @ SV1721 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4646,plain,
! [SV1722: $i,SV1421: $i,SV1043: $i,SV513: $i] :
( ( ( ~ ( c_in @ SV513 @ SV1043 @ SV1421 ) )
= $true )
| ( ( ! [SY5345: $i,SY5346: $i] :
( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SY5345 @ SV513 ) @ SY5346 )
| ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SY5345 @ SV1421 @ SY5346 ) @ ( tc_fun @ SV1421 @ SY5346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4228]) ).
thf(4647,plain,
! [SV1723: $i,SV1422: $i,SV1044: $i,SV514: $i] :
( ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SV1723 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV514 = SV1044 )
| ( SV514 = SV1723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4229]) ).
thf(4648,plain,
! [SV1724: $i,SV1423: $i,SV1045: $i,SV515: $i] :
( ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SV1724 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1045 = SV1724 )
| ( SV515 = SV1724 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4649,plain,
! [SV1425: $i,SV518: $i,SV1934: $i,SV1048: $i] :
( ( ( ( SV1048 = SV1934 )
| ~ ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1425 @ SV1934 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1425 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4650,plain,
! [SV1935: $i,SV1049: $i,SV519: $i] :
( ( ( c_in @ ( c_Pair @ SV519 @ SV1049 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1935 @ SV519 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV1049 = SV519 )
= $true )
| ( ( SV519 = SV1049 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4233]) ).
thf(4651,plain,
! [SV1725: $i,SV1427: $i,SV1052: $i,SV522: $i] :
( ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SV1725 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV522 = SV1052 )
| ( SV1052 = SV1725 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4652,plain,
! [SV1726: $i,SV1428: $i,SV1053: $i,SV523: $i] :
( ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SV1726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV523 = SV1726 )
| ( SV1053 = SV1726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4236]) ).
thf(4653,plain,
! [SV1936: $i,SV1054: $i,SV524: $i] :
( ( ( c_in @ ( c_Pair @ SV524 @ SV1054 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1936 @ SV1054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV524 = SV1054 )
= $true )
| ( ( SV524 = SV1054 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4654,plain,
! [SV1429: $i,SV1055: $i,SV1937: $i,SV525: $i] :
( ( ( ( SV525 = SV1937 )
| ~ ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1429 @ SV1937 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1429 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(4655,plain,
! [SV1430: $i,SV1938: $i,SV527: $i,SV1057: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(4656,plain,
! [SV1431: $i,SV1939: $i,SV528: $i,SV1058: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4657,plain,
! [SV1432: $i,SV1940: $i,SV529: $i,SV1059: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(4658,plain,
! [SV1433: $i,SV1941: $i,SV530: $i,SV1060: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(4659,plain,
! [SV1727: $i,SV1434: $i,SV1061: $i,SV531: $i] :
( ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5347: $i] :
( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SY5347 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5347 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SY5347 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SY5347 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5347 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4660,plain,
! [SV1728: $i,SV1435: $i,SV1062: $i,SV532: $i] :
( ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5348: $i] :
( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SY5348 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5348 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5348 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SY5348 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5348 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4661,plain,
! [SV1729: $i,SV1436: $i,SV1063: $i,SV533: $i] :
( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5349: $i] :
( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SY5349 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5349 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SY5349 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SY5349 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5349 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4662,plain,
! [SV1730: $i,SV1437: $i,SV1064: $i,SV534: $i] :
( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5350: $i] :
( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SY5350 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5350 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5350 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SY5350 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5350 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4246]) ).
thf(4663,plain,
! [SV1731: $i,SV1438: $i,SV1065: $i,SV535: $i] :
( ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4664,plain,
! [SV1732: $i,SV1439: $i,SV1066: $i,SV536: $i] :
( ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5351: $i,SY5352: $i] :
( ~ ( c_in @ ( c_Pair @ SV1732 @ SY5351 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5352 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1732 @ SY5351 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5352 @ ( v_sko__local__X2__1 @ SV1439 @ SY5352 @ SV536 @ SV1732 @ SV1066 @ SY5351 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SY5352 @ SV536 @ SV1732 @ SV1066 @ SY5351 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5352 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SY5351 )
| ( SV1732 = SY5351 )
| ( SV536 = SV1066 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4248]) ).
thf(4665,plain,
! [SV1733: $i,SV1440: $i,SV1067: $i,SV537: $i] :
( ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5353: $i,SY5354: $i] :
( ~ ( c_in @ ( c_Pair @ SV1733 @ SY5353 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5354 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SY5354 @ SV1440 @ SV1733 @ SV537 @ SY5353 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SY5353 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5354 @ ( v_sko__local__X2__1 @ SY5354 @ SV1440 @ SV1733 @ SV537 @ SY5353 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5354 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5353 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SY5353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4249]) ).
thf(4666,plain,
! [SV1734: $i,SV1441: $i,SV1068: $i,SV538: $i] :
( ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5355: $i,SY5356: $i] :
( ~ ( c_in @ ( c_Pair @ SV1734 @ SY5355 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5356 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1734 @ SY5355 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5356 @ ( v_sko__local__X2__1 @ SV1441 @ SY5356 @ SV538 @ SV1734 @ SV1068 @ SY5355 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SY5356 @ SV538 @ SV1734 @ SV1068 @ SY5355 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5356 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SY5355 )
| ( SV1734 = SY5355 )
| ( SV538 = SV1068 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4667,plain,
! [SV1735: $i,SV1442: $i,SV1069: $i,SV539: $i] :
( ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5357: $i,SY5358: $i] :
( ~ ( c_in @ ( c_Pair @ SV1735 @ SY5357 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5358 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SY5358 @ SV1442 @ SV1735 @ SV539 @ SY5357 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SY5357 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5358 @ ( v_sko__local__X2__1 @ SY5358 @ SV1442 @ SV1735 @ SV539 @ SY5357 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5358 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5357 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SY5357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4668,plain,
! [SV1736: $i,SV1443: $i,SV1070: $i,SV540: $i] :
( ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5359: $i,SY5360: $i] :
( ~ ( c_in @ ( c_Pair @ SV1736 @ SY5359 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5360 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SY5360 @ SV1443 @ SV1736 @ SV540 @ SY5359 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SY5359 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5360 @ ( v_sko__local__X1__1 @ SY5360 @ SV1443 @ SV1736 @ SV540 @ SY5359 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5360 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5359 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SY5359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4669,plain,
! [SV1737: $i,SV1444: $i,SV1071: $i,SV541: $i] :
( ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5361: $i,SY5362: $i] :
( ~ ( c_in @ ( c_Pair @ SV1737 @ SY5361 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5362 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SY5362 @ SV1444 @ SV1737 @ SV541 @ SY5361 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SY5361 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5362 @ ( v_sko__local__X1__1 @ SY5362 @ SV1444 @ SV1737 @ SV541 @ SY5361 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5362 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SY5361 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SY5361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4253]) ).
thf(4670,plain,
! [SV1445: $i,SV542: $i,SV1072: $i] :
( ( ( ~ ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_Odictator @ SV542 @ SV1445 ) )
= $true )
| ( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SV1445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4254]) ).
thf(4671,plain,
! [SV1942: $i,SV1738: $i,SV1446: $i,SV1073: $i,SV543: $i] :
( ( ! [SY5486: $i] :
( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SY5486 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
| ~ ( c_in @ SV1073 @ ( hAPP @ SY5486 @ SV543 ) @ SV1738 )
| ~ ( c_in @ SV543 @ SV1942 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4255]) ).
thf(4672,plain,
! [SV1943: $i,SV1739: $i,SV1447: $i,SV1074: $i,SV544: $i] :
( ( ! [SY5487: $i] :
( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SY5487 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
| ~ ( c_in @ SV1074 @ ( hAPP @ SY5487 @ SV544 ) @ SV1739 )
| ~ ( c_in @ SV544 @ SV1943 @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4673,plain,
! [SV1075: $i,SV1448: $i,SV1944: $i,SV545: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV545 @ SV1944 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SV1944 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 ) )
= $true )
| ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(4674,plain,
! [SV1076: $i,SV1449: $i,SV1945: $i,SV546: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV546 @ SV1945 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) )
| ~ ( c_in @ SV1945 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 ) )
= $true )
| ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4675,plain,
! [SV1946: $i,SV1740: $i,SV1450: $i,SV1077: $i,SV547: $i] :
( ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
| ! [SY5488: $i] :
( ~ ( c_in @ ( c_Pair @ SY5488 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) )
| ~ ( c_in @ SY5488 @ SV1450 @ SV1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(4676,plain,
! [SV1947: $i,SV1741: $i,SV1451: $i,SV1078: $i,SV548: $i] :
( ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
| ! [SY5489: $i] :
( ~ ( c_in @ ( c_Pair @ SY5489 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) )
| ~ ( c_in @ SY5489 @ SV1451 @ SV1741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(4677,plain,
! [SV1079: $i,SV1452: $i,SV1948: $i,SV549: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV549 @ SV1948 @ SV1452 @ SV1452 ) @ ( c_Relation_OId__on @ SV1079 @ SV1452 ) @ ( tc_prod @ SV1452 @ SV1452 ) ) )
= $true )
| ( ( c_in @ SV549 @ SV1079 @ SV1452 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(4678,plain,
! [SV1080: $i,SV1453: $i,SV550: $i] :
( ( ( c_in @ SV550 @ SV1453 @ SV1080 )
= $false )
| ( ( c_in @ ( c_Pair @ SV550 @ SV550 @ SV1080 @ SV1080 ) @ ( c_Relation_OId__on @ SV1453 @ SV1080 ) @ ( tc_prod @ SV1080 @ SV1080 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4679,plain,
! [SV1081: $i,SV1454: $i,SV551: $i,SV1949: $i] :
( ( ( ! [SY5490: $i] :
( ~ ( c_in @ ( c_Pair @ SV1949 @ SV551 @ SV1454 @ SV1454 ) @ SY5490 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SY5490 @ SV1454 ) ) )
= $true )
| ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4680,plain,
! [SV1082: $i,SV1455: $i,SV1950: $i,SV552: $i] :
( ( ( ! [SY5491: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SV1950 @ SV1455 @ SV1455 ) @ SY5491 @ ( tc_prod @ SV1455 @ SV1455 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SY5491 @ SV1455 ) ) )
= $true )
| ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(4681,plain,
! [SV1742: $i,SV1456: $i,SV1083: $i,SV553: $i] :
( ( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SV1456 @ SV1742 ) @ SV1742 )
= $true )
| ( ( ! [SY5371: $i] :
~ ( c_in @ ( c_Pair @ SY5371 @ SV553 @ SV1456 @ SV1742 ) @ SV1083 @ ( tc_prod @ SV1456 @ SV1742 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4682,plain,
! [SV1743: $i,SV1457: $i,SV1084: $i,SV554: $i] :
( ( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SV1457 @ SV1743 ) @ SV1743 )
= $true )
| ( ( ! [SY5372: $i] :
~ ( c_in @ ( c_Pair @ SY5372 @ SV554 @ SV1457 @ SV1743 ) @ SV1084 @ ( tc_prod @ SV1457 @ SV1743 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4683,plain,
! [SV1744: $i,SV1458: $i,SV1085: $i,SV555: $i] :
( ( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SV1458 @ SV1744 ) @ SV1458 )
= $true )
| ( ( ! [SY5373: $i] :
~ ( c_in @ ( c_Pair @ SV555 @ SY5373 @ SV1458 @ SV1744 ) @ SV1085 @ ( tc_prod @ SV1458 @ SV1744 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4684,plain,
! [SV1745: $i,SV1459: $i,SV1086: $i,SV556: $i] :
( ( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SV1459 @ SV1745 ) @ SV1459 )
= $true )
| ( ( ! [SY5374: $i] :
~ ( c_in @ ( c_Pair @ SV556 @ SY5374 @ SV1459 @ SV1745 ) @ SV1086 @ ( tc_prod @ SV1459 @ SV1745 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4268]) ).
thf(4685,plain,
! [SV1746: $i,SV1460: $i,SV1087: $i,SV557: $i] :
( ( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SV1746 )
= $true )
| ( ( ! [SY5375: $i,SY5376: $i] :
~ ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SY5375 @ SV1746 ) @ ( c_Product__Type_OSigma @ SY5376 @ SV1087 @ SY5375 @ SV1746 ) @ ( tc_prod @ SY5375 @ SV1746 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4686,plain,
! [SV1747: $i,SV1461: $i,SV1088: $i,SV558: $i] :
( ( ( c_in @ SV558 @ SV1088 @ SV1461 )
= $true )
| ( ( ! [SY5377: $i,SY5378: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SV1747 @ SV1461 @ SY5377 ) @ ( c_Product__Type_OSigma @ SV1088 @ SY5378 @ SV1461 @ SY5377 ) @ ( tc_prod @ SV1461 @ SY5377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4687,plain,
! [SV1748: $i,SV1462: $i,SV1089: $i,SV559: $i] :
( ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
| ( SV1089 = SV559 )
| ! [SY5379: $i] :
( ~ ( c_in @ SV559 @ SY5379 @ SV1462 )
| ~ ( c_in @ SV1089 @ SY5379 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SY5379 @ SV1748 @ SV1462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4688,plain,
! [SV1463: $i,SV1090: $i,SV1951: $i,SV560: $i] :
( ( ( ~ ( c_in @ SV560 @ SV1951 @ SV1090 )
| ~ ( c_Relation_Orefl__on @ SV1951 @ SV1463 @ SV1090 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(4689,plain,
! [SV1091: $i,SV1464: $i,SV561: $i,SV1952: $i] :
( ( ( ! [SY5492: $i] :
( ~ ( c_in @ ( c_Pair @ SV1952 @ SV561 @ SV1464 @ SV1464 ) @ SY5492 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1091 @ SY5492 @ SV1464 ) ) )
= $true )
| ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(4690,plain,
! [SV1092: $i,SV1465: $i,SV1953: $i,SV562: $i] :
( ( ( ! [SY5493: $i] :
( ~ ( c_in @ ( c_Pair @ SV562 @ SV1953 @ SV1465 @ SV1465 ) @ SY5493 @ ( tc_prod @ SV1465 @ SV1465 ) )
| ~ ( c_Relation_Orefl__on @ SV1092 @ SY5493 @ SV1465 ) ) )
= $true )
| ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(4691,plain,
! [SV1466: $i,SV1093: $i,SV1954: $i,SV563: $i] :
( ( ( ~ ( c_in @ SV563 @ SV1954 @ SV1093 )
| ~ ( c_Relation_Orefl__on @ SV1954 @ SV1466 @ SV1093 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(4692,plain,
! [SV1749: $i,SV1467: $i,SV1094: $i,SV564: $i] :
( ( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ SV1749 ) @ SV1467 ) @ ( tc_prod @ SV1467 @ SV1467 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ SV1749 @ SV1467 ) ) @ ( tc_prod @ SV1467 @ SV1467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4276]) ).
thf(4693,plain,
! [SV1750: $i,SV1468: $i,SV1095: $i,SV565: $i] :
( ( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ SV1750 @ SV1468 ) ) @ ( tc_prod @ SV1468 @ SV1468 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ SV1750 ) @ SV1468 ) @ ( tc_prod @ SV1468 @ SV1468 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4277]) ).
thf(4694,plain,
! [SV1751: $i,SV1469: $i,SV1096: $i,SV566: $i] :
( ( ( c_in @ ( c_Pair @ SV566 @ SV1096 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1751 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1096 @ SV566 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1469 @ SV1469 ) @ SV1751 ) @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4278]) ).
thf(4695,plain,
! [SV1752: $i,SV1470: $i,SV1097: $i,SV567: $i] :
( ( ( c_in @ ( c_Pair @ SV567 @ SV1097 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1470 @ SV1470 ) @ SV1752 ) @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1097 @ SV567 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1752 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4696,plain,
! [SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5494: $i,SY5495: $i,SY5496: $i,SY5497: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SY5494 ) ) )
| ! [SY5498: $i,SY5499: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SY5495 @ SY5496 @ SY5497 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5498 @ SY5496 @ SY5499 ) @ SY5494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4697,plain,
! [SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ! [SY5500: $i,SY5501: $i] :
( ! [SY5502: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
!= ( c_Fun_Ocomp @ SY5500 @ SY5501 @ SY5502 @ SV1754 @ SV1956 ) )
| ! [SY4659: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY4659 ) )
= ( hAPP @ SY5500 @ ( hAPP @ SY5501 @ SY4659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(4698,plain,
! [SV1957: $i,SV1755: $i,SV1473: $i,SV1100: $i,SV570: $i] :
( ( ! [SY5504: $i] :
( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SV1755 )
!= ( c_Pair @ SV1957 @ SY5504 @ SV1473 @ SV1755 ) )
| ( SV1100 = SY5504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4282]) ).
thf(4699,plain,
! [SV1958: $i,SV1756: $i,SV1474: $i,SV1101: $i,SV571: $i] :
( ( ! [SY5505: $i] :
( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SV1756 )
!= ( c_Pair @ SV1958 @ SY5505 @ SV1474 @ SV1756 ) )
| ( SV571 = SV1958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4283]) ).
thf(4700,plain,
! [SV1959: $i,SV1757: $i,SV1475: $i,SV1102: $i,SV572: $i] :
( ( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SV1475 @ SV1757 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1757 @ SV1475 ) @ SV1959 ) @ ( tc_prod @ SV1475 @ SV1757 ) )
| ~ ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SV1757 @ SV1475 ) @ SV1959 @ ( tc_prod @ SV1757 @ SV1475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4284]) ).
thf(4701,plain,
! [SV1960: $i,SV1758: $i,SV1476: $i,SV1103: $i,SV573: $i] :
( ( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SV1476 @ SV1758 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1758 @ SV1476 ) @ SV1960 ) @ ( tc_prod @ SV1476 @ SV1758 ) )
| ~ ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SV1758 @ SV1476 ) @ SV1960 @ ( tc_prod @ SV1758 @ SV1476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4285]) ).
thf(4702,plain,
! [SV1961: $i,SV1759: $i,SV1477: $i,SV1104: $i,SV574: $i] :
( ( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SV1477 @ SV1759 ) @ SV1961 @ ( tc_prod @ SV1477 @ SV1759 ) )
| ~ ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SV1759 @ SV1477 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1477 @ SV1759 ) @ SV1961 ) @ ( tc_prod @ SV1759 @ SV1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4703,plain,
! [SV1962: $i,SV1760: $i,SV1478: $i,SV1105: $i,SV575: $i] :
( ( ! [SY5506: $i,SY5507: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SV1478 @ SV1760 @ SV1962 @ SY5506 ) @ SV1962 @ SY5507 @ SY5506 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SV1962 @ SY5507 @ SV1760 ) @ SV1478 @ SV1760 @ SY5507 @ SY5506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4704,plain,
! [SV1963: $i,SV1761: $i,SV1480: $i,SV1107: $i,SV579: $i] :
( ( ! [SY5508: $i] :
( ( hAPP @ SV579 @ ( hAPP @ SV1107 @ SV1480 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SV1107 @ SV1761 @ SV1963 @ SY5508 ) @ SV1480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4705,plain,
! [SV1964: $i,SV1762: $i,SV1481: $i,SV1108: $i,SV580: $i] :
( ( ! [SY5509: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SV1108 @ SV1481 @ SV1762 @ SV1964 ) @ SY5509 )
= ( hAPP @ SV580 @ ( hAPP @ SV1108 @ SY5509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(4706,plain,
! [SV1763: $i,SV581: $i,SV1109: $i] :
( ( ( hBOOL @ ( hAPP @ SV1109 @ SV581 ) )
= $false )
| ( ( c_in @ SV581 @ SV1109 @ SV1763 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4707,plain,
! [SV1764: $i,SV582: $i,SV1110: $i] :
( ( ( c_in @ SV1110 @ SV582 @ SV1764 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV582 @ SV1110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4708,plain,
! [SV1765: $i,SV1121: $i,SV593: $i] :
( ( ( c_fequal @ SV593 @ SV1121 @ SV1765 )
= $false )
| ( ( SV593 = SV1121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4709,plain,
! [SV1766: $i,SV1484: $i,SV1124: $i,SV596: $i,SV5: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SV1484 ) @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) )
= $true )
| ( ( ! [SY5406: $i] :
~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SY5406 @ ( c_COMBK @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) @ SV1124 ) @ SV1124 @ SV1484 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SV1484 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4710,plain,
! [SV600: $i,SV1767: $i,SV1486: $i,SV10: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SV1486 @ SV1767 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1486 @ SV1767 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4303]) ).
thf(4711,plain,
! [SV1965: $i,SV1770: $i,SV1489: $i,SV1129: $i,SV603: $i,SV13: $i] :
( ( ! [SY5510: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SY5510 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SY5510 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4712,plain,
! [SV1966: $i,SV18: $i,SV1771: $i,SV607: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1771 @ SV18 ) @ SV1966 @ SV18 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV607 @ SV1966 @ SV18 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1771 @ SV1966 @ SV18 ) @ SV18 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(4713,plain,
! [SV19: $i,SV1967: $i,SV1772: $i,SV608: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1772 @ SV1967 @ SV19 ) @ SV19 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SV1772 @ SV19 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV608 @ SV1967 @ SV19 ) @ SV19 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4309]) ).
thf(4714,plain,
! [SV1134: $i,SV613: $i,SV24: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV24 @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4715,plain,
! [SV614: $i,SV1135: $i,SV1968: $i,SV1495: $i,SV25: $i] :
( ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SV1968 ) @ tc_bool ) )
| ! [SY5511: $i] :
~ ( c_in @ SY5511 @ SV1495 @ SV1968 ) )
= $true )
| ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4716,plain,
! [SV1774: $i,SV1496: $i,SV1136: $i,SV615: $i,SV26: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) )
| ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4717,plain,
! [SV616: $i,SV1137: $i,SV27: $i,SV1775: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV1775 @ SV27 @ SV1137 ) @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV27 @ SV616 @ ( tc_fun @ SV1137 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4315]) ).
thf(4718,plain,
! [SV617: $i,SV1497: $i,SV1138: $i,SV28: $i] :
( ( ( c_lessequals @ SV28 @ SV1138 @ ( tc_fun @ SV1497 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV28 @ ( c_Set_Oinsert @ SV617 @ SV1138 @ SV1497 ) @ ( tc_fun @ SV1497 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4719,plain,
! [SV618: $i,SV1776: $i,SV1498: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SV1498 @ SV1776 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1498 @ SV1776 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4720,plain,
! [SV41: $i,SV1147: $i,SV629: $i] :
( ( ( c_Relation_Osym @ SV629 @ SV1147 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV41 @ SV1147 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SV1147 @ SV1147 ) @ tc_bool ) ) @ SV1147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4721,plain,
! [SV1509: $i,SV1152: $i,SV636: $i,SV50: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ SV636 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV50 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV636 @ SV1509 @ ( tc_fun @ SV1152 @ tc_bool ) ) @ ( tc_fun @ SV1152 @ tc_bool ) ) )
= $false )
| ( ( c_lessequals @ SV1509 @ SV50 @ ( tc_fun @ SV1152 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4722,plain,
! [SV637: $i,SV1153: $i,SV51: $i,SV1510: $i] :
( ( ( c_lessequals @ SV1510 @ SV51 @ ( tc_fun @ SV1153 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ SV637 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV51 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV637 @ SV1510 @ ( tc_fun @ SV1153 @ tc_bool ) ) @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4723,plain,
! [SV1969: $i,SV1778: $i,SV1511: $i,SV1154: $i,SV638: $i,SV52: $i] :
( ( ! [SY5512: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SY5512 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
| ! [SY5513: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY5513 @ ( c_COMBK @ SY5512 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SY5513 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(4724,plain,
! [SV1155: $i,SV639: $i,SV53: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV639 @ SV1155 )
| ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4324]) ).
thf(4725,plain,
! [SV640: $i,SV1970: $i,SV54: $i,SV1512: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1512 @ SV54 @ ( tc_fun @ SV1970 @ tc_bool ) ) @ SV640 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1512 @ SV640 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4726,plain,
! [SV1156: $i,SV55: $i,SV1513: $i,SV641: $i] :
( ( ( hBOOL @ ( hAPP @ SV641 @ SV1513 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV641 @ ( tc_fun @ SV1156 @ tc_bool ) ) @ SV1513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4727,plain,
! [SV1157: $i,SV642: $i,SV1514: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ SV56 @ SV1514 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV642 @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV1514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4728,plain,
! [SV57: $i,SV643: $i,SV1158: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1158 @ SV643 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4328]) ).
thf(4729,plain,
! [SV1780: $i,SV1516: $i,SV1160: $i,SV645: $i,SV59: $i] :
( ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SV1780 ) @ SV1160 @ SV1780 )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SV1780 )
| ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4730,plain,
! [SV1781: $i,SV1517: $i,SV1161: $i,SV646: $i,SV60: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SV1781 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV646 @ SV1781 @ SV1161 )
| ~ ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4331]) ).
thf(4731,plain,
! [SV1971: $i,SV61: $i,SV1782: $i,SV647: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SV1782 @ SV61 ) @ SV1971 @ SV61 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1782 @ SV1971 @ SV61 ) @ SV61 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4732,plain,
! [SV62: $i,SV1972: $i,SV1783: $i,SV648: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1783 @ SV1972 @ SV62 ) @ SV62 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1783 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV648 @ SV1972 @ SV62 ) @ SV62 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4733,plain,
! [SV63: $i,SV1973: $i,SV1784: $i,SV649: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1784 @ SV1973 @ SV63 ) @ SV63 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1784 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV649 @ SV1973 @ SV63 ) @ SV63 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4734,plain,
! [SV1974: $i,SV64: $i,SV1785: $i,SV650: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ SV1785 @ SV64 ) @ SV1974 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV1974 @ SV64 ) @ SV64 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(4735,plain,
! [SV1975: $i,SV1786: $i,SV1522: $i,SV1164: $i,SV655: $i,SV71: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SV1786 @ SV1975 ) @ ( tc_fun @ SV1975 @ tc_bool ) @ SV1164 ) @ SV1164 @ SV1975 )
= ( c_Set_Oinsert @ ( c_Pair @ SV71 @ SV1522 @ SV1164 @ SV1975 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV655 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1522 @ SV1786 @ SV1975 ) @ ( tc_fun @ SV1975 @ tc_bool ) @ SV1164 ) @ SV1164 @ SV1975 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV71 @ SV655 @ SV1164 ) @ ( c_COMBK @ SV1786 @ ( tc_fun @ SV1975 @ tc_bool ) @ SV1164 ) @ SV1164 @ SV1975 ) @ ( tc_fun @ ( tc_prod @ SV1164 @ SV1975 ) @ tc_bool ) ) @ ( tc_prod @ SV1164 @ SV1975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4736,plain,
! [SV656: $i,SV1523: $i,SV72: $i] :
( ( ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SV1523 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1523 @ SV656 ) )
= $true )
| ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4337]) ).
thf(4737,plain,
! [SV658: $i,SV1165: $i,SV1976: $i,SV74: $i] :
( ( ( ~ ( c_in @ SV74 @ SV1976 @ SV1165 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1976 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) ) )
= $true )
| ( ( c_in @ SV74 @ SV658 @ SV1165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4338]) ).
thf(4738,plain,
! [SV75: $i,SV1977: $i,SV1787: $i,SV659: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1787 @ SV1977 @ SV75 ) @ SV75 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SV1787 @ SV75 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV659 @ SV1977 @ SV75 ) @ SV75 ) @ SV75 )
= $true )
| ( ( class_Lattices_Olattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4739,plain,
! [SV77: $i,SV1166: $i,SV660: $i,SV1978: $i] :
( ( ( ( ( c_Relation_Orel__comp @ SV1978 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1978 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4740,plain,
! [SV661: $i,SV1167: $i,SV1979: $i,SV78: $i] :
( ( ( ( ( c_Relation_Orel__comp @ SV78 @ SV1979 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1979 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4741,plain,
! [SV662: $i,SV1789: $i,SV1525: $i,SV79: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SV1525 @ SV1789 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1525 @ SV1789 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(4742,plain,
! [SV1526: $i,SV80: $i,SV663: $i] :
( ( ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SV1526 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SV1526 @ tc_bool ) ) )
= $true )
| ( ( SV80 = SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4743,plain,
! [SV1527: $i,SV81: $i,SV664: $i] :
( ( ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SV1527 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SV1527 @ tc_bool ) ) )
= $true )
| ( ( SV81 = SV664 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4744,plain,
! [SV82: $i,SV1790: $i,SV1528: $i] :
( ( ( SV1528 = SV1790 )
= $true )
| ( ( ~ ( c_lessequals @ SV1790 @ SV1528 @ SV82 )
| ~ ( c_lessequals @ SV1528 @ SV1790 @ SV82 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4745,plain,
! [SV83: $i,SV1791: $i,SV1529: $i] :
( ( ( SV1529 = SV1791 )
= $true )
| ( ( ~ ( c_lessequals @ SV1791 @ SV1529 @ SV83 )
| ~ ( c_lessequals @ SV1529 @ SV1791 @ SV83 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4746,plain,
! [SV84: $i,SV1792: $i,SV1530: $i] :
( ( ( SV1530 = SV1792 )
= $true )
| ( ( ~ ( c_lessequals @ SV1530 @ SV1792 @ SV84 )
| ~ ( c_lessequals @ SV1792 @ SV1530 @ SV84 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4348]) ).
thf(4747,plain,
! [SV86: $i,SV1794: $i,SV1532: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1532 @ SV1794 @ SV86 )
= SV1532 )
= $true )
| ( ( ~ ( c_lessequals @ SV1794 @ SV1532 @ SV86 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4748,plain,
! [SV87: $i,SV1795: $i,SV1533: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1533 @ SV1795 @ SV87 )
!= SV1795 )
= $true )
| ( ( c_lessequals @ SV1533 @ SV1795 @ SV87 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4749,plain,
! [SV88: $i,SV1796: $i,SV1534: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1534 @ SV1796 @ SV88 )
= SV1796 )
= $true )
| ( ( ~ ( c_lessequals @ SV1534 @ SV1796 @ SV88 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4750,plain,
! [SV1797: $i,SV1535: $i,SV1171: $i,SV668: $i,SV92: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SV1797 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV668 @ SV1797 @ SV1171 )
| ~ ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4751,plain,
! [SV1980: $i,SV93: $i,SV1798: $i,SV669: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ SV1798 @ SV93 ) @ SV1980 @ SV93 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV669 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1798 @ SV1980 @ SV93 ) @ SV93 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4752,plain,
! [SV94: $i,SV1981: $i,SV1799: $i,SV670: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1799 @ SV1981 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1799 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV670 @ SV1981 @ SV94 ) @ SV94 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4753,plain,
! [SV95: $i,SV1982: $i,SV1800: $i,SV671: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1800 @ SV1982 @ SV95 ) @ SV95 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1800 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SV1982 @ SV95 ) @ SV95 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4754,plain,
! [SV1983: $i,SV96: $i,SV1801: $i,SV672: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SV1801 @ SV96 ) @ SV1983 @ SV96 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1801 @ SV1983 @ SV96 ) @ SV96 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(4755,plain,
! [SV99: $i,SV1802: $i,SV1536: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1536 @ SV1802 @ SV99 )
= SV1536 )
= $true )
| ( ( ~ ( c_lessequals @ SV1536 @ SV1802 @ SV99 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4756,plain,
! [SV100: $i,SV1803: $i,SV1537: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1537 @ SV1803 @ SV100 )
!= SV1537 )
= $true )
| ( ( c_lessequals @ SV1537 @ SV1803 @ SV100 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4757,plain,
! [SV101: $i,SV1804: $i,SV1538: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1538 @ SV1804 @ SV101 )
= SV1804 )
= $true )
| ( ( ~ ( c_lessequals @ SV1804 @ SV1538 @ SV101 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4758,plain,
! [SV102: $i,SV1174: $i,SV1539: $i,SV675: $i] :
( ( ( ~ ( c_lessequals @ SV675 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV102 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4759,plain,
! [SV105: $i,SV1177: $i,SV1540: $i,SV678: $i] :
( ( ( ~ ( c_lessequals @ SV678 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV105 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4760,plain,
! [SV1984: $i,SV106: $i,SV1805: $i,SV679: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SV1984 @ SV106 )
| ~ ( c_lessequals @ SV1805 @ SV1984 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SV1984 @ SV106 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(4761,plain,
! [SV1985: $i,SV109: $i,SV1808: $i,SV680: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SV1985 @ SV109 )
| ~ ( c_lessequals @ SV1808 @ SV1985 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SV1985 @ SV109 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(4762,plain,
! [SV1986: $i,SV110: $i,SV1809: $i,SV681: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SV1986 @ SV110 )
| ~ ( c_lessequals @ SV1809 @ SV1986 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SV1986 @ SV110 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(4763,plain,
! [SV1987: $i,SV117: $i,SV1814: $i,SV684: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SV1814 @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ SV1987 @ SV117 ) @ SV117 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV684 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1814 @ SV1987 @ SV117 ) @ SV117 ) @ SV117 )
= $true )
| ( ( class_Lattices_Olattice @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4764,plain,
! [SV685: $i,SV1179: $i,SV118: $i] :
( ( ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1179 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4765,plain,
! [SV690: $i,SV1184: $i,SV1815: $i,SV125: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV125 @ SV1815 @ SV1184 ) @ SV690 @ ( tc_fun @ SV1184 @ tc_bool ) )
= $false )
| ( ( c_in @ SV125 @ SV690 @ SV1184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4766,plain,
! [SV692: $i,SV1550: $i,SV1186: $i,SV127: $i] :
( ( ( ~ ( c_lessequals @ SV127 @ SV1186 @ ( tc_fun @ SV1550 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV692 @ SV127 @ SV1550 )
= $true )
| ( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SV1186 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4383]) ).
thf(4767,plain,
! [SV693: $i,SV1187: $i,SV128: $i,SV1817: $i] :
( ( ( c_in @ SV1817 @ SV128 @ SV1187 )
= $true )
| ( ( ~ ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SV1817 @ SV693 @ SV1187 ) @ ( tc_fun @ SV1187 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SV1187 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4384]) ).
thf(4768,plain,
! [SV694: $i,SV1551: $i,SV1188: $i,SV129: $i] :
( ( ( ~ ( c_lessequals @ SV129 @ SV1188 @ ( tc_fun @ SV1551 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV694 @ SV129 @ SV1551 )
= $true )
| ( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SV1188 @ SV1551 ) @ ( tc_fun @ SV1551 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4769,plain,
! [SV1189: $i,SV695: $i,SV1818: $i,SV130: $i] :
( ( ( ~ ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SV1818 @ SV695 @ SV1189 ) @ ( tc_fun @ SV1189 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV1818 @ SV130 @ SV1189 )
= $true )
| ( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SV1189 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4386]) ).
thf(4770,plain,
! [SV135: $i,SV1988: $i,SV1554: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1554 @ SV1988 @ SV135 )
!= ( c_Orderings_Obot__class_Obot @ SV135 ) )
= $true )
| ( ( SV1554
= ( c_Orderings_Obot__class_Obot @ SV135 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(4771,plain,
! [SV136: $i,SV1819: $i,SV1555: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1555 @ SV1819 @ SV136 )
!= ( c_Orderings_Obot__class_Obot @ SV136 ) )
= $true )
| ( ( SV1819
= ( c_Orderings_Obot__class_Obot @ SV136 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4392]) ).
thf(4772,plain,
! [SV1989: $i,SV1820: $i,SV1556: $i,SV1194: $i,SV700: $i,SV137: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV700 @ ( tc_fun @ ( tc_prod @ SV1194 @ SV1556 ) @ tc_bool ) ) @ SV1820 @ SV1194 @ SV1556 @ SV1989 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV137 @ SV1820 @ SV1194 @ SV1556 @ SV1989 ) @ ( c_Relation_Orel__comp @ SV700 @ SV1820 @ SV1194 @ SV1556 @ SV1989 ) @ ( tc_fun @ ( tc_prod @ SV1194 @ SV1989 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(4773,plain,
! [SV1990: $i,SV1821: $i,SV1557: $i,SV1195: $i,SV701: $i,SV138: $i] :
( ( ( c_Relation_Orel__comp @ SV138 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV701 @ SV1195 @ ( tc_fun @ ( tc_prod @ SV1557 @ SV1821 ) @ tc_bool ) ) @ SV1990 @ SV1557 @ SV1821 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV138 @ SV701 @ SV1990 @ SV1557 @ SV1821 ) @ ( c_Relation_Orel__comp @ SV138 @ SV1195 @ SV1990 @ SV1557 @ SV1821 ) @ ( tc_fun @ ( tc_prod @ SV1990 @ SV1821 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(4774,plain,
! [SV1197: $i,SV703: $i,SV1822: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1822 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) ) @ ( tc_fun @ SV1197 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV140 @ SV703 @ ( tc_fun @ SV1197 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4395]) ).
thf(4775,plain,
! [SV1198: $i,SV1823: $i,SV704: $i,SV141: $i] :
( ( ( c_lessequals @ SV141 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV704 @ SV1823 @ ( tc_fun @ SV1198 @ tc_bool ) ) @ ( tc_fun @ SV1198 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV141 @ SV704 @ ( tc_fun @ SV1198 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4776,plain,
! [SV142: $i,SV1824: $i,SV705: $i] :
( ( ( c_lessequals @ SV705 @ SV1824 @ SV142 )
= $true )
| ( ( ! [SY5431: $i] :
~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1824 @ SY5431 @ SV142 ) @ SV142 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4397]) ).
thf(4777,plain,
! [SV143: $i,SV1825: $i,SV706: $i] :
( ( ( c_lessequals @ SV706 @ SV1825 @ SV143 )
= $true )
| ( ( ! [SY5432: $i] :
~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5432 @ SV1825 @ SV143 ) @ SV143 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(4778,plain,
! [SV1991: $i,SV144: $i,SV1826: $i,SV707: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SV1826 @ SV144 ) @ SV1991 @ SV144 )
| ~ ( c_lessequals @ SV707 @ SV1991 @ SV144 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(4779,plain,
! [SV1992: $i,SV145: $i,SV1827: $i,SV708: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SV1827 @ SV145 ) @ SV1992 @ SV145 )
| ~ ( c_lessequals @ SV1827 @ SV1992 @ SV145 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(4780,plain,
! [SV146: $i,SV1828: $i,SV709: $i] :
( ( ( c_lessequals @ SV709 @ SV1828 @ SV146 )
= $true )
| ( ( ! [SY5435: $i] :
~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1828 @ SY5435 @ SV146 ) @ SV146 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4781,plain,
! [SV147: $i,SV1829: $i,SV710: $i] :
( ( ( c_lessequals @ SV710 @ SV1829 @ SV147 )
= $true )
| ( ( ! [SY5436: $i] :
~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5436 @ SV1829 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(4782,plain,
! [SV719: $i,SV1834: $i,SV1564: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SV1564 @ SV1834 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1564 @ SV1834 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(4783,plain,
! [SV721: $i,SV1835: $i,SV163: $i,SV1565: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1565 @ SV163 @ ( tc_fun @ SV1835 @ tc_bool ) ) @ SV721 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4784,plain,
! [SV722: $i,SV1836: $i,SV1566: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 @ SV1566 @ ( tc_fun @ SV1836 @ tc_bool ) ) @ SV722 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV164 @ SV722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4785,plain,
! [SV165: $i,SV1208: $i,SV723: $i] :
( ( ( c_Relation_Osym @ SV723 @ SV1208 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV165 @ SV1208 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1208 @ SV1208 ) @ tc_bool ) ) @ SV1208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4412]) ).
thf(4786,plain,
! [SV1993: $i,SV1837: $i,SV1567: $i,SV1209: $i,SV724: $i,SV166: $i] :
( ( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) ) )
| ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SV1567 @ SV1837 @ SV1993 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(4787,plain,
! [SV168: $i,SV726: $i,SV1838: $i,SV1568: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1568 @ SV1838 @ SV726 @ SV726 ) @ SV168 @ ( tc_prod @ SV726 @ SV726 ) ) @ SV726 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV168 @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4414]) ).
