%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SCT073-1 : 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 : n017.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 10:38:16 AM UTC 2026
% Result : Unsatisfiable 151.67s 30.71s
% Output : CNFRefutation 151.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 550
% Syntax : Number of formulae : 5018 (3220 unt; 0 typ; 0 def)
% Number of atoms : 27363 (9512 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 102808 (5811 ~;8517 |; 0 &;88480 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 12 con; 0-7 aty)
% Number of variables : 19493 ( 0 ^;19493 !; 0 ?;19493 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1,type,
c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XDomainE__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
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__Xrefl__onI__1__1,type,
c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1,type,
c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1: $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__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__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__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__XwfI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1: $i > $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__eq__minimal__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_OLin,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(tp_c_Arrow__Order__Mirabelle_Oabove,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_Obelow,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
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_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
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_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
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_FuncSet_Osko__FuncSet__XfuncsetI__1__1,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__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__Equiv__Relations__XquotientE__1__1,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $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_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_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_Oconverse,type,
c_Relation_Oconverse: $i > $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_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_Relation_Otrans,type,
c_Relation_Otrans: $i > $i > $o ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
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_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_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Finite__Set_Ofinite_Ofinite,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(tp_class_HOL_Oord,type,
class_HOL_Oord: $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_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_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_a____,type,
v_a____: $i ).
thf(tp_v_b____,type,
v_b____: $i ).
thf(tp_v_r,type,
v_r: $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__Xlinear__alt__1,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $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_thesis____,type,
v_thesis____: $o ).
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_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(5,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(6,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(7,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(8,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(9,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(10,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(11,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
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_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(14,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(15,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(16,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(17,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(18,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(19,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(20,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(21,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
thf(22,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(23,axiom,
! [V_b: $i,V_a: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
thf(24,axiom,
! [V_Lab: $i] :
( v_thesis____
| ~ ( c_in @ V_Lab @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_Lab @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(25,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(26,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(27,axiom,
! [V_y: $i,V_x: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
thf(28,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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
thf(29,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(30,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(31,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ( V_y = V_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).
thf(32,axiom,
! [V_xa: $i,V_b: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_b @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).
thf(33,axiom,
! [V_x: $i,V_xa: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_xa @ 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_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_11) ).
thf(34,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).
thf(35,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).
thf(36,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ 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_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).
thf(37,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).
thf(38,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_b: $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_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_12) ).
thf(39,axiom,
! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_13) ).
thf(40,axiom,
! [V_xa: $i,V_x: $i,V_L: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).
thf(41,axiom,
! [V_y: $i,V_x: $i,V_L: $i,V_b: $i] :
( ( 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_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_b @ 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_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).
thf(42,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $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_a )
| ( V_y = V_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).
thf(43,axiom,
! [V_x: $i,V_a: $i,V_xa: $i,V_L: $i] :
( ( V_x = V_a )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).
thf(44,axiom,
! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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_x )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).
thf(45,axiom,
! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).
thf(46,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).
thf(47,axiom,
! [V_a: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).
thf(48,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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_11) ).
thf(49,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).
thf(50,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_x = V_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).
thf(51,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).
thf(52,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).
thf(53,axiom,
! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_12) ).
thf(54,axiom,
! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_13) ).
thf(55,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_a @ 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).
thf(56,axiom,
! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ( 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_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).
thf(57,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_b: $i,V_a: $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_b )
| ( V_x = V_b )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).
thf(58,axiom,
! [V_x: $i,V_b: $i,V_y: $i,V_L: $i] :
( ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).
thf(59,axiom,
! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).
thf(60,axiom,
! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).
thf(61,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(62,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(63,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(64,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(65,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(66,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(67,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(68,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(69,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(70,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(71,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(72,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(73,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(74,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(75,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(76,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(77,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(78,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(79,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(80,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(81,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(82,axiom,
! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).
thf(83,axiom,
! [V_L: $i] :
( ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(84,axiom,
! [V_L: $i] :
( ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(85,axiom,
c_in @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).
thf(86,axiom,
! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).
thf(87,axiom,
! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
thf(88,axiom,
! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
thf(89,axiom,
! [V_a: $i,V_b: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
thf(90,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(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_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(92,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(93,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(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_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(95,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(96,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(97,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(98,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(99,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(100,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(101,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(102,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(103,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_X: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(104,axiom,
! [V_A: $i,V_X: $i,T_a: $i,V_C: $i] :
( ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterD_0) ).
thf(105,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_xa: $i,V_A: $i,V_r: $i] :
( ~ ( c_in @ V_y @ V_x @ T_a )
| ~ ( c_in @ V_xa @ V_x @ T_a )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_xa @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
thf(106,axiom,
! [V_X: $i,V_Y: $i,V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( V_X = V_Y )
| ~ ( 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_Y @ T_a )
| ~ ( c_in @ V_x @ V_X @ T_a )
| ~ ( c_in @ V_Y @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ 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_quotient__eqI_0) ).
thf(107,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(108,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(109,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(110,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(111,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(112,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(113,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(114,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(115,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(116,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(117,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(118,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(119,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(120,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(121,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(122,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(123,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(124,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(125,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(126,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ),
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_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
thf(129,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(130,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(132,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(133,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(134,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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,
! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(136,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(137,axiom,
! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(138,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(139,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(140,axiom,
! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(141,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(142,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(143,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(144,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(145,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(146,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(147,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(148,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(149,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(150,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(151,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(152,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(153,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(154,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(155,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(156,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(157,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(158,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(159,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(160,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(161,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(162,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(163,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(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_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(165,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_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(166,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(167,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(168,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(169,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( 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(170,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 ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( 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(171,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(172,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(173,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(174,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(175,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(176,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(177,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(178,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(179,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(180,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(181,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(182,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(183,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(184,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(185,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(186,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(187,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(188,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(189,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(190,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(191,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(192,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(193,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(194,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(195,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(196,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(197,axiom,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(198,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(199,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(200,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(201,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(202,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(203,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(204,axiom,
! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_0) ).
thf(205,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(206,axiom,
! [V_A: $i,V_X: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ V_A @ V_X @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_1) ).
thf(207,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(208,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(209,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(210,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(211,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(212,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(213,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(214,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(215,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(216,axiom,
! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_1) ).
thf(217,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(218,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(219,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(220,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(221,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(222,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(223,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(224,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(225,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(226,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(227,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(228,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(229,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(230,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(231,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(232,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(233,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(234,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(235,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(236,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(237,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(238,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(239,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(240,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(241,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(242,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(243,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(244,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(245,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(246,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(247,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(248,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(249,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(250,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(251,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(252,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(253,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(254,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(255,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(256,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(257,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(258,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(259,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(260,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(261,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(262,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(263,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(264,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(265,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(266,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(267,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(268,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(269,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(270,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(271,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(272,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(273,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(274,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(275,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(276,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(277,axiom,
! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ T_a )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_0) ).
thf(278,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(279,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(280,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(281,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(282,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(283,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(284,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_B @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(285,axiom,
! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(286,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(287,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(288,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(289,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(290,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(291,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(292,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(293,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(294,axiom,
! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_1) ).
thf(295,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(296,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(297,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
thf(298,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(299,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(300,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(301,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(302,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(303,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(304,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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_refl__on__def_3) ).
thf(305,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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_refl__onI_1) ).
thf(306,axiom,
! [V_X: $i,T_a: $i,V_A: $i,V_r: $i] :
( ( c_Finite__Set_Ofinite @ V_X @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ 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 ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__equiv__class_0) ).
thf(307,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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_refl__onI_0) ).
thf(308,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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_refl__on__def_2) ).
thf(309,axiom,
! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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_wfI_2) ).
thf(310,axiom,
! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_B @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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_wfI_3) ).
thf(311,axiom,
! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(312,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(313,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(314,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( 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__image_0) ).
thf(315,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_0) ).
thf(316,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ V_B @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_1) ).
thf(317,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).
thf(318,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(319,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(320,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(321,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(322,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(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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( 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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( 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_M: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Inter_0) ).
thf(327,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(328,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(329,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(330,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(331,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 ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ 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_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(332,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 ) @ V_r @ ( 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 ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
thf(333,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(334,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(335,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(336,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(337,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(338,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(339,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(340,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(341,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(342,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(343,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(344,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(345,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(346,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(347,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(348,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(349,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(350,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(351,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(352,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(353,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(354,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(355,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(356,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(357,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(358,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(359,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(360,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(361,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(362,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(363,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(364,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(365,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(366,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(367,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(368,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(369,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(370,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(371,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(372,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(373,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(374,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(375,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(376,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(377,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(378,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(379,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(380,axiom,
! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(381,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(382,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(383,axiom,
! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(384,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(385,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(386,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(387,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(388,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(389,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(390,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(391,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(392,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(393,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(394,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
thf(395,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(396,axiom,
! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(397,axiom,
! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(398,axiom,
! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(399,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(400,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(401,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(402,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(403,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(404,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(405,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(406,axiom,
! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(407,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(408,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(409,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(410,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(411,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( 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_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
thf(412,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(413,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(414,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(415,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(416,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(417,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(418,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(419,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(420,axiom,
! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(421,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(422,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(423,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(424,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(425,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(426,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(427,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( hAPP @ V_D @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).
thf(428,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(429,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(430,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(431,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(432,axiom,
! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(433,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(434,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(435,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(436,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(437,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(438,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(439,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(440,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(441,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(442,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(443,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(444,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(445,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(446,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(447,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(448,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(449,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(450,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(451,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(452,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(453,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(454,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(455,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(456,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(457,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(458,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(459,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(460,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(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_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(476,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(477,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(478,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(479,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(480,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(481,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(482,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(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_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(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__iff_2) ).
thf(485,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(486,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(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,
! [V_r: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).
thf(490,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(491,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(492,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(493,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(494,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(495,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(496,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(497,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(498,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(499,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(500,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(501,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(502,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(503,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(504,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(505,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(506,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(507,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(508,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(509,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(510,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(511,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(512,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(513,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(514,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(515,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(516,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(517,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(518,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(519,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(520,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(521,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(522,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(523,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(524,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(525,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(526,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(527,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(528,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(529,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(530,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(531,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(532,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(533,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(534,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(535,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(536,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(537,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(538,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(539,axiom,
! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(540,axiom,
! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(541,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(542,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(543,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(544,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(545,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(546,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(547,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(548,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(549,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(550,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[549]) ).
thf(551,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(552,plain,
$false = $false,
inference(unfold_def,[status(thm)],[550]) ).
thf(553,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(554,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(555,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(556,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(557,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(558,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(559,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(560,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(561,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(562,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(563,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(564,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(565,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)],[13]) ).
thf(566,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)],[14]) ).
thf(567,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)],[15]) ).
thf(568,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(569,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)],[17]) ).
thf(570,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)],[18]) ).
thf(571,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)],[19]) ).
thf(572,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(573,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(574,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(575,plain,
( ( ! [V_b: $i,V_a: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(576,plain,
( ( ! [V_Lab: $i] :
( v_thesis____
| ~ ( c_in @ V_Lab @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_Lab @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(577,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)],[25]) ).
thf(578,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)],[26]) ).
thf(579,plain,
( ( ! [V_y: $i,V_x: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(580,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(581,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)],[29]) ).
thf(582,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)],[30]) ).
thf(583,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ( V_y = V_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(584,plain,
( ( ! [V_xa: $i,V_b: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_b @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(585,plain,
( ( ! [V_x: $i,V_xa: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_xa @ 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_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(586,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(587,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(588,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ 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_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(589,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(590,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_b: $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_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(591,plain,
( ( ! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(592,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(593,plain,
( ( ! [V_y: $i,V_x: $i,V_L: $i,V_b: $i] :
( ( 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_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_b @ 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_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(594,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $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_a )
| ( V_y = V_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(595,plain,
( ( ! [V_x: $i,V_a: $i,V_xa: $i,V_L: $i] :
( ( V_x = V_a )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(596,plain,
( ( ! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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_x )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(597,plain,
( ( ! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(598,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(599,plain,
( ( ! [V_a: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(600,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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(601,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(602,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_x = V_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(603,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(604,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(605,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(606,plain,
( ( ! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(607,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_a @ 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(608,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ( 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_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(609,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_b: $i,V_a: $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_b )
| ( V_x = V_b )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(610,plain,
( ( ! [V_x: $i,V_b: $i,V_y: $i,V_L: $i] :
( ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(611,plain,
( ( ! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(612,plain,
( ( ! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(613,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)],[61]) ).
thf(614,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)],[62]) ).
thf(615,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)],[63]) ).
thf(616,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)],[64]) ).
thf(617,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)],[65]) ).
thf(618,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)],[66]) ).
thf(619,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)],[67]) ).
thf(620,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)],[68]) ).
thf(621,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)],[69]) ).
thf(622,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)],[70]) ).
thf(623,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)],[71]) ).
thf(624,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)],[72]) ).
thf(625,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)],[73]) ).
thf(626,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)],[74]) ).
thf(627,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)],[75]) ).
thf(628,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)],[76]) ).
thf(629,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)],[77]) ).
thf(630,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)],[78]) ).
thf(631,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)],[79]) ).
thf(632,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)],[80]) ).
thf(633,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)],[81]) ).
thf(634,plain,
( ( ! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(635,plain,
( ( ! [V_L: $i] :
( ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(636,plain,
( ( ! [V_L: $i] :
( ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(637,plain,
( ( c_in @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(638,plain,
( ( ! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(639,plain,
( ( ! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(640,plain,
( ( ! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(641,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(642,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)],[90]) ).
thf(643,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)],[91]) ).
thf(644,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)],[92]) ).
thf(645,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)],[93]) ).
thf(646,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)],[94]) ).
thf(647,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)],[95]) ).
thf(648,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)],[96]) ).
thf(649,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)],[97]) ).
thf(650,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)],[98]) ).
thf(651,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)],[99]) ).
thf(652,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)],[100]) ).
thf(653,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)],[101]) ).
thf(654,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)],[102]) ).
thf(655,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_X: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(656,plain,
( ( ! [V_A: $i,V_X: $i,T_a: $i,V_C: $i] :
( ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(657,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_xa: $i,V_A: $i,V_r: $i] :
( ~ ( c_in @ V_y @ V_x @ T_a )
| ~ ( c_in @ V_xa @ V_x @ T_a )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_xa @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(658,plain,
( ( ! [V_X: $i,V_Y: $i,V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( V_X = V_Y )
| ~ ( 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_Y @ T_a )
| ~ ( c_in @ V_x @ V_X @ T_a )
| ~ ( c_in @ V_Y @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(659,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)],[107]) ).
thf(660,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)],[108]) ).
thf(661,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)],[109]) ).
thf(662,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)],[110]) ).
thf(663,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)],[111]) ).
thf(664,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)],[112]) ).
thf(665,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)],[113]) ).
thf(666,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)],[114]) ).
thf(667,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)],[115]) ).
thf(668,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)],[116]) ).
thf(669,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)],[117]) ).
thf(670,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)],[118]) ).
thf(671,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)],[119]) ).
thf(672,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)],[120]) ).
thf(673,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)],[121]) ).
thf(674,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)],[122]) ).
thf(675,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(676,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(677,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(678,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(679,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(680,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(681,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)],[129]) ).
thf(682,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(683,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(684,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)],[132]) ).
thf(685,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(686,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(687,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(688,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(689,plain,
( ( ! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(690,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)],[138]) ).
thf(691,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)],[139]) ).
thf(692,plain,
( ( ! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(693,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)],[141]) ).
thf(694,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)],[142]) ).
thf(695,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)],[143]) ).
thf(696,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)],[144]) ).
thf(697,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(698,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)],[146]) ).
thf(699,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(700,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(701,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)],[149]) ).
thf(702,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)],[150]) ).
thf(703,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)],[151]) ).
thf(704,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)],[152]) ).
thf(705,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(706,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(707,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(708,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)],[156]) ).
thf(709,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)],[157]) ).
thf(710,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(711,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)],[159]) ).
thf(712,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(713,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(714,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)],[162]) ).
thf(715,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)],[163]) ).
thf(716,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(717,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_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(718,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)],[166]) ).
thf(719,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)],[167]) ).
thf(720,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)],[168]) ).
thf(721,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( 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)],[169]) ).
thf(722,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 ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( 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)],[170]) ).
thf(723,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(724,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)],[172]) ).
thf(725,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)],[173]) ).
thf(726,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)],[174]) ).
thf(727,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)],[175]) ).
thf(728,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)],[176]) ).
thf(729,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)],[177]) ).
thf(730,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)],[178]) ).
thf(731,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)],[179]) ).
thf(732,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)],[180]) ).
thf(733,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)],[181]) ).
thf(734,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)],[182]) ).
thf(735,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)],[183]) ).
thf(736,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)],[184]) ).
thf(737,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)],[185]) ).
thf(738,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)],[186]) ).
thf(739,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)],[187]) ).
thf(740,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)],[188]) ).
thf(741,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)],[189]) ).
thf(742,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)],[190]) ).
thf(743,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)],[191]) ).
thf(744,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)],[192]) ).
thf(745,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)],[193]) ).
thf(746,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)],[194]) ).
thf(747,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)],[195]) ).
thf(748,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)],[196]) ).
thf(749,plain,
( ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(750,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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)],[198]) ).
thf(751,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)],[199]) ).
thf(752,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)],[200]) ).
thf(753,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)],[201]) ).
thf(754,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)],[202]) ).
thf(755,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)],[203]) ).
thf(756,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(757,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)],[205]) ).
thf(758,plain,
( ( ! [V_A: $i,V_X: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ V_A @ V_X @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(759,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)],[207]) ).
thf(760,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)],[208]) ).
thf(761,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)],[209]) ).
thf(762,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)],[210]) ).
thf(763,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)],[211]) ).
thf(764,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)],[212]) ).
thf(765,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)],[213]) ).
thf(766,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(767,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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)],[215]) ).
thf(768,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(769,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)],[217]) ).
thf(770,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)],[218]) ).
thf(771,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)],[219]) ).
thf(772,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)],[220]) ).
thf(773,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)],[221]) ).
thf(774,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)],[222]) ).
thf(775,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)],[223]) ).
thf(776,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)],[224]) ).
thf(777,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)],[225]) ).
thf(778,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)],[226]) ).
thf(779,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)],[227]) ).
thf(780,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)],[228]) ).
thf(781,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)],[229]) ).
thf(782,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)],[230]) ).
thf(783,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)],[231]) ).
thf(784,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)],[232]) ).
thf(785,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)],[233]) ).
thf(786,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)],[234]) ).
thf(787,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)],[235]) ).
thf(788,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)],[236]) ).
thf(789,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)],[237]) ).
thf(790,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)],[238]) ).
thf(791,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)],[239]) ).
thf(792,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)],[240]) ).
thf(793,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)],[241]) ).
thf(794,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)],[242]) ).
thf(795,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)],[243]) ).
thf(796,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)],[244]) ).
thf(797,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)],[245]) ).
thf(798,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)],[246]) ).
thf(799,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)],[247]) ).
thf(800,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)],[248]) ).
thf(801,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)],[249]) ).
thf(802,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)],[250]) ).
thf(803,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)],[251]) ).
thf(804,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)],[252]) ).
thf(805,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(806,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)],[254]) ).
thf(807,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)],[255]) ).
thf(808,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)],[256]) ).
thf(809,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)],[257]) ).
thf(810,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)],[258]) ).
thf(811,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)],[259]) ).
thf(812,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)],[260]) ).
thf(813,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)],[261]) ).
thf(814,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)],[262]) ).
thf(815,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)],[263]) ).
thf(816,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)],[264]) ).
thf(817,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)],[265]) ).
thf(818,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)],[266]) ).
thf(819,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)],[267]) ).
thf(820,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)],[268]) ).
thf(821,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)],[269]) ).
thf(822,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)],[270]) ).
thf(823,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)],[271]) ).
thf(824,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)],[272]) ).
thf(825,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)],[273]) ).
thf(826,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)],[274]) ).
thf(827,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)],[275]) ).
thf(828,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(829,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ T_a )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(830,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)],[278]) ).
thf(831,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)],[279]) ).
thf(832,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)],[280]) ).
thf(833,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)],[281]) ).
thf(834,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)],[282]) ).
thf(835,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)],[283]) ).
thf(836,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_B @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(837,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(838,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)],[286]) ).
thf(839,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)],[287]) ).
thf(840,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)],[288]) ).
thf(841,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)],[289]) ).
thf(842,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)],[290]) ).
thf(843,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)],[291]) ).
thf(844,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)],[292]) ).
thf(845,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)],[293]) ).
thf(846,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(847,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)],[295]) ).
thf(848,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)],[296]) ).
thf(849,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(850,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)],[298]) ).
thf(851,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)],[299]) ).
thf(852,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)],[300]) ).
thf(853,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)],[301]) ).
thf(854,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)],[302]) ).
thf(855,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)],[303]) ).
thf(856,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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)],[304]) ).
thf(857,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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)],[305]) ).
thf(858,plain,
( ( ! [V_X: $i,T_a: $i,V_A: $i,V_r: $i] :
( ( c_Finite__Set_Ofinite @ V_X @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ 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 ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(859,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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)],[307]) ).
thf(860,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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)],[308]) ).
thf(861,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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)],[309]) ).
thf(862,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_B @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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)],[310]) ).
thf(863,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(864,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)],[312]) ).
thf(865,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)],[313]) ).
thf(866,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( 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)],[314]) ).
thf(867,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(868,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ V_B @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(869,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(870,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)],[318]) ).
thf(871,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)],[319]) ).
thf(872,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)],[320]) ).
thf(873,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)],[321]) ).
thf(874,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)],[322]) ).
thf(875,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(876,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(877,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(878,plain,
( ( ! [V_M: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(879,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)],[327]) ).
thf(880,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)],[328]) ).
thf(881,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)],[329]) ).
thf(882,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)],[330]) ).
thf(883,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 ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ 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_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(884,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 ) @ V_r @ ( 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 ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(885,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(886,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(887,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)],[335]) ).
thf(888,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(889,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(890,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)],[338]) ).
thf(891,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)],[339]) ).
thf(892,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(893,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(894,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)],[342]) ).
thf(895,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)],[343]) ).
thf(896,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)],[344]) ).
thf(897,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)],[345]) ).
thf(898,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)],[346]) ).
thf(899,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)],[347]) ).
thf(900,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)],[348]) ).
thf(901,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)],[349]) ).
thf(902,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)],[350]) ).
thf(903,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)],[351]) ).
thf(904,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)],[352]) ).
thf(905,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)],[353]) ).
thf(906,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)],[354]) ).
thf(907,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)],[355]) ).
thf(908,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)],[356]) ).
thf(909,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)],[357]) ).
thf(910,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)],[358]) ).
thf(911,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)],[359]) ).
thf(912,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)],[360]) ).
thf(913,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)],[361]) ).
thf(914,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)],[362]) ).
thf(915,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)],[363]) ).
thf(916,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)],[364]) ).
thf(917,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)],[365]) ).
thf(918,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)],[366]) ).
thf(919,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)],[367]) ).
thf(920,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)],[368]) ).
thf(921,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)],[369]) ).
thf(922,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)],[370]) ).
thf(923,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)],[371]) ).
thf(924,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)],[372]) ).
thf(925,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)],[373]) ).
thf(926,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)],[374]) ).
thf(927,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)],[375]) ).
thf(928,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)],[376]) ).
thf(929,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)],[377]) ).
thf(930,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(931,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)],[379]) ).
thf(932,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(933,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)],[381]) ).
thf(934,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)],[382]) ).
thf(935,plain,
( ( ! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(936,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)],[384]) ).
thf(937,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)],[385]) ).
thf(938,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)],[386]) ).
thf(939,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)],[387]) ).
thf(940,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)],[388]) ).
thf(941,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)],[389]) ).
thf(942,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)],[390]) ).
thf(943,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)],[391]) ).
thf(944,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)],[392]) ).
thf(945,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)],[393]) ).
thf(946,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(947,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)],[395]) ).
thf(948,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(949,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(950,plain,
( ( ! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(951,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)],[399]) ).
thf(952,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)],[400]) ).
thf(953,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)],[401]) ).
thf(954,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)],[402]) ).
thf(955,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)],[403]) ).
thf(956,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)],[404]) ).
thf(957,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)],[405]) ).
thf(958,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(959,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)],[407]) ).
thf(960,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)],[408]) ).
thf(961,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)],[409]) ).
thf(962,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)],[410]) ).
thf(963,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( 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_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(964,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)],[412]) ).
thf(965,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)],[413]) ).
thf(966,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)],[414]) ).
thf(967,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(968,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(969,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(970,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(971,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(972,plain,
( ( ! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(973,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)],[421]) ).
thf(974,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)],[422]) ).
thf(975,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)],[423]) ).
thf(976,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)],[424]) ).
thf(977,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)],[425]) ).
thf(978,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)],[426]) ).
thf(979,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( hAPP @ V_D @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(980,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)],[428]) ).
thf(981,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(982,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(983,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(984,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(985,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)],[433]) ).
thf(986,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)],[434]) ).
thf(987,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)],[435]) ).
thf(988,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)],[436]) ).
thf(989,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)],[437]) ).
thf(990,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)],[438]) ).
thf(991,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)],[439]) ).
thf(992,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)],[440]) ).