thf(4788,plain,
! [SV169: $i,SV1994: $i,SV1210: $i,SV727: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SV1994 @ SV1210 ) @ SV169 )
| ! [SY5514: $i] :
~ ( c_lessequals @ SV727 @ SV1994 @ ( tc_fun @ SY5514 @ SV169 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(4789,plain,
! [SV728: $i,SV1569: $i,SV1211: $i,SV170: $i] :
( ( ( ~ ( c_in @ SV170 @ SV1211 @ SV1569 ) )
= $true )
| ( ( ~ ( c_in @ SV170 @ SV728 @ SV1569 ) )
= $true )
| ( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV1569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4790,plain,
! [SV729: $i,SV1570: $i,SV1212: $i,SV171: $i] :
( ( ( ~ ( c_in @ SV171 @ SV1212 @ SV1570 ) )
= $true )
| ( ( ~ ( c_in @ SV171 @ SV729 @ SV1570 ) )
= $true )
| ( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4791,plain,
! [SV730: $i,SV1213: $i,SV1839: $i,SV172: $i] :
( ( ( ~ ( c_in @ SV172 @ SV1839 @ SV1213 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1839 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV172 @ SV730 @ SV1213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(4792,plain,
! [SV173: $i,SV1214: $i,SV731: $i,SV1840: $i] :
( ( ( ~ ( c_lessequals @ SV1840 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV173 @ SV1840 @ SV1214 ) )
= $true )
| ( ( c_in @ SV173 @ SV731 @ SV1214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(4793,plain,
! [SV732: $i,SV1215: $i,SV1841: $i,SV174: $i] :
( ( ( ~ ( c_in @ SV174 @ SV1841 @ SV1215 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1841 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV174 @ SV732 @ SV1215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4794,plain,
! [SV733: $i,SV1216: $i,SV1842: $i,SV175: $i] :
( ( ( ~ ( c_in @ SV175 @ SV1842 @ SV1216 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1842 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV175 @ SV733 @ SV1216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(4795,plain,
! [SV1217: $i,SV1571: $i,SV734: $i,SV176: $i] :
( ( ( c_in @ SV176 @ SV734 @ SV1571 )
= $false )
| ( ( c_in @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV734 @ SV1217 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4796,plain,
! [SV735: $i,SV1572: $i,SV1218: $i,SV177: $i] :
( ( ( c_in @ SV177 @ SV1218 @ SV1572 )
= $false )
| ( ( c_in @ SV177 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SV1218 @ ( tc_fun @ SV1572 @ tc_bool ) ) @ SV1572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4797,plain,
! [SV740: $i,SV1219: $i,SV1843: $i,SV182: $i] :
( ( ( c_in @ SV182 @ SV1843 @ SV1219 )
= $true )
| ( ( ~ ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1843 @ SV740 @ ( tc_fun @ SV1219 @ tc_bool ) ) @ SV1219 ) )
= $true )
| ( ( c_in @ SV182 @ SV740 @ SV1219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(4798,plain,
! [SV1220: $i,SV741: $i,SV1844: $i,SV183: $i] :
( ( ( c_in @ SV183 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1844 @ SV741 @ ( tc_fun @ SV1220 @ tc_bool ) ) @ SV1220 )
= $false )
| ( ( c_in @ SV183 @ SV741 @ SV1220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(4799,plain,
! [SV1221: $i,SV1845: $i,SV742: $i,SV184: $i] :
( ( ( c_in @ SV184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV742 @ SV1845 @ ( tc_fun @ SV1221 @ tc_bool ) ) @ SV1221 )
= $false )
| ( ( c_in @ SV184 @ SV742 @ SV1221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4800,plain,
! [SV185: $i,SV1846: $i,SV743: $i] :
( ( ( c_in @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1846 @ tc_bool ) ) @ SV1846 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV743 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4801,plain,
! [SV1224: $i,SV749: $i,SV1576: $i,SV191: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) ) )
= $true )
| ( ( ! [SY5228: $i] :
( ~ ( c_in @ SV1576 @ SY5228 @ SV749 )
| ~ ( c_in @ SV191 @ SY5228 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5228 @ SV1224 @ SV749 ) ) )
= $true )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(4802,plain,
! [SV1847: $i,SV1577: $i,SV1225: $i,SV751: $i,SV194: $i] :
( ( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
!= ( c_Set_Oinsert @ SV1577 @ ( c_Set_Oinsert @ SV1847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
= $true )
| ( ( ( SV194 = SV1847 )
| ( SV194 = SV1577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(4803,plain,
! [SV1995: $i,SV1578: $i,SV1226: $i,SV752: $i,SV195: $i] :
( ( ( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
!= ( c_Set_Oinsert @ SV1578 @ ( c_Set_Oinsert @ SV1995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) )
= $true )
| ( ( ( SV752 = SV1578 )
| ( SV195 = SV1578 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(4804,plain,
! [SV1848: $i,SV1579: $i,SV1227: $i,SV753: $i,SV196: $i] :
( ( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
!= ( c_Set_Oinsert @ SV1579 @ ( c_Set_Oinsert @ SV1848 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
= $true )
| ( ( ( SV196 = SV1848 )
| ( SV753 = SV1848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(4805,plain,
! [SV1849: $i,SV1580: $i,SV1228: $i,SV754: $i,SV197: $i] :
( ( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
!= ( c_Set_Oinsert @ SV1580 @ ( c_Set_Oinsert @ SV1849 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
= $true )
| ( ( ( SV754 = SV1580 )
| ( SV754 = SV1849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4806,plain,
! [SV759: $i,SV1232: $i,SV1581: $i,SV204: $i] :
( ( ( c_in @ SV204 @ SV1581 @ SV1232 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV204 @ SV759 @ SV1232 ) @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) )
= ( c_Set_Oinsert @ SV204 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV759 @ SV1581 @ ( tc_fun @ SV1232 @ tc_bool ) ) @ SV1232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(4807,plain,
! [SV1233: $i,SV1582: $i,SV205: $i,SV760: $i] :
( ( ( c_in @ SV760 @ SV205 @ SV1582 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ ( c_Set_Oinsert @ SV760 @ SV1233 @ SV1582 ) @ ( tc_fun @ SV1582 @ tc_bool ) )
= ( c_Set_Oinsert @ SV760 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV1233 @ ( tc_fun @ SV1582 @ tc_bool ) ) @ SV1582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(4808,plain,
! [SV1850: $i,SV1583: $i,SV1234: $i,SV762: $i,SV207: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV762 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) )
| ~ ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(4809,plain,
! [SV210: $i,SV1996: $i,SV1853: $i,SV763: $i] :
( ( ( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SV1996 @ SV210 ) @ SV210 )
| ~ ( c_lessequals @ SV763 @ SV1996 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SV1853 @ SV210 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(4810,plain,
! [SV211: $i,SV1997: $i,SV1854: $i,SV764: $i] :
( ( ( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV1997 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV764 @ SV1997 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SV1854 @ SV211 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(4811,plain,
! [SV212: $i,SV1998: $i,SV1855: $i,SV765: $i] :
( ( ( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SV1998 @ SV212 ) @ SV212 )
| ~ ( c_lessequals @ SV765 @ SV1998 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SV1855 @ SV212 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4812,plain,
! [SV768: $i,SV1588: $i,SV1237: $i,SV217: $i] :
( ( ( ~ ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SV1588 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ ( tc_fun @ SV1588 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(4813,plain,
! [SV769: $i,SV1589: $i,SV1238: $i,SV218: $i] :
( ( ( ~ ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SV1589 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ ( tc_fun @ SV1589 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4814,plain,
! [SV1999: $i,SV220: $i,SV1859: $i,SV771: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV771 @ SV1859 @ SV220 ) @ SV1999 @ SV220 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV771 @ SV1999 @ SV220 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SV1999 @ SV220 ) @ SV220 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(4815,plain,
! [SV221: $i,SV2000: $i,SV1860: $i,SV772: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1860 @ SV2000 @ SV221 ) @ SV221 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SV1860 @ SV221 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV772 @ SV2000 @ SV221 ) @ SV221 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(4816,plain,
! [SV224: $i,SV1242: $i,SV1593: $i,SV775: $i] :
( ( ( ~ ( c_lessequals @ SV775 @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV224 @ SV1593 @ SV1242 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(4817,plain,
! [SV1863: $i,SV1596: $i,SV1245: $i,SV778: $i,SV229: $i] :
( ( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SV1245 @ ( tc_fun @ SV1596 @ tc_bool ) ) @ SV1596 @ SV1863 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SV1596 @ SV1863 ) @ ( c_Relation_OImage @ SV229 @ SV1245 @ SV1596 @ SV1863 ) @ ( tc_fun @ SV1863 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SV1596 @ SV1863 ) @ SV229 ) @ SV1863 @ SV1596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(4818,plain,
! [SV236: $i,SV1864: $i,SV784: $i] :
( ( ( c_lessequals @ SV784 @ SV1864 @ SV236 )
= $true )
| ( ( ! [SY5443: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5443 @ SV784 @ SV236 ) @ SV1864 @ SV236 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4819,plain,
! [SV237: $i,SV1865: $i,SV785: $i] :
( ( ( c_lessequals @ SV785 @ SV1865 @ SV237 )
= $true )
| ( ( ! [SY5444: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SY5444 @ SV237 ) @ SV1865 @ SV237 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4820,plain,
! [SV238: $i,SV2001: $i,SV1866: $i,SV786: $i] :
( ( ( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1866 @ SV2001 @ SV238 ) @ SV238 )
| ~ ( c_lessequals @ SV786 @ SV2001 @ SV238 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4460]) ).
thf(4821,plain,
! [SV239: $i,SV1867: $i,SV787: $i] :
( ( ( ! [SY5446: $i] : ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1867 @ SY5446 @ SV239 ) @ SV239 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV787 @ SV1867 @ SV239 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(4822,plain,
! [SV240: $i,SV1868: $i,SV788: $i] :
( ( ( c_lessequals @ SV788 @ SV1868 @ SV240 )
= $true )
| ( ( ! [SY5447: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5447 @ SV788 @ SV240 ) @ SV1868 @ SV240 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4462]) ).
thf(4823,plain,
! [SV241: $i,SV1869: $i,SV789: $i] :
( ( ( c_lessequals @ SV789 @ SV1869 @ SV241 )
= $true )
| ( ( ! [SY5448: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SY5448 @ SV241 ) @ SV1869 @ SV241 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(4824,plain,
! [SV790: $i,SV1249: $i,SV1870: $i,SV242: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV242 @ SV1870 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV242 @ SV790 @ ( tc_fun @ SV1249 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4825,plain,
! [SV791: $i,SV1250: $i,SV243: $i,SV1871: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1871 @ SV243 @ ( tc_fun @ SV1250 @ tc_bool ) ) @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV243 @ SV791 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4465]) ).
thf(4826,plain,
! [SV244: $i,SV1872: $i,SV792: $i] :
( ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
= $true )
| ( ( ! [SY5449: $i] :
( ~ ( c_lessequals @ SV792 @ SY5449 @ SV244 )
| ~ ( c_lessequals @ SY5449 @ SV1872 @ SV244 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4827,plain,
! [SV245: $i,SV1873: $i,SV793: $i] :
( ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
= $true )
| ( ( ! [SY5450: $i] :
( ~ ( c_lessequals @ SY5450 @ SV1873 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SY5450 @ SV245 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4828,plain,
! [SV248: $i,SV1251: $i,SV796: $i,SV1874: $i] :
( ( ( ~ ( c_lessequals @ SV1874 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV248 @ SV1874 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4468]) ).
thf(4829,plain,
! [SV249: $i,SV797: $i,SV1599: $i] :
( ( ( hBOOL @ ( hAPP @ SV1599 @ SV797 ) )
= $false )
| ( ( ! [SY5242: $i] :
~ ( c_lessequals @ SV1599 @ SV249 @ ( tc_fun @ SY5242 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4830,plain,
! [SV798: $i,SV1600: $i,SV250: $i] :
( ( ( c_lessequals @ SV250 @ SV1600 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1600 @ SV798 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4831,plain,
! [SV253: $i,SV799: $i,SV1603: $i] :
( ( ( c_Relation_Oantisym @ SV1603 @ SV799 )
= $false )
| ( ( ~ ( c_lessequals @ SV253 @ SV1603 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV253 @ SV799 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4832,plain,
! [SV800: $i,SV2002: $i,SV254: $i,SV1604: $i] :
( ( ( ~ ( c_lessequals @ SV1604 @ SV254 @ ( tc_fun @ SV2002 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1604 @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(4833,plain,
! [SV801: $i,SV1605: $i,SV255: $i] :
( ( ( c_lessequals @ SV255 @ SV1605 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1605 @ SV801 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4834,plain,
! [SV256: $i,SV1252: $i,SV802: $i,SV1875: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1875 @ SV802 @ SV1252 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV256 @ SV1875 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(4835,plain,
! [SV1876: $i,SV1606: $i,SV1253: $i,SV803: $i,SV257: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV803 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4836,plain,
! [SV1254: $i,SV806: $i,SV1607: $i,SV260: $i] :
( ( ( c_lessequals @ SV260 @ SV1607 @ ( tc_fun @ ( tc_prod @ SV806 @ SV1254 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_ODomain @ SV260 @ SV806 @ SV1254 ) @ ( c_Relation_ODomain @ SV1607 @ SV806 @ SV1254 ) @ ( tc_fun @ SV806 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4476]) ).
thf(4837,plain,
! [SV1255: $i,SV807: $i,SV261: $i] :
( ( ( c_lessequals @ SV261 @ ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) @ ( tc_fun @ SV1255 @ tc_bool ) )
= $false )
| ( ( SV261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) )
= $true )
| ( ( SV261
= ( c_Set_Oinsert @ SV807 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1255 @ tc_bool ) ) @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4838,plain,
! [SV1257: $i,SV263: $i,SV1608: $i,SV809: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV809 @ SV1608 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV263 @ SV1608 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1608 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4478]) ).
thf(4839,plain,
! [SV264: $i,SV1258: $i,SV1609: $i,SV810: $i] :
( ( ( c_lessequals @ SV810 @ SV1609 @ ( tc_fun @ SV1258 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV264 @ SV810 @ SV1258 ) @ ( c_Set_Oinsert @ SV264 @ SV1609 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4840,plain,
! [SV2003: $i,SV1877: $i,SV1610: $i,SV1260: $i,SV812: $i,SV268: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SV2003 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
| ~ ( c_lessequals @ SV812 @ SV2003 @ ( tc_fun @ SV1260 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(4841,plain,
! [SV270: $i,SV1878: $i,SV1611: $i] :
( ( ( c_lessequals @ SV1611 @ SV1878 @ SV270 )
= $true )
| ( ( c_lessequals @ SV1878 @ SV1611 @ SV270 )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(4842,plain,
! [SV814: $i,SV2004: $i,SV1879: $i,SV1262: $i,SV271: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ SV2004 @ SV2004 ) @ SV1879 @ ( tc_prod @ SV2004 @ SV2004 ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SV2004 @ SV2004 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SV2004 ) @ ( tc_prod @ SV2004 @ SV2004 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4484]) ).
thf(4843,plain,
! [SV815: $i,SV2005: $i,SV1880: $i,SV1263: $i,SV272: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ SV2005 @ SV2005 ) @ SV1880 @ ( tc_prod @ SV2005 @ SV2005 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
| ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SV2005 @ SV2005 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SV2005 ) @ ( tc_prod @ SV2005 @ SV2005 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4485]) ).
thf(4844,plain,
! [SV1264: $i,SV816: $i,SV273: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4845,plain,
! [SV274: $i,SV2006: $i,SV1612: $i,SV817: $i,SV1265: $i] :
( ( ( ! [SY5515: $i] :
( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SY5515 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SY5515 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_Relation_Osingle__valued @ SY5515 @ SV1612 @ SV2006 ) ) )
= $true )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4487]) ).
thf(4846,plain,
! [SV1881: $i,SV1613: $i,SV1266: $i,SV818: $i,SV275: $i] :
( ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
!= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
= $true )
| ( ( ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 )
| ( SV275 = SV1881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(4847,plain,
! [SV1267: $i,SV1614: $i,SV819: $i,SV276: $i] :
( ( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ SV819 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $false )
| ( ( c_in @ SV276 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV819 @ SV1267 @ ( tc_fun @ ( tc_prod @ SV1614 @ SV1614 ) @ tc_bool ) ) @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4848,plain,
! [SV820: $i,SV1615: $i,SV1268: $i,SV277: $i] :
( ( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ SV1268 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $false )
| ( ( c_in @ SV277 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1268 @ ( tc_fun @ ( tc_prod @ SV1615 @ SV1615 ) @ tc_bool ) ) @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(4849,plain,
! [SV278: $i,SV1269: $i,SV821: $i,SV1882: $i] :
( ( ( ~ ( c_lessequals @ SV1882 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV1882 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) ) )
= $true )
| ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4491]) ).
thf(4850,plain,
! [SV1616: $i,SV1273: $i,SV834: $i,SV292: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false )
| ( ( ! [SY5252: $i] :
( ~ ( c_in @ SV1616 @ SY5252 @ SV834 )
| ~ ( c_in @ SV292 @ SY5252 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5252 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4851,plain,
! [SV1274: $i,SV835: $i,SV1883: $i,SV293: $i] :
( ( ( SV293 = SV1883 )
= $true )
| ( ( ! [SY5455: $i] :
( ~ ( c_lessequals @ SY5455 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY5455 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) ) )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(4852,plain,
! [SV294: $i,SV1275: $i,SV1617: $i,SV836: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) ) )
= $true )
| ( ( ! [SY4848: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4848 @ SV294 @ SV1275 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(4853,plain,
! [SV837: $i,SV295: $i,SV1884: $i] :
( ( ( c_in @ ( c_Pair @ SV1884 @ SV1884 @ SV295 @ SV295 ) @ ( c_Transitive__Closure_Otrancl @ SV837 @ SV295 ) @ ( tc_prod @ SV295 @ SV295 ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ SV295 @ SV295 ) @ SV837 ) @ ( c_Transitive__Closure_Ortrancl @ SV837 @ SV295 ) @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV295 @ SV295 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4854,plain,
! [SV1618: $i,SV1276: $i,SV838: $i,SV296: $i] :
( ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false )
| ( ( ~ ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4855,plain,
! [SV1885: $i,SV1619: $i,SV1278: $i,SV839: $i,SV299: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SV1278 @ SV1619 @ SV1885 ) @ SV299 @ SV1619 )
= $true )
| ( ( ~ ( c_in @ SV1278 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SV1619 @ SV1885 ) @ ( tc_prod @ SV1619 @ SV1885 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4856,plain,
! [SV1279: $i,SV1620: $i,SV840: $i,SV300: $i] :
( ( ( SV300 = SV840 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV300 @ SV840 @ SV1620 @ SV1620 ) @ ( c_Transitive__Closure_Ortrancl @ SV1279 @ SV1620 ) @ ( tc_prod @ SV1620 @ SV1620 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SV1279 @ SV1620 ) @ SV840 @ SV1620 @ SV1620 ) @ SV1279 @ ( tc_prod @ SV1620 @ SV1620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(4857,plain,
! [SV301: $i,SV1621: $i,SV1280: $i,SV841: $i] :
( ( ( SV841 = SV1280 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV841 @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SV1280 @ SV1621 ) @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(4858,plain,
! [SV842: $i,SV1622: $i,SV1281: $i,SV302: $i] :
( ( ( SV302 = SV1281 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV302 @ SV1281 @ SV1622 @ SV1622 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SV1622 ) @ ( tc_prod @ SV1622 @ SV1622 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SV1281 @ SV1622 ) @ SV1622 @ SV1622 ) @ SV842 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(4859,plain,
! [SV843: $i,SV2007: $i,SV1886: $i,SV1282: $i,SV303: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SV2007 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SV2007 @ SV2007 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV2007 ) @ ( tc_prod @ SV2007 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(4860,plain,
! [SV844: $i,SV2008: $i,SV1887: $i,SV1283: $i,SV304: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SV2008 ) @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4504]) ).
thf(4861,plain,
! [SV845: $i,SV2009: $i,SV1888: $i,SV305: $i,SV1284: $i] :
( ( ( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SV2009 ) @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
| ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
| ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4505]) ).
thf(4862,plain,
! [SV846: $i,SV2010: $i,SV1889: $i,SV1285: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(4863,plain,
! [SV1623: $i,SV1286: $i,SV307: $i,SV847: $i] :
( ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( ! [SY5255: $i] :
( ~ ( c_in @ ( c_Pair @ SY5255 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_in @ ( c_Pair @ SY5255 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(4864,plain,
! [SV1287: $i,SV848: $i,SV308: $i] :
( ( ( c_in @ ( c_Pair @ SV308 @ SV848 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( SV848 = SV308 )
= $true )
| ( ( c_in @ ( c_Pair @ SV308 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV308 @ SV848 @ SV1287 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1287 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4865,plain,
! [SV849: $i,SV2011: $i,SV1890: $i,SV1288: $i,SV309: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SV2011 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
| ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SV2011 @ SV2011 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV2011 ) @ ( tc_prod @ SV2011 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4509]) ).
thf(4866,plain,
! [SV1289: $i,SV850: $i,SV310: $i] :
( ( ( c_in @ ( c_Pair @ SV310 @ SV850 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1289 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( SV850 = SV310 )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV310 @ SV850 @ SV1289 ) @ SV850 @ t_a @ t_a ) @ SV1289 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4510]) ).
thf(4867,plain,
! [SV851: $i,SV2012: $i,SV1891: $i,SV1290: $i,SV311: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(4868,plain,
! [SV1291: $i,SV1624: $i,SV852: $i,SV312: $i] :
( ( ( SV312 = SV852 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV312 @ SV852 @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SV1291 @ SV1624 ) @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(4869,plain,
! [SV853: $i,SV2013: $i,SV313: $i,SV1292: $i] :
( ( ( ! [SY5516: $i] :
( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SV2013 @ SY5516 ) @ SY5516 @ SY5516 ) @ SV2013 @ ( tc_prod @ SY5516 @ SY5516 ) )
| ~ ( c_Wellfounded_Owf @ SV2013 @ SY5516 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4513]) ).
thf(4870,plain,
! [SV854: $i,SV2014: $i,SV314: $i,SV1293: $i] :
( ( ( ! [SY5517: $i] :
( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SV2014 @ SY5517 ) @ SY5517 @ SY5517 ) @ SV2014 @ ( tc_prod @ SY5517 @ SY5517 ) )
| ~ ( c_Wellfounded_Owf @ SV2014 @ SY5517 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4514]) ).
thf(4871,plain,
! [SV855: $i,SV2015: $i,SV315: $i,SV1294: $i] :
( ( ( ! [SY5518: $i] :
( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SV2015 @ SY5518 ) @ SY5518 @ SY5518 ) @ SV2015 @ ( tc_prod @ SY5518 @ SY5518 ) )
| ~ ( c_Wellfounded_Owf @ SV2015 @ SY5518 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4515]) ).
thf(4872,plain,
! [SV856: $i,SV2016: $i,SV316: $i,SV1295: $i] :
( ( ( ! [SY5519: $i] :
( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SV2016 @ SY5519 ) @ SY5519 @ SY5519 ) @ SV2016 @ ( tc_prod @ SY5519 @ SY5519 ) )
| ~ ( c_Wellfounded_Owf @ SV2016 @ SY5519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4516]) ).
thf(4873,plain,
! [SV318: $i,SV1625: $i,SV1297: $i,SV858: $i] :
( ( ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ SV318 @ ( tc_prod @ SV1625 @ SV1625 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SV1297 @ SV1625 ) @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4874,plain,
! [SV1298: $i,SV859: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV319 @ SV859 @ t_a @ t_a ) @ SV1298 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV319 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV319 @ SV859 @ SV1298 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1298 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4875,plain,
! [SV320: $i,SV860: $i,SV1299: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1299 @ SV860 )
= $false )
| ( ( c_in @ ( c_Pair @ SV320 @ SV320 @ SV860 @ SV860 ) @ ( c_Transitive__Closure_Otrancl @ SV1299 @ SV860 ) @ ( tc_prod @ SV860 @ SV860 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(4876,plain,
! [SV1300: $i,SV1626: $i,SV861: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV1626 ) @ ( tc_prod @ SV1626 @ SV1626 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SV1300 @ SV1626 ) @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(4877,plain,
! [SV1301: $i,SV1627: $i,SV862: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ SV1301 @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SV1301 @ SV1627 ) @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(4878,plain,
! [SV863: $i,SV1628: $i,SV1302: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SV1628 ) @ ( tc_prod @ SV1628 @ SV1628 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SV1302 @ SV1628 ) @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4523]) ).
thf(4879,plain,
! [SV1303: $i,SV864: $i,SV324: $i] :
( ( ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV324 @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV324 @ SV864 @ SV1303 ) @ SV864 @ t_a @ t_a ) @ SV1303 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4524]) ).
thf(4880,plain,
! [SV325: $i,SV1629: $i,SV1304: $i,SV2017: $i,SV865: $i] :
( ( ( ~ ( c_in @ SV865 @ SV2017 @ SV1304 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4525]) ).
thf(4881,plain,
! [SV866: $i,SV1305: $i,SV326: $i,SV1630: $i] :
( ( ( ! [SY5257: $i] :
~ ( c_in @ SY5257 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) )
= $true )
| ( ( ! [SY5258: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5258 @ SV1630 @ SV1305 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4526]) ).
thf(4882,plain,
! [SV2018: $i,SV1892: $i,SV1631: $i,SV1306: $i,SV867: $i,SV327: $i] :
( ( ! [SY5520: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SV1892 @ SV2018 @ SY5520 ) @ SV867 @ SY5520 @ SV2018 ) @ SV1631 @ ( tc_prod @ SY5520 @ SV2018 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SV1892 @ SV2018 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SV1892 @ SY5520 @ SV2018 ) @ ( tc_prod @ SV1892 @ SV2018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(4883,plain,
! [SV2019: $i,SV1893: $i,SV1632: $i,SV1307: $i,SV868: $i,SV328: $i] :
( ( ! [SY5521: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SV1893 @ SV2019 @ SY5521 ) @ SV1893 @ SY5521 ) @ SV1307 @ ( tc_prod @ SV1893 @ SY5521 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SV1893 @ SV2019 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SV1893 @ SY5521 @ SV2019 ) @ ( tc_prod @ SV1893 @ SV2019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4528]) ).
thf(4884,plain,
! [SV1894: $i,SV1633: $i,SV1308: $i,SV869: $i,SV329: $i] :
( ( ( c_in @ SV329 @ ( c_FuncSet_OPi @ SV869 @ SV1308 @ SV1633 @ SV1894 ) @ ( tc_fun @ SV1633 @ SV1894 ) )
= $true )
| ( ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV869 @ SV1308 @ SV329 @ SV1633 @ SV1894 ) @ SV869 @ SV1633 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(4885,plain,
! [SV1895: $i,SV1634: $i,SV1309: $i,SV870: $i,SV330: $i] :
( ( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV870 @ SV1309 @ SV1634 @ SV1895 ) @ ( tc_fun @ SV1634 @ SV1895 ) )
= $true )
| ( ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV870 @ SV1309 @ SV330 @ SV1634 @ SV1895 ) @ SV870 @ SV1634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4886,plain,
! [SV1896: $i,SV1635: $i,SV1310: $i,SV871: $i,SV331: $i] :
( ( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SV1310 @ SV1635 @ SV1896 ) @ ( tc_fun @ SV1635 @ SV1896 ) )
= $true )
| ( ( ~ ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ ( hAPP @ SV1310 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ SV1896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(4887,plain,
! [SV1636: $i,SV1311: $i,SV332: $i,SV2020: $i,SV872: $i] :
( ( ( ! [SY5522: $i] :
( ~ ( c_in @ SV872 @ SV2020 @ SY5522 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV2020 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SY5522 ) @ SY5522 @ SV1636 ) @ ( tc_fun @ SY5522 @ SV1636 ) ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4532]) ).
thf(4888,plain,
! [SV1897: $i,SV1637: $i,SV1312: $i,SV873: $i,SV333: $i] :
( ( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SV1312 @ SV1637 @ SV1897 ) @ ( tc_fun @ SV1637 @ SV1897 ) )
= $true )
| ( ( ~ ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ ( hAPP @ SV1312 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ SV1897 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(4889,plain,
! [SV2021: $i,SV1898: $i,SV1638: $i,SV1315: $i,SV879: $i,SV339: $i] :
( ( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SV1315 @ SV1638 @ SV1898 )
= ( c_Recdef_Ocut @ SV2021 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SV2021 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) @ SV1315 @ SV1638 @ SV1638 ) @ SV879 @ ( tc_prod @ SV1638 @ SV1638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4536]) ).
thf(4890,plain,
! [SV1640: $i,SV1318: $i,SV885: $i,SV349: $i] :
( ( ( c_in @ ( c_Pair @ SV349 @ SV885 @ SV1318 @ SV1318 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1318 ) @ ( tc_prod @ SV1318 @ SV1318 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SV1318 @ SV1318 ) @ SV1640 @ ( tc_prod @ SV1318 @ SV1318 ) ) @ SV1318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4541]) ).
thf(4891,plain,
! [SV1641: $i,SV1319: $i,SV350: $i,SV886: $i] :
( ( ( c_in @ ( c_Pair @ SV886 @ SV350 @ SV1319 @ SV1319 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1319 ) @ ( tc_prod @ SV1319 @ SV1319 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1641 @ SV1319 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SV1319 @ SV1319 ) @ SV1641 @ ( tc_prod @ SV1319 @ SV1319 ) ) @ SV1319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4892,plain,
! [SV887: $i,SV1320: $i,SV1899: $i,SV351: $i] :
( ( ( ~ ( c_in @ SV351 @ SV1899 @ SV1320 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1899 @ SV887 @ SV1320 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(4893,plain,
! [SV1900: $i,SV1642: $i,SV1321: $i,SV888: $i,SV352: $i] :
( ( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SV1321 @ SV1642 ) @ SV1900 @ ( tc_prod @ SV1321 @ SV1642 ) )
= $true )
| ( ( ~ ( c_in @ SV888 @ ( c_Relation_OImage @ SV1900 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 @ SV1642 ) @ SV1642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4894,plain,
! [SV1901: $i,SV1643: $i,SV1322: $i,SV889: $i,SV353: $i] :
( ( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SV1322 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1643 @ tc_bool ) ) @ SV1643 ) @ SV1643 @ SV1901 ) @ SV1901 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1322 @ SV353 @ SV1643 @ SV1901 ) @ SV889 @ ( tc_prod @ SV1643 @ SV1901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(4895,plain,
! [SV354: $i,SV1323: $i,SV1644: $i,SV890: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) ) )
= $true )
| ( ( ! [SY4917: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4917 @ SV354 @ SV1323 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4896,plain,
! [SV355: $i,SV1324: $i,SV1645: $i,SV891: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) ) )
= $true )
| ( ( ! [SY4919: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4919 @ SV355 @ SV1324 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4897,plain,
! [SV1646: $i,SV1325: $i,SV892: $i,SV356: $i] :
( ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
| ! [SY5277: $i] :
( ~ ( c_in @ SV1646 @ SY5277 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5277 @ SV356 @ SV1325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(4898,plain,
! [SV1647: $i,SV1326: $i,SV893: $i,SV357: $i] :
( ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false )
| ( ( ! [SY5278: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5278 @ SV357 @ SV1326 )
| ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SY5278 @ SV1326 )
| ~ ( c_in @ SV893 @ SY5278 @ SV1326 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4549]) ).
thf(4899,plain,
! [SV358: $i,SV1327: $i,SV1648: $i,SV894: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) ) )
= $true )
| ( ( ! [SY5279: $i] :
( ~ ( c_in @ SV1648 @ SY5279 @ SV1327 )
| ~ ( c_in @ SV894 @ SY5279 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5279 @ SV358 @ SV1327 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(4900,plain,
! [SV1649: $i,SV1328: $i,SV895: $i,SV359: $i] :
( ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false )
| ( ( ! [SY5280: $i] :
( ~ ( c_in @ SV1649 @ SY5280 @ SV1328 )
| ~ ( c_in @ SV895 @ SY5280 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5280 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4901,plain,
! [SV896: $i,SV1650: $i,SV1329: $i,SV360: $i] :
( ( ( c_in @ ( c_Pair @ SV360 @ SV1329 @ SV1650 @ SV1650 ) @ ( c_Transitive__Closure_Otrancl @ SV896 @ SV1650 ) @ ( tc_prod @ SV1650 @ SV1650 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV360 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV896 @ SV360 @ SV1329 @ SV1650 ) @ SV1650 @ SV1650 ) @ SV896 @ ( tc_prod @ SV1650 @ SV1650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4902,plain,
! [SV361: $i,SV1651: $i,SV1330: $i,SV897: $i] :
( ( ( c_in @ ( c_Pair @ SV897 @ SV1330 @ SV1651 @ SV1651 ) @ ( c_Transitive__Closure_Otrancl @ SV361 @ SV1651 ) @ ( tc_prod @ SV1651 @ SV1651 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV361 @ SV897 @ SV1330 @ SV1651 ) @ SV1330 @ SV1651 @ SV1651 ) @ SV361 @ ( tc_prod @ SV1651 @ SV1651 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(4903,plain,
! [SV898: $i,SV1902: $i,SV1652: $i,SV362: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SV1652 @ SV1902 ) @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 )
= $true )
| ( ( ~ ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4554]) ).
thf(4904,plain,
! [SV900: $i,SV1653: $i,SV364: $i] :
( ( ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SV1653 ) ) )
= $false )
| ( ( ~ ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SV1653 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4556]) ).
thf(4905,plain,
! [SV901: $i,SV1903: $i,SV1654: $i,SV365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SV1654 @ SV1903 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SV1654 @ SV1903 ) @ SV1903 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4557]) ).
thf(4906,plain,
! [SV903: $i,SV1904: $i,SV1655: $i,SV367: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SV1655 @ SV1904 ) @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 )
= $true )
| ( ( ~ ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4907,plain,
! [SV904: $i,SV1656: $i,SV368: $i] :
( ( ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SV1656 ) ) )
= $false )
| ( ( ~ ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SV1656 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4560]) ).
thf(4908,plain,
! [SV905: $i,SV1905: $i,SV1657: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SV1657 @ SV1905 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SV1657 @ SV1905 ) @ SV1905 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(4909,plain,
! [SV1906: $i,SV1658: $i,SV1333: $i,SV906: $i,SV370: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SV1333 @ SV1658 @ SV1906 ) @ SV370 @ SV1658 )
= $true )
| ( ( ~ ( c_in @ SV906 @ ( c_Relation_OImage @ SV1333 @ SV370 @ SV1658 @ SV1906 ) @ SV1906 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(4910,plain,
! [SV1907: $i,SV1659: $i,SV1334: $i,SV907: $i,SV371: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SV1334 @ SV1659 @ SV1907 ) @ SV371 @ SV1659 )
= $true )
| ( ( ~ ( c_in @ SV907 @ ( c_Relation_OImage @ SV1334 @ SV371 @ SV1659 @ SV1907 ) @ SV1907 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(4911,plain,
! [SV372: $i,SV908: $i,SV1908: $i,SV1660: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1660 @ SV1908 @ SV908 @ SV908 ) @ SV372 @ ( tc_prod @ SV908 @ SV908 ) ) @ SV908 )
= $false )
| ( ( c_Wellfounded_Owf @ SV372 @ SV908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(4912,plain,
! [SV909: $i,SV1335: $i,SV373: $i,SV2022: $i] :
( ( ( ~ ( c_in @ SV2022 @ SV373 @ SV1335 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV909 @ SV1335 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4565]) ).
thf(4913,plain,
! [SV910: $i,SV1336: $i,SV374: $i,SV2023: $i] :
( ( ( ~ ( c_in @ SV2023 @ SV374 @ SV1336 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV910 @ SV1336 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4566]) ).
thf(4914,plain,
! [SV2024: $i,SV1909: $i,SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ! [SY5523: $i,SY5524: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SY5523 @ ( tc_prod @ SV2024 @ SV2024 ) )
| ! [SY5525: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SY5524 @ SY5524 ) @ SY5525 @ ( tc_prod @ SY5524 @ SY5524 ) )
| ! [SY5526: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5525 @ SY5523 @ SV375 @ SY5524 @ SV2024 @ SY5526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4567]) ).
thf(4915,plain,
! [SV915: $i,SV2025: $i,SV379: $i,SV1663: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1663 @ SV379 @ SV2025 ) @ SV915 ) ) )
= $true )
| ( ( SV1663 = SV915 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4569]) ).
thf(4916,plain,
! [SV1342: $i,SV382: $i,SV1665: $i,SV918: $i] :
( ( ( hBOOL @ ( hAPP @ SV918 @ SV1665 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV382 @ SV918 @ SV1342 ) @ SV1665 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4917,plain,
! [SV920: $i,SV1667: $i,SV1344: $i,SV384: $i] :
( ( ( c_in @ SV384 @ SV1344 @ SV1667 )
= $false )
| ( ( c_in @ SV384 @ ( c_Set_Oinsert @ SV920 @ SV1344 @ SV1667 ) @ SV1667 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4918,plain,
! [SV921: $i,SV1668: $i,SV1345: $i,SV385: $i] :
( ( ( c_in @ SV385 @ SV1345 @ SV1668 )
= $false )
| ( ( c_in @ SV385 @ ( c_Set_Oinsert @ SV921 @ SV1345 @ SV1668 ) @ SV1668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4919,plain,
! [SV1346: $i,SV922: $i,SV1912: $i,SV386: $i] :
( ( ( SV386 = SV1912 )
= $true )
| ( ( ~ ( c_in @ SV386 @ ( c_Set_Oinsert @ SV1912 @ SV922 @ SV1346 ) @ SV1346 ) )
= $true )
| ( ( c_in @ SV386 @ SV922 @ SV1346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4574]) ).
thf(4920,plain,
! [SV1669: $i,SV1350: $i,SV926: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
= ( c_Set_Oinsert @ SV390 @ SV1669 @ SV1350 ) )
= $false )
| ( ( ( c_in @ SV390 @ SV1669 @ SV1350 )
| ( SV926 = SV1669 )
| ( c_in @ SV390 @ SV926 @ SV1350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4921,plain,
! [SV2026: $i,SV1913: $i,SV1670: $i,SV1352: $i,SV928: $i,SV392: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
| ! [SY5527: $i] :
( ~ ( c_in @ SV1352 @ SV2026 @ SY5527 )
| ! [SY5528: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5528 @ SV392 @ SV928 @ SY5527 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SY5528 @ SY5527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4577]) ).
thf(4922,plain,
! [SV1353: $i,SV2027: $i,SV931: $i,SV398: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
| ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(4923,plain,
! [SV1354: $i,SV2028: $i,SV932: $i,SV399: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
| ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4579]) ).
thf(4924,plain,
! [SV1914: $i,SV1671: $i,SV1355: $i,SV933: $i,SV400: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SV1355 @ SV1671 @ SV1914 ) @ SV933 @ SV1671 @ SV1914 ) @ SV1355 @ ( tc_prod @ SV1671 @ SV1914 ) )
= $true )
| ( ( ~ ( c_in @ SV933 @ ( c_Relation_OImage @ SV1355 @ SV400 @ SV1671 @ SV1914 ) @ SV1914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4580]) ).
thf(4925,plain,
! [SV1915: $i,SV1672: $i,SV1356: $i,SV934: $i,SV401: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SV1356 @ SV1672 @ SV1915 ) @ SV934 @ SV1672 @ SV1915 ) @ SV1356 @ ( tc_prod @ SV1672 @ SV1915 ) )
= $true )
| ( ( ~ ( c_in @ SV934 @ ( c_Relation_OImage @ SV1356 @ SV401 @ SV1672 @ SV1915 ) @ SV1915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(4926,plain,
! [SV1673: $i,SV1357: $i,SV935: $i,SV402: $i] :
( ( ( c_in @ SV402 @ ( c_Relation_ODomain @ SV935 @ SV1357 @ SV1673 ) @ SV1357 )
= $false )
| ( ( c_in @ ( c_Pair @ SV402 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV402 @ SV935 @ SV1357 @ SV1673 ) @ SV1357 @ SV1673 ) @ SV935 @ ( tc_prod @ SV1357 @ SV1673 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4927,plain,
! [SV1674: $i,SV1358: $i,SV936: $i,SV403: $i] :
( ( ( c_in @ SV403 @ ( c_Relation_ODomain @ SV936 @ SV1358 @ SV1674 ) @ SV1358 )
= $false )
| ( ( c_in @ ( c_Pair @ SV403 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV403 @ SV936 @ SV1358 @ SV1674 ) @ SV1358 @ SV1674 ) @ SV936 @ ( tc_prod @ SV1358 @ SV1674 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4583]) ).
thf(4928,plain,
! [SV937: $i,SV404: $i,SV1916: $i,SV1675: $i] :
( ( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SV1916 ) @ t_a @ t_a ) @ SV1916 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4584]) ).
thf(4929,plain,
! [SV938: $i,SV405: $i,SV1917: $i,SV1676: $i] :
( ( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SV1917 ) @ t_a @ t_a ) @ SV1917 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(4930,plain,
! [SV940: $i,SV2029: $i,SV407: $i,SV1360: $i] :
( ( ( ! [SY5531: $i] :
( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SV2029 @ SY5531 ) @ SY5531 @ SY5531 ) @ SV2029 @ ( tc_prod @ SY5531 @ SY5531 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SV2029 @ SY5531 ) @ SY5531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4586]) ).
thf(4931,plain,
! [SV941: $i,SV2030: $i,SV408: $i,SV1677: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SV2030 ) @ t_a @ t_a ) @ SV2030 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SV2030 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4587]) ).
thf(4932,plain,
! [SV942: $i,SV2031: $i,SV409: $i,SV1678: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SV2031 ) @ t_a @ t_a ) @ SV2031 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SV2031 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4588]) ).
thf(4933,plain,
! [SV943: $i,SV2032: $i,SV410: $i,SV1361: $i] :
( ( ( ! [SY5532: $i] :
( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SV2032 @ SY5532 ) @ SY5532 @ SY5532 ) @ SV2032 @ ( tc_prod @ SY5532 @ SY5532 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SV2032 @ SY5532 ) @ SY5532 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(4934,plain,
! [SV1679: $i,SV1363: $i,SV412: $i,SV945: $i] :
( ( ( c_in @ ( c_Pair @ SV945 @ SV412 @ SV1363 @ SV1363 ) @ ( c_Transitive__Closure_Ortrancl @ SV1679 @ SV1363 ) @ ( tc_prod @ SV1363 @ SV1363 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1679 @ SV1363 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SV1363 @ SV1363 ) @ SV1679 @ ( tc_prod @ SV1363 @ SV1363 ) ) @ SV1363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4590]) ).
thf(4935,plain,
! [SV1680: $i,SV1364: $i,SV946: $i,SV413: $i] :
( ( ( c_in @ ( c_Pair @ SV413 @ SV946 @ SV1364 @ SV1364 ) @ ( c_Transitive__Closure_Ortrancl @ SV1680 @ SV1364 ) @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SV1364 @ SV1364 ) @ SV1680 @ ( tc_prod @ SV1364 @ SV1364 ) ) @ SV1364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4936,plain,
! [SV1365: $i,SV1681: $i,SV947: $i,SV414: $i] :
( ( ( c_in @ SV414 @ ( c_Relation_ORange @ SV947 @ SV1681 @ SV1365 ) @ SV1365 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV414 @ SV947 @ SV1365 @ SV1681 ) @ SV414 @ SV1681 @ SV1365 ) @ SV947 @ ( tc_prod @ SV1681 @ SV1365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4592]) ).
thf(4937,plain,
! [SV1366: $i,SV1682: $i,SV948: $i,SV415: $i] :
( ( ( c_in @ SV415 @ ( c_Relation_ORange @ SV948 @ SV1682 @ SV1366 ) @ SV1366 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV415 @ SV948 @ SV1366 @ SV1682 ) @ SV415 @ SV1682 @ SV1366 ) @ SV948 @ ( tc_prod @ SV1682 @ SV1366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4593]) ).
thf(4938,plain,
! [SV416: $i,SV1683: $i,SV1367: $i,SV949: $i] :
( ( ( c_in @ ( c_Pair @ SV949 @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Otrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV416 @ SV949 @ SV1367 @ SV1683 ) @ SV1367 @ SV1683 @ SV1683 ) @ ( c_Transitive__Closure_Ortrancl @ SV416 @ SV1683 ) @ ( tc_prod @ SV1683 @ SV1683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(4939,plain,
! [SV950: $i,SV1684: $i,SV1368: $i,SV417: $i] :
( ( ( c_in @ ( c_Pair @ SV417 @ SV1368 @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Otrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV417 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV950 @ SV417 @ SV1368 @ SV1684 ) @ SV1684 @ SV1684 ) @ ( c_Transitive__Closure_Ortrancl @ SV950 @ SV1684 ) @ ( tc_prod @ SV1684 @ SV1684 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4595]) ).
thf(4940,plain,
! [SV418: $i,SV1685: $i,SV1369: $i,SV951: $i,SV2033: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2033 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) )
| ~ ( c_in @ ( c_Pair @ SV418 @ SV2033 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(4941,plain,
! [SV419: $i,SV1686: $i,SV1370: $i,SV952: $i,SV2034: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2034 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
| ~ ( c_in @ ( c_Pair @ SV419 @ SV2034 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(4942,plain,
! [SV420: $i,SV1687: $i,SV1371: $i,SV953: $i,SV2035: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2035 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) )
| ~ ( c_in @ ( c_Pair @ SV420 @ SV2035 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(4943,plain,
! [SV2036: $i,SV1918: $i,SV1688: $i,SV1372: $i,SV954: $i,SV421: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SV1688 @ SV1918 ) @ SV2036 )
= ( hAPP @ SV421 @ SV2036 ) )
| ~ ( c_in @ ( c_Pair @ SV2036 @ SV1372 @ SV1688 @ SV1688 ) @ SV954 @ ( tc_prod @ SV1688 @ SV1688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4599]) ).