thf(993,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)],[441]) ).
thf(994,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)],[442]) ).
thf(995,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)],[443]) ).
thf(996,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)],[444]) ).
thf(997,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)],[445]) ).
thf(998,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)],[446]) ).
thf(999,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)],[447]) ).
thf(1000,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1001,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1002,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1003,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)],[451]) ).
thf(1004,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)],[452]) ).
thf(1005,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)],[453]) ).
thf(1006,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)],[454]) ).
thf(1007,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)],[455]) ).
thf(1008,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)],[456]) ).
thf(1009,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1010,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)],[458]) ).
thf(1011,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)],[459]) ).
thf(1012,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)],[460]) ).
thf(1013,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(1014,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(1015,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(1016,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(1017,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(1018,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(1019,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(1020,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(1021,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(1022,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(1023,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(1024,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(1025,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(1026,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(1027,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1028,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)],[476]) ).
thf(1029,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)],[477]) ).
thf(1030,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)],[478]) ).
thf(1031,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)],[479]) ).
thf(1032,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1033,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)],[481]) ).
thf(1034,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)],[482]) ).
thf(1035,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)],[483]) ).
thf(1036,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(1037,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1038,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)],[486]) ).
thf(1039,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(1040,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(1041,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1042,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)],[490]) ).
thf(1043,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)],[491]) ).
thf(1044,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)],[492]) ).
thf(1045,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)],[493]) ).
thf(1046,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)],[494]) ).
thf(1047,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)],[495]) ).
thf(1048,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)],[496]) ).
thf(1049,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)],[497]) ).
thf(1050,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)],[498]) ).
thf(1051,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)],[499]) ).
thf(1052,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)],[500]) ).
thf(1053,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)],[501]) ).
thf(1054,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)],[502]) ).
thf(1055,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)],[503]) ).
thf(1056,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)],[504]) ).
thf(1057,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)],[505]) ).
thf(1058,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)],[506]) ).
thf(1059,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)],[507]) ).
thf(1060,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)],[508]) ).
thf(1061,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)],[509]) ).
thf(1062,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)],[510]) ).
thf(1063,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)],[511]) ).
thf(1064,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)],[512]) ).
thf(1065,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)],[513]) ).
thf(1066,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)],[514]) ).
thf(1067,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)],[515]) ).
thf(1068,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)],[516]) ).
thf(1069,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)],[517]) ).
thf(1070,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)],[518]) ).
thf(1071,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)],[519]) ).
thf(1072,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)],[520]) ).
thf(1073,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)],[521]) ).
thf(1074,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)],[522]) ).
thf(1075,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)],[523]) ).
thf(1076,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)],[524]) ).
thf(1077,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)],[525]) ).
thf(1078,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)],[526]) ).
thf(1079,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)],[527]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1081,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1082,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1083,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1084,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)],[532]) ).
thf(1085,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)],[533]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1087,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)],[535]) ).
thf(1088,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)],[536]) ).
thf(1089,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)],[537]) ).
thf(1090,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)],[538]) ).
thf(1091,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1092,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1093,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)],[541]) ).
thf(1094,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)],[542]) ).
thf(1095,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)],[543]) ).
thf(1096,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)],[544]) ).
thf(1097,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)],[545]) ).
thf(1098,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)],[546]) ).
thf(1099,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)],[547]) ).
thf(1100,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1101,plain,
( ( ~ v_thesis____ ) = $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1102,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[552]) ).
thf(1103,plain,
( ( ~ v_thesis____ ) = $true ),
inference(copy,[status(thm)],[1101]) ).
thf(1104,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1105,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(copy,[status(thm)],[1099]) ).
thf(1106,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)],[1098]) ).
thf(1107,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(copy,[status(thm)],[1097]) ).
thf(1108,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(copy,[status(thm)],[1096]) ).
thf(1109,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)],[1095]) ).
thf(1110,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)],[1094]) ).
thf(1111,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)],[1093]) ).
thf(1112,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1113,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1114,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(copy,[status(thm)],[1090]) ).
thf(1115,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)],[1089]) ).
thf(1116,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)],[1088]) ).
thf(1117,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)],[1087]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(1119,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)],[1085]) ).
thf(1120,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)],[1084]) ).
thf(1121,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1122,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1123,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1124,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1125,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)],[1079]) ).
thf(1126,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)],[1078]) ).
thf(1127,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(copy,[status(thm)],[1077]) ).
thf(1128,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)],[1076]) ).
thf(1129,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)],[1075]) ).
thf(1130,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)],[1074]) ).
thf(1131,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)],[1073]) ).
thf(1132,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)],[1072]) ).
thf(1133,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)],[1071]) ).
thf(1134,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)],[1070]) ).
thf(1135,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)],[1069]) ).
thf(1136,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)],[1068]) ).
thf(1137,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(copy,[status(thm)],[1067]) ).
thf(1138,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(copy,[status(thm)],[1066]) ).
thf(1139,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(copy,[status(thm)],[1065]) ).
thf(1140,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(copy,[status(thm)],[1064]) ).
thf(1141,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)],[1063]) ).
thf(1142,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)],[1062]) ).
thf(1143,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)],[1061]) ).
thf(1144,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(copy,[status(thm)],[1060]) ).
thf(1145,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(copy,[status(thm)],[1059]) ).
thf(1146,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(copy,[status(thm)],[1058]) ).
thf(1147,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)],[1057]) ).
thf(1148,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)],[1056]) ).
thf(1149,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)],[1055]) ).
thf(1150,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)],[1054]) ).
thf(1151,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(copy,[status(thm)],[1053]) ).
thf(1152,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(copy,[status(thm)],[1052]) ).
thf(1153,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(copy,[status(thm)],[1051]) ).
thf(1154,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(copy,[status(thm)],[1050]) ).
thf(1155,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(copy,[status(thm)],[1049]) ).
thf(1156,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(copy,[status(thm)],[1048]) ).
thf(1157,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(copy,[status(thm)],[1047]) ).
thf(1158,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)],[1046]) ).
thf(1159,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(copy,[status(thm)],[1045]) ).
thf(1160,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(copy,[status(thm)],[1044]) ).
thf(1161,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(copy,[status(thm)],[1043]) ).
thf(1162,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)],[1042]) ).
thf(1163,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_OField @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1164,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(copy,[status(thm)],[1040]) ).
thf(1165,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)],[1039]) ).
thf(1166,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)],[1038]) ).
thf(1167,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(1168,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)],[1036]) ).
thf(1169,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(copy,[status(thm)],[1035]) ).
thf(1170,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)],[1034]) ).
thf(1171,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(copy,[status(thm)],[1033]) ).
thf(1172,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1173,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)],[1031]) ).
thf(1174,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)],[1030]) ).
thf(1175,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)],[1029]) ).
thf(1176,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)],[1028]) ).
thf(1177,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1178,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)],[1026]) ).
thf(1179,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(copy,[status(thm)],[1025]) ).
thf(1180,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(copy,[status(thm)],[1024]) ).
thf(1181,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(copy,[status(thm)],[1023]) ).
thf(1182,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(copy,[status(thm)],[1022]) ).
thf(1183,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(copy,[status(thm)],[1021]) ).
thf(1184,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(copy,[status(thm)],[1020]) ).
thf(1185,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(copy,[status(thm)],[1019]) ).
thf(1186,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(copy,[status(thm)],[1018]) ).
thf(1187,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)],[1017]) ).
thf(1188,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)],[1016]) ).
thf(1189,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(copy,[status(thm)],[1015]) ).
thf(1190,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(copy,[status(thm)],[1014]) ).
thf(1191,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)],[1013]) ).
thf(1192,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)],[1012]) ).
thf(1193,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(copy,[status(thm)],[1011]) ).
thf(1194,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(copy,[status(thm)],[1010]) ).
thf(1195,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1196,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)],[1008]) ).
thf(1197,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)],[1007]) ).
thf(1198,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(copy,[status(thm)],[1006]) ).
thf(1199,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(copy,[status(thm)],[1005]) ).
thf(1200,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)],[1004]) ).
thf(1201,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)],[1003]) ).
thf(1202,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1203,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1204,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1205,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)],[999]) ).
thf(1206,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)],[998]) ).
thf(1207,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)],[997]) ).
thf(1208,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)],[996]) ).
thf(1209,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)],[995]) ).
thf(1210,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)],[994]) ).
thf(1211,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(copy,[status(thm)],[993]) ).
thf(1212,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(copy,[status(thm)],[992]) ).
thf(1213,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)],[991]) ).
thf(1214,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)],[990]) ).
thf(1215,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)],[989]) ).
thf(1216,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(copy,[status(thm)],[988]) ).
thf(1217,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(copy,[status(thm)],[987]) ).
thf(1218,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(copy,[status(thm)],[986]) ).
thf(1219,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)],[985]) ).
thf(1220,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1221,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1222,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1223,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1224,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)],[980]) ).
thf(1225,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( hAPP @ V_D @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1226,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)],[978]) ).
thf(1227,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)],[977]) ).
thf(1228,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)],[976]) ).
thf(1229,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)],[975]) ).
thf(1230,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)],[974]) ).
thf(1231,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)],[973]) ).
thf(1232,plain,
( ( ! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(1233,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1234,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1235,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1236,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1237,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1238,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)],[966]) ).
thf(1239,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)],[965]) ).
thf(1240,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)],[964]) ).
thf(1241,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( 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_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1242,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(copy,[status(thm)],[962]) ).
thf(1243,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)],[961]) ).
thf(1244,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)],[960]) ).
thf(1245,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)],[959]) ).
thf(1246,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1247,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)],[957]) ).
thf(1248,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(copy,[status(thm)],[956]) ).
thf(1249,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(copy,[status(thm)],[955]) ).
thf(1250,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(copy,[status(thm)],[954]) ).
thf(1251,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(copy,[status(thm)],[953]) ).
thf(1252,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)],[952]) ).
thf(1253,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)],[951]) ).
thf(1254,plain,
( ( ! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1255,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1256,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1257,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)],[947]) ).
thf(1258,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1259,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(copy,[status(thm)],[945]) ).
thf(1260,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(copy,[status(thm)],[944]) ).
thf(1261,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(copy,[status(thm)],[943]) ).
thf(1262,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(copy,[status(thm)],[942]) ).
thf(1263,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(copy,[status(thm)],[941]) ).
thf(1264,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(copy,[status(thm)],[940]) ).
thf(1265,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)],[939]) ).
thf(1266,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)],[938]) ).
thf(1267,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)],[937]) ).
thf(1268,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)],[936]) ).
thf(1269,plain,
( ( ! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1270,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)],[934]) ).
thf(1271,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)],[933]) ).
thf(1272,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1273,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)],[931]) ).
thf(1274,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1275,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(copy,[status(thm)],[929]) ).
thf(1276,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(copy,[status(thm)],[928]) ).
thf(1277,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(copy,[status(thm)],[927]) ).
thf(1278,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(copy,[status(thm)],[926]) ).
thf(1279,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(copy,[status(thm)],[925]) ).
thf(1280,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(copy,[status(thm)],[924]) ).
thf(1281,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(copy,[status(thm)],[923]) ).
thf(1282,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)],[922]) ).
thf(1283,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)],[921]) ).
thf(1284,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)],[920]) ).
thf(1285,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)],[919]) ).
thf(1286,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)],[918]) ).
thf(1287,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(copy,[status(thm)],[917]) ).
thf(1288,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(copy,[status(thm)],[916]) ).
thf(1289,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)],[915]) ).
thf(1290,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)],[914]) ).
thf(1291,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)],[913]) ).
thf(1292,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)],[912]) ).
thf(1293,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(copy,[status(thm)],[911]) ).
thf(1294,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(copy,[status(thm)],[910]) ).
thf(1295,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)],[909]) ).
thf(1296,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)],[908]) ).
thf(1297,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)],[907]) ).
thf(1298,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)],[906]) ).
thf(1299,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)],[905]) ).
thf(1300,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(copy,[status(thm)],[904]) ).
thf(1301,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)],[903]) ).
thf(1302,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)],[902]) ).
thf(1303,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(copy,[status(thm)],[901]) ).
thf(1304,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(copy,[status(thm)],[900]) ).
thf(1305,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(copy,[status(thm)],[899]) ).
thf(1306,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(copy,[status(thm)],[898]) ).
thf(1307,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(copy,[status(thm)],[897]) ).
thf(1308,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(copy,[status(thm)],[896]) ).
thf(1309,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(copy,[status(thm)],[895]) ).
thf(1310,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(copy,[status(thm)],[894]) ).
thf(1311,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1312,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1313,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)],[891]) ).
thf(1314,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)],[890]) ).
thf(1315,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1316,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1317,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)],[887]) ).
thf(1318,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1319,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1320,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 ) @ V_r @ ( 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 ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1321,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 ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ 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_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1322,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(copy,[status(thm)],[882]) ).
thf(1323,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)],[881]) ).
thf(1324,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)],[880]) ).
thf(1325,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)],[879]) ).
thf(1326,plain,
( ( ! [V_M: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_M @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1327,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1328,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1329,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)],[875]) ).
thf(1330,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)],[874]) ).
thf(1331,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)],[873]) ).
thf(1332,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)],[872]) ).
thf(1333,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)],[871]) ).
thf(1334,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)],[870]) ).
thf(1335,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_C @ V_D @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ V_A @ V_B @ V_D @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1336,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ~ ( c_in @ ( hAPP @ V_f @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) ) @ V_B @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1337,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( 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 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ V_A @ V_B @ V_f @ T_a @ T_b ) @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1338,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( 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)],[866]) ).
thf(1339,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)],[865]) ).
thf(1340,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)],[864]) ).
thf(1341,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1342,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_B @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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)],[862]) ).
thf(1343,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ V_A @ V_B @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( 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)],[861]) ).
thf(1344,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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)],[860]) ).
thf(1345,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( 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)],[859]) ).
thf(1346,plain,
( ( ! [V_X: $i,T_a: $i,V_A: $i,V_r: $i] :
( ( c_Finite__Set_Ofinite @ V_X @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ 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 ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1347,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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)],[857]) ).
thf(1348,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ V_A @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( 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)],[856]) ).
thf(1349,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)],[855]) ).
thf(1350,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)],[854]) ).
thf(1351,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)],[853]) ).
thf(1352,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)],[852]) ).
thf(1353,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(copy,[status(thm)],[851]) ).
thf(1354,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(copy,[status(thm)],[850]) ).
thf(1355,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1356,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)],[848]) ).
thf(1357,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)],[847]) ).
thf(1358,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1359,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(copy,[status(thm)],[845]) ).
thf(1360,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)],[844]) ).
thf(1361,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(copy,[status(thm)],[843]) ).
thf(1362,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(copy,[status(thm)],[842]) ).
thf(1363,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)],[841]) ).
thf(1364,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(copy,[status(thm)],[840]) ).
thf(1365,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(copy,[status(thm)],[839]) ).
thf(1366,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(copy,[status(thm)],[838]) ).
thf(1367,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1368,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_B @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1369,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(copy,[status(thm)],[835]) ).
thf(1370,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)],[834]) ).
thf(1371,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)],[833]) ).
thf(1372,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(copy,[status(thm)],[832]) ).
thf(1373,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(copy,[status(thm)],[831]) ).
thf(1374,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(copy,[status(thm)],[830]) ).
thf(1375,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ T_a )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1376,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1377,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(copy,[status(thm)],[827]) ).
thf(1378,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(copy,[status(thm)],[826]) ).
thf(1379,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(copy,[status(thm)],[825]) ).
thf(1380,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)],[824]) ).
thf(1381,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)],[823]) ).
thf(1382,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)],[822]) ).
thf(1383,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(copy,[status(thm)],[821]) ).
thf(1384,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)],[820]) ).
thf(1385,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)],[819]) ).
thf(1386,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)],[818]) ).
thf(1387,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)],[817]) ).
thf(1388,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)],[816]) ).
thf(1389,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(copy,[status(thm)],[815]) ).
thf(1390,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1391,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1392,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(copy,[status(thm)],[812]) ).
thf(1393,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(copy,[status(thm)],[811]) ).
thf(1394,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(copy,[status(thm)],[810]) ).
thf(1395,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1396,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1397,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(copy,[status(thm)],[807]) ).
thf(1398,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(copy,[status(thm)],[806]) ).
thf(1399,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1400,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)],[804]) ).
thf(1401,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)],[803]) ).
thf(1402,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(copy,[status(thm)],[802]) ).
thf(1403,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(copy,[status(thm)],[801]) ).
thf(1404,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(copy,[status(thm)],[800]) ).
thf(1405,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(copy,[status(thm)],[799]) ).
thf(1406,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(copy,[status(thm)],[798]) ).
thf(1407,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)],[797]) ).
thf(1408,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(copy,[status(thm)],[796]) ).
thf(1409,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)],[795]) ).
thf(1410,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)],[794]) ).
thf(1411,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)],[793]) ).
thf(1412,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(copy,[status(thm)],[792]) ).
thf(1413,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(copy,[status(thm)],[791]) ).
thf(1414,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)],[790]) ).
thf(1415,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)],[789]) ).
thf(1416,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)],[788]) ).
thf(1417,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)],[787]) ).
thf(1418,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(copy,[status(thm)],[786]) ).
thf(1419,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)],[785]) ).
thf(1420,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)],[784]) ).
thf(1421,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(copy,[status(thm)],[783]) ).
thf(1422,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)],[782]) ).
thf(1423,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)],[781]) ).
thf(1424,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(copy,[status(thm)],[780]) ).
thf(1425,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(copy,[status(thm)],[779]) ).
thf(1426,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(copy,[status(thm)],[778]) ).
thf(1427,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(copy,[status(thm)],[777]) ).
thf(1428,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(copy,[status(thm)],[776]) ).
thf(1429,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)],[775]) ).
thf(1430,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)],[774]) ).
thf(1431,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(copy,[status(thm)],[773]) ).
thf(1432,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(copy,[status(thm)],[772]) ).
thf(1433,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)],[771]) ).
thf(1434,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)],[770]) ).
thf(1435,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)],[769]) ).
thf(1436,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1437,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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)],[767]) ).
thf(1438,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1439,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)],[765]) ).
thf(1440,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)],[764]) ).
thf(1441,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)],[763]) ).
thf(1442,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(copy,[status(thm)],[762]) ).
thf(1443,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)],[761]) ).
thf(1444,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)],[760]) ).
thf(1445,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)],[759]) ).
thf(1446,plain,
( ( ! [V_A: $i,V_X: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ V_A @ V_X @ V_r @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1447,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)],[757]) ).
thf(1448,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1449,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)],[755]) ).
thf(1450,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)],[754]) ).
thf(1451,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)],[753]) ).
thf(1452,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)],[752]) ).
thf(1453,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)],[751]) ).
thf(1454,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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(copy,[status(thm)],[750]) ).
thf(1455,plain,
( ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1456,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)],[748]) ).
thf(1457,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(copy,[status(thm)],[747]) ).
thf(1458,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(copy,[status(thm)],[746]) ).
thf(1459,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)],[745]) ).
thf(1460,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)],[744]) ).
thf(1461,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(copy,[status(thm)],[743]) ).
thf(1462,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)],[742]) ).
thf(1463,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)],[741]) ).
thf(1464,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)],[740]) ).
thf(1465,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(copy,[status(thm)],[739]) ).
thf(1466,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(copy,[status(thm)],[738]) ).
thf(1467,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(copy,[status(thm)],[737]) ).
thf(1468,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(copy,[status(thm)],[736]) ).
thf(1469,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(copy,[status(thm)],[735]) ).
thf(1470,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(copy,[status(thm)],[734]) ).
thf(1471,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)],[733]) ).
thf(1472,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(copy,[status(thm)],[732]) ).
thf(1473,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(copy,[status(thm)],[731]) ).
thf(1474,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)],[730]) ).
thf(1475,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)],[729]) ).
thf(1476,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)],[728]) ).
thf(1477,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)],[727]) ).
thf(1478,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)],[726]) ).
thf(1479,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(copy,[status(thm)],[725]) ).
thf(1480,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(copy,[status(thm)],[724]) ).
thf(1481,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1482,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 ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( 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)],[722]) ).
thf(1483,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 ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( 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)],[721]) ).
thf(1484,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)],[720]) ).
thf(1485,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)],[719]) ).
thf(1486,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)],[718]) ).
thf(1487,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_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1488,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1489,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)],[715]) ).
thf(1490,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)],[714]) ).
thf(1491,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1492,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1493,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)],[711]) ).
thf(1494,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1495,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)],[709]) ).
thf(1496,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)],[708]) ).
thf(1497,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1498,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(1499,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1500,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)],[704]) ).
thf(1501,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)],[703]) ).
thf(1502,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)],[702]) ).
thf(1503,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)],[701]) ).
thf(1504,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1505,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1506,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)],[698]) ).
thf(1507,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1508,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)],[696]) ).
thf(1509,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)],[695]) ).
thf(1510,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)],[694]) ).
thf(1511,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)],[693]) ).
thf(1512,plain,
( ( ! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1513,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)],[691]) ).
thf(1514,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)],[690]) ).
thf(1515,plain,
( ( ! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1516,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1517,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1518,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ 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)],[686]) ).
thf(1519,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1520,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)],[684]) ).
thf(1521,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1522,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1523,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)],[681]) ).
thf(1524,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1525,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(copy,[status(thm)],[679]) ).
thf(1526,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1527,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1528,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 @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1529,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1530,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(copy,[status(thm)],[674]) ).
thf(1531,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(copy,[status(thm)],[673]) ).
thf(1532,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(copy,[status(thm)],[672]) ).
thf(1533,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)],[671]) ).
thf(1534,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)],[670]) ).
thf(1535,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)],[669]) ).
thf(1536,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(copy,[status(thm)],[668]) ).
thf(1537,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)],[667]) ).
thf(1538,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)],[666]) ).
thf(1539,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(copy,[status(thm)],[665]) ).
thf(1540,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(copy,[status(thm)],[664]) ).
thf(1541,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(copy,[status(thm)],[663]) ).
thf(1542,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)],[662]) ).
thf(1543,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)],[661]) ).
thf(1544,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(copy,[status(thm)],[660]) ).
thf(1545,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(copy,[status(thm)],[659]) ).
thf(1546,plain,
( ( ! [V_X: $i,V_Y: $i,V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( V_X = V_Y )
| ~ ( 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_Y @ T_a )
| ~ ( c_in @ V_x @ V_X @ T_a )
| ~ ( c_in @ V_Y @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_X @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1547,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_xa: $i,V_A: $i,V_r: $i] :
( ~ ( c_in @ V_y @ V_x @ T_a )
| ~ ( c_in @ V_xa @ V_x @ T_a )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_xa @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1548,plain,
( ( ! [V_A: $i,V_X: $i,T_a: $i,V_C: $i] :
( ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_A @ ( c_Complete__Lattice_OInf__class_OInf @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1549,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_X: $i] :
( ( c_in @ V_A @ ( c_Complete__Lattice_OSup__class_OSup @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_A @ V_X @ T_a )
| ~ ( c_in @ V_X @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(1550,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)],[654]) ).
thf(1551,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)],[653]) ).
thf(1552,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)],[652]) ).
thf(1553,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)],[651]) ).
thf(1554,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(copy,[status(thm)],[650]) ).
thf(1555,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(copy,[status(thm)],[649]) ).
thf(1556,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)],[648]) ).
thf(1557,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)],[647]) ).
thf(1558,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)],[646]) ).
thf(1559,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)],[645]) ).
thf(1560,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(copy,[status(thm)],[644]) ).
thf(1561,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(copy,[status(thm)],[643]) ).
thf(1562,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(copy,[status(thm)],[642]) ).
thf(1563,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1564,plain,
( ( ! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(1565,plain,
( ( ! [V_L: $i,V_x: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ V_L @ V_x ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1566,plain,
( ( ! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1567,plain,
( ( c_in @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1568,plain,
( ( ! [V_L: $i] :
( ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1569,plain,
( ( ! [V_L: $i] :
( ( c_in @ ( c_Relation_Oconverse @ V_L @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1570,plain,
( ( ! [V_L: $i,V_x: $i,V_y: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_y ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1571,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)],[633]) ).
thf(1572,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)],[632]) ).
thf(1573,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(copy,[status(thm)],[631]) ).
thf(1574,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(copy,[status(thm)],[630]) ).
thf(1575,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(copy,[status(thm)],[629]) ).
thf(1576,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(copy,[status(thm)],[628]) ).
thf(1577,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(copy,[status(thm)],[627]) ).
thf(1578,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)],[626]) ).
thf(1579,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(copy,[status(thm)],[625]) ).
thf(1580,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(copy,[status(thm)],[624]) ).
thf(1581,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(copy,[status(thm)],[623]) ).
thf(1582,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(copy,[status(thm)],[622]) ).
thf(1583,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(copy,[status(thm)],[621]) ).
thf(1584,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(copy,[status(thm)],[620]) ).
thf(1585,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(copy,[status(thm)],[619]) ).
thf(1586,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(copy,[status(thm)],[618]) ).
thf(1587,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(copy,[status(thm)],[617]) ).
thf(1588,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(copy,[status(thm)],[616]) ).
thf(1589,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(copy,[status(thm)],[615]) ).