thf(4944,plain,
! [SV2037: $i,SV1919: $i,SV1689: $i,SV1373: $i,SV955: $i,SV422: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SV1689 @ SV1919 ) @ SV2037 )
= ( hAPP @ SV422 @ SV2037 ) )
| ~ ( c_in @ ( c_Pair @ SV2037 @ SV1373 @ SV1689 @ SV1689 ) @ SV955 @ ( tc_prod @ SV1689 @ SV1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(4945,plain,
! [SV1920: $i,SV1690: $i,SV956: $i,SV423: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV423 @ SV956 @ SV1690 @ SV1690 ) @ ( c_Transitive__Closure_Ortrancl @ SV1920 @ SV1690 ) @ ( tc_prod @ SV1690 @ SV1690 ) ) )
= $true )
| ( ( c_in @ SV423 @ ( c_Relation_ODomain @ SV1920 @ SV1690 @ SV1690 ) @ SV1690 )
= $true )
| ( ( SV423 = SV956 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4601]) ).
thf(4946,plain,
! [SV958: $i,SV1375: $i,SV1921: $i,SV425: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV425 @ SV1921 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1921 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 ) )
= $true )
| ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(4947,plain,
! [SV426: $i,SV1376: $i,SV959: $i,SV1922: $i] :
( ( ( ~ ( c_in @ SV1922 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV426 @ SV1922 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) )
= $true )
| ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(4948,plain,
! [SV445: $i,SV1693: $i,SV1385: $i,SV977: $i,SV2038: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2038 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV445 @ SV2038 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4611]) ).
thf(4949,plain,
! [SV446: $i,SV1694: $i,SV1386: $i,SV978: $i,SV2039: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2039 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV2039 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(4950,plain,
! [SV1695: $i,SV1387: $i,SV979: $i,SV447: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true )
| ( ( SV447 = SV979 )
= $true )
| ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Ortrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4613]) ).
thf(4951,plain,
! [SV1696: $i,SV1388: $i,SV980: $i,SV448: $i] :
( ( ( SV448 = SV980 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Ortrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Otrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(4952,plain,
! [SV1697: $i,SV1389: $i,SV981: $i,SV449: $i] :
( ( ( SV449 = SV981 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Ortrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Otrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(4953,plain,
! [SV1698: $i,SV1390: $i,SV982: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Otrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV450 @ SV982 @ SV1390 @ SV1390 ) @ ( c_Transitive__Closure_Ortrancl @ SV1698 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(4954,plain,
! [SV451: $i,SV1699: $i,SV1391: $i,SV983: $i,SV2040: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2040 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
| ~ ( c_in @ ( c_Pair @ SV451 @ SV2040 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4617]) ).
thf(4955,plain,
! [SV452: $i,SV1700: $i,SV1392: $i,SV984: $i,SV2041: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2041 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
| ~ ( c_in @ ( c_Pair @ SV452 @ SV2041 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(4956,plain,
! [SV1924: $i,SV1000: $i,SV1396: $i,SV469: $i] :
( ( ( c_Wellfounded_Owf @ SV469 @ SV1396 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV469 @ SV1000 @ SV1396 @ SV1924 ) @ SV1924 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4957,plain,
! [SV1925: $i,SV1002: $i,SV1397: $i,SV471: $i] :
( ( ( c_Relation_Osym @ SV471 @ SV1397 )
= $false )
| ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV471 @ SV1002 @ SV1397 @ SV1925 ) @ SV1925 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(4958,plain,
! [SV2042: $i,SV1926: $i,SV1701: $i,SV1398: $i,SV1005: $i,SV474: $i] :
( ( ! [SY5533: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SV1398 @ SV1701 @ SV1926 ) @ SV2042 @ SV1398 @ SV1926 @ SY5533 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SV2042 @ SV1701 @ SV1926 @ SY5533 ) @ SV1398 @ SV1701 @ SY5533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(4959,plain,
! [SV489: $i,SV1704: $i,SV1403: $i,SV1019: $i,SV2043: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2043 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
| ~ ( c_in @ ( c_Pair @ SV489 @ SV2043 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4626]) ).
thf(4960,plain,
! [SV1705: $i,SV1404: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ SV1705 @ ( tc_prod @ SV1404 @ SV1404 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ SV1404 @ SV1404 ) @ ( c_Transitive__Closure_Otrancl @ SV1705 @ SV1404 ) @ ( tc_prod @ SV1404 @ SV1404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(4961,plain,
! [SV491: $i,SV1706: $i,SV1405: $i,SV1021: $i,SV2044: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2044 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
| ~ ( c_in @ ( c_Pair @ SV491 @ SV2044 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4628]) ).
thf(4962,plain,
! [SV1707: $i,SV1408: $i,SV1024: $i,SV494: $i] :
( ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
| ~ ( c_Wellfounded_Owf @ SV1707 @ SV1408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4963,plain,
! [SV1927: $i,SV1708: $i,SV495: $i,SV1025: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_Relation_Oantisym @ SV1927 @ SV1708 ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4630]) ).
thf(4964,plain,
! [SV1928: $i,SV1709: $i,SV496: $i,SV1026: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_Relation_Oantisym @ SV1928 @ SV1709 ) )
= $true )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(4965,plain,
! [SV497: $i,SV2045: $i,SV1710: $i,SV1409: $i,SV1027: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SV2045 @ ( tc_prod @ SV1710 @ SV1710 ) )
| ! [SY5534: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2045 @ SV497 @ SV1710 @ SY5534 ) )
= $true )
| ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4632]) ).
thf(4966,plain,
! [SV1929: $i,SV1711: $i,SV1028: $i,SV498: $i] :
( ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ SV1711 @ SV1711 ) @ ( c_Relation_OId__on @ SV1929 @ SV1711 ) @ ( tc_prod @ SV1711 @ SV1711 ) )
= $false )
| ( ( SV498 = SV1028 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(4967,plain,
! [SV2046: $i,SV1930: $i,SV1712: $i,SV1410: $i,SV1029: $i,SV499: $i] :
( ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
!= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
| ! [SY5535: $i] :
( ( ( hAPP @ SV499 @ SY5535 )
= ( hAPP @ SV2046 @ SY5535 ) )
| ~ ( c_in @ ( c_Pair @ SY5535 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4634]) ).
thf(4968,plain,
! [SV502: $i,SV1032: $i,SV1412: $i] :
( ( ( c_Wellfounded_Owf @ SV1412 @ SV1032 )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV502 @ SV1032 @ SV1032 ) @ SV1412 @ ( tc_prod @ SV1032 @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4969,plain,
! [SV2047: $i,SV1931: $i,SV1714: $i,SV1413: $i,SV1033: $i,SV503: $i] :
( ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SV1714 @ SV1931 @ SV2047 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1931 @ SV503 ) @ ( hAPP @ SV1931 @ SV1033 ) @ SV2047 @ SV2047 ) @ SV1714 @ ( tc_prod @ SV2047 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(4970,plain,
! [SV1932: $i,SV1715: $i,SV1414: $i,SV1034: $i,SV504: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SV1715 @ SV1715 ) @ SV1932 @ ( tc_prod @ SV1715 @ SV1715 ) )
= $true )
| ( ( ! [SY5482: $i] :
~ ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SY5482 @ SY5482 ) @ ( c_Relation_Oinv__image @ SV1932 @ SV504 @ SV1715 @ SY5482 ) @ ( tc_prod @ SY5482 @ SY5482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(4971,plain,
! [SV1716: $i,SV1415: $i,SV505: $i,SV1035: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1716 @ SV1415 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(4972,plain,
! [SV1717: $i,SV1416: $i,SV506: $i,SV1036: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1717 @ SV1416 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(4973,plain,
! [SV2048: $i,SV1933: $i,SV1718: $i,SV1417: $i,SV1037: $i,SV507: $i] :
( ( ! [SY5536: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SY5536 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
| ! [SY5537: $i] :
( ~ ( c_in @ ( c_Pair @ SY5537 @ SV1037 @ SY5536 @ SV1718 ) @ SV2048 @ ( tc_prod @ SY5536 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5537 @ SV1417 @ SY5536 ) @ SV1933 @ ( tc_prod @ SV1417 @ SY5536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4642]) ).
thf(4974,plain,
! [SV508: $i,SV1719: $i,SV1418: $i,SV1038: $i,SV2049: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2049 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
| ~ ( c_in @ ( c_Pair @ SV508 @ SV2049 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(4975,plain,
! [SV509: $i,SV1720: $i,SV1419: $i,SV1039: $i,SV2050: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2050 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
| ~ ( c_in @ ( c_Pair @ SV509 @ SV2050 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(4976,plain,
! [SV1721: $i,SV1420: $i,SV512: $i,SV2051: $i,SV1042: $i] :
( ( ( ! [SY5538: $i] :
( ~ ( c_in @ SV1042 @ SV2051 @ SY5538 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SV2051 @ SV1420 @ SY5538 @ SV1721 ) @ ( tc_fun @ SY5538 @ SV1721 ) ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(4977,plain,
! [SV1722: $i,SV1421: $i,SV1043: $i,SV513: $i] :
( ( ( c_in @ SV513 @ SV1043 @ SV1421 )
= $false )
| ( ( ! [SY5345: $i,SY5346: $i] :
( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SY5345 @ SV513 ) @ SY5346 )
| ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SY5345 @ SV1421 @ SY5346 ) @ ( tc_fun @ SV1421 @ SY5346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(4978,plain,
! [SV1723: $i,SV1422: $i,SV1044: $i,SV514: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV514 = SV1044 )
| ( SV514 = SV1723 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SV1723 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(4979,plain,
! [SV1724: $i,SV1423: $i,SV1045: $i,SV515: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1045 = SV1724 )
| ( SV515 = SV1724 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SV1724 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(4980,plain,
! [SV1425: $i,SV518: $i,SV1934: $i,SV1048: $i] :
( ( ( SV1048 = SV1934 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1425 @ SV1934 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1425 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(4981,plain,
! [SV1725: $i,SV1427: $i,SV1052: $i,SV522: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV522 = SV1052 )
| ( SV1052 = SV1725 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SV1725 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(4982,plain,
! [SV1726: $i,SV1428: $i,SV1053: $i,SV523: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV523 = SV1726 )
| ( SV1053 = SV1726 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SV1726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(4983,plain,
! [SV1429: $i,SV1055: $i,SV1937: $i,SV525: $i] :
( ( ( SV525 = SV1937 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1429 @ SV1937 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1429 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4654]) ).
thf(4984,plain,
! [SV1430: $i,SV1938: $i,SV527: $i,SV1057: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(4985,plain,
! [SV1431: $i,SV1939: $i,SV528: $i,SV1058: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4986,plain,
! [SV1432: $i,SV1940: $i,SV529: $i,SV1059: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(4987,plain,
! [SV1433: $i,SV1941: $i,SV530: $i,SV1060: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(4988,plain,
! [SV1727: $i,SV2052: $i,SV1434: $i,SV1061: $i,SV531: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4659]) ).
thf(4989,plain,
! [SV1728: $i,SV2053: $i,SV1435: $i,SV1062: $i,SV532: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4660]) ).
thf(4990,plain,
! [SV1729: $i,SV2054: $i,SV1436: $i,SV1063: $i,SV533: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4661]) ).
thf(4991,plain,
! [SV1730: $i,SV2055: $i,SV1437: $i,SV1064: $i,SV534: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4662]) ).
thf(4992,plain,
! [SV1438: $i,SV1731: $i,SV1065: $i,SV535: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1438 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(4993,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2056: $i,SV1732: $i] :
( ( ( ! [SY5539: $i] :
( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5539 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5539 @ ( v_sko__local__X2__1 @ SV1439 @ SY5539 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SY5539 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5539 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(4994,plain,
! [SV1440: $i,SV1067: $i,SV537: $i,SV2057: $i,SV1733: $i] :
( ( ( ! [SY5540: $i] :
( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5540 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SY5540 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5540 @ ( v_sko__local__X2__1 @ SY5540 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5540 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4665]) ).
thf(4995,plain,
! [SV1068: $i,SV538: $i,SV1441: $i,SV2058: $i,SV1734: $i] :
( ( ( ! [SY5541: $i] :
( ~ ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5541 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5541 @ ( v_sko__local__X2__1 @ SV1441 @ SY5541 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SY5541 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY5541 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4666]) ).
thf(4996,plain,
! [SV1442: $i,SV1069: $i,SV539: $i,SV2059: $i,SV1735: $i] :
( ( ( ! [SY5542: $i] :
( ~ ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5542 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SY5542 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5542 @ ( v_sko__local__X2__1 @ SY5542 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5542 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(4997,plain,
! [SV1443: $i,SV1070: $i,SV540: $i,SV2060: $i,SV1736: $i] :
( ( ( ! [SY5543: $i] :
( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5543 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SY5543 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5543 @ ( v_sko__local__X1__1 @ SY5543 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5543 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4668]) ).
thf(4998,plain,
! [SV1444: $i,SV1071: $i,SV541: $i,SV2061: $i,SV1737: $i] :
( ( ( ! [SY5544: $i] :
( ~ ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SY5544 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SY5544 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SY5544 @ ( v_sko__local__X1__1 @ SY5544 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SY5544 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4669]) ).
thf(4999,plain,
! [SV1445: $i,SV542: $i,SV1072: $i] :
( ( ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_Odictator @ SV542 @ SV1445 ) )
= $true )
| ( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SV1445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4670]) ).
thf(5000,plain,
! [SV2062: $i,SV1942: $i,SV1738: $i,SV1446: $i,SV1073: $i,SV543: $i] :
( ( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SV2062 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
| ~ ( c_in @ SV1073 @ ( hAPP @ SV2062 @ SV543 ) @ SV1738 )
| ~ ( c_in @ SV543 @ SV1942 @ SV1446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4671]) ).
thf(5001,plain,
! [SV2063: $i,SV1943: $i,SV1739: $i,SV1447: $i,SV1074: $i,SV544: $i] :
( ( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SV2063 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
| ~ ( c_in @ SV1074 @ ( hAPP @ SV2063 @ SV544 ) @ SV1739 )
| ~ ( c_in @ SV544 @ SV1943 @ SV1447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4672]) ).
thf(5002,plain,
! [SV1075: $i,SV1448: $i,SV1944: $i,SV545: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV545 @ SV1944 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1944 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 ) )
= $true )
| ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4673]) ).
thf(5003,plain,
! [SV1076: $i,SV1449: $i,SV1945: $i,SV546: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV546 @ SV1945 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1945 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 ) )
= $true )
| ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(5004,plain,
! [SV1946: $i,SV1740: $i,SV1450: $i,SV1077: $i,SV547: $i] :
( ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
= $true )
| ( ( ! [SY5488: $i] :
( ~ ( c_in @ ( c_Pair @ SY5488 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) )
| ~ ( c_in @ SY5488 @ SV1450 @ SV1740 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(5005,plain,
! [SV1947: $i,SV1741: $i,SV1451: $i,SV1078: $i,SV548: $i] :
( ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
= $true )
| ( ( ! [SY5489: $i] :
( ~ ( c_in @ ( c_Pair @ SY5489 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) )
| ~ ( c_in @ SY5489 @ SV1451 @ SV1741 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5006,plain,
! [SV1079: $i,SV1452: $i,SV1948: $i,SV549: $i] :
( ( ( c_in @ ( c_Pair @ SV549 @ SV1948 @ SV1452 @ SV1452 ) @ ( c_Relation_OId__on @ SV1079 @ SV1452 ) @ ( tc_prod @ SV1452 @ SV1452 ) )
= $false )
| ( ( c_in @ SV549 @ SV1079 @ SV1452 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4677]) ).
thf(5007,plain,
! [SV1081: $i,SV2064: $i,SV1454: $i,SV551: $i,SV1949: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1949 @ SV551 @ SV1454 @ SV1454 ) @ SV2064 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SV2064 @ SV1454 ) )
= $true )
| ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4679]) ).
thf(5008,plain,
! [SV1082: $i,SV2065: $i,SV1455: $i,SV1950: $i,SV552: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV552 @ SV1950 @ SV1455 @ SV1455 ) @ SV2065 @ ( tc_prod @ SV1455 @ SV1455 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SV2065 @ SV1455 ) )
= $true )
| ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4680]) ).
thf(5009,plain,
! [SV1083: $i,SV1742: $i,SV1456: $i,SV553: $i,SV2066: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2066 @ SV553 @ SV1456 @ SV1742 ) @ SV1083 @ ( tc_prod @ SV1456 @ SV1742 ) ) )
= $true )
| ( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SV1456 @ SV1742 ) @ SV1742 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4681]) ).
thf(5010,plain,
! [SV1084: $i,SV1743: $i,SV1457: $i,SV554: $i,SV2067: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2067 @ SV554 @ SV1457 @ SV1743 ) @ SV1084 @ ( tc_prod @ SV1457 @ SV1743 ) ) )
= $true )
| ( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SV1457 @ SV1743 ) @ SV1743 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4682]) ).
thf(5011,plain,
! [SV1085: $i,SV1744: $i,SV1458: $i,SV2068: $i,SV555: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV555 @ SV2068 @ SV1458 @ SV1744 ) @ SV1085 @ ( tc_prod @ SV1458 @ SV1744 ) ) )
= $true )
| ( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SV1458 @ SV1744 ) @ SV1458 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4683]) ).
thf(5012,plain,
! [SV1086: $i,SV1745: $i,SV1459: $i,SV2069: $i,SV556: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV556 @ SV2069 @ SV1459 @ SV1745 ) @ SV1086 @ ( tc_prod @ SV1459 @ SV1745 ) ) )
= $true )
| ( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SV1459 @ SV1745 ) @ SV1459 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4684]) ).
thf(5013,plain,
! [SV1087: $i,SV1746: $i,SV2070: $i,SV557: $i,SV1460: $i] :
( ( ( ! [SY5545: $i] :
~ ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SV2070 @ SV1746 ) @ ( c_Product__Type_OSigma @ SY5545 @ SV1087 @ SV2070 @ SV1746 ) @ ( tc_prod @ SV2070 @ SV1746 ) ) )
= $true )
| ( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SV1746 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4685]) ).
thf(5014,plain,
! [SV1088: $i,SV2071: $i,SV1461: $i,SV1747: $i,SV558: $i] :
( ( ( ! [SY5546: $i] :
~ ( c_in @ ( c_Pair @ SV558 @ SV1747 @ SV1461 @ SV2071 ) @ ( c_Product__Type_OSigma @ SV1088 @ SY5546 @ SV1461 @ SV2071 ) @ ( tc_prod @ SV1461 @ SV2071 ) ) )
= $true )
| ( ( c_in @ SV558 @ SV1088 @ SV1461 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(5015,plain,
! [SV1748: $i,SV1462: $i,SV559: $i,SV1089: $i] :
( ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( ( SV1089 = SV559 )
| ! [SY5379: $i] :
( ~ ( c_in @ SV559 @ SY5379 @ SV1462 )
| ~ ( c_in @ SV1089 @ SY5379 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SY5379 @ SV1748 @ SV1462 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(5016,plain,
! [SV1463: $i,SV1090: $i,SV1951: $i,SV560: $i] :
( ( ( ~ ( c_in @ SV560 @ SV1951 @ SV1090 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1951 @ SV1463 @ SV1090 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4688]) ).
thf(5017,plain,
! [SV1091: $i,SV2072: $i,SV1464: $i,SV561: $i,SV1952: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1952 @ SV561 @ SV1464 @ SV1464 ) @ SV2072 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1091 @ SV2072 @ SV1464 ) )
= $true )
| ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4689]) ).
thf(5018,plain,
! [SV1092: $i,SV2073: $i,SV1465: $i,SV1953: $i,SV562: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV562 @ SV1953 @ SV1465 @ SV1465 ) @ SV2073 @ ( tc_prod @ SV1465 @ SV1465 ) )
| ~ ( c_Relation_Orefl__on @ SV1092 @ SV2073 @ SV1465 ) )
= $true )
| ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4690]) ).
thf(5019,plain,
! [SV1466: $i,SV1093: $i,SV1954: $i,SV563: $i] :
( ( ( ~ ( c_in @ SV563 @ SV1954 @ SV1093 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1954 @ SV1466 @ SV1093 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4691]) ).
thf(5020,plain,
! [SV1749: $i,SV1467: $i,SV1094: $i,SV564: $i] :
( ( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ SV1749 @ SV1467 ) ) @ ( tc_prod @ SV1467 @ SV1467 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV564 @ SV1094 @ SV1467 @ SV1467 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1467 @ SV1467 ) @ SV1749 ) @ SV1467 ) @ ( tc_prod @ SV1467 @ SV1467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(5021,plain,
! [SV1750: $i,SV1468: $i,SV1095: $i,SV565: $i] :
( ( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ SV1750 ) @ SV1468 ) @ ( tc_prod @ SV1468 @ SV1468 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV565 @ SV1095 @ SV1468 @ SV1468 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1468 @ SV1468 ) @ ( c_Transitive__Closure_Otrancl @ SV1750 @ SV1468 ) ) @ ( tc_prod @ SV1468 @ SV1468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(5022,plain,
! [SV1751: $i,SV1469: $i,SV566: $i,SV1096: $i] :
( ( ( c_in @ ( c_Pair @ SV1096 @ SV566 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1469 @ SV1469 ) @ SV1751 ) @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV566 @ SV1096 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1751 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(5023,plain,
! [SV1752: $i,SV1470: $i,SV567: $i,SV1097: $i] :
( ( ( c_in @ ( c_Pair @ SV1097 @ SV567 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1752 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV567 @ SV1097 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ SV1470 @ SV1470 ) @ SV1752 ) @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(5024,plain,
! [SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5547: $i,SY5548: $i,SY5549: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
| ! [SY5550: $i,SY5551: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SY5547 @ SY5548 @ SY5549 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5550 @ SY5548 @ SY5551 ) @ SV2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4696]) ).
thf(5025,plain,
! [SV2075: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ! [SY5552: $i] :
( ! [SY5553: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
!= ( c_Fun_Ocomp @ SV2075 @ SY5552 @ SY5553 @ SV1754 @ SV1956 ) )
| ! [SY5554: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY5554 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SY5552 @ SY5554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4697]) ).
thf(5026,plain,
! [SV2076: $i,SV1957: $i,SV1755: $i,SV1473: $i,SV1100: $i,SV570: $i] :
( ( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SV1755 )
!= ( c_Pair @ SV1957 @ SV2076 @ SV1473 @ SV1755 ) )
| ( SV1100 = SV2076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4698]) ).
thf(5027,plain,
! [SV1958: $i,SV1756: $i,SV1474: $i,SV1101: $i,SV571: $i] :
( ( ( ! [SY5505: $i] :
( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SV1756 )
!= ( c_Pair @ SV1958 @ SY5505 @ SV1474 @ SV1756 ) ) )
= $true )
| ( ( SV571 = SV1958 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5028,plain,
! [SV1959: $i,SV1757: $i,SV1475: $i,SV1102: $i,SV572: $i] :
( ( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SV1475 @ SV1757 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1757 @ SV1475 ) @ SV1959 ) @ ( tc_prod @ SV1475 @ SV1757 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SV1757 @ SV1475 ) @ SV1959 @ ( tc_prod @ SV1757 @ SV1475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4700]) ).
thf(5029,plain,
! [SV1960: $i,SV1758: $i,SV1476: $i,SV1103: $i,SV573: $i] :
( ( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SV1476 @ SV1758 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1758 @ SV1476 ) @ SV1960 ) @ ( tc_prod @ SV1476 @ SV1758 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SV1758 @ SV1476 ) @ SV1960 @ ( tc_prod @ SV1758 @ SV1476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(5030,plain,
! [SV1961: $i,SV1759: $i,SV1477: $i,SV1104: $i,SV574: $i] :
( ( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SV1477 @ SV1759 ) @ SV1961 @ ( tc_prod @ SV1477 @ SV1759 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SV1759 @ SV1477 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1477 @ SV1759 ) @ SV1961 ) @ ( tc_prod @ SV1759 @ SV1477 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5031,plain,
! [SV2077: $i,SV1962: $i,SV1760: $i,SV1478: $i,SV1105: $i,SV575: $i] :
( ( ! [SY5555: $i] :
( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SV1478 @ SV1760 @ SV1962 @ SV2077 ) @ SV1962 @ SY5555 @ SV2077 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SV1962 @ SY5555 @ SV1760 ) @ SV1478 @ SV1760 @ SY5555 @ SV2077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4703]) ).
thf(5032,plain,
! [SV2078: $i,SV1963: $i,SV1761: $i,SV1480: $i,SV1107: $i,SV579: $i] :
( ( ( hAPP @ SV579 @ ( hAPP @ SV1107 @ SV1480 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV579 @ SV1107 @ SV1761 @ SV1963 @ SV2078 ) @ SV1480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(5033,plain,
! [SV2079: $i,SV1964: $i,SV1762: $i,SV1481: $i,SV1108: $i,SV580: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV580 @ SV1108 @ SV1481 @ SV1762 @ SV1964 ) @ SV2079 )
= ( hAPP @ SV580 @ ( hAPP @ SV1108 @ SV2079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4705]) ).
thf(5034,plain,
! [SV596: $i,SV1124: $i,SV1484: $i,SV1766: $i,SV2080: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SV2080 @ ( c_COMBK @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) @ SV1124 ) @ SV1124 @ SV1484 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SV1484 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SV1484 ) @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4709]) ).
thf(5035,plain,
! [SV600: $i,SV1767: $i,SV1486: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SV1486 @ SV1767 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1486 @ SV1767 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(5036,plain,
! [SV2081: $i,SV1965: $i,SV1770: $i,SV1489: $i,SV1129: $i,SV603: $i,SV13: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SV2081 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV603 @ SV2081 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4711]) ).
thf(5037,plain,
! [SV613: $i,SV1134: $i,SV24: $i] :
( ( ( c_lessequals @ SV24 @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) ) @ SV24 @ SV613 @ SV613 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV24 @ SV613 ) @ SV1134 @ ( tc_fun @ ( tc_prod @ SV613 @ SV613 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4714]) ).
thf(5038,plain,
! [SV614: $i,SV1135: $i,SV1968: $i,SV1495: $i,SV25: $i] :
( ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SV1968 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY5511: $i] :
~ ( c_in @ SY5511 @ SV1495 @ SV1968 ) )
= $true )
| ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(5039,plain,
! [SV1136: $i,SV615: $i,SV1496: $i,SV1774: $i,SV26: $i] :
( ( ( ~ ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5040,plain,
! [SV618: $i,SV1776: $i,SV1498: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SV1498 @ SV1776 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1498 @ SV1776 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(5041,plain,
! [SV629: $i,SV1147: $i,SV41: $i] :
( ( ( c_Relation_Osym @ SV41 @ SV1147 )
= $false )
| ( ( c_Relation_Osym @ SV629 @ SV1147 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV629 @ ( tc_fun @ ( tc_prod @ SV1147 @ SV1147 ) @ tc_bool ) ) @ SV1147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(5042,plain,
! [SV2082: $i,SV1969: $i,SV1778: $i,SV1511: $i,SV1154: $i,SV638: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
| ! [SY5556: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY5556 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SY5556 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4723]) ).
thf(5043,plain,
! [SV53: $i,SV1155: $i,SV639: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV639 @ SV1155 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5044,plain,
! [SV640: $i,SV1970: $i,SV54: $i,SV1512: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1512 @ SV54 @ ( tc_fun @ SV1970 @ tc_bool ) ) @ SV640 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1512 @ SV640 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV54 @ SV640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(5045,plain,
! [SV57: $i,SV643: $i,SV1158: $i] :
( ( ( c_Wellfounded_Owf @ SV1158 @ SV643 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV57 @ SV643 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(5046,plain,
! [SV1160: $i,SV59: $i,SV1780: $i,SV1516: $i,SV645: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SV1780 ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SV1780 ) @ SV1160 @ SV1780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4729]) ).
thf(5047,plain,
! [SV1517: $i,SV60: $i,SV1161: $i,SV1781: $i,SV646: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV646 @ SV1781 @ SV1161 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SV1781 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(5048,plain,
! [SV72: $i,SV656: $i,SV1523: $i] :
( ( ( c_Wellfounded_Owf @ SV1523 @ SV656 )
= $false )
| ( ( c_lessequals @ SV72 @ ( c_Relation_OImage @ SV1523 @ SV72 @ SV656 @ SV656 ) @ ( tc_fun @ SV656 @ tc_bool ) )
= $false )
| ( ( SV72
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV656 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4736]) ).
thf(5049,plain,
! [SV658: $i,SV1165: $i,SV1976: $i,SV74: $i] :
( ( ( ~ ( c_in @ SV74 @ SV1976 @ SV1165 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1976 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV74 @ SV658 @ SV1165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5050,plain,
! [SV77: $i,SV1166: $i,SV660: $i,SV1978: $i] :
( ( ( ( c_Relation_Orel__comp @ SV1978 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1978 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(5051,plain,
! [SV661: $i,SV1167: $i,SV1979: $i,SV78: $i] :
( ( ( ( c_Relation_Orel__comp @ SV78 @ SV1979 @ SV1167 @ SV1167 @ SV1167 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1979 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4740]) ).
thf(5052,plain,
! [SV662: $i,SV1789: $i,SV1525: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SV1525 @ SV1789 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1525 @ SV1789 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(5053,plain,
! [SV1526: $i,SV663: $i,SV80: $i] :
( ( ( c_lessequals @ SV80 @ SV663 @ ( tc_fun @ SV1526 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV663 @ SV80 @ ( tc_fun @ SV1526 @ tc_bool ) )
= $false )
| ( ( SV80 = SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4742]) ).
thf(5054,plain,
! [SV1527: $i,SV664: $i,SV81: $i] :
( ( ( c_lessequals @ SV81 @ SV664 @ ( tc_fun @ SV1527 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV664 @ SV81 @ ( tc_fun @ SV1527 @ tc_bool ) )
= $false )
| ( ( SV81 = SV664 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4743]) ).
thf(5055,plain,
! [SV82: $i,SV1528: $i,SV1790: $i] :
( ( ( ~ ( c_lessequals @ SV1790 @ SV1528 @ SV82 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1528 @ SV1790 @ SV82 ) )
= $true )
| ( ( SV1528 = SV1790 )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(5056,plain,
! [SV83: $i,SV1529: $i,SV1791: $i] :
( ( ( ~ ( c_lessequals @ SV1791 @ SV1529 @ SV83 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1529 @ SV1791 @ SV83 ) )
= $true )
| ( ( SV1529 = SV1791 )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4745]) ).
thf(5057,plain,
! [SV84: $i,SV1792: $i,SV1530: $i] :
( ( ( ~ ( c_lessequals @ SV1530 @ SV1792 @ SV84 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1792 @ SV1530 @ SV84 ) )
= $true )
| ( ( SV1530 = SV1792 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(5058,plain,
! [SV86: $i,SV1532: $i,SV1794: $i] :
( ( ( c_lessequals @ SV1794 @ SV1532 @ SV86 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1532 @ SV1794 @ SV86 )
= SV1532 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4747]) ).
thf(5059,plain,
! [SV87: $i,SV1795: $i,SV1533: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1533 @ SV1795 @ SV87 )
= SV1795 )
= $false )
| ( ( c_lessequals @ SV1533 @ SV1795 @ SV87 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4748]) ).
thf(5060,plain,
! [SV88: $i,SV1796: $i,SV1534: $i] :
( ( ( c_lessequals @ SV1534 @ SV1796 @ SV88 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1534 @ SV1796 @ SV88 )
= SV1796 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(5061,plain,
! [SV1535: $i,SV92: $i,SV1171: $i,SV1797: $i,SV668: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV668 @ SV1797 @ SV1171 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SV1797 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5062,plain,
! [SV99: $i,SV1802: $i,SV1536: $i] :
( ( ( c_lessequals @ SV1536 @ SV1802 @ SV99 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1536 @ SV1802 @ SV99 )
= SV1536 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(5063,plain,
! [SV100: $i,SV1803: $i,SV1537: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1537 @ SV1803 @ SV100 )
= SV1537 )
= $false )
| ( ( c_lessequals @ SV1537 @ SV1803 @ SV100 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4756]) ).
thf(5064,plain,
! [SV101: $i,SV1538: $i,SV1804: $i] :
( ( ( c_lessequals @ SV1804 @ SV1538 @ SV101 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1538 @ SV1804 @ SV101 )
= SV1804 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4757]) ).
thf(5065,plain,
! [SV102: $i,SV1174: $i,SV1539: $i,SV675: $i] :
( ( ( c_lessequals @ SV675 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV102 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(5066,plain,
! [SV105: $i,SV1177: $i,SV1540: $i,SV678: $i] :
( ( ( c_lessequals @ SV678 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV105 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5067,plain,
! [SV1984: $i,SV106: $i,SV1805: $i,SV679: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SV1984 @ SV106 )
= $true )
| ( ( ~ ( c_lessequals @ SV1805 @ SV1984 @ SV106 )
| ~ ( c_lessequals @ SV679 @ SV1984 @ SV106 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4760]) ).
thf(5068,plain,
! [SV1985: $i,SV109: $i,SV1808: $i,SV680: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SV1985 @ SV109 )
= $true )
| ( ( ~ ( c_lessequals @ SV1808 @ SV1985 @ SV109 )
| ~ ( c_lessequals @ SV680 @ SV1985 @ SV109 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5069,plain,
! [SV1986: $i,SV110: $i,SV1809: $i,SV681: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SV1986 @ SV110 )
= $true )
| ( ( ~ ( c_lessequals @ SV1809 @ SV1986 @ SV110 )
| ~ ( c_lessequals @ SV681 @ SV1986 @ SV110 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5070,plain,
! [SV685: $i,SV118: $i,SV1179: $i] :
( ( ( c_lessequals @ SV1179 @ SV118 @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV118 @ ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) @ ( tc_fun @ ( tc_prod @ SV685 @ SV685 ) @ tc_bool ) )
= $false )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV118 @ SV685 )
= ( c_Transitive__Closure_Ortrancl @ SV1179 @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(5071,plain,
! [SV692: $i,SV1550: $i,SV1186: $i,SV127: $i] :
( ( ( c_lessequals @ SV127 @ SV1186 @ ( tc_fun @ SV1550 @ tc_bool ) )
= $false )
| ( ( c_in @ SV692 @ SV127 @ SV1550 )
= $true )
| ( ( c_lessequals @ SV127 @ ( c_Set_Oinsert @ SV692 @ SV1186 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(5072,plain,
! [SV1187: $i,SV693: $i,SV1817: $i,SV128: $i] :
( ( ( c_lessequals @ SV128 @ ( c_Set_Oinsert @ SV1817 @ SV693 @ SV1187 ) @ ( tc_fun @ SV1187 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1817 @ SV128 @ SV1187 )
= $true )
| ( ( c_lessequals @ SV128 @ SV693 @ ( tc_fun @ SV1187 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(5073,plain,
! [SV694: $i,SV1551: $i,SV1188: $i,SV129: $i] :
( ( ( c_lessequals @ SV129 @ SV1188 @ ( tc_fun @ SV1551 @ tc_bool ) )
= $false )
| ( ( c_in @ SV694 @ SV129 @ SV1551 )
= $true )
| ( ( c_lessequals @ SV129 @ ( c_Set_Oinsert @ SV694 @ SV1188 @ SV1551 ) @ ( tc_fun @ SV1551 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4768]) ).
thf(5074,plain,
! [SV1189: $i,SV695: $i,SV1818: $i,SV130: $i] :
( ( ( c_lessequals @ SV130 @ ( c_Set_Oinsert @ SV1818 @ SV695 @ SV1189 ) @ ( tc_fun @ SV1189 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1818 @ SV130 @ SV1189 )
= $true )
| ( ( c_lessequals @ SV130 @ SV695 @ ( tc_fun @ SV1189 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(5075,plain,
! [SV135: $i,SV1988: $i,SV1554: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1554 @ SV1988 @ SV135 )
= ( c_Orderings_Obot__class_Obot @ SV135 ) )
= $false )
| ( ( SV1554
= ( c_Orderings_Obot__class_Obot @ SV135 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(5076,plain,
! [SV136: $i,SV1819: $i,SV1555: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1555 @ SV1819 @ SV136 )
= ( c_Orderings_Obot__class_Obot @ SV136 ) )
= $false )
| ( ( SV1819
= ( c_Orderings_Obot__class_Obot @ SV136 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(5077,plain,
! [SV142: $i,SV2083: $i,SV1824: $i,SV705: $i] :
( ( ( ~ ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1824 @ SV2083 @ SV142 ) @ SV142 ) )
= $true )
| ( ( c_lessequals @ SV705 @ SV1824 @ SV142 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4776]) ).
thf(5078,plain,
! [SV143: $i,SV1825: $i,SV2084: $i,SV706: $i] :
( ( ( ~ ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2084 @ SV1825 @ SV143 ) @ SV143 ) )
= $true )
| ( ( c_lessequals @ SV706 @ SV1825 @ SV143 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4777]) ).
thf(5079,plain,
! [SV1991: $i,SV144: $i,SV1826: $i,SV707: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SV1826 @ SV144 ) @ SV1991 @ SV144 )
= $true )
| ( ( ~ ( c_lessequals @ SV707 @ SV1991 @ SV144 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(5080,plain,
! [SV1992: $i,SV145: $i,SV1827: $i,SV708: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SV1827 @ SV145 ) @ SV1992 @ SV145 )
= $true )
| ( ( ~ ( c_lessequals @ SV1827 @ SV1992 @ SV145 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(5081,plain,
! [SV146: $i,SV2085: $i,SV1828: $i,SV709: $i] :
( ( ( ~ ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1828 @ SV2085 @ SV146 ) @ SV146 ) )
= $true )
| ( ( c_lessequals @ SV709 @ SV1828 @ SV146 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4780]) ).
thf(5082,plain,
! [SV147: $i,SV1829: $i,SV2086: $i,SV710: $i] :
( ( ( ~ ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2086 @ SV1829 @ SV147 ) @ SV147 ) )
= $true )
| ( ( c_lessequals @ SV710 @ SV1829 @ SV147 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4781]) ).
thf(5083,plain,
! [SV719: $i,SV1834: $i,SV1564: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SV1564 @ SV1834 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1564 @ SV1834 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(5084,plain,
! [SV723: $i,SV1208: $i,SV165: $i] :
( ( ( c_Relation_Osym @ SV165 @ SV1208 )
= $false )
| ( ( c_Relation_Osym @ SV723 @ SV1208 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1208 @ SV1208 ) @ tc_bool ) ) @ SV1208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4785]) ).
thf(5085,plain,
! [SV1993: $i,SV1837: $i,SV1567: $i,SV1209: $i,SV724: $i,SV166: $i] :
( ( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) )
!= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SV1567 @ SV1837 @ SV1993 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(5086,plain,
! [SV169: $i,SV1994: $i,SV1210: $i,SV727: $i] :
( ( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SV1994 @ SV1210 ) @ SV169 )
= $true )
| ( ( ! [SY5514: $i] :
~ ( c_lessequals @ SV727 @ SV1994 @ ( tc_fun @ SY5514 @ SV169 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4788]) ).
thf(5087,plain,
! [SV728: $i,SV1569: $i,SV1211: $i,SV170: $i] :
( ( ( c_in @ SV170 @ SV1211 @ SV1569 )
= $false )
| ( ( ~ ( c_in @ SV170 @ SV728 @ SV1569 ) )
= $true )
| ( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV1569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4789]) ).
thf(5088,plain,
! [SV729: $i,SV1570: $i,SV1212: $i,SV171: $i] :
( ( ( c_in @ SV171 @ SV1212 @ SV1570 )
= $false )
| ( ( ~ ( c_in @ SV171 @ SV729 @ SV1570 ) )
= $true )
| ( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(5089,plain,
! [SV730: $i,SV1213: $i,SV1839: $i,SV172: $i] :
( ( ( c_in @ SV172 @ SV1839 @ SV1213 )
= $false )
| ( ( ~ ( c_lessequals @ SV1839 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV172 @ SV730 @ SV1213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4791]) ).
thf(5090,plain,
! [SV173: $i,SV1214: $i,SV731: $i,SV1840: $i] :
( ( ( c_lessequals @ SV1840 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV173 @ SV1840 @ SV1214 ) )
= $true )
| ( ( c_in @ SV173 @ SV731 @ SV1214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4792]) ).
thf(5091,plain,
! [SV732: $i,SV1215: $i,SV1841: $i,SV174: $i] :
( ( ( c_in @ SV174 @ SV1841 @ SV1215 )
= $false )
| ( ( ~ ( c_lessequals @ SV1841 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV174 @ SV732 @ SV1215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(5092,plain,
! [SV733: $i,SV1216: $i,SV1842: $i,SV175: $i] :
( ( ( c_in @ SV175 @ SV1842 @ SV1216 )
= $false )
| ( ( ~ ( c_lessequals @ SV1842 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV175 @ SV733 @ SV1216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4794]) ).
thf(5093,plain,
! [SV1219: $i,SV740: $i,SV1843: $i,SV182: $i] :
( ( ( c_in @ SV182 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1843 @ SV740 @ ( tc_fun @ SV1219 @ tc_bool ) ) @ SV1219 )
= $false )
| ( ( c_in @ SV182 @ SV1843 @ SV1219 )
= $true )
| ( ( c_in @ SV182 @ SV740 @ SV1219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5094,plain,
! [SV1224: $i,SV749: $i,SV1576: $i,SV191: $i] :
( ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ! [SY5228: $i] :
( ~ ( c_in @ SV1576 @ SY5228 @ SV749 )
| ~ ( c_in @ SV191 @ SY5228 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5228 @ SV1224 @ SV749 ) ) )
= $true )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4801]) ).
thf(5095,plain,
! [SV1847: $i,SV1577: $i,SV1225: $i,SV751: $i,SV194: $i] :
( ( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
= ( c_Set_Oinsert @ SV1577 @ ( c_Set_Oinsert @ SV1847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
= $false )
| ( ( ( SV194 = SV1847 )
| ( SV194 = SV1577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(5096,plain,
! [SV1995: $i,SV1578: $i,SV1226: $i,SV752: $i,SV195: $i] :
( ( ( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
= ( c_Set_Oinsert @ SV1578 @ ( c_Set_Oinsert @ SV1995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) )
= $false )
| ( ( ( SV752 = SV1578 )
| ( SV195 = SV1578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5097,plain,
! [SV1848: $i,SV1579: $i,SV1227: $i,SV753: $i,SV196: $i] :
( ( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
= ( c_Set_Oinsert @ SV1579 @ ( c_Set_Oinsert @ SV1848 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
= $false )
| ( ( ( SV196 = SV1848 )
| ( SV753 = SV1848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(5098,plain,
! [SV1849: $i,SV1580: $i,SV1228: $i,SV754: $i,SV197: $i] :
( ( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
= ( c_Set_Oinsert @ SV1580 @ ( c_Set_Oinsert @ SV1849 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
= $false )
| ( ( ( SV754 = SV1580 )
| ( SV754 = SV1849 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(5099,plain,
! [SV1583: $i,SV207: $i,SV1234: $i,SV1850: $i,SV762: $i] :
( ( ( ~ ( c_lessequals @ SV762 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5100,plain,
! [SV210: $i,SV1996: $i,SV1853: $i,SV763: $i] :
( ( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SV1996 @ SV210 ) @ SV210 )
= $true )
| ( ( ~ ( c_lessequals @ SV763 @ SV1996 @ SV210 )
| ~ ( c_lessequals @ SV763 @ SV1853 @ SV210 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4809]) ).
thf(5101,plain,
! [SV211: $i,SV1997: $i,SV1854: $i,SV764: $i] :
( ( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV1997 @ SV211 ) @ SV211 )
= $true )
| ( ( ~ ( c_lessequals @ SV764 @ SV1997 @ SV211 )
| ~ ( c_lessequals @ SV764 @ SV1854 @ SV211 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5102,plain,
! [SV212: $i,SV1998: $i,SV1855: $i,SV765: $i] :
( ( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SV1998 @ SV212 ) @ SV212 )
= $true )
| ( ( ~ ( c_lessequals @ SV765 @ SV1998 @ SV212 )
| ~ ( c_lessequals @ SV765 @ SV1855 @ SV212 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5103,plain,
! [SV768: $i,SV1588: $i,SV1237: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SV1588 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ ( tc_fun @ SV1588 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(5104,plain,
! [SV769: $i,SV1589: $i,SV1238: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SV1589 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ ( tc_fun @ SV1589 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(5105,plain,
! [SV224: $i,SV1242: $i,SV1593: $i,SV775: $i] :
( ( ( c_lessequals @ SV775 @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV224 @ SV1593 @ SV1242 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(5106,plain,
! [SV1245: $i,SV778: $i,SV229: $i,SV1863: $i,SV1596: $i] :
( ( ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ SV1596 @ SV1863 ) @ SV229 ) @ SV1863 @ SV1596 )
= $false )
| ( ( ( c_Relation_OImage @ SV229 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV778 @ SV1245 @ ( tc_fun @ SV1596 @ tc_bool ) ) @ SV1596 @ SV1863 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV229 @ SV778 @ SV1596 @ SV1863 ) @ ( c_Relation_OImage @ SV229 @ SV1245 @ SV1596 @ SV1863 ) @ ( tc_fun @ SV1863 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(5107,plain,
! [SV1864: $i,SV236: $i,SV784: $i,SV2087: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2087 @ SV784 @ SV236 ) @ SV1864 @ SV236 ) )
= $true )
| ( ( c_lessequals @ SV784 @ SV1864 @ SV236 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4818]) ).
thf(5108,plain,
! [SV1865: $i,SV237: $i,SV2088: $i,SV785: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SV2088 @ SV237 ) @ SV1865 @ SV237 ) )
= $true )
| ( ( c_lessequals @ SV785 @ SV1865 @ SV237 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4819]) ).
thf(5109,plain,
! [SV238: $i,SV2001: $i,SV1866: $i,SV786: $i] :
( ( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1866 @ SV2001 @ SV238 ) @ SV238 )
= $true )
| ( ( ~ ( c_lessequals @ SV786 @ SV2001 @ SV238 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5110,plain,
! [SV239: $i,SV2089: $i,SV1867: $i,SV787: $i] :
( ( ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1867 @ SV2089 @ SV239 ) @ SV239 )
= $true )
| ( ( ~ ( c_lessequals @ SV787 @ SV1867 @ SV239 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4821]) ).
thf(5111,plain,
! [SV1868: $i,SV240: $i,SV788: $i,SV2090: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2090 @ SV788 @ SV240 ) @ SV1868 @ SV240 ) )
= $true )
| ( ( c_lessequals @ SV788 @ SV1868 @ SV240 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV240 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4822]) ).
thf(5112,plain,
! [SV1869: $i,SV241: $i,SV2091: $i,SV789: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SV2091 @ SV241 ) @ SV1869 @ SV241 ) )
= $true )
| ( ( c_lessequals @ SV789 @ SV1869 @ SV241 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(5113,plain,
! [SV1872: $i,SV244: $i,SV2092: $i,SV792: $i] :
( ( ( ~ ( c_lessequals @ SV792 @ SV2092 @ SV244 )
| ~ ( c_lessequals @ SV2092 @ SV1872 @ SV244 ) )
= $true )
| ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4826]) ).
thf(5114,plain,
! [SV793: $i,SV245: $i,SV1873: $i,SV2093: $i] :
( ( ( ~ ( c_lessequals @ SV2093 @ SV1873 @ SV245 )
| ~ ( c_lessequals @ SV793 @ SV2093 @ SV245 ) )
= $true )
| ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4827]) ).
thf(5115,plain,
! [SV248: $i,SV1251: $i,SV796: $i,SV1874: $i] :
( ( ( c_lessequals @ SV1874 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV248 @ SV1874 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4828]) ).
thf(5116,plain,
! [SV797: $i,SV2094: $i,SV249: $i,SV1599: $i] :
( ( ( ~ ( c_lessequals @ SV1599 @ SV249 @ ( tc_fun @ SV2094 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1599 @ SV797 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4829]) ).
thf(5117,plain,
! [SV250: $i,SV798: $i,SV1600: $i] :
( ( ( c_Wellfounded_Owf @ SV1600 @ SV798 )
= $false )
| ( ( c_lessequals @ SV250 @ SV1600 @ ( tc_fun @ ( tc_prod @ SV798 @ SV798 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV250 @ SV798 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(5118,plain,
! [SV799: $i,SV1603: $i,SV253: $i] :
( ( ( c_lessequals @ SV253 @ SV1603 @ ( tc_fun @ ( tc_prod @ SV799 @ SV799 ) @ tc_bool ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1603 @ SV799 )
= $false )
| ( ( c_Relation_Oantisym @ SV253 @ SV799 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(5119,plain,
! [SV800: $i,SV2002: $i,SV254: $i,SV1604: $i] :
( ( ( c_lessequals @ SV1604 @ SV254 @ ( tc_fun @ SV2002 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1604 @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(5120,plain,
! [SV255: $i,SV801: $i,SV1605: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1605 @ SV801 )
= $false )
| ( ( c_lessequals @ SV255 @ SV1605 @ ( tc_fun @ ( tc_prod @ SV801 @ SV801 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV255 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4833]) ).
thf(5121,plain,
! [SV256: $i,SV1252: $i,SV802: $i,SV1875: $i] :
( ( ( c_Relation_Osingle__valued @ SV1875 @ SV802 @ SV1252 )
= $false )
| ( ( ~ ( c_lessequals @ SV256 @ SV1875 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(5122,plain,
! [SV1606: $i,SV257: $i,SV1253: $i,SV1876: $i,SV803: $i] :
( ( ( ~ ( c_lessequals @ SV803 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4835]) ).
thf(5123,plain,
! [SV1257: $i,SV263: $i,SV1608: $i,SV809: $i] :
( ( ( hBOOL @ ( hAPP @ SV809 @ SV1608 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV263 @ SV1608 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(5124,plain,
! [SV2003: $i,SV1877: $i,SV1610: $i,SV1260: $i,SV812: $i,SV268: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SV2003 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV812 @ SV2003 @ ( tc_fun @ SV1260 @ tc_bool ) )
| ~ ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(5125,plain,
! [SV814: $i,SV2004: $i,SV1879: $i,SV1262: $i,SV271: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ SV2004 @ SV2004 ) @ SV1879 @ ( tc_prod @ SV2004 @ SV2004 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
| ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SV2004 @ SV2004 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SV2004 ) @ ( tc_prod @ SV2004 @ SV2004 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(5126,plain,
! [SV815: $i,SV2005: $i,SV1880: $i,SV1263: $i,SV272: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ SV2005 @ SV2005 ) @ SV1880 @ ( tc_prod @ SV2005 @ SV2005 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
| ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SV2005 @ SV2005 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SV2005 ) @ ( tc_prod @ SV2005 @ SV2005 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5127,plain,
! [SV273: $i,SV1264: $i,SV816: $i] :
( ( ( c_lessequals @ ( c_Relation_OId @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) @ SV273 @ SV816 @ SV816 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV273 @ SV816 ) @ SV1264 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4844]) ).
thf(5128,plain,
! [SV274: $i,SV2095: $i,SV2006: $i,SV1612: $i,SV817: $i,SV1265: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 ) )
= $true )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4845]) ).
thf(5129,plain,
! [SV1881: $i,SV1613: $i,SV1266: $i,SV818: $i,SV275: $i] :
( ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
= $false )
| ( ( ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 )
| ( SV275 = SV1881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4846]) ).
thf(5130,plain,
! [SV278: $i,SV1269: $i,SV821: $i,SV1882: $i] :
( ( ( c_lessequals @ SV1882 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV1882 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) ) )
= $true )
| ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5131,plain,
! [SV1273: $i,SV292: $i,SV834: $i,SV2096: $i,SV1616: $i] :
( ( ( ~ ( c_in @ SV1616 @ SV2096 @ SV834 )
| ~ ( c_in @ SV292 @ SV2096 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) )
= $true )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4850]) ).
thf(5132,plain,
! [SV1883: $i,SV293: $i,SV1274: $i,SV835: $i,SV2097: $i] :
( ( ( ~ ( c_lessequals @ SV2097 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SV2097 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) )
= $true )
| ( ( SV293 = SV1883 )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(5133,plain,
! [SV294: $i,SV1275: $i,SV1617: $i,SV836: $i] :
( ( ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
= $false )
| ( ( ! [SY4848: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4848 @ SV294 @ SV1275 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(5134,plain,
! [SV838: $i,SV1276: $i,SV296: $i,SV1618: $i] :
( ( ( ~ ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 ) )
= $true )
| ( ( ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5135,plain,
! [SV1885: $i,SV1619: $i,SV839: $i,SV299: $i,SV1278: $i] :
( ( ( c_in @ SV1278 @ ( c_Product__Type_OSigma @ SV299 @ SV839 @ SV1619 @ SV1885 ) @ ( tc_prod @ SV1619 @ SV1885 ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV299 @ SV839 @ SV1278 @ SV1619 @ SV1885 ) @ SV299 @ SV1619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(5136,plain,
! [SV1279: $i,SV1620: $i,SV840: $i,SV300: $i] :
( ( ( c_in @ ( c_Pair @ SV300 @ SV840 @ SV1620 @ SV1620 ) @ ( c_Transitive__Closure_Ortrancl @ SV1279 @ SV1620 ) @ ( tc_prod @ SV1620 @ SV1620 ) )
= $false )
| ( ( SV300 = SV840 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV300 @ SV840 @ SV1279 @ SV1620 ) @ SV840 @ SV1620 @ SV1620 ) @ SV1279 @ ( tc_prod @ SV1620 @ SV1620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(5137,plain,
! [SV301: $i,SV1621: $i,SV1280: $i,SV841: $i] :
( ( ( c_in @ ( c_Pair @ SV841 @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) )
= $false )
| ( ( SV841 = SV1280 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV301 @ SV841 @ SV1280 @ SV1621 ) @ SV1280 @ SV1621 @ SV1621 ) @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV1621 ) @ ( tc_prod @ SV1621 @ SV1621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5138,plain,
! [SV842: $i,SV1622: $i,SV1281: $i,SV302: $i] :
( ( ( c_in @ ( c_Pair @ SV302 @ SV1281 @ SV1622 @ SV1622 ) @ ( c_Transitive__Closure_Ortrancl @ SV842 @ SV1622 ) @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false )
| ( ( SV302 = SV1281 )
= $true )
| ( ( c_in @ ( c_Pair @ SV302 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV842 @ SV302 @ SV1281 @ SV1622 ) @ SV1622 @ SV1622 ) @ SV842 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(5139,plain,
! [SV843: $i,SV2007: $i,SV1886: $i,SV1282: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SV2007 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SV2007 @ SV2007 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV2007 ) @ ( tc_prod @ SV2007 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4859]) ).
thf(5140,plain,
! [SV844: $i,SV2008: $i,SV1887: $i,SV1283: $i,SV304: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SV2008 ) @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
| ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4860]) ).
thf(5141,plain,
! [SV845: $i,SV2009: $i,SV1888: $i,SV305: $i,SV1284: $i] :
( ( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SV2009 ) @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
| ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(5142,plain,
! [SV846: $i,SV2010: $i,SV1889: $i,SV1285: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(5143,plain,
! [SV847: $i,SV1623: $i,SV1286: $i,SV307: $i,SV2098: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4863]) ).
thf(5144,plain,
! [SV849: $i,SV2011: $i,SV1890: $i,SV1288: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SV2011 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
| ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SV2011 @ SV2011 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV2011 ) @ ( tc_prod @ SV2011 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5145,plain,
! [SV851: $i,SV2012: $i,SV1891: $i,SV1290: $i,SV311: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(5146,plain,
! [SV1291: $i,SV1624: $i,SV852: $i,SV312: $i] :
( ( ( c_in @ ( c_Pair @ SV312 @ SV852 @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) )
= $false )
| ( ( SV312 = SV852 )
= $true )
| ( ( c_in @ ( c_Pair @ SV312 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV312 @ SV852 @ SV1291 @ SV1624 ) @ SV1624 @ SV1624 ) @ ( c_Transitive__Closure_Ortrancl @ SV1291 @ SV1624 ) @ ( tc_prod @ SV1624 @ SV1624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(5147,plain,
! [SV853: $i,SV2099: $i,SV2013: $i,SV313: $i,SV1292: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SV2013 @ SV2099 ) @ SV2099 @ SV2099 ) @ SV2013 @ ( tc_prod @ SV2099 @ SV2099 ) )
| ~ ( c_Wellfounded_Owf @ SV2013 @ SV2099 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4869]) ).
thf(5148,plain,
! [SV854: $i,SV2100: $i,SV2014: $i,SV314: $i,SV1293: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SV2014 @ SV2100 ) @ SV2100 @ SV2100 ) @ SV2014 @ ( tc_prod @ SV2100 @ SV2100 ) )
| ~ ( c_Wellfounded_Owf @ SV2014 @ SV2100 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4870]) ).
thf(5149,plain,
! [SV855: $i,SV2101: $i,SV2015: $i,SV315: $i,SV1294: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SV2015 @ SV2101 ) @ SV2101 @ SV2101 ) @ SV2015 @ ( tc_prod @ SV2101 @ SV2101 ) )
| ~ ( c_Wellfounded_Owf @ SV2015 @ SV2101 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4871]) ).
thf(5150,plain,
! [SV856: $i,SV2102: $i,SV2016: $i,SV316: $i,SV1295: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SV2016 @ SV2102 ) @ SV2102 @ SV2102 ) @ SV2016 @ ( tc_prod @ SV2102 @ SV2102 ) )
| ~ ( c_Wellfounded_Owf @ SV2016 @ SV2102 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4872]) ).
thf(5151,plain,
! [SV318: $i,SV1625: $i,SV1297: $i,SV858: $i] :
( ( ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV858 @ SV1297 @ SV1625 @ SV1625 ) @ SV318 @ ( tc_prod @ SV1625 @ SV1625 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV318 @ SV858 @ SV1297 @ SV1625 ) @ SV1297 @ SV1625 @ SV1625 ) @ ( c_Transitive__Closure_Otrancl @ SV318 @ SV1625 ) @ ( tc_prod @ SV1625 @ SV1625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4873]) ).
thf(5152,plain,
! [SV1300: $i,SV1626: $i,SV861: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV1626 ) @ ( tc_prod @ SV1626 @ SV1626 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV321 @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV321 @ SV861 @ SV1300 @ SV1626 ) @ SV861 @ SV1626 @ SV1626 ) @ SV1300 @ ( tc_prod @ SV1626 @ SV1626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4876]) ).
thf(5153,plain,
! [SV1301: $i,SV1627: $i,SV862: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV322 @ SV862 @ SV1627 @ SV1627 ) @ SV1301 @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV322 @ SV862 @ SV1301 @ SV1627 ) @ SV1627 @ SV1627 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5154,plain,
! [SV863: $i,SV1628: $i,SV1302: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ ( c_Transitive__Closure_Otrancl @ SV863 @ SV1628 ) @ ( tc_prod @ SV1628 @ SV1628 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV323 @ SV1302 @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV323 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV863 @ SV323 @ SV1302 @ SV1628 ) @ SV1628 @ SV1628 ) @ SV863 @ ( tc_prod @ SV1628 @ SV1628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(5155,plain,
! [SV325: $i,SV1629: $i,SV1304: $i,SV2017: $i,SV865: $i] :
( ( ( ~ ( c_in @ SV865 @ SV2017 @ SV1304 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(5156,plain,
! [SV866: $i,SV1305: $i,SV326: $i,SV1630: $i,SV2103: $i] :
( ( ( ~ ( c_in @ SV2103 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) )
= $true )
| ( ( ! [SY5258: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5258 @ SV1630 @ SV1305 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4881]) ).
thf(5157,plain,
! [SV2104: $i,SV2018: $i,SV1892: $i,SV1631: $i,SV1306: $i,SV867: $i,SV327: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SV1892 @ SV2018 @ SV2104 ) @ SV867 @ SV2104 @ SV2018 ) @ SV1631 @ ( tc_prod @ SV2104 @ SV2018 ) )
| ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SV1892 @ SV2018 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SV1892 @ SV2104 @ SV2018 ) @ ( tc_prod @ SV1892 @ SV2018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4882]) ).
thf(5158,plain,
! [SV2105: $i,SV2019: $i,SV1893: $i,SV1632: $i,SV1307: $i,SV868: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SV1893 @ SV2019 @ SV2105 ) @ SV1893 @ SV2105 ) @ SV1307 @ ( tc_prod @ SV1893 @ SV2105 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SV1893 @ SV2019 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SV1893 @ SV2105 @ SV2019 ) @ ( tc_prod @ SV1893 @ SV2019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4883]) ).
thf(5159,plain,
! [SV1896: $i,SV1635: $i,SV1310: $i,SV871: $i,SV331: $i] :
( ( ( c_in @ ( hAPP @ SV331 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ ( hAPP @ SV1310 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV871 @ SV1310 @ SV331 @ SV1635 @ SV1896 ) ) @ SV1896 )
= $false )
| ( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV871 @ SV1310 @ SV1635 @ SV1896 ) @ ( tc_fun @ SV1635 @ SV1896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5160,plain,
! [SV1636: $i,SV1311: $i,SV332: $i,SV2106: $i,SV2020: $i,SV872: $i] :
( ( ( ~ ( c_in @ SV872 @ SV2020 @ SV2106 )
| ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV2020 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SV2106 ) @ SV2106 @ SV1636 ) @ ( tc_fun @ SV2106 @ SV1636 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4887]) ).
thf(5161,plain,
! [SV1897: $i,SV1637: $i,SV1312: $i,SV873: $i,SV333: $i] :
( ( ( c_in @ ( hAPP @ SV333 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ ( hAPP @ SV1312 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV873 @ SV1312 @ SV333 @ SV1637 @ SV1897 ) ) @ SV1897 )
= $false )
| ( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV873 @ SV1312 @ SV1637 @ SV1897 ) @ ( tc_fun @ SV1637 @ SV1897 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5162,plain,
! [SV2021: $i,SV1898: $i,SV1638: $i,SV1315: $i,SV879: $i,SV339: $i] :
( ( ( ( c_Recdef_Ocut @ SV339 @ SV879 @ SV1315 @ SV1638 @ SV1898 )
= ( c_Recdef_Ocut @ SV2021 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV339 @ SV2021 @ SV879 @ SV1315 @ SV1638 @ SV1898 ) @ SV1315 @ SV1638 @ SV1638 ) @ SV879 @ ( tc_prod @ SV1638 @ SV1638 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(5163,plain,
! [SV1640: $i,SV1318: $i,SV349: $i,SV885: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV885 @ SV349 @ SV1318 @ SV1318 ) @ SV1640 @ ( tc_prod @ SV1318 @ SV1318 ) ) @ SV1318 )
= $false )
| ( ( c_in @ ( c_Pair @ SV349 @ SV885 @ SV1318 @ SV1318 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1318 ) @ ( tc_prod @ SV1318 @ SV1318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(5164,plain,
! [SV350: $i,SV886: $i,SV1319: $i,SV1641: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1641 @ SV1319 )
= $false )
| ( ( c_in @ ( c_Pair @ SV886 @ SV350 @ SV1319 @ SV1319 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1319 ) @ ( tc_prod @ SV1319 @ SV1319 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV350 @ SV886 @ SV1319 @ SV1319 ) @ SV1641 @ ( tc_prod @ SV1319 @ SV1319 ) ) @ SV1319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5165,plain,
! [SV887: $i,SV1320: $i,SV1899: $i,SV351: $i] :
( ( ( c_in @ SV351 @ SV1899 @ SV1320 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1899 @ SV887 @ SV1320 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5166,plain,
! [SV1642: $i,SV1321: $i,SV352: $i,SV1900: $i,SV888: $i] :
( ( ( c_in @ SV888 @ ( c_Relation_OImage @ SV1900 @ ( c_Set_Oinsert @ SV352 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 @ SV1642 ) @ SV1642 )
= $false )
| ( ( c_in @ ( c_Pair @ SV352 @ SV888 @ SV1321 @ SV1642 ) @ SV1900 @ ( tc_prod @ SV1321 @ SV1642 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(5167,plain,
! [SV889: $i,SV1901: $i,SV1643: $i,SV353: $i,SV1322: $i] :
( ( ( c_in @ ( c_Pair @ SV1322 @ SV353 @ SV1643 @ SV1901 ) @ SV889 @ ( tc_prod @ SV1643 @ SV1901 ) )
= $false )
| ( ( c_in @ SV353 @ ( c_Relation_OImage @ SV889 @ ( c_Set_Oinsert @ SV1322 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1643 @ tc_bool ) ) @ SV1643 ) @ SV1643 @ SV1901 ) @ SV1901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4894]) ).
thf(5168,plain,
! [SV354: $i,SV1323: $i,SV1644: $i,SV890: $i] :
( ( ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
= $false )
| ( ( ! [SY4917: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4917 @ SV354 @ SV1323 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4895]) ).
thf(5169,plain,
! [SV355: $i,SV1324: $i,SV1645: $i,SV891: $i] :
( ( ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
= $false )
| ( ( ! [SY4919: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4919 @ SV355 @ SV1324 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4896]) ).
thf(5170,plain,
! [SV356: $i,SV1325: $i,SV1646: $i,SV892: $i] :
( ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
= $true )
| ( ( ! [SY5277: $i] :
( ~ ( c_in @ SV1646 @ SY5277 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5277 @ SV356 @ SV1325 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(5171,plain,
! [SV1647: $i,SV893: $i,SV1326: $i,SV357: $i,SV2107: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
| ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SV2107 @ SV1326 )
| ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4898]) ).
thf(5172,plain,
! [SV358: $i,SV1327: $i,SV1648: $i,SV894: $i] :
( ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ! [SY5279: $i] :
( ~ ( c_in @ SV1648 @ SY5279 @ SV1327 )
| ~ ( c_in @ SV894 @ SY5279 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5279 @ SV358 @ SV1327 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(5173,plain,
! [SV359: $i,SV895: $i,SV1328: $i,SV2108: $i,SV1649: $i] :
( ( ( ~ ( c_in @ SV1649 @ SV2108 @ SV1328 )
| ~ ( c_in @ SV895 @ SV2108 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4900]) ).
thf(5174,plain,
! [SV362: $i,SV1902: $i,SV1652: $i,SV898: $i] :
( ( ( c_in @ SV898 @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV362 @ SV1652 @ SV1902 ) @ ( c_Wellfounded_Oacc @ SV1652 @ SV1902 ) @ SV1902 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV362 @ SV898 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(5175,plain,
! [SV364: $i,SV1653: $i,SV900: $i] :
( ( ( c_in @ SV900 @ ( c_Wellfounded_Oacc @ SV1653 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV364 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV364 @ SV1653 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV364 @ SV900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4904]) ).
thf(5176,plain,
! [SV901: $i,SV1903: $i,SV1654: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SV1654 @ SV1903 ) ) )
= $false )
| ( ( ~ ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SV1654 @ SV1903 ) @ SV1903 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5177,plain,
! [SV367: $i,SV1904: $i,SV1655: $i,SV903: $i] :
( ( ( c_in @ SV903 @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV367 @ SV1655 @ SV1904 ) @ ( c_Wellfounded_Oacc @ SV1655 @ SV1904 ) @ SV1904 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV367 @ SV903 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5178,plain,
! [SV368: $i,SV1656: $i,SV904: $i] :
( ( ( c_in @ SV904 @ ( c_Wellfounded_Oacc @ SV1656 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV368 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV368 @ SV1656 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV368 @ SV904 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(5179,plain,
! [SV905: $i,SV1905: $i,SV1657: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SV1657 @ SV1905 ) ) )
= $false )
| ( ( ~ ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SV1657 @ SV1905 ) @ SV1905 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(5180,plain,
! [SV1906: $i,SV1658: $i,SV370: $i,SV1333: $i,SV906: $i] :
( ( ( c_in @ SV906 @ ( c_Relation_OImage @ SV1333 @ SV370 @ SV1658 @ SV1906 ) @ SV1906 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV370 @ SV906 @ SV1333 @ SV1658 @ SV1906 ) @ SV370 @ SV1658 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4909]) ).
thf(5181,plain,
! [SV1907: $i,SV1659: $i,SV371: $i,SV1334: $i,SV907: $i] :
( ( ( c_in @ SV907 @ ( c_Relation_OImage @ SV1334 @ SV371 @ SV1659 @ SV1907 ) @ SV1907 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV371 @ SV907 @ SV1334 @ SV1659 @ SV1907 ) @ SV371 @ SV1659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(5182,plain,
! [SV909: $i,SV1335: $i,SV373: $i,SV2022: $i] :
( ( ( c_in @ SV2022 @ SV373 @ SV1335 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV909 @ SV1335 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5183,plain,
! [SV910: $i,SV1336: $i,SV374: $i,SV2023: $i] :
( ( ( c_in @ SV2023 @ SV374 @ SV1336 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV910 @ SV1336 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5184,plain,
! [SV2109: $i,SV2024: $i,SV1909: $i,SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ! [SY5557: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
| ! [SY5558: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SY5557 @ SY5557 ) @ SY5558 @ ( tc_prod @ SY5557 @ SY5557 ) )
| ! [SY5559: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5558 @ SV2109 @ SV375 @ SY5557 @ SV2024 @ SY5559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4914]) ).
thf(5185,plain,
! [SV915: $i,SV2025: $i,SV379: $i,SV1663: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1663 @ SV379 @ SV2025 ) @ SV915 ) )
= $false )
| ( ( SV1663 = SV915 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV379 @ SV915 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4915]) ).
thf(5186,plain,
! [SV1346: $i,SV922: $i,SV1912: $i,SV386: $i] :
( ( ( c_in @ SV386 @ ( c_Set_Oinsert @ SV1912 @ SV922 @ SV1346 ) @ SV1346 )
= $false )
| ( ( SV386 = SV1912 )
= $true )
| ( ( c_in @ SV386 @ SV922 @ SV1346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4919]) ).
thf(5187,plain,
! [SV926: $i,SV1350: $i,SV1669: $i,SV390: $i] :
( ( ( c_in @ SV390 @ SV1669 @ SV1350 )
= $true )
| ( ( ( SV926 = SV1669 )
| ( c_in @ SV390 @ SV926 @ SV1350 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
= ( c_Set_Oinsert @ SV390 @ SV1669 @ SV1350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5188,plain,
! [SV2026: $i,SV1913: $i,SV1670: $i,SV1352: $i,SV928: $i,SV392: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true )
| ( ( ! [SY5527: $i] :
( ~ ( c_in @ SV1352 @ SV2026 @ SY5527 )
| ! [SY5528: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5528 @ SV392 @ SV928 @ SY5527 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SY5528 @ SY5527 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5189,plain,
! [SV1353: $i,SV2027: $i,SV931: $i,SV398: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) ) )
= $true )
| ( ( ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5190,plain,
! [SV1354: $i,SV2028: $i,SV932: $i,SV399: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) ) )
= $true )
| ( ( ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5191,plain,
! [SV1914: $i,SV1671: $i,SV400: $i,SV1355: $i,SV933: $i] :
( ( ( c_in @ SV933 @ ( c_Relation_OImage @ SV1355 @ SV400 @ SV1671 @ SV1914 ) @ SV1914 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV400 @ SV933 @ SV1355 @ SV1671 @ SV1914 ) @ SV933 @ SV1671 @ SV1914 ) @ SV1355 @ ( tc_prod @ SV1671 @ SV1914 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4924]) ).
thf(5192,plain,
! [SV1915: $i,SV1672: $i,SV401: $i,SV1356: $i,SV934: $i] :
( ( ( c_in @ SV934 @ ( c_Relation_OImage @ SV1356 @ SV401 @ SV1672 @ SV1915 ) @ SV1915 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV401 @ SV934 @ SV1356 @ SV1672 @ SV1915 ) @ SV934 @ SV1672 @ SV1915 ) @ SV1356 @ ( tc_prod @ SV1672 @ SV1915 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5193,plain,
! [SV937: $i,SV1916: $i,SV404: $i,SV1675: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SV1916 ) @ t_a @ t_a ) @ SV1916 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4928]) ).
thf(5194,plain,
! [SV938: $i,SV1917: $i,SV405: $i,SV1676: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SV1917 ) @ t_a @ t_a ) @ SV1917 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(5195,plain,
! [SV940: $i,SV2110: $i,SV2029: $i,SV407: $i,SV1360: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SV2029 @ SV2110 ) @ SV2110 @ SV2110 ) @ SV2029 @ ( tc_prod @ SV2110 @ SV2110 ) )
| ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SV2029 @ SV2110 ) @ SV2110 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4930]) ).
thf(5196,plain,
! [SV941: $i,SV2030: $i,SV408: $i,SV1677: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SV2030 ) @ t_a @ t_a ) @ SV2030 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SV2030 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(5197,plain,
! [SV942: $i,SV2031: $i,SV409: $i,SV1678: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SV2031 ) @ t_a @ t_a ) @ SV2031 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SV2031 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(5198,plain,
! [SV943: $i,SV2111: $i,SV2032: $i,SV410: $i,SV1361: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SV2032 @ SV2111 ) @ SV2111 @ SV2111 ) @ SV2032 @ ( tc_prod @ SV2111 @ SV2111 ) )
| ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SV2032 @ SV2111 ) @ SV2111 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4933]) ).
thf(5199,plain,
! [SV412: $i,SV945: $i,SV1363: $i,SV1679: $i] :
( ( ( c_Wellfounded_Owf @ SV1679 @ SV1363 )
= $false )
| ( ( c_in @ ( c_Pair @ SV945 @ SV412 @ SV1363 @ SV1363 ) @ ( c_Transitive__Closure_Ortrancl @ SV1679 @ SV1363 ) @ ( tc_prod @ SV1363 @ SV1363 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV412 @ SV945 @ SV1363 @ SV1363 ) @ SV1679 @ ( tc_prod @ SV1363 @ SV1363 ) ) @ SV1363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5200,plain,
! [SV1680: $i,SV1364: $i,SV413: $i,SV946: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV946 @ SV413 @ SV1364 @ SV1364 ) @ SV1680 @ ( tc_prod @ SV1364 @ SV1364 ) ) @ SV1364 )
= $false )
| ( ( c_in @ ( c_Pair @ SV413 @ SV946 @ SV1364 @ SV1364 ) @ ( c_Transitive__Closure_Ortrancl @ SV1680 @ SV1364 ) @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4935]) ).
thf(5201,plain,
! [SV418: $i,SV1685: $i,SV1369: $i,SV951: $i,SV2033: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2033 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV418 @ SV2033 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(5202,plain,
! [SV419: $i,SV1686: $i,SV1370: $i,SV952: $i,SV2034: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2034 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV419 @ SV2034 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4941]) ).
thf(5203,plain,
! [SV420: $i,SV1687: $i,SV1371: $i,SV953: $i,SV2035: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2035 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV420 @ SV2035 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4942]) ).
thf(5204,plain,
! [SV2036: $i,SV1918: $i,SV1688: $i,SV1372: $i,SV954: $i,SV421: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SV1688 @ SV1918 ) @ SV2036 )
= ( hAPP @ SV421 @ SV2036 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2036 @ SV1372 @ SV1688 @ SV1688 ) @ SV954 @ ( tc_prod @ SV1688 @ SV1688 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4943]) ).
thf(5205,plain,
! [SV2037: $i,SV1919: $i,SV1689: $i,SV1373: $i,SV955: $i,SV422: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SV1689 @ SV1919 ) @ SV2037 )
= ( hAPP @ SV422 @ SV2037 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2037 @ SV1373 @ SV1689 @ SV1689 ) @ SV955 @ ( tc_prod @ SV1689 @ SV1689 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4944]) ).
thf(5206,plain,
! [SV1920: $i,SV1690: $i,SV956: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ SV956 @ SV1690 @ SV1690 ) @ ( c_Transitive__Closure_Ortrancl @ SV1920 @ SV1690 ) @ ( tc_prod @ SV1690 @ SV1690 ) )
= $false )
| ( ( c_in @ SV423 @ ( c_Relation_ODomain @ SV1920 @ SV1690 @ SV1690 ) @ SV1690 )
= $true )
| ( ( SV423 = SV956 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(5207,plain,
! [SV958: $i,SV1375: $i,SV1921: $i,SV425: $i] :
( ( ( c_in @ ( c_Pair @ SV425 @ SV1921 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) )
= $false )
| ( ( ~ ( c_in @ SV1921 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 ) )
= $true )
| ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5208,plain,
! [SV426: $i,SV1376: $i,SV959: $i,SV1922: $i] :
( ( ( c_in @ SV1922 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV426 @ SV1922 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) )
= $true )
| ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5209,plain,
! [SV445: $i,SV1693: $i,SV1385: $i,SV977: $i,SV2038: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2038 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV445 @ SV2038 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4948]) ).
thf(5210,plain,
! [SV446: $i,SV1694: $i,SV1386: $i,SV978: $i,SV2039: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2039 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV446 @ SV2039 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4949]) ).
thf(5211,plain,
! [SV1695: $i,SV1387: $i,SV979: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $false )
| ( ( SV447 = SV979 )
= $true )
| ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Ortrancl @ SV1695 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5212,plain,
! [SV1696: $i,SV1388: $i,SV980: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Ortrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
= $false )
| ( ( SV448 = SV980 )
= $true )
| ( ( c_in @ ( c_Pair @ SV448 @ SV980 @ SV1388 @ SV1388 ) @ ( c_Transitive__Closure_Otrancl @ SV1696 @ SV1388 ) @ ( tc_prod @ SV1388 @ SV1388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4951]) ).
thf(5213,plain,
! [SV1697: $i,SV1389: $i,SV981: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Ortrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
= $false )
| ( ( SV449 = SV981 )
= $true )
| ( ( c_in @ ( c_Pair @ SV449 @ SV981 @ SV1389 @ SV1389 ) @ ( c_Transitive__Closure_Otrancl @ SV1697 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5214,plain,
! [SV451: $i,SV1699: $i,SV1391: $i,SV983: $i,SV2040: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2040 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV451 @ SV2040 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5215,plain,
! [SV452: $i,SV1700: $i,SV1392: $i,SV984: $i,SV2041: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2041 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV452 @ SV2041 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5216,plain,
! [SV2112: $i,SV2042: $i,SV1926: $i,SV1701: $i,SV1398: $i,SV1005: $i,SV474: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV474 @ SV1005 @ SV1398 @ SV1701 @ SV1926 ) @ SV2042 @ SV1398 @ SV1926 @ SV2112 )
= ( c_Relation_Orel__comp @ SV474 @ ( c_Relation_Orel__comp @ SV1005 @ SV2042 @ SV1701 @ SV1926 @ SV2112 ) @ SV1398 @ SV1701 @ SV2112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4958]) ).
thf(5217,plain,
! [SV489: $i,SV1704: $i,SV1403: $i,SV1019: $i,SV2043: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2043 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV489 @ SV2043 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4959]) ).
thf(5218,plain,
! [SV491: $i,SV1706: $i,SV1405: $i,SV1021: $i,SV2044: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2044 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV491 @ SV2044 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5219,plain,
! [SV1707: $i,SV1408: $i,SV494: $i,SV1024: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1707 @ SV1408 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(5220,plain,
! [SV1927: $i,SV1708: $i,SV495: $i,SV1025: $i] :
( ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
| ~ ( c_Relation_Oantisym @ SV1927 @ SV1708 ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4963]) ).
thf(5221,plain,
! [SV1928: $i,SV1709: $i,SV496: $i,SV1026: $i] :
( ( ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
| ~ ( c_Relation_Oantisym @ SV1928 @ SV1709 ) )
= $true )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4964]) ).
thf(5222,plain,
! [SV497: $i,SV2045: $i,SV1710: $i,SV1409: $i,SV1027: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SV2045 @ ( tc_prod @ SV1710 @ SV1710 ) ) )
= $true )
| ( ( ! [SY5534: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2045 @ SV497 @ SV1710 @ SY5534 ) )
= $true )
| ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4965]) ).
thf(5223,plain,
! [SV2046: $i,SV1930: $i,SV1712: $i,SV1410: $i,SV1029: $i,SV499: $i] :
( ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
!= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
= $true )
| ( ( ! [SY5535: $i] :
( ( ( hAPP @ SV499 @ SY5535 )
= ( hAPP @ SV2046 @ SY5535 ) )
| ~ ( c_in @ ( c_Pair @ SY5535 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4967]) ).
thf(5224,plain,
! [SV2047: $i,SV1931: $i,SV1714: $i,SV1413: $i,SV1033: $i,SV503: $i] :
( ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SV1714 @ SV1931 @ SV2047 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1931 @ SV503 ) @ ( hAPP @ SV1931 @ SV1033 ) @ SV2047 @ SV2047 ) @ SV1714 @ ( tc_prod @ SV2047 @ SV2047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4969]) ).
thf(5225,plain,
! [SV1715: $i,SV504: $i,SV1932: $i,SV2113: $i,SV1414: $i,SV1034: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SV2113 @ SV2113 ) @ ( c_Relation_Oinv__image @ SV1932 @ SV504 @ SV1715 @ SV2113 ) @ ( tc_prod @ SV2113 @ SV2113 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SV1715 @ SV1715 ) @ SV1932 @ ( tc_prod @ SV1715 @ SV1715 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4970]) ).
thf(5226,plain,
! [SV1716: $i,SV1415: $i,SV505: $i,SV1035: $i] :
( ( ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1716 @ SV1415 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4971]) ).
thf(5227,plain,
! [SV1717: $i,SV1416: $i,SV506: $i,SV1036: $i] :
( ( ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1717 @ SV1416 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5228,plain,
! [SV2114: $i,SV2048: $i,SV1933: $i,SV1718: $i,SV1417: $i,SV1037: $i,SV507: $i] :
( ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
| ! [SY5560: $i] :
( ~ ( c_in @ ( c_Pair @ SY5560 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5560 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4973]) ).
thf(5229,plain,
! [SV508: $i,SV1719: $i,SV1418: $i,SV1038: $i,SV2049: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2049 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV508 @ SV2049 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5230,plain,
! [SV509: $i,SV1720: $i,SV1419: $i,SV1039: $i,SV2050: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2050 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV509 @ SV2050 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5231,plain,
! [SV1721: $i,SV1420: $i,SV512: $i,SV2115: $i,SV2051: $i,SV1042: $i] :
( ( ( ~ ( c_in @ SV1042 @ SV2051 @ SV2115 )
| ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SV2051 @ SV1420 @ SV2115 @ SV1721 ) @ ( tc_fun @ SV2115 @ SV1721 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4976]) ).
thf(5232,plain,
! [SV1421: $i,SV1043: $i,SV2116: $i,SV513: $i,SV1722: $i] :
( ( ( ! [SY5561: $i] :
( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SV2116 @ SV513 ) @ SY5561 )
| ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SV2116 @ SV1421 @ SY5561 ) @ ( tc_fun @ SV1421 @ SY5561 ) ) ) )
= $true )
| ( ( c_in @ SV513 @ SV1043 @ SV1421 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4977]) ).
thf(5233,plain,
! [SV1723: $i,SV1422: $i,SV1044: $i,SV514: $i] :
( ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV514 = SV1044 )
| ( SV514 = SV1723 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SV1723 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5234,plain,
! [SV1724: $i,SV1423: $i,SV1045: $i,SV515: $i] :
( ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1045 = SV1724 )
| ( SV515 = SV1724 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SV1724 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4979]) ).
thf(5235,plain,
! [SV1934: $i,SV1425: $i,SV1048: $i,SV518: $i] :
( ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1425 @ SV1934 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1048 = SV1934 )
= $true )
| ( ( c_in @ ( c_Pair @ SV518 @ SV1048 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1425 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5236,plain,
! [SV1725: $i,SV1427: $i,SV1052: $i,SV522: $i] :
( ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV522 = SV1052 )
| ( SV1052 = SV1725 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SV1725 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(5237,plain,
! [SV1726: $i,SV1428: $i,SV1053: $i,SV523: $i] :
( ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV523 = SV1726 )
| ( SV1053 = SV1726 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SV1726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4982]) ).
thf(5238,plain,
! [SV1937: $i,SV1429: $i,SV1055: $i,SV525: $i] :
( ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1429 @ SV1937 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV525 = SV1937 )
= $true )
| ( ( c_in @ ( c_Pair @ SV525 @ SV1055 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1429 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4983]) ).
thf(5239,plain,
! [SV1430: $i,SV1938: $i,SV527: $i,SV1057: $i] :
( ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5240,plain,
! [SV1431: $i,SV1939: $i,SV528: $i,SV1058: $i] :
( ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4985]) ).
thf(5241,plain,
! [SV1432: $i,SV1940: $i,SV529: $i,SV1059: $i] :
( ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4986]) ).
thf(5242,plain,
! [SV1433: $i,SV1941: $i,SV530: $i,SV1060: $i] :
( ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5243,plain,
! [SV1727: $i,SV2052: $i,SV1434: $i,SV1061: $i,SV531: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(5244,plain,
! [SV1728: $i,SV2053: $i,SV1435: $i,SV1062: $i,SV532: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4989]) ).
thf(5245,plain,
! [SV1729: $i,SV2054: $i,SV1436: $i,SV1063: $i,SV533: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4990]) ).
thf(5246,plain,
! [SV1730: $i,SV2055: $i,SV1437: $i,SV1064: $i,SV534: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4991]) ).
thf(5247,plain,
! [SV1438: $i,SV1731: $i,SV1065: $i,SV535: $i] :
( ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1438 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4992]) ).
thf(5248,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2117: $i,SV2056: $i,SV1732: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4993]) ).
thf(5249,plain,
! [SV1440: $i,SV1067: $i,SV537: $i,SV2118: $i,SV2057: $i,SV1733: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4994]) ).
thf(5250,plain,
! [SV1068: $i,SV538: $i,SV1441: $i,SV2119: $i,SV2058: $i,SV1734: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4995]) ).
thf(5251,plain,
! [SV1442: $i,SV1069: $i,SV539: $i,SV2120: $i,SV2059: $i,SV1735: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4996]) ).
thf(5252,plain,
! [SV1443: $i,SV1070: $i,SV540: $i,SV2121: $i,SV2060: $i,SV1736: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4997]) ).