thf(1590,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(copy,[status(thm)],[614]) ).
thf(1591,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(copy,[status(thm)],[613]) ).
thf(1592,plain,
( ( ! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(1593,plain,
( ( ! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1594,plain,
( ( ! [V_x: $i,V_b: $i,V_y: $i,V_L: $i] :
( ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(1595,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_b: $i,V_a: $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_b )
| ( V_x = V_b )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(1596,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ( 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_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_a @ 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_xa = V_a ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1597,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_a @ 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(1598,plain,
( ( ! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(1599,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(1600,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(1601,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(1602,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_x = V_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(1603,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1604,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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1605,plain,
( ( ! [V_a: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1606,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ( V_x = V_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1607,plain,
( ( ! [V_x: $i,V_L: $i,V_a: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(1608,plain,
( ( ! [V_b: $i,V_y: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ 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_x )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(1609,plain,
( ( ! [V_x: $i,V_a: $i,V_xa: $i,V_L: $i] :
( ( V_x = V_a )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1610,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $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_a )
| ( V_y = V_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(1611,plain,
( ( ! [V_y: $i,V_x: $i,V_L: $i,V_b: $i] :
( ( 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_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_b @ 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_b ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1612,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i,V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1613,plain,
( ( ! [V_xa: $i,V_a: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1614,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_b: $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_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_x @ V_b ) @ ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1615,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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_b )
| ~ ( c_in @ ( c_Pair @ V_a @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1616,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ 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_b )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1617,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( 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_Oabove @ V_L @ V_xa @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1618,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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 ) )
| ~ ( c_in @ ( c_Pair @ V_b @ 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 ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(1619,plain,
( ( ! [V_x: $i,V_xa: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_xa @ 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_xa )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_xa )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_xa ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(1620,plain,
( ( ! [V_xa: $i,V_b: $i,V_L: $i,V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_xa @ V_b @ 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_xa = V_x )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_x = V_b )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_x @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1621,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ V_L @ V_a @ V_b ) @ ( 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_a )
| ( V_y = V_a )
| ( V_x = V_y )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1622,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)],[582]) ).
thf(1623,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)],[581]) ).
thf(1624,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(1625,plain,
( ( ! [V_y: $i,V_x: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1626,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)],[578]) ).
thf(1627,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(copy,[status(thm)],[577]) ).
thf(1628,plain,
( ( ! [V_Lab: $i] :
( v_thesis____
| ~ ( c_in @ V_Lab @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_Lab @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1629,plain,
( ( ! [V_b: $i,V_a: $i,V_L: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( 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 ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ V_L @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1630,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1631,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1632,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1633,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)],[571]) ).
thf(1634,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)],[570]) ).
thf(1635,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)],[569]) ).
thf(1636,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1637,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)],[567]) ).
thf(1638,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)],[566]) ).
thf(1639,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)],[565]) ).
thf(1640,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)],[564]) ).
thf(1641,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1642,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1643,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1644,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1645,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1646,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1647,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1648,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1649,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1650,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1651,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1652,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1653,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( c_Recdef_Ocut @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
!= ( c_Recdef_Ocut @ SX5 @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ( ( hAPP @ SX0 @ SX6 )
= ( hAPP @ SX5 @ SX6 ) )
| ~ ( c_in @ ( c_Pair @ SX6 @ SX2 @ SX3 @ SX3 ) @ SX1 @ ( tc_prod @ SX3 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1531]) ).
thf(1654,plain,
( ( v_a____ != v_b____ )
= $true ),
inference(unfold_def,[status(thm)],[1630]) ).
thf(1655,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SX0 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX1 @ SX2 @ SX0 )
!= SX2 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1263]) ).
thf(1656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SX0 @ SX1 @ SX1 ) @ SX0 @ SX1 @ SX1 @ SX1 )
!= SX0 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SX0 @ SX1 @ SX1 ) @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1518]) ).
thf(1657,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) )
!= SX1 )
| ( c_lessequals @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1267]) ).
thf(1658,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SX0 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SX1 @ SX2 @ SX0 )
!= SX1 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1659,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Product__Type_OSigma @ SX0 @ ( c_COMBK @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) @ SX3 ) @ SX3 @ SX2 )
!= ( c_Product__Type_OSigma @ SX4 @ ( c_COMBK @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) @ SX3 ) @ SX3 @ SX2 ) )
| ~ ( c_in @ SX5 @ SX1 @ SX2 )
| ( SX0 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1372]) ).
thf(1660,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX3 @ ( tc_fun @ SX2 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SX0 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SX1 @ SX3 @ ( tc_fun @ SX2 @ tc_bool ) ) @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( c_lessequals @ SX3 @ SX0 @ ( tc_fun @ SX2 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1239]) ).
thf(1661,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Pair @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Pair @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX1 = SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1622]) ).
thf(1662,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Relation_Oconverse @ SX0 @ SX1 @ SX1 )
!= SX0 )
| ( c_Relation_Osym @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1505]) ).
thf(1663,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Set_Oinsert @ SX0 @ SX3 @ SX2 ) )
| ( c_in @ SX0 @ SX3 @ SX2 )
| ( c_in @ SX0 @ SX1 @ SX2 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1218]) ).
thf(1664,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) )
!= ( hAPP @ SX1 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
| ( ( c_Recdef_Ocut @ SX0 @ SX2 @ SX3 @ SX4 @ SX5 )
= ( c_Recdef_Ocut @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1423]) ).
thf(1665,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Pair @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Pair @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX0 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1623]) ).
thf(1666,plain,
v_thesis____ = $false,
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1667,plain,
! [SV1: $i] :
( ( ! [SY1970: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ SV1 @ SY1970 ) @ SY1970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1668,plain,
! [SV2: $i] :
( ( ! [SY1971: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV2 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1971 @ SY1971 @ SV2 )
= SY1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1669,plain,
! [SV3: $i] :
( ( ! [SY1972: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SV3 @ ( tc_fun @ SY1972 @ tc_bool ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1670,plain,
! [SV4: $i] :
( ( ! [SY1973: $i,SY1974: $i,SY1975: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV4 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1973 @ SY1974 @ SV4 ) @ SY1975 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1973 @ SY1975 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1974 @ SY1975 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1671,plain,
! [SV5: $i] :
( ( ! [SY1976: $i,SY1977: $i,SY1978: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV5 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1976 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1977 @ SY1978 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1976 @ SY1977 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1976 @ SY1978 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1672,plain,
! [SV6: $i] :
( ( ! [SY1979: $i,SY1980: $i,SY1981: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1979 @ SY1980 @ ( tc_fun @ SY1981 @ tc_bool ) ) @ ( tc_fun @ SY1981 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SY1979 @ ( tc_fun @ SY1981 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SY1980 @ ( tc_fun @ SY1981 @ tc_bool ) ) @ ( tc_fun @ SY1981 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1673,plain,
! [SV7: $i] :
( ( ! [SY1982: $i,SY1983: $i,SY1984: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SY1982 @ ( tc_fun @ SY1983 @ tc_bool ) ) @ SY1984 @ ( tc_fun @ SY1983 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV7 @ SY1984 @ ( tc_fun @ SY1983 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1982 @ SY1984 @ ( tc_fun @ SY1983 @ tc_bool ) ) @ ( tc_fun @ SY1983 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1674,plain,
! [SV8: $i] :
( ( ! [SY1985: $i,SY1986: $i,SY1987: $i,SY1988: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV8 @ SY1985 @ ( tc_fun @ SY1986 @ tc_bool ) ) @ SY1987 @ SY1986 @ SY1988 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV8 @ SY1987 @ SY1986 @ SY1988 ) @ ( c_Product__Type_OSigma @ SY1985 @ SY1987 @ SY1986 @ SY1988 ) @ ( tc_fun @ ( tc_prod @ SY1986 @ SY1988 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1675,plain,
! [SV9: $i] :
( ( ! [SY1989: $i,SY1990: $i,SY1991: $i,SY1992: $i,SY1993: $i] :
( ( c_in @ ( hAPP @ SV9 @ SY1989 ) @ SY1990 @ SY1991 )
| ~ ( c_in @ SY1989 @ SY1992 @ SY1993 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SY1992 @ SY1993 @ SY1991 ) @ SY1990 @ ( tc_fun @ SY1991 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1676,plain,
! [SV10: $i] :
( ( ! [SY1994: $i,SY1995: $i,SY1996: $i,SY1997: $i] :
( ( c_Finite__Set_Ofinite @ SV10 @ SY1994 )
| ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SY1995 @ SY1996 @ SY1997 @ SY1994 ) @ ( tc_fun @ SY1994 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY1996 @ SY1997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1677,plain,
! [SV11: $i] :
( ( ! [SY1998: $i,SY1999: $i,SY2000: $i] :
( ( c_lessequals @ SV11 @ SY1998 @ ( tc_fun @ SY1999 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY2000 @ SV11 @ SY1999 ) @ SY1998 @ ( tc_fun @ SY1999 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1678,plain,
! [SV12: $i] :
( ( ! [SY2001: $i,SY2002: $i,SY2003: $i] :
( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SY2001 @ SY2002 @ SY2003 ) @ ( tc_fun @ SY2003 @ tc_bool ) )
| ~ ( c_lessequals @ SV12 @ SY2002 @ ( tc_fun @ SY2003 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1679,plain,
! [SV13: $i] :
( ( ! [SY2004: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV13 @ ( c_Relation_OId @ SY2004 ) @ ( tc_fun @ ( tc_prod @ SY2004 @ SY2004 ) @ tc_bool ) ) @ SY2004 )
= ( c_Transitive__Closure_Ortrancl @ SV13 @ SY2004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1680,plain,
! [SV14: $i] :
( ( ! [SY2005: $i,SY2006: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV14 @ SY2005 ) @ ( c_Transitive__Closure_Ortrancl @ SY2006 @ SY2005 ) @ ( tc_fun @ ( tc_prod @ SY2005 @ SY2005 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV14 @ SY2006 @ ( tc_fun @ ( tc_prod @ SY2005 @ SY2005 ) @ tc_bool ) ) @ SY2005 ) @ ( tc_fun @ ( tc_prod @ SY2005 @ SY2005 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1681,plain,
! [SV15: $i] :
( ( ! [SY2007: $i,SY2008: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV15 )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SY2007 @ SY2008 @ SV15 ) @ SV15 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2007 @ ( c_Complete__Lattice_OInf__class_OInf @ SY2008 @ SV15 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1682,plain,
! [SV16: $i] :
( ( ! [SY2009: $i,SY2010: $i,SY2011: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV16 @ SY2009 @ SY2010 ) @ SY2011 @ ( tc_fun @ SY2010 @ tc_bool ) )
= ( c_Set_Oinsert @ SV16 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2009 @ SY2011 @ ( tc_fun @ SY2010 @ tc_bool ) ) @ SY2010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1683,plain,
! [SV17: $i] :
( ( ! [SY2012: $i,SY2013: $i,SY2014: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ ( c_Set_Oinsert @ SY2012 @ SY2013 @ SY2014 ) @ ( tc_fun @ SY2014 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2012 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ SY2013 @ ( tc_fun @ SY2014 @ tc_bool ) ) @ SY2014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1684,plain,
! [SV18: $i] :
( ( ! [SY2015: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ SV18 @ SY2015 ) @ SY2015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1685,plain,
! [SV19: $i] :
( ( ! [SY2016: $i] :
( ( c_Relation_Otrans @ SV19 @ SY2016 )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV19 @ SY2016 @ SY2016 ) @ SY2016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1686,plain,
! [SV20: $i] :
( ( ! [SY2017: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV20 @ SY2017 @ SY2017 ) @ SY2017 )
| ~ ( c_Relation_Otrans @ SV20 @ SY2017 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1687,plain,
! [SV21: $i] :
( ( ! [SY2018: $i,SY2019: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV21 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2018 @ SY2019 @ SV21 ) @ SV21 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2018 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2019 @ SV21 ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1688,plain,
! [SV22: $i] :
( ( ! [SY2020: $i,SY2021: $i,SY2022: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV22 @ SY2020 @ SY2021 ) @ ( c_Set_Oinsert @ SV22 @ SY2022 @ SY2021 ) @ ( tc_fun @ SY2021 @ tc_bool ) )
= ( c_Set_Oinsert @ SV22 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2020 @ SY2022 @ ( tc_fun @ SY2021 @ tc_bool ) ) @ SY2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1689,plain,
! [SV23: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ( c_Set_Oinsert @ SV23 @ ( c_Set_Oinsert @ SV23 @ SY2023 @ SY2024 ) @ SY2024 )
= ( c_Set_Oinsert @ SV23 @ SY2023 @ SY2024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1690,plain,
! [SV24: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i] :
( ( hBOOL @ ( hAPP @ SV24 @ SY2025 ) )
| ( SY2026 = SY2025 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2026 @ SV24 @ SY2027 ) @ SY2025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1691,plain,
! [SV25: $i] :
( ( ! [SY2028: $i,SY2029: $i,SY2030: $i,SY2031: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV25 @ SY2028 @ SY2029 @ SY2030 ) @ SY2031 @ ( tc_prod @ SY2029 @ SY2030 ) ) @ SY2029 @ SY2030 )
= ( c_Set_Oinsert @ SV25 @ ( c_Relation_ODomain @ SY2031 @ SY2029 @ SY2030 ) @ SY2029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1692,plain,
! [SV26: $i] :
( ( ! [SY2032: $i,SY2033: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SY2032 @ ( tc_fun @ ( tc_prod @ SY2033 @ SY2033 ) @ tc_bool ) ) @ SY2033 )
| ~ ( c_Relation_Osym @ SY2032 @ SY2033 )
| ~ ( c_Relation_Osym @ SV26 @ SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1693,plain,
! [SV27: $i] :
( ( ! [SY2034: $i,SY2035: $i,SY2036: $i,SY2037: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 @ SY2034 @ ( tc_fun @ ( tc_prod @ SY2035 @ SY2036 ) @ tc_bool ) ) @ SY2037 @ SY2035 @ SY2036 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV27 @ SY2037 @ SY2035 @ SY2036 ) @ ( c_Relation_OImage @ SY2034 @ SY2037 @ SY2035 @ SY2036 ) @ ( tc_fun @ SY2036 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1694,plain,
! [SV28: $i] :
( ( ! [SY2038: $i,SY2039: $i,SY2040: $i,SY2041: $i] :
( ( c_Relation_OImage @ SV28 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2038 @ SY2039 @ ( tc_fun @ SY2040 @ tc_bool ) ) @ SY2040 @ SY2041 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV28 @ SY2038 @ SY2040 @ SY2041 ) @ ( c_Relation_OImage @ SV28 @ SY2039 @ SY2040 @ SY2041 ) @ ( tc_fun @ SY2041 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1695,plain,
! [SV29: $i] :
( ( ! [SY2042: $i,SY2043: $i,SY2044: $i] :
( ( c_Set_Oinsert @ SV29 @ ( c_Set_Oinsert @ SY2042 @ SY2043 @ SY2044 ) @ SY2044 )
= ( c_Set_Oinsert @ SY2042 @ ( c_Set_Oinsert @ SV29 @ SY2043 @ SY2044 ) @ SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1696,plain,
! [SV30: $i] :
( ( ! [SY2045: $i,SY2046: $i,SY2047: $i] :
( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2045 @ SY2046 @ ( tc_fun @ ( tc_prod @ SY2047 @ SY2047 ) @ tc_bool ) ) @ SY2047 ) @ ( tc_prod @ SY2047 @ SY2047 ) )
| ~ ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SY2046 @ SY2047 ) @ ( tc_prod @ SY2047 @ SY2047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1697,plain,
! [SV31: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i] :
( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2048 @ SY2049 @ ( tc_fun @ ( tc_prod @ SY2050 @ SY2050 ) @ tc_bool ) ) @ SY2050 ) @ ( tc_prod @ SY2050 @ SY2050 ) )
| ~ ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SY2048 @ SY2050 ) @ ( tc_prod @ SY2050 @ SY2050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1698,plain,
! [SV32: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2051 @ SY2052 @ ( tc_fun @ SY2053 @ tc_bool ) ) @ ( tc_fun @ SY2053 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2051 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SY2052 @ ( tc_fun @ SY2053 @ tc_bool ) ) @ ( tc_fun @ SY2053 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1699,plain,
! [SV33: $i] :
( ( ! [SY2054: $i,SY2055: $i,SY2056: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ SY2054 @ ( tc_fun @ SY2055 @ tc_bool ) ) @ SY2056 @ ( tc_fun @ SY2055 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2054 @ SY2056 @ ( tc_fun @ SY2055 @ tc_bool ) ) @ ( tc_fun @ SY2055 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1700,plain,
! [SV34: $i] :
( ( ! [SY2057: $i,SY2058: $i,SY2059: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV34 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2057 @ SY2058 @ SV34 ) @ SY2059 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2057 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2058 @ SY2059 @ SV34 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1701,plain,
! [SV35: $i] :
( ( ! [SY2060: $i,SY2061: $i,SY2062: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2060 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2061 @ SY2062 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2061 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2060 @ SY2062 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1702,plain,
! [SV36: $i] :
( ( ! [SY2063: $i,SY2064: $i,SY2065: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2063 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2064 @ SY2065 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2064 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2063 @ SY2065 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1703,plain,
! [SV37: $i] :
( ( ! [SY2066: $i,SY2067: $i,SY2068: $i] :
( ~ ( class_Lattices_Olattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2066 @ SY2067 @ SV37 ) @ SY2068 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2066 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2067 @ SY2068 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1704,plain,
! [SV38: $i] :
( ( ! [SY2069: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV38 @ SY2069 ) @ ( c_Relation_OId @ SY2069 ) @ ( tc_fun @ ( tc_prod @ SY2069 @ SY2069 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV38 @ SY2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1705,plain,
! [SV39: $i] :
( ( ! [SY2070: $i,SY2071: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV39 @ SY2070 @ ( tc_fun @ SY2071 @ tc_bool ) )
= SV39 )
| ~ ( c_lessequals @ SV39 @ SY2070 @ ( tc_fun @ SY2071 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1706,plain,
! [SV40: $i] :
( ( ! [SY2072: $i,SY2073: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV40 @ SY2072 @ ( tc_fun @ SY2073 @ tc_bool ) )
= SY2072 )
| ~ ( c_lessequals @ SY2072 @ SV40 @ ( tc_fun @ SY2073 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1707,plain,
! [SV41: $i] :
( ( ! [SY2074: $i,SY2075: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2074 @ SY2075 @ SV41 )
= SY2074 )
| ~ ( c_lessequals @ SY2074 @ SY2075 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1708,plain,
! [SV42: $i] :
( ( ! [SY2076: $i,SY2077: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV42 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2076 @ SY2077 @ SV42 )
= SY2077 )
| ~ ( c_lessequals @ SY2077 @ SY2076 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1709,plain,
! [SV43: $i] :
( ( ! [SY2078: $i,SY2079: $i,SY2080: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SY2078 @ ( tc_fun @ SY2079 @ tc_bool ) ) @ SY2080 @ ( tc_fun @ SY2079 @ tc_bool ) )
| ~ ( c_lessequals @ SY2078 @ SY2080 @ ( tc_fun @ SY2079 @ tc_bool ) )
| ~ ( c_lessequals @ SV43 @ SY2080 @ ( tc_fun @ SY2079 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1710,plain,
! [SV44: $i] :
( ( ! [SY2081: $i,SY2082: $i] : ( c_lessequals @ SV44 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2081 @ SV44 @ ( tc_fun @ SY2082 @ tc_bool ) ) @ ( tc_fun @ SY2082 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1711,plain,
! [SV45: $i] :
( ( ! [SY2083: $i,SY2084: $i] : ( c_lessequals @ SV45 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV45 @ SY2083 @ ( tc_fun @ SY2084 @ tc_bool ) ) @ ( tc_fun @ SY2084 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1712,plain,
! [SV46: $i] :
( ( ! [SY2085: $i,SY2086: $i,SY2087: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SY2085 @ ( tc_fun @ SY2086 @ tc_bool ) ) @ SY2087 @ ( tc_fun @ SY2086 @ tc_bool ) )
| ~ ( c_lessequals @ SY2085 @ SY2087 @ ( tc_fun @ SY2086 @ tc_bool ) )
| ~ ( c_lessequals @ SV46 @ SY2087 @ ( tc_fun @ SY2086 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1713,plain,
! [SV47: $i] :
( ( ! [SY2088: $i,SY2089: $i,SY2090: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV47 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2088 @ SY2089 @ SV47 ) @ SY2090 @ SV47 )
| ~ ( c_lessequals @ SY2089 @ SY2090 @ SV47 )
| ~ ( c_lessequals @ SY2088 @ SY2090 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1714,plain,
! [SV48: $i] :
( ( ! [SY2091: $i,SY2092: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV48 )
| ( c_lessequals @ SY2091 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2091 @ SY2092 @ SV48 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1715,plain,
! [SV49: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV49 )
| ( c_lessequals @ SY2093 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2094 @ SY2093 @ SV49 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1716,plain,
! [SV50: $i] :
( ( ! [SY2095: $i,SY2096: $i,SY2097: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV50 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2095 @ SY2096 @ SV50 ) @ SY2097 @ SV50 )
| ~ ( c_lessequals @ SY2096 @ SY2097 @ SV50 )
| ~ ( c_lessequals @ SY2095 @ SY2097 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1717,plain,
! [SV51: $i] :
( ( ! [SY2098: $i,SY2099: $i,SY2100: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV51 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2098 @ SY2099 @ SV51 ) @ SY2100 @ SV51 )
| ~ ( c_lessequals @ SY2099 @ SY2100 @ SV51 )