thf(5253,plain,
! [SV1444: $i,SV1071: $i,SV541: $i,SV2122: $i,SV2061: $i,SV1737: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4998]) ).
thf(5254,plain,
! [SV1072: $i,SV1445: $i,SV542: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ SV542 @ SV1445 )
= $false )
| ( ( c_in @ SV1072 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( hAPP @ SV542 @ SV1072 )
= ( hAPP @ SV1072 @ SV1445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4999]) ).
thf(5255,plain,
! [SV2062: $i,SV1942: $i,SV1738: $i,SV1446: $i,SV1073: $i,SV543: $i] :
( ( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SV2062 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
= $true )
| ( ( ~ ( c_in @ SV1073 @ ( hAPP @ SV2062 @ SV543 ) @ SV1738 )
| ~ ( c_in @ SV543 @ SV1942 @ SV1446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(5256,plain,
! [SV2063: $i,SV1943: $i,SV1739: $i,SV1447: $i,SV1074: $i,SV544: $i] :
( ( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SV2063 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
= $true )
| ( ( ~ ( c_in @ SV1074 @ ( hAPP @ SV2063 @ SV544 ) @ SV1739 )
| ~ ( c_in @ SV544 @ SV1943 @ SV1447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(5257,plain,
! [SV1075: $i,SV1448: $i,SV1944: $i,SV545: $i] :
( ( ( c_in @ ( c_Pair @ SV545 @ SV1944 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) )
= $false )
| ( ( ~ ( c_in @ SV1944 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 ) )
= $true )
| ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5258,plain,
! [SV1076: $i,SV1449: $i,SV1945: $i,SV546: $i] :
( ( ( c_in @ ( c_Pair @ SV546 @ SV1945 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) )
= $false )
| ( ( ~ ( c_in @ SV1945 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 ) )
= $true )
| ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5259,plain,
! [SV1450: $i,SV1077: $i,SV1946: $i,SV1740: $i,SV547: $i,SV2123: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2123 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) )
| ~ ( c_in @ SV2123 @ SV1450 @ SV1740 ) )
= $true )
| ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5004]) ).
thf(5260,plain,
! [SV1451: $i,SV1078: $i,SV1947: $i,SV1741: $i,SV548: $i,SV2124: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2124 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) )
| ~ ( c_in @ SV2124 @ SV1451 @ SV1741 ) )
= $true )
| ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5005]) ).
thf(5261,plain,
! [SV1081: $i,SV2064: $i,SV1454: $i,SV551: $i,SV1949: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1949 @ SV551 @ SV1454 @ SV1454 ) @ SV2064 @ ( tc_prod @ SV1454 @ SV1454 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SV2064 @ SV1454 ) )
= $true )
| ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5262,plain,
! [SV1082: $i,SV2065: $i,SV1455: $i,SV1950: $i,SV552: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV552 @ SV1950 @ SV1455 @ SV1455 ) @ SV2065 @ ( tc_prod @ SV1455 @ SV1455 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SV2065 @ SV1455 ) )
= $true )
| ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5263,plain,
! [SV1083: $i,SV1742: $i,SV1456: $i,SV553: $i,SV2066: $i] :
( ( ( c_in @ ( c_Pair @ SV2066 @ SV553 @ SV1456 @ SV1742 ) @ SV1083 @ ( tc_prod @ SV1456 @ SV1742 ) )
= $false )
| ( ( c_in @ SV553 @ ( c_Relation_ORange @ SV1083 @ SV1456 @ SV1742 ) @ SV1742 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5264,plain,
! [SV1084: $i,SV1743: $i,SV1457: $i,SV554: $i,SV2067: $i] :
( ( ( c_in @ ( c_Pair @ SV2067 @ SV554 @ SV1457 @ SV1743 ) @ SV1084 @ ( tc_prod @ SV1457 @ SV1743 ) )
= $false )
| ( ( c_in @ SV554 @ ( c_Relation_ORange @ SV1084 @ SV1457 @ SV1743 ) @ SV1743 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5010]) ).
thf(5265,plain,
! [SV1085: $i,SV1744: $i,SV1458: $i,SV2068: $i,SV555: $i] :
( ( ( c_in @ ( c_Pair @ SV555 @ SV2068 @ SV1458 @ SV1744 ) @ SV1085 @ ( tc_prod @ SV1458 @ SV1744 ) )
= $false )
| ( ( c_in @ SV555 @ ( c_Relation_ODomain @ SV1085 @ SV1458 @ SV1744 ) @ SV1458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5011]) ).
thf(5266,plain,
! [SV1086: $i,SV1745: $i,SV1459: $i,SV2069: $i,SV556: $i] :
( ( ( c_in @ ( c_Pair @ SV556 @ SV2069 @ SV1459 @ SV1745 ) @ SV1086 @ ( tc_prod @ SV1459 @ SV1745 ) )
= $false )
| ( ( c_in @ SV556 @ ( c_Relation_ODomain @ SV1086 @ SV1459 @ SV1745 ) @ SV1459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5267,plain,
! [SV1087: $i,SV2125: $i,SV1746: $i,SV2070: $i,SV557: $i,SV1460: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SV2070 @ SV1746 ) @ ( c_Product__Type_OSigma @ SV2125 @ SV1087 @ SV2070 @ SV1746 ) @ ( tc_prod @ SV2070 @ SV1746 ) ) )
= $true )
| ( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SV1746 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5013]) ).
thf(5268,plain,
! [SV2126: $i,SV1088: $i,SV2071: $i,SV1461: $i,SV1747: $i,SV558: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV558 @ SV1747 @ SV1461 @ SV2071 ) @ ( c_Product__Type_OSigma @ SV1088 @ SV2126 @ SV1461 @ SV2071 ) @ ( tc_prod @ SV1461 @ SV2071 ) ) )
= $true )
| ( ( c_in @ SV558 @ SV1088 @ SV1461 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5014]) ).
thf(5269,plain,
! [SV1748: $i,SV1462: $i,SV559: $i,SV1089: $i] :
( ( ( SV1089 = SV559 )
= $true )
| ( ( ! [SY5379: $i] :
( ~ ( c_in @ SV559 @ SY5379 @ SV1462 )
| ~ ( c_in @ SV1089 @ SY5379 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SY5379 @ SV1748 @ SV1462 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5270,plain,
! [SV1463: $i,SV1090: $i,SV1951: $i,SV560: $i] :
( ( ( c_in @ SV560 @ SV1951 @ SV1090 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1951 @ SV1463 @ SV1090 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5271,plain,
! [SV1091: $i,SV2072: $i,SV1464: $i,SV561: $i,SV1952: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1952 @ SV561 @ SV1464 @ SV1464 ) @ SV2072 @ ( tc_prod @ SV1464 @ SV1464 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1091 @ SV2072 @ SV1464 ) )
= $true )
| ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5272,plain,
! [SV1092: $i,SV2073: $i,SV1465: $i,SV1953: $i,SV562: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV562 @ SV1953 @ SV1465 @ SV1465 ) @ SV2073 @ ( tc_prod @ SV1465 @ SV1465 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1092 @ SV2073 @ SV1465 ) )
= $true )
| ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5018]) ).
thf(5273,plain,
! [SV1466: $i,SV1093: $i,SV1954: $i,SV563: $i] :
( ( ( c_in @ SV563 @ SV1954 @ SV1093 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1954 @ SV1466 @ SV1093 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5274,plain,
! [SV2127: $i,SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5562: $i,SY5563: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
| ! [SY5564: $i,SY5565: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SY5562 @ SY5563 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5564 @ SY5562 @ SY5565 ) @ SV2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5024]) ).
thf(5275,plain,
! [SV2128: $i,SV2075: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ! [SY5566: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
!= ( c_Fun_Ocomp @ SV2075 @ SV2128 @ SY5566 @ SV1754 @ SV1956 ) )
| ! [SY5567: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY5567 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SV2128 @ SY5567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5025]) ).
thf(5276,plain,
! [SV2076: $i,SV1957: $i,SV1755: $i,SV1473: $i,SV1100: $i,SV570: $i] :
( ( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SV1755 )
!= ( c_Pair @ SV1957 @ SV2076 @ SV1473 @ SV1755 ) )
= $true )
| ( ( SV1100 = SV2076 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5277,plain,
! [SV2129: $i,SV1958: $i,SV1756: $i,SV1474: $i,SV1101: $i,SV571: $i] :
( ( ( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SV1756 )
!= ( c_Pair @ SV1958 @ SV2129 @ SV1474 @ SV1756 ) )
= $true )
| ( ( SV571 = SV1958 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5027]) ).
thf(5278,plain,
! [SV1959: $i,SV1475: $i,SV1757: $i,SV572: $i,SV1102: $i] :
( ( ( c_in @ ( c_Pair @ SV1102 @ SV572 @ SV1757 @ SV1475 ) @ SV1959 @ ( tc_prod @ SV1757 @ SV1475 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1102 @ SV1475 @ SV1757 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1757 @ SV1475 ) @ SV1959 ) @ ( tc_prod @ SV1475 @ SV1757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5279,plain,
! [SV1960: $i,SV1476: $i,SV1758: $i,SV573: $i,SV1103: $i] :
( ( ( c_in @ ( c_Pair @ SV1103 @ SV573 @ SV1758 @ SV1476 ) @ SV1960 @ ( tc_prod @ SV1758 @ SV1476 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1103 @ SV1476 @ SV1758 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1758 @ SV1476 ) @ SV1960 ) @ ( tc_prod @ SV1476 @ SV1758 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5280,plain,
! [SV1961: $i,SV1477: $i,SV1759: $i,SV574: $i,SV1104: $i] :
( ( ( c_in @ ( c_Pair @ SV1104 @ SV574 @ SV1759 @ SV1477 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV1477 @ SV1759 ) @ SV1961 ) @ ( tc_prod @ SV1759 @ SV1477 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV574 @ SV1104 @ SV1477 @ SV1759 ) @ SV1961 @ ( tc_prod @ SV1477 @ SV1759 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5281,plain,
! [SV2130: $i,SV2077: $i,SV1962: $i,SV1760: $i,SV1478: $i,SV1105: $i,SV575: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ ( c_Fun_Ocomp @ SV1105 @ SV1478 @ SV1760 @ SV1962 @ SV2077 ) @ SV1962 @ SV2130 @ SV2077 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV575 @ SV1105 @ SV1962 @ SV2130 @ SV1760 ) @ SV1478 @ SV1760 @ SV2130 @ SV2077 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5031]) ).
thf(5282,plain,
! [SV596: $i,SV1124: $i,SV1484: $i,SV1766: $i,SV2080: $i,SV5: $i] :
( ( ( c_lessequals @ SV5 @ ( c_Product__Type_OSigma @ SV2080 @ ( c_COMBK @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) @ SV1124 ) @ SV1124 @ SV1484 ) @ ( tc_fun @ ( tc_prod @ SV1124 @ SV1484 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV5 @ SV596 @ SV1124 @ SV1484 ) @ SV1766 @ ( tc_fun @ SV1484 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5283,plain,
! [SV600: $i,SV10: $i,SV1767: $i,SV1486: $i] :
( ( ( c_Wellfounded_Owf @ SV1486 @ SV1767 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV10 @ SV1486 @ SV1767 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5284,plain,
! [SV2081: $i,SV1965: $i,SV1770: $i,SV1489: $i,SV1129: $i,SV603: $i,SV13: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SV2081 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV603 @ SV2081 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5036]) ).
thf(5285,plain,
! [SV614: $i,SV1135: $i,SV1968: $i,SV1495: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SV1968 ) @ tc_bool ) )
= $false )
| ( ( ! [SY5511: $i] :
~ ( c_in @ SY5511 @ SV1495 @ SV1968 ) )
= $true )
| ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5286,plain,
! [SV1136: $i,SV615: $i,SV1496: $i,SV1774: $i,SV26: $i] :
( ( ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) )
= $false )
| ( ( ! [SY4717: $i] :
~ ( c_in @ SY4717 @ SV615 @ SV1136 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5287,plain,
! [SV618: $i,SV29: $i,SV1776: $i,SV1498: $i] :
( ( ( c_Wellfounded_Owf @ SV1498 @ SV1776 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV29 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV29 @ SV1498 @ SV1776 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5288,plain,
! [SV2082: $i,SV1969: $i,SV1778: $i,SV1511: $i,SV1154: $i,SV638: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
= $true )
| ( ( ! [SY5556: $i] :
( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SY5556 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SY5556 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5042]) ).
thf(5289,plain,
! [SV53: $i,SV1155: $i,SV639: $i] :
( ( ( c_Wellfounded_Owf @ SV639 @ SV1155 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV53 @ SV1155 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5290,plain,
! [SV1158: $i,SV643: $i,SV57: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV57 @ SV643 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 )
= $true )
| ( ( c_Wellfounded_Owf @ SV1158 @ SV643 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5291,plain,
! [SV1160: $i,SV59: $i,SV1780: $i,SV1516: $i,SV645: $i] :
( ( ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SV1780 )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SV1780 ) @ SV1160 @ SV1780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5046]) ).
thf(5292,plain,
! [SV1517: $i,SV60: $i,SV1161: $i,SV1781: $i,SV646: $i] :
( ( ( c_Relation_Orefl__on @ SV646 @ SV1781 @ SV1161 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SV1781 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5047]) ).
thf(5293,plain,
! [SV658: $i,SV1165: $i,SV1976: $i,SV74: $i] :
( ( ( c_in @ SV74 @ SV1976 @ SV1165 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1976 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV74 @ SV658 @ SV1165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5294,plain,
! [SV77: $i,SV1166: $i,SV660: $i,SV1978: $i] :
( ( ( ( c_Relation_Orel__comp @ SV1978 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $false )
| ( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1978 @ SV77 @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV77 @ SV660 @ SV1166 @ SV1166 @ SV1166 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1166 @ SV1166 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5050]) ).
thf(5295,plain,
! [SV661: $i,SV1167: $i,SV1979: $i,SV78: $i] :
( ( ( ( c_Relation_Orel__comp @ SV78 @ SV1979 @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $false )
| ( ( ( c_Relation_Orel__comp @ SV78 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1979 @ SV661 @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV78 @ SV661 @ SV1167 @ SV1167 @ SV1167 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1167 @ SV1167 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5051]) ).
thf(5296,plain,
! [SV662: $i,SV79: $i,SV1789: $i,SV1525: $i] :
( ( ( c_Wellfounded_Owf @ SV1525 @ SV1789 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV79 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV79 @ SV1525 @ SV1789 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV79 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5297,plain,
! [SV82: $i,SV1528: $i,SV1790: $i] :
( ( ( c_lessequals @ SV1790 @ SV1528 @ SV82 )
= $false )
| ( ( ~ ( c_lessequals @ SV1528 @ SV1790 @ SV82 ) )
= $true )
| ( ( SV1528 = SV1790 )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5298,plain,
! [SV83: $i,SV1529: $i,SV1791: $i] :
( ( ( c_lessequals @ SV1791 @ SV1529 @ SV83 )
= $false )
| ( ( ~ ( c_lessequals @ SV1529 @ SV1791 @ SV83 ) )
= $true )
| ( ( SV1529 = SV1791 )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5299,plain,
! [SV84: $i,SV1792: $i,SV1530: $i] :
( ( ( c_lessequals @ SV1530 @ SV1792 @ SV84 )
= $false )
| ( ( ~ ( c_lessequals @ SV1792 @ SV1530 @ SV84 ) )
= $true )
| ( ( SV1530 = SV1792 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5300,plain,
! [SV1535: $i,SV92: $i,SV1171: $i,SV1797: $i,SV668: $i] :
( ( ( c_Relation_Orefl__on @ SV668 @ SV1797 @ SV1171 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SV1797 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5301,plain,
! [SV675: $i,SV1174: $i,SV1539: $i,SV102: $i] :
( ( ( c_lessequals @ SV102 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV675 @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV102 @ SV675 @ ( tc_fun @ SV1174 @ tc_bool ) ) @ SV1539 @ ( tc_fun @ SV1174 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5065]) ).
thf(5302,plain,
! [SV678: $i,SV1177: $i,SV1540: $i,SV105: $i] :
( ( ( c_lessequals @ SV105 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV678 @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV105 @ SV678 @ ( tc_fun @ SV1177 @ tc_bool ) ) @ SV1540 @ ( tc_fun @ SV1177 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5066]) ).
thf(5303,plain,
! [SV679: $i,SV106: $i,SV1984: $i,SV1805: $i] :
( ( ( ~ ( c_lessequals @ SV1805 @ SV1984 @ SV106 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV679 @ SV1984 @ SV106 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SV1984 @ SV106 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5304,plain,
! [SV680: $i,SV109: $i,SV1985: $i,SV1808: $i] :
( ( ( ~ ( c_lessequals @ SV1808 @ SV1985 @ SV109 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV680 @ SV1985 @ SV109 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SV1985 @ SV109 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5305,plain,
! [SV681: $i,SV110: $i,SV1986: $i,SV1809: $i] :
( ( ( ~ ( c_lessequals @ SV1809 @ SV1986 @ SV110 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV681 @ SV1986 @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SV1986 @ SV110 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5306,plain,
! [SV142: $i,SV2083: $i,SV1824: $i,SV705: $i] :
( ( ( c_lessequals @ SV705 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1824 @ SV2083 @ SV142 ) @ SV142 )
= $false )
| ( ( c_lessequals @ SV705 @ SV1824 @ SV142 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5077]) ).
thf(5307,plain,
! [SV143: $i,SV1825: $i,SV2084: $i,SV706: $i] :
( ( ( c_lessequals @ SV706 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2084 @ SV1825 @ SV143 ) @ SV143 )
= $false )
| ( ( c_lessequals @ SV706 @ SV1825 @ SV143 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5078]) ).
thf(5308,plain,
! [SV1826: $i,SV144: $i,SV1991: $i,SV707: $i] :
( ( ( c_lessequals @ SV707 @ SV1991 @ SV144 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV707 @ SV1826 @ SV144 ) @ SV1991 @ SV144 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5079]) ).
thf(5309,plain,
! [SV708: $i,SV145: $i,SV1992: $i,SV1827: $i] :
( ( ( c_lessequals @ SV1827 @ SV1992 @ SV145 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV708 @ SV1827 @ SV145 ) @ SV1992 @ SV145 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5080]) ).
thf(5310,plain,
! [SV146: $i,SV2085: $i,SV1828: $i,SV709: $i] :
( ( ( c_lessequals @ SV709 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1828 @ SV2085 @ SV146 ) @ SV146 )
= $false )
| ( ( c_lessequals @ SV709 @ SV1828 @ SV146 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5311,plain,
! [SV147: $i,SV1829: $i,SV2086: $i,SV710: $i] :
( ( ( c_lessequals @ SV710 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2086 @ SV1829 @ SV147 ) @ SV147 )
= $false )
| ( ( c_lessequals @ SV710 @ SV1829 @ SV147 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5312,plain,
! [SV719: $i,SV160: $i,SV1834: $i,SV1564: $i] :
( ( ( c_Wellfounded_Owf @ SV1564 @ SV1834 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV160 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV160 @ SV1564 @ SV1834 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV160 @ SV719 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5313,plain,
! [SV1993: $i,SV1837: $i,SV1567: $i,SV1209: $i,SV724: $i,SV166: $i] :
( ( ( ( hAPP @ SV166 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) )
= ( hAPP @ SV724 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV166 @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV166 @ SV1209 @ SV1567 @ SV1837 @ SV1993 )
= ( c_Recdef_Ocut @ SV724 @ SV1209 @ SV1567 @ SV1837 @ SV1993 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5314,plain,
! [SV1210: $i,SV169: $i,SV2131: $i,SV1994: $i,SV727: $i] :
( ( ( ~ ( c_lessequals @ SV727 @ SV1994 @ ( tc_fun @ SV2131 @ SV169 ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SV1994 @ SV1210 ) @ SV169 )
= $true )
| ( ( class_HOL_Oord @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5086]) ).
thf(5315,plain,
! [SV1211: $i,SV1569: $i,SV728: $i,SV170: $i] :
( ( ( c_in @ SV170 @ SV728 @ SV1569 )
= $false )
| ( ( c_in @ SV170 @ SV1211 @ SV1569 )
= $false )
| ( ( c_in @ SV170 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV728 @ SV1211 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV1569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5316,plain,
! [SV1212: $i,SV1570: $i,SV729: $i,SV171: $i] :
( ( ( c_in @ SV171 @ SV729 @ SV1570 )
= $false )
| ( ( c_in @ SV171 @ SV1212 @ SV1570 )
= $false )
| ( ( c_in @ SV171 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV729 @ SV1212 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5088]) ).
thf(5317,plain,
! [SV172: $i,SV1213: $i,SV730: $i,SV1839: $i] :
( ( ( c_lessequals @ SV1839 @ SV730 @ ( tc_fun @ SV1213 @ tc_bool ) )
= $false )
| ( ( c_in @ SV172 @ SV1839 @ SV1213 )
= $false )
| ( ( c_in @ SV172 @ SV730 @ SV1213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5089]) ).
thf(5318,plain,
! [SV731: $i,SV1214: $i,SV1840: $i,SV173: $i] :
( ( ( c_in @ SV173 @ SV1840 @ SV1214 )
= $false )
| ( ( c_lessequals @ SV1840 @ SV731 @ ( tc_fun @ SV1214 @ tc_bool ) )
= $false )
| ( ( c_in @ SV173 @ SV731 @ SV1214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5090]) ).
thf(5319,plain,
! [SV174: $i,SV1215: $i,SV732: $i,SV1841: $i] :
( ( ( c_lessequals @ SV1841 @ SV732 @ ( tc_fun @ SV1215 @ tc_bool ) )
= $false )
| ( ( c_in @ SV174 @ SV1841 @ SV1215 )
= $false )
| ( ( c_in @ SV174 @ SV732 @ SV1215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5320,plain,
! [SV175: $i,SV1216: $i,SV733: $i,SV1842: $i] :
( ( ( c_lessequals @ SV1842 @ SV733 @ ( tc_fun @ SV1216 @ tc_bool ) )
= $false )
| ( ( c_in @ SV175 @ SV1842 @ SV1216 )
= $false )
| ( ( c_in @ SV175 @ SV733 @ SV1216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5092]) ).
thf(5321,plain,
! [SV1224: $i,SV191: $i,SV749: $i,SV2132: $i,SV1576: $i] :
( ( ( ~ ( c_in @ SV1576 @ SV2132 @ SV749 )
| ~ ( c_in @ SV191 @ SV2132 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5094]) ).
thf(5322,plain,
! [SV1225: $i,SV751: $i,SV1577: $i,SV1847: $i,SV194: $i] :
( ( ( SV194 = SV1847 )
= $true )
| ( ( SV194 = SV1577 )
= $true )
| ( ( ( c_Set_Oinsert @ SV194 @ ( c_Set_Oinsert @ SV751 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 )
= ( c_Set_Oinsert @ SV1577 @ ( c_Set_Oinsert @ SV1847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ SV1225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(5323,plain,
! [SV1995: $i,SV1226: $i,SV195: $i,SV1578: $i,SV752: $i] :
( ( ( SV752 = SV1578 )
= $true )
| ( ( SV195 = SV1578 )
= $true )
| ( ( ( c_Set_Oinsert @ SV195 @ ( c_Set_Oinsert @ SV752 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 )
= ( c_Set_Oinsert @ SV1578 @ ( c_Set_Oinsert @ SV1995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) @ SV1226 ) @ SV1226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(5324,plain,
! [SV1579: $i,SV1227: $i,SV753: $i,SV1848: $i,SV196: $i] :
( ( ( SV196 = SV1848 )
= $true )
| ( ( SV753 = SV1848 )
= $true )
| ( ( ( c_Set_Oinsert @ SV196 @ ( c_Set_Oinsert @ SV753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 )
= ( c_Set_Oinsert @ SV1579 @ ( c_Set_Oinsert @ SV1848 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1227 @ tc_bool ) ) @ SV1227 ) @ SV1227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5097]) ).
thf(5325,plain,
! [SV1228: $i,SV197: $i,SV1849: $i,SV1580: $i,SV754: $i] :
( ( ( SV754 = SV1580 )
= $true )
| ( ( SV754 = SV1849 )
= $true )
| ( ( ( c_Set_Oinsert @ SV197 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 )
= ( c_Set_Oinsert @ SV1580 @ ( c_Set_Oinsert @ SV1849 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1228 ) @ SV1228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5098]) ).
thf(5326,plain,
! [SV1583: $i,SV207: $i,SV1234: $i,SV1850: $i,SV762: $i] :
( ( ( c_lessequals @ SV762 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5327,plain,
! [SV1853: $i,SV210: $i,SV1996: $i,SV763: $i] :
( ( ( ~ ( c_lessequals @ SV763 @ SV1996 @ SV210 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV763 @ SV1853 @ SV210 ) )
= $true )
| ( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SV1996 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(5328,plain,
! [SV1854: $i,SV211: $i,SV1997: $i,SV764: $i] :
( ( ( ~ ( c_lessequals @ SV764 @ SV1997 @ SV211 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV764 @ SV1854 @ SV211 ) )
= $true )
| ( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV1997 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5329,plain,
! [SV1855: $i,SV212: $i,SV1998: $i,SV765: $i] :
( ( ( ~ ( c_lessequals @ SV765 @ SV1998 @ SV212 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV765 @ SV1855 @ SV212 ) )
= $true )
| ( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SV1998 @ SV212 ) @ SV212 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5102]) ).
thf(5330,plain,
! [SV1237: $i,SV1588: $i,SV768: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ SV768 @ ( tc_fun @ SV1588 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV217 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV217 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV768 @ SV1237 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ ( tc_fun @ SV1588 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5331,plain,
! [SV1238: $i,SV1589: $i,SV769: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ SV769 @ ( tc_fun @ SV1589 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV218 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV218 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV769 @ SV1238 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ ( tc_fun @ SV1589 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5332,plain,
! [SV775: $i,SV1242: $i,SV1593: $i,SV224: $i] :
( ( ( c_in @ SV224 @ SV1593 @ SV1242 )
= $false )
| ( ( c_lessequals @ SV775 @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV224 @ SV775 @ SV1242 ) @ SV1593 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5333,plain,
! [SV1864: $i,SV236: $i,SV784: $i,SV2087: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2087 @ SV784 @ SV236 ) @ SV1864 @ SV236 )
= $false )
| ( ( c_lessequals @ SV784 @ SV1864 @ SV236 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5334,plain,
! [SV1865: $i,SV237: $i,SV2088: $i,SV785: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV785 @ SV2088 @ SV237 ) @ SV1865 @ SV237 )
= $false )
| ( ( c_lessequals @ SV785 @ SV1865 @ SV237 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5335,plain,
! [SV1866: $i,SV238: $i,SV2001: $i,SV786: $i] :
( ( ( c_lessequals @ SV786 @ SV2001 @ SV238 )
= $false )
| ( ( c_lessequals @ SV786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1866 @ SV2001 @ SV238 ) @ SV238 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5336,plain,
! [SV2089: $i,SV239: $i,SV1867: $i,SV787: $i] :
( ( ( c_lessequals @ SV787 @ SV1867 @ SV239 )
= $false )
| ( ( c_lessequals @ SV787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1867 @ SV2089 @ SV239 ) @ SV239 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5337,plain,
! [SV1868: $i,SV240: $i,SV788: $i,SV2090: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2090 @ SV788 @ SV240 ) @ SV1868 @ SV240 )
= $false )
| ( ( c_lessequals @ SV788 @ SV1868 @ SV240 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5338,plain,
! [SV1869: $i,SV241: $i,SV2091: $i,SV789: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV789 @ SV2091 @ SV241 ) @ SV1869 @ SV241 )
= $false )
| ( ( c_lessequals @ SV789 @ SV1869 @ SV241 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5339,plain,
! [SV1872: $i,SV244: $i,SV2092: $i,SV792: $i] :
( ( ( ~ ( c_lessequals @ SV792 @ SV2092 @ SV244 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2092 @ SV1872 @ SV244 ) )
= $true )
| ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5113]) ).
thf(5340,plain,
! [SV793: $i,SV245: $i,SV1873: $i,SV2093: $i] :
( ( ( ~ ( c_lessequals @ SV2093 @ SV1873 @ SV245 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV793 @ SV2093 @ SV245 ) )
= $true )
| ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5114]) ).
thf(5341,plain,
! [SV796: $i,SV1251: $i,SV1874: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV1874 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1874 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV248 @ SV796 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5342,plain,
! [SV797: $i,SV2094: $i,SV249: $i,SV1599: $i] :
( ( ( c_lessequals @ SV1599 @ SV249 @ ( tc_fun @ SV2094 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1599 @ SV797 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV797 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5343,plain,
! [SV2002: $i,SV254: $i,SV800: $i,SV1604: $i] :
( ( ( hBOOL @ ( hAPP @ SV1604 @ SV800 ) )
= $false )
| ( ( c_lessequals @ SV1604 @ SV254 @ ( tc_fun @ SV2002 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV800 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5344,plain,
! [SV1252: $i,SV802: $i,SV1875: $i,SV256: $i] :
( ( ( c_lessequals @ SV256 @ SV1875 @ ( tc_fun @ ( tc_prod @ SV802 @ SV1252 ) @ tc_bool ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1875 @ SV802 @ SV1252 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV256 @ SV802 @ SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5345,plain,
! [SV1606: $i,SV257: $i,SV1253: $i,SV1876: $i,SV803: $i] :
( ( ( c_lessequals @ SV803 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5346,plain,
! [SV1257: $i,SV809: $i,SV1608: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP @ SV263 @ SV1608 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV809 @ SV1608 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV809 @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5123]) ).
thf(5347,plain,
! [SV1610: $i,SV1877: $i,SV268: $i,SV1260: $i,SV2003: $i,SV812: $i] :
( ( ( ~ ( c_lessequals @ SV812 @ SV2003 @ ( tc_fun @ SV1260 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SV2003 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5348,plain,
! [SV1879: $i,SV2004: $i,SV814: $i,SV1262: $i,SV271: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SV2004 @ SV2004 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SV2004 ) @ ( tc_prod @ SV2004 @ SV2004 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ SV2004 @ SV2004 ) @ SV1879 @ ( tc_prod @ SV2004 @ SV2004 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5349,plain,
! [SV1880: $i,SV2005: $i,SV815: $i,SV1263: $i,SV272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SV2005 @ SV2005 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SV2005 ) @ ( tc_prod @ SV2005 @ SV2005 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ SV2005 @ SV2005 ) @ SV1880 @ ( tc_prod @ SV2005 @ SV2005 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5350,plain,
! [SV274: $i,SV2095: $i,SV2006: $i,SV1612: $i,SV817: $i,SV1265: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 ) )
= $true )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5351,plain,
! [SV1613: $i,SV1881: $i,SV275: $i,SV1266: $i,SV818: $i] :
( ( ( ! [SY4839: $i] :
~ ( c_in @ SY4839 @ SV818 @ SV1266 ) )
= $true )
| ( ( SV275 = SV1881 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5352,plain,
! [SV821: $i,SV1269: $i,SV1882: $i,SV278: $i] :
( ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV1882 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $false )
| ( ( c_lessequals @ SV1882 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1269 @ SV1269 ) @ tc_bool ) )
= $false )
| ( ( c_in @ SV278 @ ( c_Transitive__Closure_Otrancl @ SV821 @ SV1269 ) @ ( tc_prod @ SV1269 @ SV1269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5130]) ).
thf(5353,plain,
! [SV1273: $i,SV292: $i,SV834: $i,SV2096: $i,SV1616: $i] :
( ( ( ~ ( c_in @ SV1616 @ SV2096 @ SV834 ) )
= $true )
| ( ( ~ ( c_in @ SV292 @ SV2096 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) )
= $true )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5131]) ).
thf(5354,plain,
! [SV1883: $i,SV293: $i,SV1274: $i,SV835: $i,SV2097: $i] :
( ( ( ~ ( c_lessequals @ SV2097 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SV2097 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) )
= $true )
| ( ( SV293 = SV1883 )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5132]) ).
thf(5355,plain,
! [SV1617: $i,SV836: $i,SV1275: $i,SV294: $i,SV2133: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2133 @ SV294 @ SV1275 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5133]) ).
thf(5356,plain,
! [SV838: $i,SV1276: $i,SV296: $i,SV1618: $i] :
( ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
| ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5134]) ).
thf(5357,plain,
! [SV1886: $i,SV2007: $i,SV843: $i,SV1282: $i,SV303: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SV2007 @ SV2007 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV2007 ) @ ( tc_prod @ SV2007 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5139]) ).
thf(5358,plain,
! [SV1887: $i,SV2008: $i,SV844: $i,SV1283: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SV2008 ) @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5359,plain,
! [SV1888: $i,SV2009: $i,SV845: $i,SV1284: $i,SV305: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SV2009 ) @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5360,plain,
! [SV846: $i,SV2010: $i,SV1889: $i,SV1285: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
| ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5361,plain,
! [SV847: $i,SV1623: $i,SV1286: $i,SV307: $i,SV2098: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5362,plain,
! [SV1890: $i,SV2011: $i,SV849: $i,SV1288: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SV2011 @ SV2011 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV2011 ) @ ( tc_prod @ SV2011 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5144]) ).
thf(5363,plain,
! [SV851: $i,SV2012: $i,SV1891: $i,SV1290: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
| ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5364,plain,
! [SV853: $i,SV2099: $i,SV2013: $i,SV313: $i,SV1292: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SV2013 @ SV2099 ) @ SV2099 @ SV2099 ) @ SV2013 @ ( tc_prod @ SV2099 @ SV2099 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2013 @ SV2099 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5147]) ).
thf(5365,plain,
! [SV854: $i,SV2100: $i,SV2014: $i,SV314: $i,SV1293: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SV2014 @ SV2100 ) @ SV2100 @ SV2100 ) @ SV2014 @ ( tc_prod @ SV2100 @ SV2100 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2014 @ SV2100 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5366,plain,
! [SV855: $i,SV2101: $i,SV2015: $i,SV315: $i,SV1294: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SV2015 @ SV2101 ) @ SV2101 @ SV2101 ) @ SV2015 @ ( tc_prod @ SV2101 @ SV2101 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2015 @ SV2101 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5367,plain,
! [SV856: $i,SV2102: $i,SV2016: $i,SV316: $i,SV1295: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SV2016 @ SV2102 ) @ SV2102 @ SV2102 ) @ SV2016 @ ( tc_prod @ SV2102 @ SV2102 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2016 @ SV2102 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5368,plain,
! [SV325: $i,SV1629: $i,SV1304: $i,SV2017: $i,SV865: $i] :
( ( ( c_in @ SV865 @ SV2017 @ SV1304 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5369,plain,
! [SV866: $i,SV1305: $i,SV326: $i,SV1630: $i,SV2103: $i] :
( ( ( c_in @ SV2103 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
= $false )
| ( ( ! [SY5258: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5258 @ SV1630 @ SV1305 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5370,plain,
! [SV2104: $i,SV2018: $i,SV1892: $i,SV1631: $i,SV1306: $i,SV867: $i,SV327: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SV1892 @ SV2018 @ SV2104 ) @ SV867 @ SV2104 @ SV2018 ) @ SV1631 @ ( tc_prod @ SV2104 @ SV2018 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV327 @ SV867 @ SV1892 @ SV2018 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SV1892 @ SV2104 @ SV2018 ) @ ( tc_prod @ SV1892 @ SV2018 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5371,plain,
! [SV2105: $i,SV2019: $i,SV1893: $i,SV1632: $i,SV1307: $i,SV868: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SV1893 @ SV2019 @ SV2105 ) @ SV1893 @ SV2105 ) @ SV1307 @ ( tc_prod @ SV1893 @ SV2105 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV328 @ SV868 @ SV1893 @ SV2019 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SV1893 @ SV2105 @ SV2019 ) @ ( tc_prod @ SV1893 @ SV2019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5158]) ).
thf(5372,plain,
! [SV1636: $i,SV1311: $i,SV332: $i,SV2106: $i,SV2020: $i,SV872: $i] :
( ( ( ~ ( c_in @ SV872 @ SV2020 @ SV2106 ) )
= $true )
| ( ( ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV2020 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SV2106 ) @ SV2106 @ SV1636 ) @ ( tc_fun @ SV2106 @ SV1636 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(5373,plain,
! [SV351: $i,SV1320: $i,SV887: $i,SV1899: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1899 @ SV887 @ SV1320 )
= $false )
| ( ( c_in @ SV351 @ SV1899 @ SV1320 )
= $false )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV887 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 @ SV1320 ) @ SV1320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5374,plain,
! [SV1644: $i,SV890: $i,SV1323: $i,SV354: $i,SV2134: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2134 @ SV354 @ SV1323 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5168]) ).
thf(5375,plain,
! [SV1645: $i,SV891: $i,SV1324: $i,SV355: $i,SV2135: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2135 @ SV355 @ SV1324 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5169]) ).
thf(5376,plain,
! [SV892: $i,SV356: $i,SV1325: $i,SV2136: $i,SV1646: $i] :
( ( ( ~ ( c_in @ SV1646 @ SV2136 @ SV1325 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2136 @ SV356 @ SV1325 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5170]) ).
thf(5377,plain,
! [SV1647: $i,SV893: $i,SV1326: $i,SV357: $i,SV2107: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SV2107 @ SV1326 )
| ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5171]) ).
thf(5378,plain,
! [SV358: $i,SV894: $i,SV1327: $i,SV2137: $i,SV1648: $i] :
( ( ( ~ ( c_in @ SV1648 @ SV2137 @ SV1327 )
| ~ ( c_in @ SV894 @ SV2137 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5172]) ).
thf(5379,plain,
! [SV359: $i,SV895: $i,SV1328: $i,SV2108: $i,SV1649: $i] :
( ( ( ~ ( c_in @ SV1649 @ SV2108 @ SV1328 ) )
= $true )
| ( ( ~ ( c_in @ SV895 @ SV2108 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5380,plain,
! [SV365: $i,SV1903: $i,SV1654: $i,SV901: $i] :
( ( ( c_in @ SV901 @ ( c_Wellfounded_Oacc @ SV1654 @ SV1903 ) @ SV1903 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV365 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV365 @ SV1654 @ SV1903 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5381,plain,
! [SV369: $i,SV1905: $i,SV1657: $i,SV905: $i] :
( ( ( c_in @ SV905 @ ( c_Wellfounded_Oacc @ SV1657 @ SV1905 ) @ SV1905 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV369 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV369 @ SV1657 @ SV1905 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV369 @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5382,plain,
! [SV373: $i,SV2022: $i,SV1335: $i,SV909: $i] :
( ( ( c_Wellfounded_Owf @ SV909 @ SV1335 )
= $false )
| ( ( c_in @ SV2022 @ SV373 @ SV1335 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV373 @ SV909 @ SV1335 ) @ SV373 @ SV1335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5182]) ).
thf(5383,plain,
! [SV374: $i,SV2023: $i,SV1336: $i,SV910: $i] :
( ( ( c_Wellfounded_Owf @ SV910 @ SV1336 )
= $false )
| ( ( c_in @ SV2023 @ SV374 @ SV1336 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV374 @ SV910 @ SV1336 ) @ SV374 @ SV1336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5384,plain,
! [SV2138: $i,SV2109: $i,SV2024: $i,SV1909: $i,SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
| ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
| ! [SY5568: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SY5568 @ ( tc_prod @ SV2138 @ SV2138 ) )
| ! [SY5569: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5568 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5184]) ).
thf(5385,plain,
! [SV1350: $i,SV390: $i,SV1669: $i,SV926: $i] :
( ( ( SV926 = SV1669 )
= $true )
| ( ( c_in @ SV390 @ SV926 @ SV1350 )
= $true )
| ( ( c_in @ SV390 @ SV1669 @ SV1350 )
= $true )
| ( ( ( c_Set_Oinsert @ SV390 @ SV926 @ SV1350 )
= ( c_Set_Oinsert @ SV390 @ SV1669 @ SV1350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5386,plain,
! [SV1913: $i,SV1670: $i,SV928: $i,SV392: $i,SV2139: $i,SV2026: $i,SV1352: $i] :
( ( ( ~ ( c_in @ SV1352 @ SV2026 @ SV2139 )
| ! [SY5570: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5570 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SY5570 @ SV2139 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5188]) ).
thf(5387,plain,
! [SV1353: $i,SV2027: $i,SV931: $i,SV398: $i] :
( ( ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
= $false )
| ( ( ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 )
| ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5189]) ).
thf(5388,plain,
! [SV1354: $i,SV2028: $i,SV932: $i,SV399: $i] :
( ( ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
= $false )
| ( ( ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 )
| ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5190]) ).
thf(5389,plain,
! [SV937: $i,SV1916: $i,SV404: $i,SV1675: $i] :
( ( ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SV1916 ) @ t_a @ t_a ) @ SV1916 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5193]) ).
thf(5390,plain,
! [SV938: $i,SV1917: $i,SV405: $i,SV1676: $i] :
( ( ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SV1917 ) @ t_a @ t_a ) @ SV1917 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5391,plain,
! [SV940: $i,SV2110: $i,SV2029: $i,SV407: $i,SV1360: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SV2029 @ SV2110 ) @ SV2110 @ SV2110 ) @ SV2029 @ ( tc_prod @ SV2110 @ SV2110 ) ) )
= $true )
| ( ( ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SV2029 @ SV2110 ) @ SV2110 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5392,plain,
! [SV941: $i,SV2030: $i,SV408: $i,SV1677: $i] :
( ( ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SV2030 ) @ t_a @ t_a ) @ SV2030 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SV2030 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5196]) ).
thf(5393,plain,
! [SV942: $i,SV2031: $i,SV409: $i,SV1678: $i] :
( ( ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SV2031 ) @ t_a @ t_a ) @ SV2031 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SV2031 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5394,plain,
! [SV943: $i,SV2111: $i,SV2032: $i,SV410: $i,SV1361: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SV2032 @ SV2111 ) @ SV2111 @ SV2111 ) @ SV2032 @ ( tc_prod @ SV2111 @ SV2111 ) ) )
= $true )
| ( ( ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SV2032 @ SV2111 ) @ SV2111 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5395,plain,
! [SV418: $i,SV1685: $i,SV1369: $i,SV951: $i,SV2033: $i] :
( ( ( c_in @ ( c_Pair @ SV2033 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV418 @ SV2033 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5201]) ).
thf(5396,plain,
! [SV419: $i,SV1686: $i,SV1370: $i,SV952: $i,SV2034: $i] :
( ( ( c_in @ ( c_Pair @ SV2034 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV419 @ SV2034 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5397,plain,
! [SV420: $i,SV1687: $i,SV1371: $i,SV953: $i,SV2035: $i] :
( ( ( c_in @ ( c_Pair @ SV2035 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV420 @ SV2035 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5398,plain,
! [SV1918: $i,SV421: $i,SV954: $i,SV1688: $i,SV1372: $i,SV2036: $i] :
( ( ( c_in @ ( c_Pair @ SV2036 @ SV1372 @ SV1688 @ SV1688 ) @ SV954 @ ( tc_prod @ SV1688 @ SV1688 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV421 @ SV954 @ SV1372 @ SV1688 @ SV1918 ) @ SV2036 )
= ( hAPP @ SV421 @ SV2036 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5204]) ).
thf(5399,plain,
! [SV1919: $i,SV422: $i,SV955: $i,SV1689: $i,SV1373: $i,SV2037: $i] :
( ( ( c_in @ ( c_Pair @ SV2037 @ SV1373 @ SV1689 @ SV1689 ) @ SV955 @ ( tc_prod @ SV1689 @ SV1689 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV422 @ SV955 @ SV1373 @ SV1689 @ SV1919 ) @ SV2037 )
= ( hAPP @ SV422 @ SV2037 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5400,plain,
! [SV425: $i,SV1375: $i,SV958: $i,SV1921: $i] :
( ( ( c_in @ SV1921 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $false )
| ( ( c_in @ ( c_Pair @ SV425 @ SV1921 @ SV1375 @ SV1375 ) @ ( c_Transitive__Closure_Ortrancl @ SV958 @ SV1375 ) @ ( tc_prod @ SV1375 @ SV1375 ) )
= $false )
| ( ( c_in @ SV425 @ ( c_Wellfounded_Oacc @ SV958 @ SV1375 ) @ SV1375 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5207]) ).
thf(5401,plain,
! [SV959: $i,SV1376: $i,SV1922: $i,SV426: $i] :
( ( ( c_in @ ( c_Pair @ SV426 @ SV1922 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV959 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
= $false )
| ( ( c_in @ SV1922 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $false )
| ( ( c_in @ SV426 @ ( c_Wellfounded_Oacc @ SV959 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5402,plain,
! [SV445: $i,SV1693: $i,SV1385: $i,SV977: $i,SV2038: $i] :
( ( ( c_in @ ( c_Pair @ SV2038 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV445 @ SV2038 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5403,plain,
! [SV446: $i,SV1694: $i,SV1386: $i,SV978: $i,SV2039: $i] :
( ( ( c_in @ ( c_Pair @ SV2039 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV446 @ SV2039 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5404,plain,
! [SV451: $i,SV1699: $i,SV1391: $i,SV983: $i,SV2040: $i] :
( ( ( c_in @ ( c_Pair @ SV2040 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV451 @ SV2040 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5405,plain,
! [SV452: $i,SV1700: $i,SV1392: $i,SV984: $i,SV2041: $i] :
( ( ( c_in @ ( c_Pair @ SV2041 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV452 @ SV2041 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5215]) ).
thf(5406,plain,
! [SV489: $i,SV1704: $i,SV1403: $i,SV1019: $i,SV2043: $i] :
( ( ( c_in @ ( c_Pair @ SV2043 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV489 @ SV2043 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5407,plain,
! [SV491: $i,SV1706: $i,SV1405: $i,SV1021: $i,SV2044: $i] :
( ( ( c_in @ ( c_Pair @ SV2044 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV491 @ SV2044 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5218]) ).
thf(5408,plain,
! [SV1707: $i,SV1408: $i,SV494: $i,SV1024: $i] :
( ( ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1707 @ SV1408 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5219]) ).
thf(5409,plain,
! [SV1927: $i,SV1708: $i,SV1025: $i,SV495: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV1927 @ SV1708 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5410,plain,
! [SV1928: $i,SV1709: $i,SV1026: $i,SV496: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV1928 @ SV1709 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5411,plain,
! [SV497: $i,SV2045: $i,SV1710: $i,SV1409: $i,SV1027: $i] :
( ( ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SV2045 @ ( tc_prod @ SV1710 @ SV1710 ) )
= $false )
| ( ( ! [SY5534: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2045 @ SV497 @ SV1710 @ SY5534 ) )
= $true )
| ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5412,plain,
! [SV2046: $i,SV1930: $i,SV1712: $i,SV1410: $i,SV1029: $i,SV499: $i] :
( ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
= $false )
| ( ( ! [SY5535: $i] :
( ( ( hAPP @ SV499 @ SY5535 )
= ( hAPP @ SV2046 @ SY5535 ) )
| ~ ( c_in @ ( c_Pair @ SY5535 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5413,plain,
! [SV1413: $i,SV1714: $i,SV2047: $i,SV1033: $i,SV503: $i,SV1931: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV1931 @ SV503 ) @ ( hAPP @ SV1931 @ SV1033 ) @ SV2047 @ SV2047 ) @ SV1714 @ ( tc_prod @ SV2047 @ SV2047 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ SV1413 @ SV1413 ) @ ( c_Relation_Oinv__image @ SV1714 @ SV1931 @ SV2047 @ SV1413 ) @ ( tc_prod @ SV1413 @ SV1413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5414,plain,
! [SV1715: $i,SV504: $i,SV1932: $i,SV2113: $i,SV1414: $i,SV1034: $i] :
( ( ( c_in @ ( c_Pair @ SV1034 @ SV1414 @ SV2113 @ SV2113 ) @ ( c_Relation_Oinv__image @ SV1932 @ SV504 @ SV1715 @ SV2113 ) @ ( tc_prod @ SV2113 @ SV2113 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( hAPP @ SV504 @ SV1034 ) @ ( hAPP @ SV504 @ SV1414 ) @ SV1715 @ SV1715 ) @ SV1932 @ ( tc_prod @ SV1715 @ SV1715 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5225]) ).
thf(5415,plain,
! [SV505: $i,SV1035: $i,SV1415: $i,SV1716: $i] :
( ( ( c_Relation_Osym @ SV1716 @ SV1415 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1035 @ SV505 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ SV1415 @ SV1415 ) @ SV1716 @ ( tc_prod @ SV1415 @ SV1415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5226]) ).
thf(5416,plain,
! [SV506: $i,SV1036: $i,SV1416: $i,SV1717: $i] :
( ( ( c_Relation_Osym @ SV1717 @ SV1416 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1036 @ SV506 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ SV1416 @ SV1416 ) @ SV1717 @ ( tc_prod @ SV1416 @ SV1416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5417,plain,
! [SV2114: $i,SV2048: $i,SV1933: $i,SV1718: $i,SV1417: $i,SV1037: $i,SV507: $i] :
( ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
= $true )
| ( ( ! [SY5560: $i] :
( ~ ( c_in @ ( c_Pair @ SY5560 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SY5560 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(5418,plain,
! [SV508: $i,SV1719: $i,SV1418: $i,SV1038: $i,SV2049: $i] :
( ( ( c_in @ ( c_Pair @ SV2049 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV508 @ SV2049 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5229]) ).
thf(5419,plain,
! [SV509: $i,SV1720: $i,SV1419: $i,SV1039: $i,SV2050: $i] :
( ( ( c_in @ ( c_Pair @ SV2050 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV509 @ SV2050 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5230]) ).
thf(5420,plain,
! [SV1721: $i,SV1420: $i,SV512: $i,SV2115: $i,SV2051: $i,SV1042: $i] :
( ( ( ~ ( c_in @ SV1042 @ SV2051 @ SV2115 ) )
= $true )
| ( ( ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SV2051 @ SV1420 @ SV2115 @ SV1721 ) @ ( tc_fun @ SV2115 @ SV1721 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5421,plain,
! [SV1421: $i,SV1043: $i,SV2140: $i,SV2116: $i,SV513: $i,SV1722: $i] :
( ( ( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SV2116 @ SV513 ) @ SV2140 )
| ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SV2116 @ SV1421 @ SV2140 ) @ ( tc_fun @ SV1421 @ SV2140 ) ) )
= $true )
| ( ( c_in @ SV513 @ SV1043 @ SV1421 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5232]) ).
thf(5422,plain,
! [SV1422: $i,SV1723: $i,SV1044: $i,SV514: $i] :
( ( ( SV514 = SV1044 )
= $true )
| ( ( SV514 = SV1723 )
= $true )
| ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1422 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV514 @ SV1044 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1422 @ SV1723 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(5423,plain,
! [SV1423: $i,SV515: $i,SV1724: $i,SV1045: $i] :
( ( ( SV1045 = SV1724 )
= $true )
| ( ( SV515 = SV1724 )
= $true )
| ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1423 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV515 @ SV1045 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1423 @ SV1724 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5424,plain,
! [SV1427: $i,SV1725: $i,SV1052: $i,SV522: $i] :
( ( ( SV522 = SV1052 )
= $true )
| ( ( SV1052 = SV1725 )
= $true )
| ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1427 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV522 @ SV1052 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1427 @ SV1725 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5236]) ).
thf(5425,plain,
! [SV1428: $i,SV1053: $i,SV1726: $i,SV523: $i] :
( ( ( SV523 = SV1726 )
= $true )
| ( ( SV1053 = SV1726 )
= $true )
| ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1428 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV523 @ SV1053 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1428 @ SV1726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5426,plain,
! [SV1430: $i,SV1938: $i,SV527: $i,SV1057: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5239]) ).
thf(5427,plain,
! [SV1939: $i,SV1431: $i,SV1058: $i,SV528: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5240]) ).
thf(5428,plain,
! [SV1432: $i,SV1940: $i,SV529: $i,SV1059: $i] :
( ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5241]) ).
thf(5429,plain,
! [SV1941: $i,SV1433: $i,SV1060: $i,SV530: $i] :
( ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5242]) ).
thf(5430,plain,
! [SV1727: $i,SV2052: $i,SV1434: $i,SV1061: $i,SV531: $i] :
( ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5431,plain,
! [SV1728: $i,SV2053: $i,SV1435: $i,SV1062: $i,SV532: $i] :
( ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5432,plain,
! [SV1729: $i,SV2054: $i,SV1436: $i,SV1063: $i,SV533: $i] :
( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5245]) ).
thf(5433,plain,
! [SV1730: $i,SV2055: $i,SV1437: $i,SV1064: $i,SV534: $i] :
( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5246]) ).
thf(5434,plain,
! [SV1065: $i,SV535: $i,SV1438: $i,SV1731: $i] :
( ( ( ~ ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_Ounanimity @ SV1438 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(5435,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2117: $i,SV2056: $i,SV1732: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5248]) ).
thf(5436,plain,
! [SV1440: $i,SV1067: $i,SV537: $i,SV2118: $i,SV2057: $i,SV1733: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5437,plain,
! [SV1068: $i,SV538: $i,SV1441: $i,SV2119: $i,SV2058: $i,SV1734: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5438,plain,
! [SV1442: $i,SV1069: $i,SV539: $i,SV2120: $i,SV2059: $i,SV1735: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5251]) ).
thf(5439,plain,
! [SV1443: $i,SV1070: $i,SV540: $i,SV2121: $i,SV2060: $i,SV1736: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5252]) ).
thf(5440,plain,
! [SV1444: $i,SV1071: $i,SV541: $i,SV2122: $i,SV2061: $i,SV1737: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5253]) ).
thf(5441,plain,
! [SV1446: $i,SV1942: $i,SV1738: $i,SV543: $i,SV2062: $i,SV1073: $i] :
( ( ( ~ ( c_in @ SV1073 @ ( hAPP @ SV2062 @ SV543 ) @ SV1738 ) )
= $true )
| ( ( ~ ( c_in @ SV543 @ SV1942 @ SV1446 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SV2062 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5442,plain,
! [SV1447: $i,SV1943: $i,SV1739: $i,SV544: $i,SV2063: $i,SV1074: $i] :
( ( ( ~ ( c_in @ SV1074 @ ( hAPP @ SV2063 @ SV544 ) @ SV1739 ) )
= $true )
| ( ( ~ ( c_in @ SV544 @ SV1943 @ SV1447 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SV2063 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5256]) ).
thf(5443,plain,
! [SV545: $i,SV1448: $i,SV1075: $i,SV1944: $i] :
( ( ( c_in @ SV1944 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $false )
| ( ( c_in @ ( c_Pair @ SV545 @ SV1944 @ SV1448 @ SV1448 ) @ SV1075 @ ( tc_prod @ SV1448 @ SV1448 ) )
= $false )
| ( ( c_in @ SV545 @ ( c_Wellfounded_Oacc @ SV1075 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5444,plain,
! [SV546: $i,SV1449: $i,SV1076: $i,SV1945: $i] :
( ( ( c_in @ SV1945 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $false )
| ( ( c_in @ ( c_Pair @ SV546 @ SV1945 @ SV1449 @ SV1449 ) @ SV1076 @ ( tc_prod @ SV1449 @ SV1449 ) )
= $false )
| ( ( c_in @ SV546 @ ( c_Wellfounded_Oacc @ SV1076 @ SV1449 ) @ SV1449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5445,plain,
! [SV1450: $i,SV1077: $i,SV1946: $i,SV1740: $i,SV547: $i,SV2123: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2123 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2123 @ SV1450 @ SV1740 ) )
= $true )
| ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5259]) ).
thf(5446,plain,
! [SV1451: $i,SV1078: $i,SV1947: $i,SV1741: $i,SV548: $i,SV2124: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2124 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2124 @ SV1451 @ SV1741 ) )
= $true )
| ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5260]) ).
thf(5447,plain,
! [SV1081: $i,SV2064: $i,SV1454: $i,SV551: $i,SV1949: $i] :
( ( ( c_in @ ( c_Pair @ SV1949 @ SV551 @ SV1454 @ SV1454 ) @ SV2064 @ ( tc_prod @ SV1454 @ SV1454 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1081 @ SV2064 @ SV1454 ) )
= $true )
| ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5261]) ).
thf(5448,plain,
! [SV1082: $i,SV2065: $i,SV1455: $i,SV1950: $i,SV552: $i] :
( ( ( c_in @ ( c_Pair @ SV552 @ SV1950 @ SV1455 @ SV1455 ) @ SV2065 @ ( tc_prod @ SV1455 @ SV1455 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1082 @ SV2065 @ SV1455 ) )
= $true )
| ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5449,plain,
! [SV1087: $i,SV2125: $i,SV1746: $i,SV2070: $i,SV557: $i,SV1460: $i] :
( ( ( c_in @ ( c_Pair @ SV1460 @ SV557 @ SV2070 @ SV1746 ) @ ( c_Product__Type_OSigma @ SV2125 @ SV1087 @ SV2070 @ SV1746 ) @ ( tc_prod @ SV2070 @ SV1746 ) )
= $false )
| ( ( c_in @ SV557 @ ( hAPP @ SV1087 @ SV1460 ) @ SV1746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5267]) ).
thf(5450,plain,
! [SV2126: $i,SV1088: $i,SV2071: $i,SV1461: $i,SV1747: $i,SV558: $i] :
( ( ( c_in @ ( c_Pair @ SV558 @ SV1747 @ SV1461 @ SV2071 ) @ ( c_Product__Type_OSigma @ SV1088 @ SV2126 @ SV1461 @ SV2071 ) @ ( tc_prod @ SV1461 @ SV2071 ) )
= $false )
| ( ( c_in @ SV558 @ SV1088 @ SV1461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5451,plain,
! [SV1748: $i,SV1089: $i,SV1462: $i,SV2141: $i,SV559: $i] :
( ( ( ~ ( c_in @ SV559 @ SV2141 @ SV1462 )
| ~ ( c_in @ SV1089 @ SV2141 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 ) )
= $true )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5269]) ).
thf(5452,plain,
! [SV560: $i,SV1090: $i,SV1463: $i,SV1951: $i] :
( ( ( c_Relation_Orefl__on @ SV1951 @ SV1463 @ SV1090 )
= $false )
| ( ( c_in @ SV560 @ SV1951 @ SV1090 )
= $false )
| ( ( c_in @ ( c_Pair @ SV560 @ SV560 @ SV1090 @ SV1090 ) @ SV1463 @ ( tc_prod @ SV1090 @ SV1090 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5270]) ).
thf(5453,plain,
! [SV1091: $i,SV2072: $i,SV1464: $i,SV561: $i,SV1952: $i] :
( ( ( c_in @ ( c_Pair @ SV1952 @ SV561 @ SV1464 @ SV1464 ) @ SV2072 @ ( tc_prod @ SV1464 @ SV1464 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1091 @ SV2072 @ SV1464 ) )
= $true )
| ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5454,plain,
! [SV1092: $i,SV2073: $i,SV1465: $i,SV1953: $i,SV562: $i] :
( ( ( c_in @ ( c_Pair @ SV562 @ SV1953 @ SV1465 @ SV1465 ) @ SV2073 @ ( tc_prod @ SV1465 @ SV1465 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1092 @ SV2073 @ SV1465 ) )
= $true )
| ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5455,plain,
! [SV563: $i,SV1093: $i,SV1466: $i,SV1954: $i] :
( ( ( c_Relation_Orefl__on @ SV1954 @ SV1466 @ SV1093 )
= $false )
| ( ( c_in @ SV563 @ SV1954 @ SV1093 )
= $false )
| ( ( c_in @ ( c_Pair @ SV563 @ SV563 @ SV1093 @ SV1093 ) @ SV1466 @ ( tc_prod @ SV1093 @ SV1093 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5456,plain,
! [SV2142: $i,SV2127: $i,SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ! [SY5571: $i] :
( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
| ! [SY5572: $i,SY5573: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SY5571 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5572 @ SV2142 @ SY5573 ) @ SV2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5274]) ).
thf(5457,plain,
! [SV2128: $i,SV2075: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ( ! [SY5566: $i] :
( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
!= ( c_Fun_Ocomp @ SV2075 @ SV2128 @ SY5566 @ SV1754 @ SV1956 ) ) )
= $true )
| ( ( ! [SY5567: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY5567 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SV2128 @ SY5567 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5275]) ).
thf(5458,plain,
! [SV2076: $i,SV1957: $i,SV1755: $i,SV1473: $i,SV1100: $i,SV570: $i] :
( ( ( ( c_Pair @ SV570 @ SV1100 @ SV1473 @ SV1755 )
= ( c_Pair @ SV1957 @ SV2076 @ SV1473 @ SV1755 ) )
= $false )
| ( ( SV1100 = SV2076 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5459,plain,
! [SV2129: $i,SV1958: $i,SV1756: $i,SV1474: $i,SV1101: $i,SV571: $i] :
( ( ( ( c_Pair @ SV571 @ SV1101 @ SV1474 @ SV1756 )
= ( c_Pair @ SV1958 @ SV2129 @ SV1474 @ SV1756 ) )
= $false )
| ( ( SV571 = SV1958 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5277]) ).
thf(5460,plain,
! [SV1129: $i,SV1965: $i,SV13: $i,SV1770: $i,SV1489: $i,SV2081: $i,SV603: $i] :
( ( ( ~ ( c_lessequals @ SV603 @ SV2081 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SV2081 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5284]) ).
thf(5461,plain,
! [SV614: $i,SV1135: $i,SV25: $i,SV1968: $i,SV1495: $i,SV2143: $i] :
( ( ( ~ ( c_in @ SV2143 @ SV1495 @ SV1968 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SV1968 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5285]) ).
thf(5462,plain,
! [SV1496: $i,SV1774: $i,SV26: $i,SV1136: $i,SV615: $i,SV2144: $i] :
( ( ( ~ ( c_in @ SV2144 @ SV615 @ SV1136 ) )
= $true )
| ( ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5286]) ).
thf(5463,plain,
! [SV1154: $i,SV1969: $i,SV52: $i,SV1511: $i,SV1778: $i,SV2082: $i,SV2145: $i,SV638: $i] :
( ( ( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SV2145 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2145 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5288]) ).
thf(5464,plain,
! [SV639: $i,SV1155: $i,SV53: $i] :
( ( ( c_Wellfounded_Owf @ SV53 @ SV1155 )
= $false )
| ( ( c_Wellfounded_Owf @ SV639 @ SV1155 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV53 @ SV639 @ SV1155 @ SV1155 @ SV1155 ) @ SV53 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV53 @ SV639 @ ( tc_fun @ ( tc_prod @ SV1155 @ SV1155 ) @ tc_bool ) ) @ SV1155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5465,plain,
! [SV1158: $i,SV643: $i,SV57: $i] :
( ( ( c_Wellfounded_Owf @ SV57 @ SV643 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV1158 @ ( tc_fun @ ( tc_prod @ SV643 @ SV643 ) @ tc_bool ) ) @ SV643 )
= $true )
| ( ( c_Wellfounded_Owf @ SV1158 @ SV643 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV57 @ SV643 @ SV643 ) @ ( c_Relation_ORange @ SV1158 @ SV643 @ SV643 ) @ ( tc_fun @ SV643 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV643 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5290]) ).
thf(5466,plain,
! [SV1780: $i,SV645: $i,SV1516: $i,SV1160: $i,SV59: $i] :
( ( ( c_Relation_Osingle__valued @ SV59 @ SV1160 @ SV1516 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV645 @ SV1516 @ SV1780 )
= $false )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV59 @ SV645 @ SV1160 @ SV1516 @ SV1780 ) @ SV1160 @ SV1780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(5467,plain,
! [SV1781: $i,SV646: $i,SV1161: $i,SV1517: $i,SV60: $i] :
( ( ( c_Relation_Orefl__on @ SV60 @ SV1517 @ SV1161 )
= $false )
| ( ( c_Relation_Orefl__on @ SV646 @ SV1781 @ SV1161 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV646 @ ( tc_fun @ SV1161 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1517 @ SV1781 @ ( tc_fun @ ( tc_prod @ SV1161 @ SV1161 ) @ tc_bool ) ) @ SV1161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5468,plain,
! [SV74: $i,SV1165: $i,SV658: $i,SV1976: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1976 @ SV658 @ ( tc_fun @ SV1165 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV74 @ SV1976 @ SV1165 )
= $false )
| ( ( c_in @ SV74 @ SV658 @ SV1165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5293]) ).
thf(5469,plain,
! [SV82: $i,SV1790: $i,SV1528: $i] :
( ( ( c_lessequals @ SV1528 @ SV1790 @ SV82 )
= $false )
| ( ( c_lessequals @ SV1790 @ SV1528 @ SV82 )
= $false )
| ( ( SV1528 = SV1790 )
= $true )
| ( ( class_Orderings_Oorder @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5297]) ).
thf(5470,plain,
! [SV83: $i,SV1791: $i,SV1529: $i] :
( ( ( c_lessequals @ SV1529 @ SV1791 @ SV83 )
= $false )
| ( ( c_lessequals @ SV1791 @ SV1529 @ SV83 )
= $false )
| ( ( SV1529 = SV1791 )
= $true )
| ( ( class_Orderings_Oorder @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5471,plain,
! [SV84: $i,SV1530: $i,SV1792: $i] :
( ( ( c_lessequals @ SV1792 @ SV1530 @ SV84 )
= $false )
| ( ( c_lessequals @ SV1530 @ SV1792 @ SV84 )
= $false )
| ( ( SV1530 = SV1792 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5472,plain,
! [SV1797: $i,SV668: $i,SV1171: $i,SV1535: $i,SV92: $i] :
( ( ( c_Relation_Orefl__on @ SV92 @ SV1535 @ SV1171 )
= $false )
| ( ( c_Relation_Orefl__on @ SV668 @ SV1797 @ SV1171 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV92 @ SV668 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1535 @ SV1797 @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1171 ) @ tc_bool ) ) @ SV1171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5300]) ).
thf(5473,plain,
! [SV679: $i,SV106: $i,SV1984: $i,SV1805: $i] :
( ( ( c_lessequals @ SV1805 @ SV1984 @ SV106 )
= $false )
| ( ( ~ ( c_lessequals @ SV679 @ SV1984 @ SV106 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SV1984 @ SV106 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5474,plain,
! [SV680: $i,SV109: $i,SV1985: $i,SV1808: $i] :
( ( ( c_lessequals @ SV1808 @ SV1985 @ SV109 )
= $false )
| ( ( ~ ( c_lessequals @ SV680 @ SV1985 @ SV109 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SV1985 @ SV109 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5304]) ).
thf(5475,plain,
! [SV681: $i,SV110: $i,SV1986: $i,SV1809: $i] :
( ( ( c_lessequals @ SV1809 @ SV1986 @ SV110 )
= $false )
| ( ( ~ ( c_lessequals @ SV681 @ SV1986 @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SV1986 @ SV110 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5476,plain,
! [SV1210: $i,SV169: $i,SV2131: $i,SV1994: $i,SV727: $i] :
( ( ( c_lessequals @ SV727 @ SV1994 @ ( tc_fun @ SV2131 @ SV169 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV727 @ SV1210 ) @ ( hAPP @ SV1994 @ SV1210 ) @ SV169 )
= $true )
| ( ( class_HOL_Oord @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5477,plain,
! [SV1224: $i,SV191: $i,SV749: $i,SV2132: $i,SV1576: $i] :
( ( ( ~ ( c_in @ SV1576 @ SV2132 @ SV749 ) )
= $true )
| ( ( ~ ( c_in @ SV191 @ SV2132 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5321]) ).
thf(5478,plain,
! [SV1850: $i,SV762: $i,SV1234: $i,SV1583: $i,SV207: $i] :
( ( ( c_lessequals @ SV207 @ SV1583 @ ( tc_fun @ SV1234 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV762 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV207 @ SV762 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1583 @ SV1850 @ ( tc_fun @ SV1234 @ tc_bool ) ) @ ( tc_fun @ SV1234 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5326]) ).
thf(5479,plain,
! [SV1853: $i,SV210: $i,SV1996: $i,SV763: $i] :
( ( ( c_lessequals @ SV763 @ SV1996 @ SV210 )
= $false )
| ( ( ~ ( c_lessequals @ SV763 @ SV1853 @ SV210 ) )
= $true )
| ( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SV1996 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5327]) ).
thf(5480,plain,
! [SV1854: $i,SV211: $i,SV1997: $i,SV764: $i] :
( ( ( c_lessequals @ SV764 @ SV1997 @ SV211 )
= $false )
| ( ( ~ ( c_lessequals @ SV764 @ SV1854 @ SV211 ) )
= $true )
| ( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV1997 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5328]) ).
thf(5481,plain,
! [SV1855: $i,SV212: $i,SV1998: $i,SV765: $i] :
( ( ( c_lessequals @ SV765 @ SV1998 @ SV212 )
= $false )
| ( ( ~ ( c_lessequals @ SV765 @ SV1855 @ SV212 ) )
= $true )
| ( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SV1998 @ SV212 ) @ SV212 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5329]) ).
thf(5482,plain,
! [SV1872: $i,SV244: $i,SV2092: $i,SV792: $i] :
( ( ( c_lessequals @ SV792 @ SV2092 @ SV244 )
= $false )
| ( ( ~ ( c_lessequals @ SV2092 @ SV1872 @ SV244 ) )
= $true )
| ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5483,plain,
! [SV793: $i,SV245: $i,SV1873: $i,SV2093: $i] :
( ( ( c_lessequals @ SV2093 @ SV1873 @ SV245 )
= $false )
| ( ( ~ ( c_lessequals @ SV793 @ SV2093 @ SV245 ) )
= $true )
| ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5340]) ).
thf(5484,plain,
! [SV1876: $i,SV803: $i,SV1253: $i,SV1606: $i,SV257: $i] :
( ( ( c_lessequals @ SV257 @ SV1606 @ ( tc_fun @ SV1253 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV803 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV803 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1606 @ SV1876 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5345]) ).
thf(5485,plain,
! [SV1610: $i,SV1877: $i,SV268: $i,SV1260: $i,SV2003: $i,SV812: $i] :
( ( ( c_lessequals @ SV812 @ SV2003 @ ( tc_fun @ SV1260 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SV2003 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5486,plain,
! [SV1879: $i,SV2004: $i,SV814: $i,SV1262: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SV2004 @ SV2004 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SV2004 ) @ ( tc_prod @ SV2004 @ SV2004 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ SV2004 @ SV2004 ) @ SV1879 @ ( tc_prod @ SV2004 @ SV2004 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5487,plain,
! [SV1880: $i,SV2005: $i,SV815: $i,SV1263: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SV2005 @ SV2005 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SV2005 ) @ ( tc_prod @ SV2005 @ SV2005 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ SV2005 @ SV2005 ) @ SV1880 @ ( tc_prod @ SV2005 @ SV2005 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5488,plain,
! [SV274: $i,SV2095: $i,SV2006: $i,SV1612: $i,SV817: $i,SV1265: $i] :
( ( ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
| ~ ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 ) )
= $true )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5489,plain,
! [SV1613: $i,SV1881: $i,SV275: $i,SV1266: $i,SV818: $i,SV2146: $i] :
( ( ( ~ ( c_in @ SV2146 @ SV818 @ SV1266 ) )
= $true )
| ( ( SV275 = SV1881 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5351]) ).
thf(5490,plain,
! [SV1273: $i,SV292: $i,SV834: $i,SV2096: $i,SV1616: $i] :
( ( ( c_in @ SV1616 @ SV2096 @ SV834 )
= $false )
| ( ( ~ ( c_in @ SV292 @ SV2096 @ SV834 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) )
= $true )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5491,plain,
! [SV1883: $i,SV293: $i,SV1274: $i,SV835: $i,SV2097: $i] :
( ( ( c_lessequals @ SV2097 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SV2097 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) ) )
= $true )
| ( ( SV293 = SV1883 )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5492,plain,
! [SV1617: $i,SV836: $i,SV1275: $i,SV294: $i,SV2133: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2133 @ SV294 @ SV1275 )
= $false )
| ( ( c_in @ ( c_Pair @ SV836 @ SV1617 @ SV1275 @ SV1275 ) @ SV294 @ ( tc_prod @ SV1275 @ SV1275 ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV836 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( c_Relation_OImage @ SV294 @ ( c_Set_Oinsert @ SV1617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1275 @ tc_bool ) ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5493,plain,
! [SV1618: $i,SV1276: $i,SV296: $i,SV838: $i] :
( ( ( ~ ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5356]) ).
thf(5494,plain,
! [SV1886: $i,SV2007: $i,SV843: $i,SV1282: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SV2007 @ SV2007 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV2007 ) @ ( tc_prod @ SV2007 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5357]) ).
thf(5495,plain,
! [SV1887: $i,SV2008: $i,SV844: $i,SV1283: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SV2008 ) @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5496,plain,
! [SV1888: $i,SV2009: $i,SV845: $i,SV1284: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SV2009 ) @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5497,plain,
! [SV1889: $i,SV2010: $i,SV846: $i,SV1285: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5360]) ).
thf(5498,plain,
! [SV847: $i,SV1623: $i,SV1286: $i,SV307: $i,SV2098: $i] :
( ( ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
| ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5499,plain,
! [SV1890: $i,SV2011: $i,SV849: $i,SV1288: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SV2011 @ SV2011 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV2011 ) @ ( tc_prod @ SV2011 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5500,plain,
! [SV1891: $i,SV2012: $i,SV851: $i,SV1290: $i,SV311: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5363]) ).
thf(5501,plain,
! [SV853: $i,SV2099: $i,SV2013: $i,SV313: $i,SV1292: $i] :
( ( ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SV2013 @ SV2099 ) @ SV2099 @ SV2099 ) @ SV2013 @ ( tc_prod @ SV2099 @ SV2099 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2013 @ SV2099 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5502,plain,
! [SV854: $i,SV2100: $i,SV2014: $i,SV314: $i,SV1293: $i] :
( ( ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SV2014 @ SV2100 ) @ SV2100 @ SV2100 ) @ SV2014 @ ( tc_prod @ SV2100 @ SV2100 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2014 @ SV2100 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5365]) ).
thf(5503,plain,
! [SV855: $i,SV2101: $i,SV2015: $i,SV315: $i,SV1294: $i] :
( ( ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SV2015 @ SV2101 ) @ SV2101 @ SV2101 ) @ SV2015 @ ( tc_prod @ SV2101 @ SV2101 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2015 @ SV2101 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5504,plain,
! [SV856: $i,SV2102: $i,SV2016: $i,SV316: $i,SV1295: $i] :
( ( ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SV2016 @ SV2102 ) @ SV2102 @ SV2102 ) @ SV2016 @ ( tc_prod @ SV2102 @ SV2102 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2016 @ SV2102 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5505,plain,
! [SV2017: $i,SV325: $i,SV1304: $i,SV865: $i,SV1629: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 ) )
= $true )
| ( ( c_in @ SV865 @ SV2017 @ SV1304 )
= $false )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5506,plain,
! [SV866: $i,SV326: $i,SV2103: $i,SV1305: $i,SV1630: $i,SV2147: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2147 @ SV1630 @ SV1305 ) )
= $true )
| ( ( c_in @ SV2103 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
= $false )
| ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5369]) ).
thf(5507,plain,
! [SV2104: $i,SV1631: $i,SV1306: $i,SV2018: $i,SV1892: $i,SV867: $i,SV327: $i] :
( ( ( c_in @ ( c_Pair @ SV327 @ SV867 @ SV1892 @ SV2018 ) @ ( c_Relation_Orel__comp @ SV1306 @ SV1631 @ SV1892 @ SV2104 @ SV2018 ) @ ( tc_prod @ SV1892 @ SV2018 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV327 @ SV867 @ SV1306 @ SV1631 @ SV1892 @ SV2018 @ SV2104 ) @ SV867 @ SV2104 @ SV2018 ) @ SV1631 @ ( tc_prod @ SV2104 @ SV2018 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5370]) ).
thf(5508,plain,
! [SV2105: $i,SV1632: $i,SV1307: $i,SV2019: $i,SV1893: $i,SV868: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ SV868 @ SV1893 @ SV2019 ) @ ( c_Relation_Orel__comp @ SV1307 @ SV1632 @ SV1893 @ SV2105 @ SV2019 ) @ ( tc_prod @ SV1893 @ SV2019 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV868 @ SV1307 @ SV1632 @ SV1893 @ SV2019 @ SV2105 ) @ SV1893 @ SV2105 ) @ SV1307 @ ( tc_prod @ SV1893 @ SV2105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5371]) ).
thf(5509,plain,
! [SV1636: $i,SV1311: $i,SV332: $i,SV2106: $i,SV2020: $i,SV872: $i] :
( ( ( c_in @ SV872 @ SV2020 @ SV2106 )
= $false )
| ( ( ~ ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV2020 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SV2106 ) @ SV2106 @ SV1636 ) @ ( tc_fun @ SV2106 @ SV1636 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5510,plain,
! [SV1644: $i,SV890: $i,SV1323: $i,SV354: $i,SV2134: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2134 @ SV354 @ SV1323 )
= $false )
| ( ( c_in @ ( c_Pair @ SV890 @ SV1644 @ SV1323 @ SV1323 ) @ SV354 @ ( tc_prod @ SV1323 @ SV1323 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV890 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 )
= ( c_Relation_OImage @ SV354 @ ( c_Set_Oinsert @ SV1644 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ SV1323 @ SV1323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5511,plain,
! [SV1645: $i,SV891: $i,SV1324: $i,SV355: $i,SV2135: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2135 @ SV355 @ SV1324 )
= $false )
| ( ( c_in @ ( c_Pair @ SV891 @ SV1645 @ SV1324 @ SV1324 ) @ SV355 @ ( tc_prod @ SV1324 @ SV1324 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV891 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 )
= ( c_Relation_OImage @ SV355 @ ( c_Set_Oinsert @ SV1645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1324 ) @ SV1324 @ SV1324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5512,plain,
! [SV892: $i,SV356: $i,SV1325: $i,SV2136: $i,SV1646: $i] :
( ( ( ~ ( c_in @ SV1646 @ SV2136 @ SV1325 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2136 @ SV356 @ SV1325 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5376]) ).
thf(5513,plain,
! [SV1647: $i,SV893: $i,SV1326: $i,SV357: $i,SV2107: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
| ~ ( c_in @ SV1647 @ SV2107 @ SV1326 )
| ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5514,plain,
! [SV358: $i,SV894: $i,SV1327: $i,SV2137: $i,SV1648: $i] :
( ( ( ~ ( c_in @ SV1648 @ SV2137 @ SV1327 ) )
= $true )
| ( ( ~ ( c_in @ SV894 @ SV2137 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5378]) ).
thf(5515,plain,
! [SV359: $i,SV895: $i,SV1328: $i,SV2108: $i,SV1649: $i] :
( ( ( c_in @ SV1649 @ SV2108 @ SV1328 )
= $false )
| ( ( ~ ( c_in @ SV895 @ SV2108 @ SV1328 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5379]) ).
thf(5516,plain,
! [SV2138: $i,SV2109: $i,SV2024: $i,SV1909: $i,SV1661: $i,SV1337: $i,SV911: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
| ! [SY5568: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SY5568 @ ( tc_prod @ SV2138 @ SV2138 ) )
| ! [SY5569: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5568 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5569 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5384]) ).
thf(5517,plain,
! [SV1913: $i,SV1670: $i,SV928: $i,SV392: $i,SV2139: $i,SV2026: $i,SV1352: $i] :
( ( ( ~ ( c_in @ SV1352 @ SV2026 @ SV2139 ) )
= $true )
| ( ( ! [SY5570: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5570 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SY5570 @ SV2139 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5386]) ).
thf(5518,plain,
! [SV398: $i,SV2027: $i,SV1353: $i,SV931: $i] :
( ( ( ! [SY4959: $i] :
~ ( c_in @ SY4959 @ SV931 @ SV1353 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
= $false )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5387]) ).
thf(5519,plain,
! [SV399: $i,SV2028: $i,SV1354: $i,SV932: $i] :
( ( ( ! [SY4961: $i] :
~ ( c_in @ SY4961 @ SV932 @ SV1354 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
= $false )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5388]) ).
thf(5520,plain,
! [SV404: $i,SV1675: $i,SV1916: $i,SV937: $i] :
( ( ( c_in @ SV937 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1675 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV404 @ SV1916 ) @ t_a @ t_a ) @ SV1916 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1675 @ ( c_Wellfounded_Oacc @ SV1916 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV404 @ SV937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5521,plain,
! [SV405: $i,SV1676: $i,SV1917: $i,SV938: $i] :
( ( ( c_in @ SV938 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1676 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV405 @ SV1917 ) @ t_a @ t_a ) @ SV1917 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1676 @ ( c_Wellfounded_Oacc @ SV1917 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV938 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5522,plain,
! [SV940: $i,SV2110: $i,SV2029: $i,SV407: $i,SV1360: $i] :
( ( ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SV2029 @ SV2110 ) @ SV2110 @ SV2110 ) @ SV2029 @ ( tc_prod @ SV2110 @ SV2110 ) )
= $false )
| ( ( ~ ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SV2029 @ SV2110 ) @ SV2110 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5523,plain,
! [SV408: $i,SV1677: $i,SV2030: $i,SV941: $i] :
( ( ( c_in @ SV941 @ ( c_Wellfounded_Oacc @ SV2030 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1677 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV408 @ SV2030 ) @ t_a @ t_a ) @ SV2030 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV1677 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ SV941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5524,plain,
! [SV409: $i,SV1678: $i,SV2031: $i,SV942: $i] :
( ( ( c_in @ SV942 @ ( c_Wellfounded_Oacc @ SV2031 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1678 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV409 @ SV2031 ) @ t_a @ t_a ) @ SV2031 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV1678 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV409 @ SV942 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5525,plain,
! [SV943: $i,SV2111: $i,SV2032: $i,SV410: $i,SV1361: $i] :
( ( ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SV2032 @ SV2111 ) @ SV2111 @ SV2111 ) @ SV2032 @ ( tc_prod @ SV2111 @ SV2111 ) )
= $false )
| ( ( ~ ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SV2032 @ SV2111 ) @ SV2111 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5526,plain,
! [SV951: $i,SV1685: $i,SV1369: $i,SV2033: $i,SV418: $i] :
( ( ( c_in @ ( c_Pair @ SV418 @ SV2033 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2033 @ SV951 @ SV1369 @ SV1369 ) @ SV1685 @ ( tc_prod @ SV1369 @ SV1369 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV418 @ SV951 @ SV1369 @ SV1369 ) @ ( c_Transitive__Closure_Ortrancl @ SV1685 @ SV1369 ) @ ( tc_prod @ SV1369 @ SV1369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5527,plain,
! [SV952: $i,SV1686: $i,SV1370: $i,SV2034: $i,SV419: $i] :
( ( ( c_in @ ( c_Pair @ SV419 @ SV2034 @ SV1370 @ SV1370 ) @ SV1686 @ ( tc_prod @ SV1370 @ SV1370 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2034 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV419 @ SV952 @ SV1370 @ SV1370 ) @ ( c_Transitive__Closure_Otrancl @ SV1686 @ SV1370 ) @ ( tc_prod @ SV1370 @ SV1370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5528,plain,
! [SV953: $i,SV1687: $i,SV1371: $i,SV2035: $i,SV420: $i] :
( ( ( c_in @ ( c_Pair @ SV420 @ SV2035 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2035 @ SV953 @ SV1371 @ SV1371 ) @ SV1687 @ ( tc_prod @ SV1371 @ SV1371 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV420 @ SV953 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Otrancl @ SV1687 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5529,plain,
! [SV977: $i,SV1693: $i,SV1385: $i,SV2038: $i,SV445: $i] :
( ( ( c_in @ ( c_Pair @ SV445 @ SV2038 @ SV1385 @ SV1385 ) @ SV1693 @ ( tc_prod @ SV1385 @ SV1385 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2038 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1693 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5402]) ).
thf(5530,plain,
! [SV978: $i,SV1694: $i,SV1386: $i,SV2039: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV2039 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2039 @ SV978 @ SV1386 @ SV1386 ) @ SV1694 @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1694 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(5531,plain,
! [SV983: $i,SV1699: $i,SV1391: $i,SV2040: $i,SV451: $i] :
( ( ( c_in @ ( c_Pair @ SV451 @ SV2040 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2040 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Ortrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV451 @ SV983 @ SV1391 @ SV1391 ) @ ( c_Transitive__Closure_Otrancl @ SV1699 @ SV1391 ) @ ( tc_prod @ SV1391 @ SV1391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5404]) ).
thf(5532,plain,
! [SV984: $i,SV1700: $i,SV1392: $i,SV2041: $i,SV452: $i] :
( ( ( c_in @ ( c_Pair @ SV452 @ SV2041 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2041 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV452 @ SV984 @ SV1392 @ SV1392 ) @ ( c_Transitive__Closure_Otrancl @ SV1700 @ SV1392 ) @ ( tc_prod @ SV1392 @ SV1392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5405]) ).
thf(5533,plain,
! [SV1019: $i,SV1704: $i,SV1403: $i,SV2043: $i,SV489: $i] :
( ( ( c_in @ ( c_Pair @ SV489 @ SV2043 @ SV1403 @ SV1403 ) @ SV1704 @ ( tc_prod @ SV1403 @ SV1403 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2043 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ SV1403 @ SV1403 ) @ ( c_Transitive__Closure_Ortrancl @ SV1704 @ SV1403 ) @ ( tc_prod @ SV1403 @ SV1403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5534,plain,
! [SV1021: $i,SV1706: $i,SV1405: $i,SV2044: $i,SV491: $i] :
( ( ( c_in @ ( c_Pair @ SV491 @ SV2044 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2044 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV491 @ SV1021 @ SV1405 @ SV1405 ) @ ( c_Transitive__Closure_Ortrancl @ SV1706 @ SV1405 ) @ ( tc_prod @ SV1405 @ SV1405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5535,plain,
! [SV494: $i,SV1024: $i,SV1408: $i,SV1707: $i] :
( ( ( c_Wellfounded_Owf @ SV1707 @ SV1408 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1024 @ SV494 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ SV1408 @ SV1408 ) @ SV1707 @ ( tc_prod @ SV1408 @ SV1408 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5536,plain,
! [SV1927: $i,SV1708: $i,SV1025: $i,SV495: $i] :
( ( ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV1927 @ SV1708 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5537,plain,
! [SV1928: $i,SV1709: $i,SV1026: $i,SV496: $i] :
( ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV1928 @ SV1709 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5410]) ).