| ~ ( c_lessequals @ SY2098 @ SY2100 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1718,plain,
! [SV52: $i] :
( ( ! [SY2101: $i,SY2102: $i] :
( ~ ( class_Lattices_Olattice @ SV52 )
| ( c_lessequals @ SY2101 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2102 @ SY2101 @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1719,plain,
! [SV53: $i] :
( ( ! [SY2103: $i,SY2104: $i] :
( ~ ( class_Lattices_Olattice @ SV53 )
| ( c_lessequals @ SY2103 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2103 @ SY2104 @ SV53 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1720,plain,
! [SV54: $i] :
( ( ! [SY2105: $i,SY2106: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV54 @ SY2105 @ ( tc_fun @ SY2106 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2105 @ SV54 @ ( tc_fun @ SY2106 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1721,plain,
! [SV55: $i] :
( ( ! [SY2107: $i,SY2108: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2107 @ SY2108 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2108 @ SY2107 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1722,plain,
! [SV56: $i] :
( ( ! [SY2109: $i,SY2110: $i] :
( ~ ( class_Lattices_Olattice @ SV56 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2109 @ SY2110 @ SV56 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2110 @ SY2109 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1723,plain,
! [SV57: $i] :
( ( ! [SY2111: $i,SY2112: $i,SY2113: $i] :
( ~ ( class_Lattices_Olattice @ SV57 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2111 @ SY2112 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2111 @ SY2113 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2111 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2112 @ SY2113 @ SV57 ) @ SV57 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1724,plain,
! [SV58: $i] :
( ( ! [SY2114: $i,SY2115: $i,SY2116: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SY2114 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2114 @ SY2116 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2116 @ SV58 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( tc_fun @ SY2115 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV58 @ SY2114 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2114 @ SY2116 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2116 @ SV58 @ ( tc_fun @ SY2115 @ tc_bool ) ) @ ( tc_fun @ SY2115 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1725,plain,
! [SV59: $i] :
( ( ! [SY2117: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ SV59 @ SY2117 @ SY2117 ) @ SY2117 )
= ( c_Relation_OField @ SV59 @ SY2117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1726,plain,
! [SV60: $i] :
( ( ! [SY2118: $i,SY2119: $i,SY2120: $i] :
( ( c_in @ SV60 @ SY2118 @ SY2119 )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SY2120 @ SY2119 ) @ SY2118 @ ( tc_fun @ SY2119 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1727,plain,
! [SV61: $i] :
( ( ! [SY2121: $i,SY2122: $i,SY2123: $i,SY2124: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SY2121 @ ( tc_fun @ SY2122 @ tc_bool ) ) @ SY2123 @ SY2122 @ SY2124 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV61 @ SY2123 @ SY2122 @ SY2124 ) @ ( c_Product__Type_OSigma @ SY2121 @ SY2123 @ SY2122 @ SY2124 ) @ ( tc_fun @ ( tc_prod @ SY2122 @ SY2124 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1728,plain,
! [SV62: $i] :
( ( ! [SY2125: $i,SY2126: $i,SY2127: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SY2125 @ SY2126 ) @ SY2127 ) )
| ~ ( hBOOL @ ( hAPP @ SY2125 @ SY2127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1729,plain,
! [SV63: $i] :
( ( ! [SY2128: $i,SY2129: $i,SY2130: $i,SY2131: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SY2128 ) @ ( c_Set_Oimage @ SV63 @ SY2129 @ SY2130 @ SY2131 ) @ SY2131 )
= ( c_Set_Oimage @ SV63 @ SY2129 @ SY2130 @ SY2131 ) )
| ~ ( c_in @ SY2128 @ SY2129 @ SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1730,plain,
! [SV64: $i] :
( ( ! [SY2132: $i,SY2133: $i,SY2134: $i] :
( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SY2132 @ SY2133 @ SY2134 ) @ ( tc_fun @ SY2134 @ tc_bool ) )
| ~ ( c_lessequals @ SV64 @ SY2133 @ ( tc_fun @ SY2134 @ tc_bool ) )
| ( c_in @ SY2132 @ SV64 @ SY2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1731,plain,
! [SV65: $i] :
( ( ! [SY2135: $i,SY2136: $i,SY2137: $i] :
( ( c_lessequals @ SV65 @ SY2135 @ ( tc_fun @ SY2136 @ tc_bool ) )
| ( c_in @ SY2137 @ SV65 @ SY2136 )
| ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SY2137 @ SY2135 @ SY2136 ) @ ( tc_fun @ SY2136 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1732,plain,
! [SV66: $i] :
( ( ! [SY2138: $i,SY2139: $i,SY2140: $i] :
( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SY2138 @ SY2139 @ SY2140 ) @ ( tc_fun @ SY2140 @ tc_bool ) )
| ~ ( c_lessequals @ SV66 @ SY2139 @ ( tc_fun @ SY2140 @ tc_bool ) )
| ( c_in @ SY2138 @ SV66 @ SY2140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1733,plain,
! [SV67: $i] :
( ( ! [SY2141: $i,SY2142: $i,SY2143: $i] :
( ( c_lessequals @ SV67 @ SY2141 @ ( tc_fun @ SY2142 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SY2143 @ SY2141 @ SY2142 ) @ ( tc_fun @ SY2142 @ tc_bool ) )
| ( c_in @ SY2143 @ SV67 @ SY2142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1734,plain,
! [SV68: $i] :
( ( ! [SY2144: $i,SY2145: $i,SY2146: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SY2144 @ ( tc_fun @ ( tc_prod @ SY2145 @ SY2146 ) @ tc_bool ) ) @ SY2145 @ SY2146 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV68 @ SY2145 @ SY2146 ) @ ( c_Relation_Oconverse @ SY2144 @ SY2145 @ SY2146 ) @ ( tc_fun @ ( tc_prod @ SY2146 @ SY2145 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1735,plain,
! [SV69: $i] :
( ( ! [SY2147: $i,SY2148: $i,SY2149: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Set_Oinsert @ SY2147 @ SY2148 @ SY2149 ) @ ( tc_fun @ SY2149 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SY2148 @ ( tc_fun @ SY2149 @ tc_bool ) ) )
| ( c_in @ SY2147 @ SV69 @ SY2149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1736,plain,
! [SV70: $i] :
( ( ! [SY2150: $i,SY2151: $i,SY2152: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV70 @ SY2150 @ SY2151 ) @ SY2152 @ ( tc_fun @ SY2151 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2150 @ SY2152 @ ( tc_fun @ SY2151 @ tc_bool ) ) )
| ( c_in @ SV70 @ SY2152 @ SY2151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1737,plain,
! [SV71: $i] :
( ( ! [SY2153: $i,SY2154: $i,SY2155: $i,SY2156: $i,SY2157: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SY2153 @ ( tc_fun @ ( tc_prod @ SY2154 @ SY2155 ) @ tc_bool ) ) @ SY2156 @ SY2154 @ SY2155 @ SY2157 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SY2156 @ SY2154 @ SY2155 @ SY2157 ) @ ( c_Relation_Orel__comp @ SY2153 @ SY2156 @ SY2154 @ SY2155 @ SY2157 ) @ ( tc_fun @ ( tc_prod @ SY2154 @ SY2157 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1738,plain,
! [SV72: $i] :
( ( ! [SY2158: $i,SY2159: $i,SY2160: $i,SY2161: $i,SY2162: $i] :
( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2158 @ SY2159 @ ( tc_fun @ ( tc_prod @ SY2160 @ SY2161 ) @ tc_bool ) ) @ SY2162 @ SY2160 @ SY2161 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SY2158 @ SY2162 @ SY2160 @ SY2161 ) @ ( c_Relation_Orel__comp @ SV72 @ SY2159 @ SY2162 @ SY2160 @ SY2161 ) @ ( tc_fun @ ( tc_prod @ SY2162 @ SY2161 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1739,plain,
! [SV73: $i] :
( ( ! [SY2163: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ SV73 @ SY2163 ) @ SY2163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1740,plain,
! [SV74: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV74 @ SY2164 @ ( tc_fun @ ( tc_prod @ SY2165 @ SY2165 ) @ tc_bool ) ) @ SY2165 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV74 @ SY2165 ) @ ( c_Relation_OField @ SY2164 @ SY2165 ) @ ( tc_fun @ SY2165 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1741,plain,
! [SV75: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i] :
( ( c_lessequals @ SV75 @ SY2166 @ ( tc_fun @ SY2167 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2168 @ SY2166 @ ( tc_fun @ SY2167 @ tc_bool ) ) @ ( tc_fun @ SY2167 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1742,plain,
! [SV76: $i] :
( ( ! [SY2169: $i,SY2170: $i,SY2171: $i] :
( ( c_lessequals @ SV76 @ SY2169 @ ( tc_fun @ SY2170 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2169 @ SY2171 @ ( tc_fun @ SY2170 @ tc_bool ) ) @ ( tc_fun @ SY2170 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1743,plain,
! [SV77: $i] :
( ( ! [SY2172: $i,SY2173: $i,SY2174: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ( c_lessequals @ SY2172 @ SY2173 @ SV77 )
| ~ ( c_lessequals @ SY2172 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2173 @ SY2174 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1744,plain,
! [SV78: $i] :
( ( ! [SY2175: $i,SY2176: $i,SY2177: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ( c_lessequals @ SY2175 @ SY2176 @ SV78 )
| ~ ( c_lessequals @ SY2175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2177 @ SY2176 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1745,plain,
! [SV79: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV79 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2178 @ SY2179 @ SV79 ) @ SY2180 @ SV79 )
| ~ ( c_lessequals @ SY2178 @ SY2180 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1746,plain,
! [SV80: $i] :
( ( ! [SY2181: $i,SY2182: $i,SY2183: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV80 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2181 @ SY2182 @ SV80 ) @ SY2183 @ SV80 )
| ~ ( c_lessequals @ SY2182 @ SY2183 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1747,plain,
! [SV81: $i] :
( ( ! [SY2184: $i,SY2185: $i,SY2186: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV81 )
| ( c_lessequals @ SY2184 @ SY2185 @ SV81 )
| ~ ( c_lessequals @ SY2184 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2185 @ SY2186 @ SV81 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1748,plain,
! [SV82: $i] :
( ( ! [SY2187: $i,SY2188: $i,SY2189: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( c_lessequals @ SY2187 @ SY2188 @ SV82 )
| ~ ( c_lessequals @ SY2187 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2189 @ SY2188 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1749,plain,
! [SV83: $i] :
( ( ! [SY2190: $i,SY2191: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV83 @ SY2190 @ ( tc_fun @ SY2191 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2190 @ SV83 @ ( tc_fun @ SY2191 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1750,plain,
! [SV84: $i] :
( ( ! [SY2192: $i,SY2193: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV84 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2192 @ SY2193 @ SV84 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2193 @ SY2192 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1751,plain,
! [SV85: $i] :
( ( ! [SY2194: $i,SY2195: $i] :
( ~ ( class_Lattices_Olattice @ SV85 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2194 @ SY2195 @ SV85 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2195 @ SY2194 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1752,plain,
! [SV86: $i] :
( ( ! [SY2196: $i,SY2197: $i,SY2198: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV86 @ SY2196 @ ( tc_fun @ ( tc_prod @ SY2197 @ SY2198 ) @ tc_bool ) ) @ SY2197 @ SY2198 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV86 @ SY2197 @ SY2198 ) @ ( c_Relation_ODomain @ SY2196 @ SY2197 @ SY2198 ) @ ( tc_fun @ SY2197 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1753,plain,
! [SV87: $i] :
( ( ! [SY2199: $i,SY2200: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SY2199 @ ( tc_fun @ SY2200 @ tc_bool ) ) @ ( tc_fun @ SY2200 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SY2199 @ ( tc_fun @ SY2200 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1754,plain,
! [SV88: $i] :
( ( ! [SY2201: $i,SY2202: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2201 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2201 @ SY2202 @ SV88 ) @ SV88 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2201 @ SY2202 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1755,plain,
! [SV89: $i] :
( ( ! [SY2203: $i,SY2204: $i] :
( ~ ( class_Lattices_Olattice @ SV89 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2203 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2203 @ SY2204 @ SV89 ) @ SV89 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2203 @ SY2204 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1756,plain,
! [SV90: $i] :
( ( ! [SY2205: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV90 )
| ( c_Finite__Set_Ofinite @ SY2205 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1757,plain,
! [SV91: $i] :
( ( ! [SY2206: $i,SY2207: $i,SY2208: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV91 @ SY2206 @ ( tc_fun @ ( tc_prod @ SY2207 @ SY2208 ) @ tc_bool ) ) @ SY2207 @ SY2208 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV91 @ SY2207 @ SY2208 ) @ ( c_Relation_ORange @ SY2206 @ SY2207 @ SY2208 ) @ ( tc_fun @ SY2208 @ tc_bool ) ) @ ( tc_fun @ SY2208 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1758,plain,
! [SV92: $i] :
( ( ! [SY2209: $i,SY2210: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV92 @ SY2209 ) @ ( c_Transitive__Closure_Ortrancl @ SY2210 @ SY2209 ) @ ( tc_fun @ ( tc_prod @ SY2209 @ SY2209 ) @ tc_bool ) ) @ SY2209 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV92 @ SY2210 @ ( tc_fun @ ( tc_prod @ SY2209 @ SY2209 ) @ tc_bool ) ) @ SY2209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1759,plain,
! [SV93: $i] :