thf(5538,plain,
! [SV1409: $i,SV1027: $i,SV2148: $i,SV1710: $i,SV497: $i,SV2045: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent @ SV2045 @ SV497 @ SV1710 @ SV2148 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SV2045 @ ( tc_prod @ SV1710 @ SV1710 ) )
= $false )
| ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5411]) ).
thf(5539,plain,
! [SV1930: $i,SV1029: $i,SV1712: $i,SV1410: $i,SV2046: $i,SV2149: $i,SV499: $i] :
( ( ( ( ( hAPP @ SV499 @ SV2149 )
= ( hAPP @ SV2046 @ SV2149 ) )
| ~ ( c_in @ ( c_Pair @ SV2149 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(5540,plain,
! [SV1933: $i,SV1417: $i,SV507: $i,SV2048: $i,SV1718: $i,SV2114: $i,SV1037: $i,SV2150: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2150 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) )
| ~ ( c_in @ ( c_Pair @ SV507 @ SV2150 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5417]) ).
thf(5541,plain,
! [SV1038: $i,SV1719: $i,SV1418: $i,SV2049: $i,SV508: $i] :
( ( ( c_in @ ( c_Pair @ SV508 @ SV2049 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2049 @ SV1038 @ SV1418 @ SV1418 ) @ SV1719 @ ( tc_prod @ SV1418 @ SV1418 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV508 @ SV1038 @ SV1418 @ SV1418 ) @ ( c_Transitive__Closure_Otrancl @ SV1719 @ SV1418 ) @ ( tc_prod @ SV1418 @ SV1418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5418]) ).
thf(5542,plain,
! [SV1039: $i,SV1720: $i,SV1419: $i,SV2050: $i,SV509: $i] :
( ( ( c_in @ ( c_Pair @ SV509 @ SV2050 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2050 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV509 @ SV1039 @ SV1419 @ SV1419 ) @ ( c_Transitive__Closure_Otrancl @ SV1720 @ SV1419 ) @ ( tc_prod @ SV1419 @ SV1419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5543,plain,
! [SV1721: $i,SV1420: $i,SV512: $i,SV2115: $i,SV2051: $i,SV1042: $i] :
( ( ( c_in @ SV1042 @ SV2051 @ SV2115 )
= $false )
| ( ( ~ ( c_in @ SV512 @ ( c_FuncSet_OPi @ SV2051 @ SV1420 @ SV2115 @ SV1721 ) @ ( tc_fun @ SV2115 @ SV1721 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(5544,plain,
! [SV1421: $i,SV1043: $i,SV2140: $i,SV2116: $i,SV513: $i,SV1722: $i] :
( ( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SV2116 @ SV513 ) @ SV2140 )
= $true )
| ( ( ~ ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SV2116 @ SV1421 @ SV2140 ) @ ( tc_fun @ SV1421 @ SV2140 ) ) )
= $true )
| ( ( c_in @ SV513 @ SV1043 @ SV1421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5421]) ).
thf(5545,plain,
! [SV1430: $i,SV1938: $i,SV527: $i,SV1057: $i] :
( ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5546,plain,
! [SV1939: $i,SV1431: $i,SV1058: $i,SV528: $i] :
( ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5547,plain,
! [SV1940: $i,SV1432: $i,SV1059: $i,SV529: $i] :
( ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5548,plain,
! [SV1433: $i,SV1941: $i,SV530: $i,SV1060: $i] :
( ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5429]) ).
thf(5549,plain,
! [SV1434: $i,SV1727: $i,SV2052: $i,SV1061: $i,SV531: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5550,plain,
! [SV1435: $i,SV2053: $i,SV1728: $i,SV1062: $i,SV532: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5551,plain,
! [SV1436: $i,SV1729: $i,SV2054: $i,SV1063: $i,SV533: $i] :
( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5432]) ).
thf(5552,plain,
! [SV1437: $i,SV2055: $i,SV1730: $i,SV1064: $i,SV534: $i] :
( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5433]) ).
thf(5553,plain,
! [SV1065: $i,SV535: $i,SV1438: $i,SV1731: $i] :
( ( ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_Ounanimity @ SV1438 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5434]) ).
thf(5554,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2117: $i,SV2056: $i,SV1732: $i] :
( ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5555,plain,
! [SV1440: $i,SV1067: $i,SV537: $i,SV2118: $i,SV2057: $i,SV1733: $i] :
( ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5556,plain,
! [SV1068: $i,SV538: $i,SV1441: $i,SV2119: $i,SV2058: $i,SV1734: $i] :
( ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5557,plain,
! [SV1442: $i,SV1069: $i,SV539: $i,SV2120: $i,SV2059: $i,SV1735: $i] :
( ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5558,plain,
! [SV1443: $i,SV1070: $i,SV540: $i,SV2121: $i,SV2060: $i,SV1736: $i] :
( ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5559,plain,
! [SV1444: $i,SV1071: $i,SV541: $i,SV2122: $i,SV2061: $i,SV1737: $i] :
( ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5440]) ).
thf(5560,plain,
! [SV1446: $i,SV1942: $i,SV1738: $i,SV543: $i,SV2062: $i,SV1073: $i] :
( ( ( c_in @ SV1073 @ ( hAPP @ SV2062 @ SV543 ) @ SV1738 )
= $false )
| ( ( ~ ( c_in @ SV543 @ SV1942 @ SV1446 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SV2062 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5561,plain,
! [SV1447: $i,SV1943: $i,SV1739: $i,SV544: $i,SV2063: $i,SV1074: $i] :
( ( ( c_in @ SV1074 @ ( hAPP @ SV2063 @ SV544 ) @ SV1739 )
= $false )
| ( ( ~ ( c_in @ SV544 @ SV1943 @ SV1447 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SV2063 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5562,plain,
! [SV1450: $i,SV1077: $i,SV1946: $i,SV1740: $i,SV547: $i,SV2123: $i] :
( ( ( c_in @ ( c_Pair @ SV2123 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) )
= $false )
| ( ( ~ ( c_in @ SV2123 @ SV1450 @ SV1740 ) )
= $true )
| ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5563,plain,
! [SV1451: $i,SV1078: $i,SV1947: $i,SV1741: $i,SV548: $i,SV2124: $i] :
( ( ( c_in @ ( c_Pair @ SV2124 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) )
= $false )
| ( ( ~ ( c_in @ SV2124 @ SV1451 @ SV1741 ) )
= $true )
| ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5564,plain,
! [SV551: $i,SV1949: $i,SV1454: $i,SV2064: $i,SV1081: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1081 @ SV2064 @ SV1454 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1949 @ SV551 @ SV1454 @ SV1454 ) @ SV2064 @ ( tc_prod @ SV1454 @ SV1454 ) )
= $false )
| ( ( c_in @ SV551 @ SV1081 @ SV1454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5565,plain,
! [SV1950: $i,SV552: $i,SV1455: $i,SV2065: $i,SV1082: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1082 @ SV2065 @ SV1455 )
= $false )
| ( ( c_in @ ( c_Pair @ SV552 @ SV1950 @ SV1455 @ SV1455 ) @ SV2065 @ ( tc_prod @ SV1455 @ SV1455 ) )
= $false )
| ( ( c_in @ SV552 @ SV1082 @ SV1455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5566,plain,
! [SV1748: $i,SV1089: $i,SV1462: $i,SV2141: $i,SV559: $i] :
( ( ( ~ ( c_in @ SV559 @ SV2141 @ SV1462 ) )
= $true )
| ( ( ~ ( c_in @ SV1089 @ SV2141 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 ) )
= $true )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5451]) ).
thf(5567,plain,
! [SV561: $i,SV1952: $i,SV1464: $i,SV2072: $i,SV1091: $i] :
( ( ( c_Relation_Orefl__on @ SV1091 @ SV2072 @ SV1464 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1952 @ SV561 @ SV1464 @ SV1464 ) @ SV2072 @ ( tc_prod @ SV1464 @ SV1464 ) )
= $false )
| ( ( c_in @ SV561 @ SV1091 @ SV1464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5568,plain,
! [SV1953: $i,SV562: $i,SV1465: $i,SV2073: $i,SV1092: $i] :
( ( ( c_Relation_Orefl__on @ SV1092 @ SV2073 @ SV1465 )
= $false )
| ( ( c_in @ ( c_Pair @ SV562 @ SV1953 @ SV1465 @ SV1465 ) @ SV2073 @ ( tc_prod @ SV1465 @ SV1465 ) )
= $false )
| ( ( c_in @ SV562 @ SV1092 @ SV1465 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5454]) ).
thf(5569,plain,
! [SV2151: $i,SV2142: $i,SV2127: $i,SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
| ! [SY5574: $i,SY5575: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SV2151 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5574 @ SV2142 @ SY5575 ) @ SV2074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5456]) ).
thf(5570,plain,
! [SV2152: $i,SV2128: $i,SV2075: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
!= ( c_Fun_Ocomp @ SV2075 @ SV2128 @ SV2152 @ SV1754 @ SV1956 ) )
= $true )
| ( ( ! [SY5567: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY5567 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SV2128 @ SY5567 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5457]) ).
thf(5571,plain,
! [SV1129: $i,SV1965: $i,SV13: $i,SV1770: $i,SV1489: $i,SV2081: $i,SV603: $i] :
( ( ( c_lessequals @ SV603 @ SV2081 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SV2081 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5572,plain,
! [SV614: $i,SV1135: $i,SV25: $i,SV1968: $i,SV1495: $i,SV2143: $i] :
( ( ( c_in @ SV2143 @ SV1495 @ SV1968 )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV25 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( c_Product__Type_OSigma @ SV614 @ ( c_COMBK @ SV1495 @ ( tc_fun @ SV1968 @ tc_bool ) @ SV1135 ) @ SV1135 @ SV1968 ) @ ( tc_fun @ ( tc_prod @ SV1135 @ SV1968 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV25 @ SV614 @ ( tc_fun @ SV1135 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5573,plain,
! [SV1496: $i,SV1774: $i,SV26: $i,SV1136: $i,SV615: $i,SV2144: $i] :
( ( ( c_in @ SV2144 @ SV615 @ SV1136 )
= $false )
| ( ( c_lessequals @ SV26 @ SV1774 @ ( tc_fun @ SV1496 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV26 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( c_Product__Type_OSigma @ SV1774 @ ( c_COMBK @ SV615 @ ( tc_fun @ SV1136 @ tc_bool ) @ SV1496 ) @ SV1496 @ SV1136 ) @ ( tc_fun @ ( tc_prod @ SV1496 @ SV1136 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5574,plain,
! [SV1154: $i,SV1969: $i,SV52: $i,SV1511: $i,SV1778: $i,SV2082: $i,SV2145: $i,SV638: $i] :
( ( ( ~ ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SV2145 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2145 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5463]) ).
thf(5575,plain,
! [SV1805: $i,SV106: $i,SV1984: $i,SV679: $i] :
( ( ( c_lessequals @ SV679 @ SV1984 @ SV106 )
= $false )
| ( ( c_lessequals @ SV1805 @ SV1984 @ SV106 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV679 @ SV1805 @ SV106 ) @ SV1984 @ SV106 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(5576,plain,
! [SV1808: $i,SV109: $i,SV1985: $i,SV680: $i] :
( ( ( c_lessequals @ SV680 @ SV1985 @ SV109 )
= $false )
| ( ( c_lessequals @ SV1808 @ SV1985 @ SV109 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1808 @ SV109 ) @ SV1985 @ SV109 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5577,plain,
! [SV1809: $i,SV110: $i,SV1986: $i,SV681: $i] :
( ( ( c_lessequals @ SV681 @ SV1986 @ SV110 )
= $false )
| ( ( c_lessequals @ SV1809 @ SV1986 @ SV110 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1809 @ SV110 ) @ SV1986 @ SV110 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5578,plain,
! [SV1224: $i,SV191: $i,SV749: $i,SV2132: $i,SV1576: $i] :
( ( ( c_in @ SV1576 @ SV2132 @ SV749 )
= $false )
| ( ( ~ ( c_in @ SV191 @ SV2132 @ SV749 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5477]) ).
thf(5579,plain,
! [SV1996: $i,SV210: $i,SV1853: $i,SV763: $i] :
( ( ( c_lessequals @ SV763 @ SV1853 @ SV210 )
= $false )
| ( ( c_lessequals @ SV763 @ SV1996 @ SV210 )
= $false )
| ( ( c_lessequals @ SV763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1853 @ SV1996 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5580,plain,
! [SV1997: $i,SV211: $i,SV1854: $i,SV764: $i] :
( ( ( c_lessequals @ SV764 @ SV1854 @ SV211 )
= $false )
| ( ( c_lessequals @ SV764 @ SV1997 @ SV211 )
= $false )
| ( ( c_lessequals @ SV764 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV1997 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5480]) ).
thf(5581,plain,
! [SV1998: $i,SV212: $i,SV1855: $i,SV765: $i] :
( ( ( c_lessequals @ SV765 @ SV1855 @ SV212 )
= $false )
| ( ( c_lessequals @ SV765 @ SV1998 @ SV212 )
= $false )
| ( ( c_lessequals @ SV765 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1855 @ SV1998 @ SV212 ) @ SV212 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5481]) ).
thf(5582,plain,
! [SV792: $i,SV244: $i,SV1872: $i,SV2092: $i] :
( ( ( c_lessequals @ SV2092 @ SV1872 @ SV244 )
= $false )
| ( ( c_lessequals @ SV792 @ SV2092 @ SV244 )
= $false )
| ( ( c_lessequals @ SV792 @ SV1872 @ SV244 )
= $true )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5583,plain,
! [SV1873: $i,SV245: $i,SV2093: $i,SV793: $i] :
( ( ( c_lessequals @ SV793 @ SV2093 @ SV245 )
= $false )
| ( ( c_lessequals @ SV2093 @ SV1873 @ SV245 )
= $false )
| ( ( c_lessequals @ SV793 @ SV1873 @ SV245 )
= $true )
| ( ( class_Orderings_Opreorder @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5584,plain,
! [SV2003: $i,SV812: $i,SV1610: $i,SV1260: $i,SV1877: $i,SV268: $i] :
( ( ( c_lessequals @ SV268 @ SV1877 @ ( tc_fun @ ( tc_prod @ SV1260 @ SV1610 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV812 @ SV2003 @ ( tc_fun @ SV1260 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV268 @ SV812 @ SV1260 @ SV1610 ) @ ( c_Relation_OImage @ SV1877 @ SV2003 @ SV1260 @ SV1610 ) @ ( tc_fun @ SV1610 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5485]) ).
thf(5585,plain,
! [SV271: $i,SV1879: $i,SV2004: $i,SV1262: $i,SV814: $i] :
( ( ( c_in @ ( c_Pair @ SV814 @ SV1262 @ SV2004 @ SV2004 ) @ ( c_Transitive__Closure_Ortrancl @ SV1879 @ SV2004 ) @ ( tc_prod @ SV2004 @ SV2004 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV1262 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV271 @ SV1262 @ SV1879 @ SV2004 ) @ SV2004 @ SV2004 ) @ SV1879 @ ( tc_prod @ SV2004 @ SV2004 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV814 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(5586,plain,
! [SV272: $i,SV1880: $i,SV2005: $i,SV815: $i,SV1263: $i] :
( ( ( c_in @ ( c_Pair @ SV1263 @ SV815 @ SV2005 @ SV2005 ) @ ( c_Transitive__Closure_Ortrancl @ SV1880 @ SV2005 ) @ ( tc_prod @ SV2005 @ SV2005 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV1263 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV272 @ SV1263 @ SV1880 @ SV2005 ) @ SV2005 @ SV2005 ) @ SV1880 @ ( tc_prod @ SV2005 @ SV2005 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV815 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5487]) ).
thf(5587,plain,
! [SV817: $i,SV2095: $i,SV2006: $i,SV1612: $i,SV274: $i,SV1265: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5588,plain,
! [SV1613: $i,SV1881: $i,SV275: $i,SV1266: $i,SV818: $i,SV2146: $i] :
( ( ( c_in @ SV2146 @ SV818 @ SV1266 )
= $false )
| ( ( SV275 = SV1881 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV275 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 )
= ( c_Product__Type_OSigma @ SV1881 @ ( c_COMBK @ SV818 @ ( tc_fun @ SV1266 @ tc_bool ) @ SV1613 ) @ SV1613 @ SV1266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5589,plain,
! [SV1616: $i,SV1273: $i,SV834: $i,SV2096: $i,SV292: $i] :
( ( ( ~ ( c_in @ SV292 @ SV2096 @ SV834 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) )
= $true )
| ( ( c_in @ SV1616 @ SV2096 @ SV834 )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5490]) ).
thf(5590,plain,
! [SV835: $i,SV2097: $i,SV1274: $i,SV1883: $i,SV293: $i] :
( ( ( c_in @ ( c_Pair @ SV293 @ SV1883 @ SV1274 @ SV1274 ) @ ( c_Transitive__Closure_Ortrancl @ SV2097 @ SV1274 ) @ ( tc_prod @ SV1274 @ SV1274 ) )
= $false )
| ( ( c_lessequals @ SV2097 @ ( c_Product__Type_OSigma @ SV835 @ ( c_COMBK @ SV835 @ ( tc_fun @ SV1274 @ tc_bool ) @ SV1274 ) @ SV1274 @ SV1274 ) @ ( tc_fun @ ( tc_prod @ SV1274 @ SV1274 ) @ tc_bool ) )
= $false )
| ( ( SV293 = SV1883 )
= $true )
| ( ( c_in @ SV293 @ SV835 @ SV1274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5591,plain,
! [SV1618: $i,SV1276: $i,SV296: $i,SV838: $i] :
( ( ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV296 @ SV1276 )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5592,plain,
! [SV303: $i,SV1886: $i,SV2007: $i,SV1282: $i,SV843: $i] :
( ( ( c_in @ ( c_Pair @ SV843 @ SV1282 @ SV2007 @ SV2007 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV2007 ) @ ( tc_prod @ SV2007 @ SV2007 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV1282 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV303 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV303 @ SV1282 @ SV1886 @ SV2007 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV303 @ SV843 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5593,plain,
! [SV304: $i,SV1887: $i,SV2008: $i,SV1283: $i,SV844: $i] :
( ( ( c_in @ ( c_Pair @ SV844 @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV1283 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV304 @ SV1283 @ SV1887 @ SV2008 ) @ SV1283 @ SV2008 @ SV2008 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV2008 ) @ ( tc_prod @ SV2008 @ SV2008 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV844 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5594,plain,
! [SV305: $i,SV1888: $i,SV2009: $i,SV845: $i,SV1284: $i] :
( ( ( c_in @ ( c_Pair @ SV1284 @ SV845 @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV1284 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1284 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV305 @ SV1284 @ SV1888 @ SV2009 ) @ SV2009 @ SV2009 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV2009 ) @ ( tc_prod @ SV2009 @ SV2009 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ SV845 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5595,plain,
! [SV1889: $i,SV2010: $i,SV846: $i,SV1285: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5596,plain,
! [SV307: $i,SV1623: $i,SV1286: $i,SV847: $i,SV2098: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5498]) ).
thf(5597,plain,
! [SV309: $i,SV1890: $i,SV2011: $i,SV849: $i,SV1288: $i] :
( ( ( c_in @ ( c_Pair @ SV1288 @ SV849 @ SV2011 @ SV2011 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV2011 ) @ ( tc_prod @ SV2011 @ SV2011 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV1288 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV309 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV309 @ SV1288 @ SV1890 @ SV2011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV849 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5598,plain,
! [SV1891: $i,SV2012: $i,SV851: $i,SV1290: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5599,plain,
! [SV853: $i,SV313: $i,SV1292: $i,SV2099: $i,SV2013: $i] :
( ( ( c_Wellfounded_Owf @ SV2013 @ SV2099 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1292 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV313 @ SV2013 @ SV2099 ) @ SV2099 @ SV2099 ) @ SV2013 @ ( tc_prod @ SV2099 @ SV2099 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV1292 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV313 @ SV853 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(5600,plain,
! [SV854: $i,SV314: $i,SV1293: $i,SV2100: $i,SV2014: $i] :
( ( ( c_Wellfounded_Owf @ SV2014 @ SV2100 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1293 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV314 @ SV2014 @ SV2100 ) @ SV2100 @ SV2100 ) @ SV2014 @ ( tc_prod @ SV2100 @ SV2100 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV1293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV854 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5502]) ).
thf(5601,plain,
! [SV855: $i,SV315: $i,SV1294: $i,SV2101: $i,SV2015: $i] :
( ( ( c_Wellfounded_Owf @ SV2015 @ SV2101 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1294 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV315 @ SV2015 @ SV2101 ) @ SV2101 @ SV2101 ) @ SV2015 @ ( tc_prod @ SV2101 @ SV2101 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV1294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV315 @ SV855 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5503]) ).
thf(5602,plain,
! [SV856: $i,SV316: $i,SV1295: $i,SV2102: $i,SV2016: $i] :
( ( ( c_Wellfounded_Owf @ SV2016 @ SV2102 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1295 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV316 @ SV2016 @ SV2102 ) @ SV2102 @ SV2102 ) @ SV2016 @ ( tc_prod @ SV2102 @ SV2102 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV1295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5504]) ).
thf(5603,plain,
! [SV2017: $i,SV325: $i,SV1304: $i,SV865: $i,SV1629: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 ) )
= $true )
| ( ( c_in @ SV865 @ SV2017 @ SV1304 )
= $false )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5505]) ).
thf(5604,plain,
! [SV866: $i,SV326: $i,SV2103: $i,SV1305: $i,SV1630: $i,SV2147: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2147 @ SV1630 @ SV1305 )
= $false )
| ( ( c_in @ SV2103 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( c_Relation_OImage @ SV1630 @ ( c_Set_Oinsert @ SV866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 ) @ SV1305 @ SV1305 ) @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1305 )
= $false )
| ( ( c_in @ ( c_Pair @ SV326 @ SV866 @ SV1305 @ SV1305 ) @ SV1630 @ ( tc_prod @ SV1305 @ SV1305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5506]) ).
thf(5605,plain,
! [SV872: $i,SV2106: $i,SV1636: $i,SV1311: $i,SV2020: $i,SV332: $i] :
( ( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV2020 @ ( c_COMBK @ SV1311 @ ( tc_fun @ SV1636 @ tc_bool ) @ SV2106 ) @ SV2106 @ SV1636 ) @ ( tc_fun @ SV2106 @ SV1636 ) )
= $false )
| ( ( c_in @ SV872 @ SV2020 @ SV2106 )
= $false )
| ( ( c_in @ ( hAPP @ SV332 @ SV872 ) @ SV1311 @ SV1636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(5606,plain,
! [SV892: $i,SV356: $i,SV1325: $i,SV2136: $i,SV1646: $i] :
( ( ( c_in @ SV1646 @ SV2136 @ SV1325 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2136 @ SV356 @ SV1325 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5607,plain,
! [SV2107: $i,SV357: $i,SV1326: $i,SV1647: $i,SV893: $i] :
( ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
= $true )
| ( ( ~ ( c_in @ SV1647 @ SV2107 @ SV1326 )
| ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
= $false )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5513]) ).
thf(5608,plain,
! [SV358: $i,SV894: $i,SV1327: $i,SV2137: $i,SV1648: $i] :
( ( ( c_in @ SV1648 @ SV2137 @ SV1327 )
= $false )
| ( ( ~ ( c_in @ SV894 @ SV2137 @ SV1327 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5609,plain,
! [SV1649: $i,SV359: $i,SV1328: $i,SV2108: $i,SV895: $i] :
( ( ( ~ ( c_in @ SV895 @ SV2108 @ SV1328 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) )
= $true )
| ( ( c_in @ SV1649 @ SV2108 @ SV1328 )
= $false )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5515]) ).
thf(5610,plain,
! [SV375: $i,SV2138: $i,SV1661: $i,SV911: $i,SV2109: $i,SV2024: $i,SV1909: $i,SV1337: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) ) )
= $true )
| ( ( ! [SY5568: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SY5568 @ ( tc_prod @ SV2138 @ SV2138 ) )
| ! [SY5569: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5568 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5569 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5516]) ).
thf(5611,plain,
! [SV1913: $i,SV1670: $i,SV928: $i,SV392: $i,SV2139: $i,SV2026: $i,SV1352: $i] :
( ( ( c_in @ SV1352 @ SV2026 @ SV2139 )
= $false )
| ( ( ! [SY5570: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5570 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SY5570 @ SV2139 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5517]) ).
thf(5612,plain,
! [SV398: $i,SV2027: $i,SV1353: $i,SV931: $i,SV2153: $i] :
( ( ( ~ ( c_in @ SV2153 @ SV931 @ SV1353 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
= $false )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5518]) ).
thf(5613,plain,
! [SV399: $i,SV2028: $i,SV1354: $i,SV932: $i,SV2154: $i] :
( ( ( ~ ( c_in @ SV2154 @ SV932 @ SV1354 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
= $false )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5519]) ).
thf(5614,plain,
! [SV407: $i,SV1360: $i,SV2110: $i,SV2029: $i,SV940: $i] :
( ( ( c_in @ SV940 @ ( c_Wellfounded_Oacc @ SV2029 @ SV2110 ) @ SV2110 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1360 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV407 @ SV2029 @ SV2110 ) @ SV2110 @ SV2110 ) @ SV2029 @ ( tc_prod @ SV2110 @ SV2110 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV1360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5522]) ).
thf(5615,plain,
! [SV410: $i,SV1361: $i,SV2111: $i,SV2032: $i,SV943: $i] :
( ( ( c_in @ SV943 @ ( c_Wellfounded_Oacc @ SV2032 @ SV2111 ) @ SV2111 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1361 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV410 @ SV2032 @ SV2111 ) @ SV2111 @ SV2111 ) @ SV2032 @ ( tc_prod @ SV2111 @ SV2111 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV1361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV410 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5616,plain,
! [SV1025: $i,SV495: $i,SV1708: $i,SV1927: $i] :
( ( ( c_Relation_Oantisym @ SV1927 @ SV1708 )
= $false )
| ( ( c_in @ ( c_Pair @ SV495 @ SV1025 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ SV1708 @ SV1708 ) @ SV1927 @ ( tc_prod @ SV1708 @ SV1708 ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5617,plain,
! [SV1026: $i,SV496: $i,SV1709: $i,SV1928: $i] :
( ( ( c_Relation_Oantisym @ SV1928 @ SV1709 )
= $false )
| ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1026 @ SV496 @ SV1709 @ SV1709 ) @ SV1928 @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( SV496 = SV1026 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5537]) ).
thf(5618,plain,
! [SV1409: $i,SV1027: $i,SV2148: $i,SV1710: $i,SV497: $i,SV2045: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV2045 @ SV497 @ SV1710 @ SV2148 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1409 @ SV1710 @ SV1710 ) @ SV2045 @ ( tc_prod @ SV1710 @ SV1710 ) )
= $false )
| ( ( ( hAPP @ SV497 @ SV1027 )
= ( hAPP @ SV497 @ SV1409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(5619,plain,
! [SV1930: $i,SV1029: $i,SV1712: $i,SV1410: $i,SV2046: $i,SV2149: $i,SV499: $i] :
( ( ( ( hAPP @ SV499 @ SV2149 )
= ( hAPP @ SV2046 @ SV2149 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2149 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5539]) ).
thf(5620,plain,
! [SV1933: $i,SV1417: $i,SV507: $i,SV2048: $i,SV1718: $i,SV2114: $i,SV1037: $i,SV2150: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2150 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV507 @ SV2150 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5540]) ).
thf(5621,plain,
! [SV1042: $i,SV1721: $i,SV2115: $i,SV1420: $i,SV2051: $i,SV512: $i] :
( ( ( c_in @ SV512 @ ( c_FuncSet_OPi @ SV2051 @ SV1420 @ SV2115 @ SV1721 ) @ ( tc_fun @ SV2115 @ SV1721 ) )
= $false )
| ( ( c_in @ SV1042 @ SV2051 @ SV2115 )
= $false )
| ( ( c_in @ ( hAPP @ SV512 @ SV1042 ) @ ( hAPP @ SV1420 @ SV1042 ) @ SV1721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(5622,plain,
! [SV513: $i,SV2140: $i,SV1421: $i,SV2116: $i,SV1043: $i,SV1722: $i] :
( ( ( c_in @ SV1722 @ ( c_FuncSet_OPi @ SV1043 @ SV2116 @ SV1421 @ SV2140 ) @ ( tc_fun @ SV1421 @ SV2140 ) )
= $false )
| ( ( c_in @ ( hAPP @ SV1722 @ SV513 ) @ ( hAPP @ SV2116 @ SV513 ) @ SV2140 )
= $true )
| ( ( c_in @ SV513 @ SV1043 @ SV1421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5544]) ).
thf(5623,plain,
! [SV1938: $i,SV1430: $i,SV1057: $i,SV527: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5545]) ).
thf(5624,plain,
! [SV1431: $i,SV1939: $i,SV528: $i,SV1058: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5546]) ).
thf(5625,plain,
! [SV1059: $i,SV529: $i,SV1432: $i,SV1940: $i] :
( ( ( ~ ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(5626,plain,
! [SV530: $i,SV1060: $i,SV1941: $i,SV1433: $i] :
( ( ( ~ ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(5627,plain,
! [SV1434: $i,SV1727: $i,SV2052: $i,SV1061: $i,SV531: $i] :
( ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5549]) ).
thf(5628,plain,
! [SV1435: $i,SV2053: $i,SV1728: $i,SV1062: $i,SV532: $i] :
( ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5550]) ).
thf(5629,plain,
! [SV1436: $i,SV2054: $i,SV1729: $i,SV1063: $i,SV533: $i] :
( ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5630,plain,
! [SV1437: $i,SV1730: $i,SV2055: $i,SV1064: $i,SV534: $i] :
( ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5552]) ).
thf(5631,plain,
! [SV1065: $i,SV535: $i,SV1731: $i,SV1438: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ SV1438 )
= $false )
| ( ( c_in @ SV1731 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1731 @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ SV535 @ SV1065 @ SV1731 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV535 @ SV1065 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1438 @ SV1731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5553]) ).
thf(5632,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2117: $i,SV2056: $i,SV1732: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5554]) ).
thf(5633,plain,
! [SV2057: $i,SV1733: $i,SV2118: $i,SV1440: $i,SV1067: $i,SV537: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5555]) ).
thf(5634,plain,
! [SV1068: $i,SV538: $i,SV1441: $i,SV2119: $i,SV2058: $i,SV1734: $i] :
( ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5556]) ).
thf(5635,plain,
! [SV2059: $i,SV1735: $i,SV2120: $i,SV1442: $i,SV1069: $i,SV539: $i] :
( ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5557]) ).
thf(5636,plain,
! [SV2060: $i,SV1736: $i,SV2121: $i,SV1443: $i,SV1070: $i,SV540: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5558]) ).
thf(5637,plain,
! [SV2061: $i,SV1737: $i,SV2122: $i,SV1444: $i,SV1071: $i,SV541: $i] :
( ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5559]) ).
thf(5638,plain,
! [SV1738: $i,SV2062: $i,SV1073: $i,SV1446: $i,SV1942: $i,SV543: $i] :
( ( ( c_in @ SV543 @ SV1942 @ SV1446 )
= $false )
| ( ( c_in @ SV1073 @ ( hAPP @ SV2062 @ SV543 ) @ SV1738 )
= $false )
| ( ( c_in @ ( c_Pair @ SV543 @ SV1073 @ SV1446 @ SV1738 ) @ ( c_Product__Type_OSigma @ SV1942 @ SV2062 @ SV1446 @ SV1738 ) @ ( tc_prod @ SV1446 @ SV1738 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5560]) ).
thf(5639,plain,
! [SV1739: $i,SV2063: $i,SV1074: $i,SV1447: $i,SV1943: $i,SV544: $i] :
( ( ( c_in @ SV544 @ SV1943 @ SV1447 )
= $false )
| ( ( c_in @ SV1074 @ ( hAPP @ SV2063 @ SV544 ) @ SV1739 )
= $false )
| ( ( c_in @ ( c_Pair @ SV544 @ SV1074 @ SV1447 @ SV1739 ) @ ( c_Product__Type_OSigma @ SV1943 @ SV2063 @ SV1447 @ SV1739 ) @ ( tc_prod @ SV1447 @ SV1739 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5640,plain,
! [SV1077: $i,SV1946: $i,SV547: $i,SV1740: $i,SV1450: $i,SV2123: $i] :
( ( ( c_in @ SV2123 @ SV1450 @ SV1740 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2123 @ SV547 @ SV1740 @ SV1946 ) @ SV1077 @ ( tc_prod @ SV1740 @ SV1946 ) )
= $false )
| ( ( c_in @ SV547 @ ( c_Relation_OImage @ SV1077 @ SV1450 @ SV1740 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(5641,plain,
! [SV1078: $i,SV1947: $i,SV548: $i,SV1741: $i,SV1451: $i,SV2124: $i] :
( ( ( c_in @ SV2124 @ SV1451 @ SV1741 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2124 @ SV548 @ SV1741 @ SV1947 ) @ SV1078 @ ( tc_prod @ SV1741 @ SV1947 ) )
= $false )
| ( ( c_in @ SV548 @ ( c_Relation_OImage @ SV1078 @ SV1451 @ SV1741 @ SV1947 ) @ SV1947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5563]) ).
thf(5642,plain,
! [SV1748: $i,SV1089: $i,SV1462: $i,SV2141: $i,SV559: $i] :
( ( ( c_in @ SV559 @ SV2141 @ SV1462 )
= $false )
| ( ( ~ ( c_in @ SV1089 @ SV2141 @ SV1462 )
| ~ ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 ) )
= $true )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5566]) ).
thf(5643,plain,
! [SV2151: $i,SV2142: $i,SV2127: $i,SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
!= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
= $true )
| ( ( ! [SY5574: $i,SY5575: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SV2151 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5574 @ SV2142 @ SY5575 ) @ SV2074 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5569]) ).
thf(5644,plain,
! [SV2152: $i,SV2128: $i,SV2075: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV1099: $i,SV569: $i] :
( ( ( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
= ( c_Fun_Ocomp @ SV2075 @ SV2128 @ SV2152 @ SV1754 @ SV1956 ) )
= $false )
| ( ( ! [SY5567: $i] :
( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SY5567 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SV2128 @ SY5567 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5570]) ).
thf(5645,plain,
! [SV1770: $i,SV2081: $i,SV603: $i,SV1489: $i,SV1129: $i,SV1965: $i,SV13: $i] :
( ( ( c_lessequals @ SV13 @ SV1965 @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1489 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV603 @ SV2081 @ ( tc_fun @ ( tc_prod @ SV1489 @ SV1770 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV13 @ SV603 @ SV1129 @ SV1489 @ SV1770 ) @ ( c_Relation_Orel__comp @ SV1965 @ SV2081 @ SV1129 @ SV1489 @ SV1770 ) @ ( tc_fun @ ( tc_prod @ SV1129 @ SV1770 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5571]) ).
thf(5646,plain,
! [SV1154: $i,SV1969: $i,SV52: $i,SV1511: $i,SV1778: $i,SV2082: $i,SV2145: $i,SV638: $i] :
( ( ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SV2145 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2145 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5574]) ).
thf(5647,plain,
! [SV1576: $i,SV1224: $i,SV749: $i,SV2132: $i,SV191: $i] :
( ( ( ~ ( c_in @ SV191 @ SV2132 @ SV749 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 ) )
= $true )
| ( ( c_in @ SV1576 @ SV2132 @ SV749 )
= $false )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5648,plain,
! [SV817: $i,SV2095: $i,SV2006: $i,SV1612: $i,SV274: $i,SV1265: $i] :
( ( ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(5649,plain,
! [SV1616: $i,SV1273: $i,SV834: $i,SV2096: $i,SV292: $i] :
( ( ( c_in @ SV292 @ SV2096 @ SV834 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
| ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) ) )
= $true )
| ( ( c_in @ SV1616 @ SV2096 @ SV834 )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5589]) ).
thf(5650,plain,
! [SV1618: $i,SV838: $i,SV1276: $i,SV296: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV296 @ SV1276 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5591]) ).
thf(5651,plain,
! [SV306: $i,SV1889: $i,SV2010: $i,SV846: $i,SV1285: $i] :
( ( ( c_in @ ( c_Pair @ SV1285 @ SV846 @ SV2010 @ SV2010 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV2010 ) @ ( tc_prod @ SV2010 @ SV2010 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV1285 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV306 @ SV1285 @ SV1889 @ SV2010 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ SV846 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5652,plain,
! [SV307: $i,SV1623: $i,SV1286: $i,SV847: $i,SV2098: $i] :
( ( ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5596]) ).
thf(5653,plain,
! [SV311: $i,SV1891: $i,SV2012: $i,SV1290: $i,SV851: $i] :
( ( ( c_in @ ( c_Pair @ SV851 @ SV1290 @ SV2012 @ SV2012 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV2012 ) @ ( tc_prod @ SV2012 @ SV2012 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV1290 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV311 @ SV1290 @ SV1891 @ SV2012 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5654,plain,
! [SV325: $i,SV865: $i,SV1304: $i,SV1629: $i,SV2017: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2017 @ SV1629 @ SV1304 )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV865 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV1629 @ ( c_Set_Oinsert @ SV325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $false )
| ( ( c_in @ SV865 @ SV2017 @ SV1304 )
= $false )
| ( ( c_in @ ( c_Pair @ SV325 @ SV865 @ SV1304 @ SV1304 ) @ SV1629 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5603]) ).
thf(5655,plain,
! [SV892: $i,SV1646: $i,SV1325: $i,SV356: $i,SV2136: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2136 @ SV356 @ SV1325 )
= $false )
| ( ( c_in @ SV1646 @ SV2136 @ SV1325 )
= $false )
| ( ( c_in @ ( c_Pair @ SV892 @ SV1646 @ SV1325 @ SV1325 ) @ SV356 @ ( tc_prod @ SV1325 @ SV1325 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV892 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 )
= ( c_Relation_OImage @ SV356 @ ( c_Set_Oinsert @ SV1646 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 @ SV1325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(5656,plain,
! [SV357: $i,SV893: $i,SV1326: $i,SV2107: $i,SV1647: $i] :
( ( ( ~ ( c_in @ SV1647 @ SV2107 @ SV1326 ) )
= $true )
| ( ( ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
= $false )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5607]) ).
thf(5657,plain,
! [SV1648: $i,SV358: $i,SV1327: $i,SV2137: $i,SV894: $i] :
( ( ( ~ ( c_in @ SV894 @ SV2137 @ SV1327 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 ) )
= $true )
| ( ( c_in @ SV1648 @ SV2137 @ SV1327 )
= $false )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5608]) ).
thf(5658,plain,
! [SV1649: $i,SV359: $i,SV1328: $i,SV2108: $i,SV895: $i] :
( ( ( c_in @ SV895 @ SV2108 @ SV1328 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
| ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) ) )
= $true )
| ( ( c_in @ SV1649 @ SV2108 @ SV1328 )
= $false )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5609]) ).
thf(5659,plain,
! [SV375: $i,SV2138: $i,SV1661: $i,SV911: $i,SV2109: $i,SV2024: $i,SV1909: $i,SV1337: $i] :
( ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ! [SY5568: $i] :
( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SY5568 @ ( tc_prod @ SV2138 @ SV2138 ) )
| ! [SY5569: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5568 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5569 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(5660,plain,
! [SV1352: $i,SV2026: $i,SV1913: $i,SV1670: $i,SV2139: $i,SV928: $i,SV392: $i,SV2155: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2155 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SV2155 @ SV2139 ) )
= $true )
| ( ( c_in @ SV1352 @ SV2026 @ SV2139 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5661,plain,
! [SV398: $i,SV2027: $i,SV1353: $i,SV931: $i,SV2153: $i] :
( ( ( c_in @ SV2153 @ SV931 @ SV1353 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2027 @ SV1353 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
= $false )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5612]) ).
thf(5662,plain,
! [SV399: $i,SV2028: $i,SV1354: $i,SV932: $i,SV2154: $i] :
( ( ( c_in @ SV2154 @ SV932 @ SV1354 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2028 @ SV1354 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
= $false )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(5663,plain,
! [SV1930: $i,SV2046: $i,SV499: $i,SV1029: $i,SV1712: $i,SV1410: $i,SV2149: $i] :
( ( ( c_in @ ( c_Pair @ SV2149 @ SV1410 @ SV1712 @ SV1712 ) @ SV1029 @ ( tc_prod @ SV1712 @ SV1712 ) )
= $false )
| ( ( ( hAPP @ SV499 @ SV2149 )
= ( hAPP @ SV2046 @ SV2149 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV499 @ SV1029 @ SV1410 @ SV1712 @ SV1930 )
= ( c_Recdef_Ocut @ SV2046 @ SV1029 @ SV1410 @ SV1712 @ SV1930 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5619]) ).
thf(5664,plain,
! [SV1933: $i,SV1417: $i,SV507: $i,SV2048: $i,SV1718: $i,SV2114: $i,SV1037: $i,SV2150: $i] :
( ( ( c_in @ ( c_Pair @ SV2150 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV507 @ SV2150 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5620]) ).
thf(5665,plain,
! [SV1938: $i,SV1430: $i,SV1057: $i,SV527: $i] :
( ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(5666,plain,
! [SV1431: $i,SV1939: $i,SV528: $i,SV1058: $i] :
( ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(5667,plain,
! [SV1059: $i,SV529: $i,SV1432: $i,SV1940: $i] :
( ( ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV529 = SV1059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5625]) ).
thf(5668,plain,
! [SV530: $i,SV1060: $i,SV1941: $i,SV1433: $i] :
( ( ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1060 = SV530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5669,plain,
! [SV1434: $i,SV2052: $i,SV1727: $i,SV1061: $i,SV531: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(5670,plain,
! [SV1435: $i,SV1728: $i,SV2053: $i,SV1062: $i,SV532: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5628]) ).
thf(5671,plain,
! [SV1063: $i,SV533: $i,SV1436: $i,SV1729: $i,SV2054: $i] :
( ( ( ~ ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5629]) ).
thf(5672,plain,
! [SV1064: $i,SV534: $i,SV1437: $i,SV2055: $i,SV1730: $i] :
( ( ( ~ ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5630]) ).
thf(5673,plain,
! [SV1066: $i,SV536: $i,SV1439: $i,SV2117: $i,SV2056: $i,SV1732: $i] :
( ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(5674,plain,
! [SV2057: $i,SV1733: $i,SV2118: $i,SV1440: $i,SV1067: $i,SV537: $i] :
( ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5675,plain,
! [SV2058: $i,SV1734: $i,SV2119: $i,SV1441: $i,SV1068: $i,SV538: $i] :
( ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5634]) ).
thf(5676,plain,
! [SV1069: $i,SV539: $i,SV1442: $i,SV2120: $i,SV2059: $i,SV1735: $i] :
( ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5635]) ).
thf(5677,plain,
! [SV2060: $i,SV1736: $i,SV2121: $i,SV1443: $i,SV1070: $i,SV540: $i] :
( ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5678,plain,
! [SV1071: $i,SV541: $i,SV1444: $i,SV2122: $i,SV2061: $i,SV1737: $i] :
( ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5637]) ).
thf(5679,plain,
! [SV559: $i,SV1748: $i,SV1462: $i,SV2141: $i,SV1089: $i] :
( ( ( ~ ( c_in @ SV1089 @ SV2141 @ SV1462 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 ) )
= $true )
| ( ( c_in @ SV559 @ SV2141 @ SV1462 )
= $false )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5642]) ).
thf(5680,plain,
! [SV2151: $i,SV2142: $i,SV2127: $i,SV2074: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV1098: $i,SV568: $i] :
( ( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
= $false )
| ( ( ! [SY5574: $i,SY5575: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SV2151 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SY5574 @ SV2142 @ SY5575 ) @ SV2074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(5681,plain,
! [SV2152: $i,SV1956: $i,SV1754: $i,SV1472: $i,SV2128: $i,SV2075: $i,SV2156: $i,SV1099: $i,SV569: $i] :
( ( ( ( hAPP @ SV569 @ ( hAPP @ SV1099 @ SV2156 ) )
= ( hAPP @ SV2075 @ ( hAPP @ SV2128 @ SV2156 ) ) )
= $true )
| ( ( ( c_Fun_Ocomp @ SV569 @ SV1099 @ SV1472 @ SV1754 @ SV1956 )
= ( c_Fun_Ocomp @ SV2075 @ SV2128 @ SV2152 @ SV1754 @ SV1956 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(5682,plain,
! [SV1778: $i,SV2082: $i,SV638: $i,SV1154: $i,SV1511: $i,SV2145: $i,SV1969: $i,SV52: $i] :
( ( ( c_lessequals @ SV52 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2145 @ ( tc_fun @ SV1511 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1511 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1511 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV638 @ ( c_Product__Type_OSigma @ SV2145 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1511 ) @ SV1511 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1511 @ SV1778 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV52 @ SV638 @ SV1154 @ SV1511 @ SV1778 ) @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV2082 @ ( tc_fun @ SV1778 @ tc_bool ) @ SV1154 ) @ SV1154 @ SV1778 ) @ ( tc_fun @ ( tc_prod @ SV1154 @ SV1778 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5646]) ).
thf(5683,plain,
! [SV1576: $i,SV1224: $i,SV749: $i,SV2132: $i,SV191: $i] :
( ( ( c_in @ SV191 @ SV2132 @ SV749 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 ) )
= $true )
| ( ( c_in @ SV1576 @ SV2132 @ SV749 )
= $false )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5647]) ).
thf(5684,plain,
! [SV817: $i,SV274: $i,SV1265: $i,SV2006: $i,SV1612: $i,SV2095: $i] :
( ( ( c_Relation_Osingle__valued @ SV2095 @ SV1612 @ SV2006 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1265 @ SV274 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1265 @ SV817 @ SV1612 @ SV2006 ) @ SV2095 @ ( tc_prod @ SV1612 @ SV2006 ) )
= $false )
| ( ( SV274 = SV817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5648]) ).
thf(5685,plain,
! [SV1616: $i,SV292: $i,SV834: $i,SV1273: $i,SV2096: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) )
= $true )
| ( ( c_in @ SV292 @ SV2096 @ SV834 )
= $false )
| ( ( c_in @ SV1616 @ SV2096 @ SV834 )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5649]) ).
thf(5686,plain,
! [SV1618: $i,SV838: $i,SV1276: $i,SV296: $i] :
( ( ( c_Relation_Oantisym @ SV296 @ SV1276 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
| ( SV838 = SV1618 ) )
= $true )
| ( ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(5687,plain,
! [SV307: $i,SV847: $i,SV2098: $i,SV1286: $i,SV1623: $i] :
( ( ( c_Relation_Osingle__valued @ SV1623 @ SV1286 @ SV1286 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2098 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2098 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV847 @ SV307 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV307 @ SV847 @ SV1286 @ SV1286 ) @ ( c_Transitive__Closure_Ortrancl @ SV1623 @ SV1286 ) @ ( tc_prod @ SV1286 @ SV1286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5652]) ).
thf(5688,plain,
! [SV357: $i,SV893: $i,SV1326: $i,SV2107: $i,SV1647: $i] :
( ( ( c_in @ SV1647 @ SV2107 @ SV1326 )
= $false )
| ( ( ~ ( c_in @ SV893 @ SV2107 @ SV1326 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
= $false )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(5689,plain,
! [SV1648: $i,SV358: $i,SV1327: $i,SV2137: $i,SV894: $i] :
( ( ( c_in @ SV894 @ SV2137 @ SV1327 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 ) )
= $true )
| ( ( c_in @ SV1648 @ SV2137 @ SV1327 )
= $false )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5657]) ).
thf(5690,plain,
! [SV1649: $i,SV895: $i,SV1328: $i,SV359: $i,SV2108: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) )
= $true )
| ( ( c_in @ SV895 @ SV2108 @ SV1328 )
= $false )
| ( ( c_in @ SV1649 @ SV2108 @ SV1328 )
= $false )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5658]) ).
thf(5691,plain,
! [SV1909: $i,SV1337: $i,SV2024: $i,SV375: $i,SV2109: $i,SV2157: $i,SV2138: $i,SV1661: $i,SV911: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SV2157 @ ( tc_prod @ SV2138 @ SV2138 ) )
| ! [SY5576: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2157 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5576 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5692,plain,
! [SV1352: $i,SV2026: $i,SV1913: $i,SV1670: $i,SV2139: $i,SV928: $i,SV392: $i,SV2155: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2155 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SV2155 @ SV2139 ) )
= $true )
| ( ( c_in @ SV1352 @ SV2026 @ SV2139 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5660]) ).
thf(5693,plain,
! [SV398: $i,SV931: $i,SV2153: $i,SV1353: $i,SV2027: $i] :
( ( ( c_Wellfounded_Owf @ SV2027 @ SV1353 )
= $false )
| ( ( c_in @ SV2153 @ SV931 @ SV1353 )
= $false )
| ( ( c_in @ ( c_Pair @ SV398 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV931 @ SV2027 @ SV1353 ) @ SV1353 @ SV1353 ) @ SV2027 @ ( tc_prod @ SV1353 @ SV1353 ) )
= $false )
| ( ( c_in @ SV398 @ SV931 @ SV1353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5661]) ).
thf(5694,plain,
! [SV399: $i,SV932: $i,SV2154: $i,SV1354: $i,SV2028: $i] :
( ( ( c_Wellfounded_Owf @ SV2028 @ SV1354 )
= $false )
| ( ( c_in @ SV2154 @ SV932 @ SV1354 )
= $false )
| ( ( c_in @ ( c_Pair @ SV399 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV932 @ SV2028 @ SV1354 ) @ SV1354 @ SV1354 ) @ SV2028 @ ( tc_prod @ SV1354 @ SV1354 ) )
= $false )
| ( ( c_in @ SV399 @ SV932 @ SV1354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(5695,plain,
! [SV2048: $i,SV1718: $i,SV1037: $i,SV1933: $i,SV2114: $i,SV1417: $i,SV2150: $i,SV507: $i] :
( ( ( c_in @ ( c_Pair @ SV507 @ SV2150 @ SV1417 @ SV2114 ) @ SV1933 @ ( tc_prod @ SV1417 @ SV2114 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2150 @ SV1037 @ SV2114 @ SV1718 ) @ SV2048 @ ( tc_prod @ SV2114 @ SV1718 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ SV1417 @ SV1718 ) @ ( c_Relation_Orel__comp @ SV1933 @ SV2048 @ SV1417 @ SV2114 @ SV1718 ) @ ( tc_prod @ SV1417 @ SV1718 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(5696,plain,
! [SV1057: $i,SV527: $i,SV1430: $i,SV1938: $i] :
( ( ( ~ ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5665]) ).
thf(5697,plain,
! [SV528: $i,SV1058: $i,SV1939: $i,SV1431: $i] :
( ( ( ~ ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5666]) ).
thf(5698,plain,
! [SV1940: $i,SV1059: $i,SV529: $i,SV1432: $i] :
( ( ( ~ ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( SV529 = SV1059 )
= $true )
| ( ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5667]) ).
thf(5699,plain,
! [SV1433: $i,SV530: $i,SV1060: $i,SV1941: $i] :
( ( ( ~ ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( SV1060 = SV530 )
= $true )
| ( ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5668]) ).
thf(5700,plain,
! [SV1434: $i,SV2052: $i,SV1727: $i,SV1061: $i,SV531: $i] :
( ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(5701,plain,
! [SV1435: $i,SV1728: $i,SV2053: $i,SV1062: $i,SV532: $i] :
( ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5670]) ).
thf(5702,plain,
! [SV1063: $i,SV533: $i,SV1436: $i,SV1729: $i,SV2054: $i] :
( ( ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1436 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5671]) ).
thf(5703,plain,
! [SV1064: $i,SV534: $i,SV1437: $i,SV2055: $i,SV1730: $i] :
( ( ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1437 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(5704,plain,
! [SV2056: $i,SV1732: $i,SV2117: $i,SV1439: $i,SV1066: $i,SV536: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5673]) ).
thf(5705,plain,
! [SV1067: $i,SV537: $i,SV1440: $i,SV2118: $i,SV2057: $i,SV1733: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5674]) ).
thf(5706,plain,
! [SV2058: $i,SV538: $i,SV1734: $i,SV1068: $i,SV1441: $i,SV2119: $i] :
( ( ( ~ ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5675]) ).
thf(5707,plain,
! [SV1069: $i,SV1735: $i,SV539: $i,SV2059: $i,SV2120: $i,SV1442: $i] :
( ( ( ~ ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5676]) ).
thf(5708,plain,
! [SV1070: $i,SV540: $i,SV1443: $i,SV2121: $i,SV2060: $i,SV1736: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5677]) ).
thf(5709,plain,
! [SV1071: $i,SV1737: $i,SV541: $i,SV2061: $i,SV2122: $i,SV1444: $i] :
( ( ( ~ ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5678]) ).
thf(5710,plain,
! [SV559: $i,SV1748: $i,SV1462: $i,SV2141: $i,SV1089: $i] :
( ( ( c_in @ SV1089 @ SV2141 @ SV1462 )
= $false )
| ( ( ~ ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 ) )
= $true )
| ( ( c_in @ SV559 @ SV2141 @ SV1462 )
= $false )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5711,plain,
! [SV2074: $i,SV2158: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV2151: $i,SV2142: $i,SV2127: $i,SV1098: $i,SV568: $i] :
( ( ( ! [SY5577: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SV2151 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SV2158 @ SV2142 @ SY5577 ) @ SV2074 ) ) )
= $true )
| ( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(5712,plain,
! [SV1576: $i,SV191: $i,SV749: $i,SV1224: $i,SV2132: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2132 @ SV1224 @ SV749 )
= $false )
| ( ( c_in @ SV191 @ SV2132 @ SV749 )
= $false )
| ( ( c_in @ SV1576 @ SV2132 @ SV749 )
= $false )
| ( ( c_in @ ( c_Pair @ SV191 @ SV1576 @ SV749 @ SV749 ) @ SV1224 @ ( tc_prod @ SV749 @ SV749 ) )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1576 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV749 ) @ SV1224 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(5713,plain,
! [SV1616: $i,SV292: $i,SV834: $i,SV1273: $i,SV2096: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2096 @ SV1273 @ SV834 )
= $false )
| ( ( c_in @ ( c_Pair @ SV292 @ SV1616 @ SV834 @ SV834 ) @ SV1273 @ ( tc_prod @ SV834 @ SV834 ) )
= $true )
| ( ( c_in @ SV292 @ SV2096 @ SV834 )
= $false )
| ( ( c_in @ SV1616 @ SV2096 @ SV834 )
= $false )
| ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV292 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV834 ) @ SV1273 @ SV834 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5685]) ).
thf(5714,plain,
! [SV1618: $i,SV838: $i,SV1276: $i,SV296: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 ) )
= $true )
| ( ( SV838 = SV1618 )
= $true )
| ( ( c_Relation_Oantisym @ SV296 @ SV1276 )
= $false )
| ( ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5686]) ).
thf(5715,plain,
! [SV357: $i,SV1647: $i,SV1326: $i,SV2107: $i,SV893: $i] :
( ( ( c_in @ SV893 @ SV2107 @ SV1326 )
= $false )
| ( ( c_in @ SV1647 @ SV2107 @ SV1326 )
= $false )
| ( ( c_in @ ( c_Pair @ SV893 @ SV1647 @ SV1326 @ SV1326 ) @ SV357 @ ( tc_prod @ SV1326 @ SV1326 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2107 @ SV357 @ SV1326 )
= $false )
| ( ( ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 )
= ( c_Relation_OImage @ SV357 @ ( c_Set_Oinsert @ SV1647 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1326 @ tc_bool ) ) @ SV1326 ) @ SV1326 @ SV1326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5688]) ).
thf(5716,plain,
! [SV1648: $i,SV894: $i,SV1327: $i,SV358: $i,SV2137: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2137 @ SV358 @ SV1327 )
= $false )
| ( ( c_in @ SV894 @ SV2137 @ SV1327 )
= $false )
| ( ( c_in @ SV1648 @ SV2137 @ SV1327 )
= $false )
| ( ( c_in @ ( c_Pair @ SV894 @ SV1648 @ SV1327 @ SV1327 ) @ SV358 @ ( tc_prod @ SV1327 @ SV1327 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 )
= ( c_Relation_OImage @ SV358 @ ( c_Set_Oinsert @ SV1648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1327 @ tc_bool ) ) @ SV1327 ) @ SV1327 @ SV1327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(5717,plain,
! [SV1649: $i,SV895: $i,SV1328: $i,SV359: $i,SV2108: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2108 @ SV359 @ SV1328 )
= $false )
| ( ( c_in @ ( c_Pair @ SV895 @ SV1649 @ SV1328 @ SV1328 ) @ SV359 @ ( tc_prod @ SV1328 @ SV1328 ) )
= $true )
| ( ( c_in @ SV895 @ SV2108 @ SV1328 )
= $false )
| ( ( c_in @ SV1649 @ SV2108 @ SV1328 )
= $false )
| ( ( ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 )
= ( c_Relation_OImage @ SV359 @ ( c_Set_Oinsert @ SV1649 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1328 ) @ SV1328 @ SV1328 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(5718,plain,
! [SV1909: $i,SV1337: $i,SV2024: $i,SV375: $i,SV2109: $i,SV2157: $i,SV2138: $i,SV1661: $i,SV911: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SV2157 @ ( tc_prod @ SV2138 @ SV2138 ) ) )
= $true )
| ( ( ! [SY5576: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2157 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5576 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5691]) ).
thf(5719,plain,
! [SV1352: $i,SV2026: $i,SV1913: $i,SV1670: $i,SV2139: $i,SV928: $i,SV392: $i,SV2155: $i] :
( ( ( c_Equiv__Relations_Ocongruent2 @ SV2155 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2026 @ SV2155 @ SV2139 ) )
= $true )
| ( ( c_in @ SV1352 @ SV2026 @ SV2139 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5692]) ).
thf(5720,plain,
! [SV1057: $i,SV527: $i,SV1430: $i,SV1938: $i] :
( ( ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV527 = SV1057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(5721,plain,
! [SV528: $i,SV1058: $i,SV1939: $i,SV1431: $i] :
( ( ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1058 = SV528 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5722,plain,
! [SV1940: $i,SV1059: $i,SV529: $i,SV1432: $i] :
( ( ( c_in @ SV1432 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( SV529 = SV1059 )
= $true )
| ( ( c_in @ SV1940 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1432 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1940 @ ( v_sko__local__X3__1 @ SV1432 @ SV1940 @ SV529 @ SV1059 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1059 @ SV529 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1940 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV529 @ SV1059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1432 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(5723,plain,
! [SV1433: $i,SV530: $i,SV1060: $i,SV1941: $i] :
( ( ( c_in @ SV1941 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( SV1060 = SV530 )
= $true )
| ( ( c_in @ SV1433 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1941 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1433 @ ( v_sko__local__X3__1 @ SV1941 @ SV1433 @ SV1060 @ SV530 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1060 @ SV530 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1941 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV530 @ SV1060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1433 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(5724,plain,
! [SV1061: $i,SV531: $i,SV1434: $i,SV1727: $i,SV2052: $i] :
( ( ( ~ ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5700]) ).
thf(5725,plain,
! [SV1062: $i,SV532: $i,SV1435: $i,SV2053: $i,SV1728: $i] :
( ( ( ~ ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5701]) ).
thf(5726,plain,
! [SV1063: $i,SV533: $i,SV2054: $i,SV1436: $i,SV1729: $i] :
( ( ( ~ ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1436 ) )
= $true )
| ( ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5702]) ).
thf(5727,plain,
! [SV1064: $i,SV534: $i,SV1730: $i,SV1437: $i,SV2055: $i] :
( ( ( ~ ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1437 ) )
= $true )
| ( ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(5728,plain,
! [SV2056: $i,SV1732: $i,SV2117: $i,SV1439: $i,SV1066: $i,SV536: $i] :
( ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(5729,plain,
! [SV1067: $i,SV537: $i,SV1440: $i,SV2118: $i,SV2057: $i,SV1733: $i] :
( ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5730,plain,
! [SV2058: $i,SV538: $i,SV1734: $i,SV1068: $i,SV1441: $i,SV2119: $i] :
( ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(5731,plain,
! [SV1069: $i,SV1735: $i,SV539: $i,SV2059: $i,SV2120: $i,SV1442: $i] :
( ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(5732,plain,
! [SV1070: $i,SV540: $i,SV1443: $i,SV2121: $i,SV2060: $i,SV1736: $i] :
( ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(5733,plain,
! [SV1071: $i,SV1737: $i,SV541: $i,SV2061: $i,SV2122: $i,SV1444: $i] :
( ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(5734,plain,
! [SV559: $i,SV1089: $i,SV1462: $i,SV1748: $i,SV2141: $i] :
( ( ( c_Relation_Ototal__on @ SV2141 @ SV1748 @ SV1462 )
= $false )
| ( ( c_in @ SV1089 @ SV2141 @ SV1462 )
= $false )
| ( ( c_in @ SV559 @ SV2141 @ SV1462 )
= $false )
| ( ( SV1089 = SV559 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1089 @ SV559 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV559 @ SV1089 @ SV1462 @ SV1462 ) @ SV1748 @ ( tc_prod @ SV1462 @ SV1462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5735,plain,
! [SV2074: $i,SV2159: $i,SV2158: $i,SV1955: $i,SV1753: $i,SV1471: $i,SV2151: $i,SV2142: $i,SV2127: $i,SV1098: $i,SV568: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV568 @ SV1098 @ SV2127 @ SV2142 @ SV2151 ) @ SV1471 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1753 @ SV1955 @ SV2158 @ SV2142 @ SV2159 ) @ SV2074 ) )
= $true )
| ( ( ( hAPP @ SV568 @ ( hAPP @ SV1098 @ SV1471 ) )
= ( hAPP @ SV1753 @ ( hAPP @ SV1955 @ SV2074 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5711]) ).
thf(5736,plain,
! [SV1618: $i,SV838: $i,SV1276: $i,SV296: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV296 @ SV1276 )
= $false )
| ( ( SV838 = SV1618 )
= $true )
| ( ( c_Relation_Oantisym @ SV296 @ SV1276 )
= $false )
| ( ( c_in @ SV838 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( c_in @ SV1618 @ ( c_Relation_OField @ SV296 @ SV1276 ) @ SV1276 )
= $false )
| ( ( ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 )
= ( c_Relation_OImage @ SV296 @ ( c_Set_Oinsert @ SV1618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1276 ) @ SV1276 @ SV1276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(5737,plain,
! [SV1909: $i,SV1337: $i,SV2024: $i,SV375: $i,SV2109: $i,SV2157: $i,SV2138: $i,SV1661: $i,SV911: $i] :
( ( ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SV2157 @ ( tc_prod @ SV2138 @ SV2138 ) )
= $false )
| ( ( ! [SY5576: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2157 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SY5576 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(5738,plain,
! [SV1352: $i,SV1913: $i,SV1670: $i,SV928: $i,SV392: $i,SV2139: $i,SV2155: $i,SV2026: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2026 @ SV2155 @ SV2139 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent2 @ SV2155 @ SV392 @ SV928 @ SV2139 @ SV1670 @ SV1913 )
= $false )
| ( ( c_in @ SV1352 @ SV2026 @ SV2139 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV392 @ ( hAPP @ SV928 @ SV1352 ) @ SV1670 @ SV1913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5739,plain,
! [SV1938: $i,SV1057: $i,SV527: $i,SV1430: $i] :
( ( ( ~ ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( SV527 = SV1057 )
= $true )
| ( ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5720]) ).
thf(5740,plain,
! [SV1431: $i,SV528: $i,SV1058: $i,SV1939: $i] :
( ( ( ~ ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( SV1058 = SV528 )
= $true )
| ( ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5721]) ).
thf(5741,plain,
! [SV1061: $i,SV531: $i,SV1434: $i,SV1727: $i,SV2052: $i] :
( ( ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1434 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(5742,plain,
! [SV1062: $i,SV532: $i,SV1435: $i,SV2053: $i,SV1728: $i] :
( ( ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( 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 @ SV1435 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(5743,plain,
! [SV1063: $i,SV533: $i,SV2054: $i,SV1436: $i,SV1729: $i] :
( ( ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1436 ) )
= $true )
| ( ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(5744,plain,
! [SV1064: $i,SV534: $i,SV1730: $i,SV1437: $i,SV2055: $i] :
( ( ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1437 ) )
= $true )
| ( ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5727]) ).
thf(5745,plain,
! [SV2056: $i,SV536: $i,SV1732: $i,SV1066: $i,SV1439: $i,SV2117: $i] :
( ( ( ~ ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5728]) ).
thf(5746,plain,
! [SV1067: $i,SV1733: $i,SV537: $i,SV2057: $i,SV2118: $i,SV1440: $i] :
( ( ( ~ ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5729]) ).
thf(5747,plain,
! [SV2119: $i,SV2058: $i,SV538: $i,SV1734: $i,SV1068: $i,SV1441: $i] :
( ( ( ~ ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5730]) ).
thf(5748,plain,
! [SV1442: $i,SV1069: $i,SV1735: $i,SV539: $i,SV2059: $i,SV2120: $i] :
( ( ( ~ ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5731]) ).
thf(5749,plain,
! [SV1070: $i,SV1736: $i,SV540: $i,SV2060: $i,SV2121: $i,SV1443: $i] :
( ( ( ~ ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5732]) ).
thf(5750,plain,
! [SV1444: $i,SV1071: $i,SV1737: $i,SV541: $i,SV2061: $i,SV2122: $i] :
( ( ( ~ ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(5751,plain,
! [SV1909: $i,SV1337: $i,SV1661: $i,SV911: $i,SV2160: $i,SV2024: $i,SV2138: $i,SV375: $i,SV2109: $i,SV2157: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2157 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SV2160 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SV2157 @ ( tc_prod @ SV2138 @ SV2138 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5737]) ).
thf(5752,plain,
! [SV1938: $i,SV1057: $i,SV527: $i,SV1430: $i] :
( ( ( c_in @ SV1430 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( SV527 = SV1057 )
= $true )
| ( ( c_in @ SV1938 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1430 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1938 @ ( v_sko__local__X3__1 @ SV1430 @ SV1938 @ SV527 @ SV1057 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1057 @ SV527 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1938 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV527 @ SV1057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1430 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(5753,plain,
! [SV1431: $i,SV528: $i,SV1058: $i,SV1939: $i] :
( ( ( c_in @ SV1939 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( SV1058 = SV528 )
= $true )
| ( ( c_in @ SV1431 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1939 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1431 @ ( v_sko__local__X3__1 @ SV1939 @ SV1431 @ SV1058 @ SV528 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV528 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1939 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV528 @ SV1058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1431 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(5754,plain,
! [SV1061: $i,SV531: $i,SV2052: $i,SV1434: $i,SV1727: $i] :
( ( ( ~ ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1434 ) )
= $true )
| ( ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5755,plain,
! [SV1062: $i,SV532: $i,SV1728: $i,SV1435: $i,SV2053: $i] :
( ( ( ~ ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1435 ) )
= $true )
| ( ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5756,plain,
! [SV1063: $i,SV533: $i,SV2054: $i,SV1729: $i,SV1436: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV1436 )
= $false )
| ( ( c_in @ SV1729 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2054 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1729 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2054 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV533 @ SV1063 @ SV1729 @ SV2054 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV2054 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV533 @ SV1063 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1436 @ SV1729 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(5757,plain,
! [SV1064: $i,SV534: $i,SV1730: $i,SV2055: $i,SV1437: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV1437 )
= $false )
| ( ( c_in @ SV2055 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1730 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2055 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1730 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV534 @ SV1064 @ SV2055 @ SV1730 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV2055 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV534 @ SV1064 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1437 @ SV1730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(5758,plain,
! [SV2056: $i,SV536: $i,SV1732: $i,SV1066: $i,SV1439: $i,SV2117: $i] :
( ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(5759,plain,
! [SV1067: $i,SV1733: $i,SV537: $i,SV2057: $i,SV2118: $i,SV1440: $i] :
( ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5746]) ).
thf(5760,plain,
! [SV2119: $i,SV2058: $i,SV538: $i,SV1734: $i,SV1068: $i,SV1441: $i] :
( ( ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV1068 = SV1734 )
| ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(5761,plain,
! [SV1442: $i,SV1069: $i,SV1735: $i,SV539: $i,SV2059: $i,SV2120: $i] :
( ( ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV2059 = SV539 )
| ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5748]) ).
thf(5762,plain,
! [SV1070: $i,SV1736: $i,SV540: $i,SV2060: $i,SV2121: $i,SV1443: $i] :
( ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(5763,plain,
! [SV1444: $i,SV1071: $i,SV1737: $i,SV541: $i,SV2061: $i,SV2122: $i] :
( ( ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV2061 = SV541 )
| ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(5764,plain,
! [SV1909: $i,SV1337: $i,SV1661: $i,SV911: $i,SV2160: $i,SV2024: $i,SV2138: $i,SV375: $i,SV2109: $i,SV2157: $i] :
( ( ( c_Equiv__Relations_Ocongruent2 @ SV2157 @ SV2109 @ SV375 @ SV2138 @ SV2024 @ SV2160 )
= $false )
| ( ( c_in @ ( c_Pair @ SV911 @ SV1661 @ SV2138 @ SV2138 ) @ SV2157 @ ( tc_prod @ SV2138 @ SV2138 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1337 @ SV1909 @ SV2024 @ SV2024 ) @ SV2109 @ ( tc_prod @ SV2024 @ SV2024 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV911 ) @ SV1337 )
= ( hAPP @ ( hAPP @ SV375 @ SV1661 ) @ SV1909 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5751]) ).
thf(5765,plain,
! [SV1061: $i,SV531: $i,SV2052: $i,SV1434: $i,SV1727: $i] :
( ( ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1434 ) )
= $true )
| ( ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(5766,plain,
! [SV1062: $i,SV532: $i,SV1728: $i,SV1435: $i,SV2053: $i] :
( ( ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Arrow__Order__Mirabelle_OIIA @ SV1435 ) )
= $true )
| ( ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5767,plain,
! [SV2117: $i,SV2056: $i,SV536: $i,SV1732: $i,SV1066: $i,SV1439: $i] :
( ( ( ~ ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5758]) ).
thf(5768,plain,
! [SV1440: $i,SV1067: $i,SV1733: $i,SV537: $i,SV2057: $i,SV2118: $i] :
( ( ( ~ ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5759]) ).
thf(5769,plain,
! [SV2119: $i,SV1441: $i,SV2058: $i,SV538: $i,SV1734: $i,SV1068: $i] :
( ( ( SV1068 = SV1734 )
= $true )
| ( ( ( SV538 = SV2058 )
| ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5760]) ).
thf(5770,plain,
! [SV1442: $i,SV2120: $i,SV1069: $i,SV1735: $i,SV539: $i,SV2059: $i] :
( ( ( SV2059 = SV539 )
= $true )
| ( ( ( SV1735 = SV1069 )
| ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5761]) ).
thf(5771,plain,
! [SV1443: $i,SV1070: $i,SV1736: $i,SV540: $i,SV2060: $i,SV2121: $i] :
( ( ( ~ ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true )
| ( ( ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5762]) ).
thf(5772,plain,
! [SV1444: $i,SV2122: $i,SV1071: $i,SV1737: $i,SV541: $i,SV2061: $i] :
( ( ( SV2061 = SV541 )
= $true )
| ( ( ( SV1737 = SV1071 )
| ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5763]) ).
thf(5773,plain,
! [SV1061: $i,SV531: $i,SV2052: $i,SV1727: $i,SV1434: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV1434 )
= $false )
| ( ( c_in @ SV1727 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2052 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1727 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2052 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV531 @ SV1061 @ SV1727 @ SV2052 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV2052 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV531 @ SV1061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1434 @ SV1727 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(5774,plain,
! [SV1062: $i,SV532: $i,SV1728: $i,SV2053: $i,SV1435: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ SV1435 )
= $false )
| ( ( c_in @ SV2053 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1728 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2053 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1728 @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ SV532 @ SV1062 @ SV2053 @ SV1728 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV2053 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV532 @ SV1062 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1435 @ SV1728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5775,plain,
! [SV2117: $i,SV2056: $i,SV536: $i,SV1732: $i,SV1066: $i,SV1439: $i] :
( ( ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV1066 = SV1732 )
| ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5767]) ).
thf(5776,plain,
! [SV1440: $i,SV1067: $i,SV1733: $i,SV537: $i,SV2057: $i,SV2118: $i] :
( ( ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV2057 = SV537 )
| ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(5777,plain,
! [SV2119: $i,SV1441: $i,SV1068: $i,SV1734: $i,SV2058: $i,SV538: $i] :
( ( ( SV538 = SV2058 )
= $true )
| ( ( ( SV1734 = SV2058 )
| ( SV538 = SV1068 ) )
= $true )
| ( ( SV1068 = SV1734 )
= $true )
| ( ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5769]) ).
thf(5778,plain,
! [SV1442: $i,SV2120: $i,SV2059: $i,SV539: $i,SV1069: $i,SV1735: $i] :
( ( ( SV1735 = SV1069 )
= $true )
| ( ( ( SV539 = SV1069 )
| ( SV1735 = SV2059 ) )
= $true )
| ( ( SV2059 = SV539 )
= $true )
| ( ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5770]) ).
thf(5779,plain,
! [SV1443: $i,SV1070: $i,SV1736: $i,SV540: $i,SV2060: $i,SV2121: $i] :
( ( ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( ( SV2060 = SV540 )
| ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(5780,plain,
! [SV1444: $i,SV2122: $i,SV2061: $i,SV541: $i,SV1071: $i,SV1737: $i] :
( ( ( SV1737 = SV1071 )
= $true )
| ( ( ( SV541 = SV1071 )
| ( SV1737 = SV2061 ) )
= $true )
| ( ( SV2061 = SV541 )
= $true )
| ( ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5772]) ).
thf(5781,plain,
! [SV2117: $i,SV1439: $i,SV2056: $i,SV536: $i,SV1732: $i,SV1066: $i] :
( ( ( SV1066 = SV1732 )
= $true )
| ( ( ( SV536 = SV2056 )
| ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5775]) ).
thf(5782,plain,
! [SV1440: $i,SV2118: $i,SV1067: $i,SV1733: $i,SV537: $i,SV2057: $i] :
( ( ( SV2057 = SV537 )
= $true )
| ( ( ( SV1733 = SV1067 )
| ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5776]) ).
thf(5783,plain,
! [SV2119: $i,SV1441: $i,SV1068: $i,SV538: $i,SV2058: $i,SV1734: $i] :
( ( ( SV1734 = SV2058 )
= $true )
| ( ( SV538 = SV1068 )
= $true )
| ( ( SV538 = SV2058 )
= $true )
| ( ( SV1068 = SV1734 )
= $true )
| ( ( c_in @ SV1441 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2119 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1441 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2119 @ ( v_sko__local__X2__1 @ SV1441 @ SV2119 @ SV538 @ SV1734 @ SV1068 @ SV2058 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1734 @ SV2058 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2119 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV538 @ SV1068 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(5784,plain,
! [SV1442: $i,SV2120: $i,SV2059: $i,SV1735: $i,SV1069: $i,SV539: $i] :
( ( ( SV539 = SV1069 )
= $true )
| ( ( SV1735 = SV2059 )
= $true )
| ( ( SV1735 = SV1069 )
= $true )
| ( ( SV2059 = SV539 )
= $true )
| ( ( c_in @ SV2120 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1442 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2120 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1442 @ ( v_sko__local__X2__1 @ SV2120 @ SV1442 @ SV1735 @ SV539 @ SV2059 @ SV1069 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1735 @ SV2059 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2120 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV539 @ SV1069 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1442 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5778]) ).
thf(5785,plain,
! [SV1443: $i,SV2121: $i,SV1070: $i,SV1736: $i,SV540: $i,SV2060: $i] :
( ( ( SV2060 = SV540 )
= $true )
| ( ( ( SV1736 = SV1070 )
| ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5779]) ).
thf(5786,plain,
! [SV1444: $i,SV2122: $i,SV2061: $i,SV1737: $i,SV1071: $i,SV541: $i] :
( ( ( SV541 = SV1071 )
= $true )
| ( ( SV1737 = SV2061 )
= $true )
| ( ( SV1737 = SV1071 )
= $true )
| ( ( SV2061 = SV541 )
= $true )
| ( ( c_in @ SV2122 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1444 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2122 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1444 @ ( v_sko__local__X1__1 @ SV2122 @ SV1444 @ SV1737 @ SV541 @ SV2061 @ SV1071 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1737 @ SV2061 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2122 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV541 @ SV1071 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1444 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5780]) ).
thf(5787,plain,
! [SV2117: $i,SV1439: $i,SV1066: $i,SV1732: $i,SV2056: $i,SV536: $i] :
( ( ( SV536 = SV2056 )
= $true )
| ( ( ( SV1732 = SV2056 )
| ( SV536 = SV1066 ) )
= $true )
| ( ( SV1066 = SV1732 )
= $true )
| ( ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5788,plain,
! [SV1440: $i,SV2118: $i,SV2057: $i,SV537: $i,SV1067: $i,SV1733: $i] :
( ( ( SV1733 = SV1067 )
= $true )
| ( ( ( SV537 = SV1067 )
| ( SV1733 = SV2057 ) )
= $true )
| ( ( SV2057 = SV537 )
= $true )
| ( ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5782]) ).
thf(5789,plain,
! [SV1443: $i,SV2121: $i,SV2060: $i,SV540: $i,SV1070: $i,SV1736: $i] :
( ( ( SV1736 = SV1070 )
= $true )
| ( ( ( SV540 = SV1070 )
| ( SV1736 = SV2060 ) )
= $true )
| ( ( SV2060 = SV540 )
= $true )
| ( ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5785]) ).
thf(5790,plain,
! [SV2117: $i,SV1439: $i,SV1066: $i,SV536: $i,SV2056: $i,SV1732: $i] :
( ( ( SV1732 = SV2056 )
= $true )
| ( ( SV536 = SV1066 )
= $true )
| ( ( SV536 = SV2056 )
= $true )
| ( ( SV1066 = SV1732 )
= $true )
| ( ( c_in @ SV1439 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV2117 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1439 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2117 @ ( v_sko__local__X2__1 @ SV1439 @ SV2117 @ SV536 @ SV1732 @ SV1066 @ SV2056 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1732 @ SV2056 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2117 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV536 @ SV1066 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1439 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5787]) ).
thf(5791,plain,
! [SV1440: $i,SV2118: $i,SV2057: $i,SV1733: $i,SV1067: $i,SV537: $i] :
( ( ( SV537 = SV1067 )
= $true )
| ( ( SV1733 = SV2057 )
= $true )
| ( ( SV1733 = SV1067 )
= $true )
| ( ( SV2057 = SV537 )
= $true )
| ( ( c_in @ SV2118 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1440 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2118 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1440 @ ( v_sko__local__X2__1 @ SV2118 @ SV1440 @ SV1733 @ SV537 @ SV2057 @ SV1067 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1733 @ SV2057 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2118 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV537 @ SV1067 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5788]) ).
thf(5792,plain,
! [SV1443: $i,SV2121: $i,SV2060: $i,SV1736: $i,SV1070: $i,SV540: $i] :
( ( ( SV540 = SV1070 )
= $true )
| ( ( SV1736 = SV2060 )
= $true )
| ( ( SV1736 = SV1070 )
= $true )
| ( ( SV2060 = SV540 )
= $true )
| ( ( c_in @ SV2121 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV1443 @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV2121 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ SV1443 @ ( v_sko__local__X1__1 @ SV2121 @ SV1443 @ SV1736 @ SV540 @ SV2060 @ SV1070 ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1736 @ SV2060 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV2121 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV540 @ SV1070 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ SV1443 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5789]) ).
thf(5793,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1501,5792,5791,5790,5786,5784,5783,5774,5773,5764,5757,5756,5753,5752,5738,5736,5735,5734,5723,5722,5717,5716,5715,5713,5712,5695,5694,5693,5687,5684,5682,5681,5663,5655,5654,5653,5651,5645,5641,5640,5639,5638,5631,5622,5621,5618,5617,5616,5615,5614,5605,5604,5602,5601,5600,5599,5597,5594,5593,5592,5590,5588,5586,5585,5584,5583,5582,5581,5580,5579,5577,5576,5575,5573,5572,5568,5567,5565,5564,5542,5541,5535,5534,5533,5532,5531,5530,5529,5528,5527,5526,5524,5523,5521,5520,5511,5510,5508,5507,5492,5484,5478,5476,5472,5471,5470,5469,5468,5467,5466,5465,5464,5459,5458,5455,5452,5450,5449,5444,5443,5425,5424,5423,5422,5416,5415,5414,5413,5401,5400,5399,5398,5385,5383,5382,5381,5380,5373,5352,5346,5344,5343,5342,5341,5338,5337,5336,5335,5334,5333,5332,5331,5330,5325,5324,5323,5322,5320,5319,5318,5317,5316,5315,5313,5312,5311,5310,5309,5308,5307,5306,5302,5301,5296,5295,5294,5287,5283,5282,5281,5280,5279,5278,5266,5265,5264,5263,5254,5238,5235,5216,5213,5212,5211,5206,5200,5199,5192,5191,5186,5185,5181,5180,5178,5177,5175,5174,5167,5166,5164,5163,5162,5161,5159,5154,5153,5152,5151,5146,5138,5137,5136,5135,5127,5120,5118,5117,5106,5093,5084,5076,5075,5074,5073,5072,5071,5070,5064,5063,5062,5060,5059,5058,5054,5053,5048,5044,5041,5037,5033,5032,5023,5022,5021,5020,5006,4968,4966,4960,4957,4956,4953,4939,4938,4937,4936,4927,4926,4918,4917,4916,4911,4902,4901,4885,4884,4879,4875,4874,4866,4864,4853,4848,4847,4841,4839,4837,4836,4825,4824,4815,4814,4807,4806,4800,4799,4798,4796,4795,4787,4784,4783,4775,4774,4773,4772,4765,4763,4754,4753,4752,4751,4738,4735,4734,4733,4732,4731,4727,4726,4722,4721,4718,4717,4713,4712,4708,4707,4706,4678,4653,4650,4636,4635,4625,4624,4623,4619,4610,4609,4608,4607,4606,4605,4604,4576,4571,4568,4558,4555,4540,4539,4538,4537,4535,4534,4517,4493,4492,4482,4480,4457,4456,4454,4453,4452,4448,4445,4444,4440,4439,4435,4434,4424,4408,4407,4406,4405,4404,4403,4390,4389,4388,4387,4382,4380,4379,4376,4375,4374,4373,4370,4369,4362,4361,4355,4354,4353,4349,4340,4329,4320,4319,4311,4310,4307,4305,4304,4300,4299,4298,4297,4296,4295,4294,4293,4292,4234,4231,4204,4202,4199,4198,4197,4196,4195,4181,4180,4179,4177,4176,4173,4172,4169,4156,4151,4142,4133,4130,4095,4094,4093,4052,4051,4050,4049,4025,4024,4010,4007,4001,4000,3984,3983,3975,3974,3973,3972,3951,3946,3920,3919,3915,3873,3872,3871,3870,3853,3852,3851,3848,3847,3846,3845,3844,3843,3842,3833,3832,3828,3823,3821,3820,3805,3804,3803,3753,3747,3743,3722,3721,3717,3716,3712,3702,3701,3646,3642,3641,3640,3633,3630,3600,3555,3554,3546,3527,3498,3487,3486,3458,3457,3455,3440,3434,3432,3431,3427,3418,3394,3385,3384,3354,3331,3325,3317,3297,3293,3292,3290,3209,3208,3186,3185,3183,3182,3178,3176,3171,3169,3167,3166,3165,3164,3163,3158,3155,3140,3137,3136,3098,3095,3094,3048,3043,3042,3041,2989,2988,2986,2985,2984,2963,2962,2951,2950,2939,2938,2910,2899,2896,2874,2780,2779,2757,2756,2746,2745,2727,2725,2719,2711,2699,2693,2682,2590,2570,2548,2399,2380,2379,2317,2315,2306,2275,2238,2235,2121,2111,2110,2109,2108,2107,2106,2105,2104,2103,2093,2089,2074,1979,1959,1894,1649]) ).
thf(5794,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT061-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n016.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 14:25:44 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 177.64/29.93 ....
% 177.64/29.93
% 177.64/29.93 No.of.Axioms: 613
% 177.64/29.93
% 177.64/29.93 Length.of.Defs: 0
% 177.64/29.93
% 177.64/29.93 Contains.Choice.Funs: false
% 177.64/29.93 .................................................................................................................................................................................................................................................................................................
% 177.64/29.93
% 177.64/29.93 ********************************
% 177.64/29.93 * All subproblems solved! *
% 177.64/29.93 ********************************
% 177.64/29.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:613,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5793,loop_count:0,foatp_calls:1,translation:fof_full)
% 177.64/29.93
% 177.64/29.93 %**** Beginning of derivation protocol ****
% 177.64/29.93 % SZS output start CNFRefutation
% See solution above
% 177.64/30.01
% 177.64/30.01 %**** End of derivation protocol ****
% 177.64/30.01 %**** no. of clauses in derivation: 5794 ****
% 177.64/30.01 %**** clause counter: 5793 ****
% 177.64/30.01
% 177.64/30.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:613,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5793,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------