( ( ! [SY2211: $i,SY2212: $i,SY2213: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ SY2211 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2212 @ SV93 @ ( tc_fun @ SY2213 @ tc_bool ) ) @ SY2211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1760,plain,
! [SV94: $i] :
( ( ! [SY2214: $i,SY2215: $i,SY2216: $i] :
( ( hBOOL @ ( hAPP @ SV94 @ SY2214 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SY2215 @ ( tc_fun @ SY2216 @ tc_bool ) ) @ SY2214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1761,plain,
! [SV95: $i] :
( ( ! [SY2217: $i,SY2218: $i,SY2219: $i,SY2220: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV95 @ SY2217 @ SY2218 @ SY2219 ) @ SY2220 @ ( tc_prod @ SY2218 @ SY2219 ) ) @ SY2218 @ SY2219 )
= ( c_Set_Oinsert @ SY2217 @ ( c_Relation_ORange @ SY2220 @ SY2218 @ SY2219 ) @ SY2219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1762,plain,
! [SV96: $i] :
( ( ! [SY2221: $i,SY2222: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SY2221 @ ( tc_fun @ ( tc_prod @ SY2222 @ SY2222 ) @ tc_bool ) ) @ SY2222 )
| ~ ( c_Relation_Osym @ SY2221 @ SY2222 )
| ~ ( c_Relation_Osym @ SV96 @ SY2222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1763,plain,
! [SV97: $i] :
( ( ! [SY2223: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV97 @ SY2223 )
= SV97 )
| ~ ( c_Relation_Otrans @ SV97 @ SY2223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1764,plain,
! [SV98: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SY2224 @ ( tc_fun @ SY2225 @ tc_bool ) ) @ SY2225 )
| ~ ( c_Finite__Set_Ofinite @ SY2224 @ SY2225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1765,plain,
! [SV99: $i] :
( ( ! [SY2226: $i,SY2227: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SY2226 @ ( tc_fun @ SY2227 @ tc_bool ) ) @ SY2227 )
| ~ ( c_Finite__Set_Ofinite @ SV99 @ SY2227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1766,plain,
! [SV100: $i] :
( ( ! [SY2228: $i,SY2229: $i,SY2230: $i] :
( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2228 @ SY2229 @ ( tc_fun @ SY2230 @ tc_bool ) ) @ SY2230 )
| ~ ( c_in @ SV100 @ SY2229 @ SY2230 )
| ~ ( c_in @ SV100 @ SY2228 @ SY2230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1767,plain,
! [SV101: $i] :
( ( ! [SY2231: $i,SY2232: $i,SY2233: $i] :
( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2231 @ SY2232 @ ( tc_fun @ SY2233 @ tc_bool ) ) @ SY2233 )
| ~ ( c_in @ SV101 @ SY2232 @ SY2233 )
| ~ ( c_in @ SV101 @ SY2231 @ SY2233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1768,plain,
! [SV102: $i] :
( ( ! [SY2234: $i,SY2235: $i,SY2236: $i] :
( ( c_in @ SV102 @ ( c_Set_Oinsert @ SY2234 @ SY2235 @ SY2236 ) @ SY2236 )
| ~ ( c_in @ SV102 @ SY2235 @ SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1769,plain,
! [SV103: $i] :
( ( ! [SY2237: $i,SY2238: $i,SY2239: $i] :
( ( c_in @ SV103 @ ( c_Set_Oinsert @ SY2237 @ SY2238 @ SY2239 ) @ SY2239 )
| ~ ( c_in @ SV103 @ SY2238 @ SY2239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1770,plain,
! [SV104: $i] :
( ( ! [SY2240: $i,SY2241: $i,SY2242: $i] :
( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2240 @ SY2241 @ ( tc_fun @ SY2242 @ tc_bool ) ) @ SY2242 )
| ~ ( c_in @ SV104 @ SY2240 @ SY2242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1771,plain,
! [SV105: $i] :
( ( ! [SY2243: $i,SY2244: $i,SY2245: $i] :
( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2243 @ SY2244 @ ( tc_fun @ SY2245 @ tc_bool ) ) @ SY2245 )
| ~ ( c_in @ SV105 @ SY2244 @ SY2245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1772,plain,
! [SV106: $i] :
( ( ! [SY2246: $i,SY2247: $i,SY2248: $i] :
( ( c_in @ SV106 @ SY2246 @ SY2247 )
| ( SV106 = SY2248 )
| ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SY2248 @ SY2246 @ SY2247 ) @ SY2247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1773,plain,
! [SV107: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i] :
( ( c_in @ SV107 @ SY2249 @ SY2250 )
| ( c_in @ SV107 @ SY2251 @ SY2250 )
| ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2251 @ SY2249 @ ( tc_fun @ SY2250 @ tc_bool ) ) @ SY2250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1774,plain,
! [SV108: $i] :
( ( ! [SY2252: $i,SY2253: $i] : ( c_in @ SV108 @ ( c_Set_Oinsert @ SV108 @ SY2252 @ SY2253 ) @ SY2253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1775,plain,
! [SV109: $i] :
( ( ! [SY2254: $i,SY2255: $i] : ( c_in @ SV109 @ ( c_Set_Oinsert @ SV109 @ SY2254 @ SY2255 ) @ SY2255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1776,plain,
! [SV110: $i] :
( ( ! [SY2256: $i,SY2257: $i] : ( c_in @ SV110 @ ( c_Set_Oinsert @ SV110 @ SY2256 @ SY2257 ) @ SY2257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1777,plain,
! [SV111: $i] :
( ( ! [SY2258: $i,SY2259: $i,SY2260: $i] :
( ( c_in @ SV111 @ SY2258 @ SY2259 )
| ~ ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2260 @ SY2258 @ ( tc_fun @ SY2259 @ tc_bool ) ) @ SY2259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1778,plain,
! [SV112: $i] :
( ( ! [SY2261: $i,SY2262: $i,SY2263: $i] :
( ( c_in @ SV112 @ SY2261 @ SY2262 )
| ~ ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2261 @ SY2263 @ ( tc_fun @ SY2262 @ tc_bool ) ) @ SY2262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1779,plain,
! [SV113: $i] :
( ( ! [SY2264: $i,SY2265: $i] :
( ( ( c_Set_Oinsert @ SV113 @ SY2264 @ SY2265 )
= SY2264 )
| ~ ( c_in @ SV113 @ SY2264 @ SY2265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1780,plain,
! [SV114: $i] :
( ( ! [SY2266: $i,SY2267: $i,SY2268: $i,SY2269: $i] :
( ~ ( c_in @ SV114 @ SY2266 @ SY2267 )
| ( c_in @ ( hAPP @ SY2268 @ SV114 ) @ ( c_Set_Oimage @ SY2268 @ SY2266 @ SY2267 @ SY2269 ) @ SY2269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1781,plain,
! [SV115: $i] :
( ( ! [SY2270: $i,SY2271: $i,SY2272: $i,SY2273: $i] :
( ~ ( c_in @ SV115 @ SY2270 @ SY2271 )
| ( c_in @ ( hAPP @ SY2272 @ SV115 ) @ ( c_Set_Oimage @ SY2272 @ SY2270 @ SY2271 @ SY2273 ) @ SY2273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1782,plain,
! [SV116: $i] :
( ( ! [SY2274: $i,SY2275: $i,SY2276: $i,SY2277: $i] :
( ( c_in @ ( hAPP @ SV116 @ SY2274 ) @ ( c_Set_Oimage @ SV116 @ SY2275 @ SY2276 @ SY2277 ) @ SY2277 )
| ~ ( c_in @ SY2274 @ SY2275 @ SY2276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1783,plain,
! [SV117: $i] :
( ( ! [SY2278: $i,SY2279: $i,SY2280: $i,SY2281: $i] :
( ( c_in @ ( hAPP @ SV117 @ SY2278 ) @ ( c_Set_Oimage @ SV117 @ SY2279 @ SY2280 @ SY2281 ) @ SY2281 )
| ~ ( c_in @ SY2278 @ SY2279 @ SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1784,plain,
! [SV118: $i] :
( ( ! [SY2282: $i,SY2283: $i,SY2284: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SY2282 @ SY2283 @ SY2284 ) @ SY2283 @ SY2284 @ SY2284 ) @ SV118 @ ( tc_prod @ SY2284 @ SY2284 ) )
| ~ ( c_in @ ( c_Pair @ SY2282 @ SY2283 @ SY2284 @ SY2284 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SY2284 ) @ ( tc_prod @ SY2284 @ SY2284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1785,plain,
! [SV119: $i] :
( ( ! [SY2285: $i,SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SY2285 @ SY2286 @ SY2287 ) @ ( c_Product__Type_OSigma @ SY2288 @ SY2289 @ SY2286 @ SY2287 ) @ ( tc_fun @ ( tc_prod @ SY2286 @ SY2287 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SY2285 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SY2285 @ SY2289 @ SY2286 @ SY2287 ) ) @ ( hAPP @ SY2289 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SY2285 @ SY2289 @ SY2286 @ SY2287 ) ) @ ( tc_fun @ SY2287 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SY2288 @ ( tc_fun @ SY2286 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1786,plain,
! [SV120: $i] :
( ( ! [SY2290: $i,SY2291: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SY2290 @ ( tc_fun @ ( tc_prod @ SY2291 @ SY2291 ) @ tc_bool ) ) @ SY2291 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SY2290 @ SY2291 @ SY2291 @ SY2291 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SY2291 @ SY2291 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2290 @ SY2291 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SY2291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1787,plain,
! [SV121: $i] :
( ( ! [SY2292: $i,SY2293: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SY2292 ) @ SY2293 @ ( tc_fun @ ( tc_prod @ SY2292 @ SY2292 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SY2292 ) @ SY2293 @ ( tc_fun @ ( tc_prod @ SY2292 @ SY2292 ) @ tc_bool ) ) @ SV121 @ SY2292 @ SY2292 @ SY2292 ) @ SY2293 @ ( tc_fun @ ( tc_prod @ SY2292 @ SY2292 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV121 @ SY2293 @ ( tc_fun @ ( tc_prod @ SY2292 @ SY2292 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1788,plain,
! [SV122: $i] :
( ( ! [SY2294: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV122 @ SY2294 ) @ ( c_Relation_OId @ SY2294 ) @ ( tc_fun @ ( tc_prod @ SY2294 @ SY2294 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV122 @ SY2294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1789,plain,
! [SV123: $i] :
( ( ! [SY2295: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV123 @ ( c_Relation_OId @ SY2295 ) @ ( tc_fun @ ( tc_prod @ SY2295 @ SY2295 ) @ tc_bool ) ) @ SY2295 )
= ( c_Transitive__Closure_Ortrancl @ SV123 @ SY2295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1790,plain,
! [SV124: $i] :
( ( ! [SY2296: $i,SY2297: $i,SY2298: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 @ SY2296 @ ( tc_fun @ ( tc_prod @ SY2297 @ SY2298 ) @ tc_bool ) ) @ SY2297 @ SY2298 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV124 @ SY2297 @ SY2298 ) @ ( c_Relation_ODomain @ SY2296 @ SY2297 @ SY2298 ) @ ( tc_fun @ SY2297 @ tc_bool ) ) @ ( tc_fun @ SY2297 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1791,plain,
! [SV125: $i] :
( ( ! [SY2299: $i,SY2300: $i] : ( c_lessequals @ SV125 @ ( c_Set_Oinsert @ SY2299 @ SV125 @ SY2300 ) @ ( tc_fun @ SY2300 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1792,plain,
! [SV126: $i] :
( ( ! [SY2301: $i,SY2302: $i] :
( ( c_Finite__Set_Ofinite @ SV126 @ SY2301 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY2302 @ SV126 @ SY2301 ) @ SY2301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1793,plain,
! [SV127: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV127 @ SY2303 @ SY2304 ) @ SY2304 )
| ~ ( c_Finite__Set_Ofinite @ SY2303 @ SY2304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1794,plain,
! [SV128: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SY2305 @ SY2306 @ SY2307 ) @ SY2307 )
| ~ ( c_Relation_Otrans @ SV128 @ SY2306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1795,plain,
! [SV129: $i] :
( ( ! [SY2308: $i,SY2309: $i,SY2310: $i,SY2311: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV129 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2308 @ SY2309 @ ( tc_fun @ SY2310 @ tc_bool ) ) @ SY2310 @ SY2311 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV129 @ SY2308 @ SY2310 @ SY2311 ) @ ( c_Set_Oimage @ SV129 @ SY2309 @ SY2310 @ SY2311 ) @ ( tc_fun @ SY2311 @ tc_bool ) ) @ ( tc_fun @ SY2311 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1796,plain,
! [SV130: $i] :
( ( ! [SY2312: $i,SY2313: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SY2312 @ ( tc_fun @ SY2313 @ tc_bool ) ) @ SY2313 )
| ~ ( c_Finite__Set_Ofinite @ SY2312 @ SY2313 )
| ~ ( c_Finite__Set_Ofinite @ SV130 @ SY2313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1797,plain,
! [SV131: $i] :
( ( ! [SY2314: $i,SY2315: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SY2314 @ ( tc_fun @ SY2315 @ tc_bool ) ) @ SY2315 )
| ~ ( c_Finite__Set_Ofinite @ SY2314 @ SY2315 )
| ~ ( c_Finite__Set_Ofinite @ SV131 @ SY2315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1798,plain,
! [SV132: $i] :
( ( ! [SY2316: $i,SY2317: $i,SY2318: $i,SY2319: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV132 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2316 @ SY2317 @ ( tc_fun @ SY2318 @ tc_bool ) ) @ SY2318 @ SY2319 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV132 @ SY2316 @ SY2318 @ SY2319 ) @ ( c_Relation_OImage @ SV132 @ SY2317 @ SY2318 @ SY2319 ) @ ( tc_fun @ SY2319 @ tc_bool ) ) @ ( tc_fun @ SY2319 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1799,plain,
! [SV133: $i] :
( ( ! [SY2320: $i,SY2321: $i,SY2322: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SY2320 @ ( tc_fun @ SY2321 @ tc_bool ) ) @ SY2322 @ ( tc_fun @ SY2321 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2320 @ SY2322 @ ( tc_fun @ SY2321 @ tc_bool ) ) @ ( tc_fun @ SY2321 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2322 @ SV133 @ ( tc_fun @ SY2321 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1800,plain,
! [SV134: $i] :
( ( ! [SY2323: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ ( c_Relation_OId @ SY2323 ) @ ( tc_fun @ ( tc_prod @ SY2323 @ SY2323 ) @ tc_bool ) ) @ SY2323 )
| ~ ( c_Relation_Otrans @ SV134 @ SY2323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1801,plain,
! [SV135: $i] :
( ( ! [SY2324: $i,SY2325: $i,SY2326: $i] :
( ( hBOOL @ ( hAPP @ SV135 @ SY2324 ) )
| ( hBOOL @ ( hAPP @ SY2325 @ SY2324 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2325 @ SV135 @ ( tc_fun @ SY2326 @ tc_bool ) ) @ SY2324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1802,plain,
! [SV136: $i] :
( ( ! [SY2327: $i,SY2328: $i,SY2329: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SY2327 @ ( tc_fun @ SY2328 @ tc_bool ) ) @ SY2329 ) )
| ~ ( hBOOL @ ( hAPP @ SY2327 @ SY2329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1803,plain,
! [SV137: $i] :
( ( ! [SY2330: $i,SY2331: $i,SY2332: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SY2330 @ ( tc_fun @ SY2331 @ tc_bool ) ) @ SY2332 ) )
| ~ ( hBOOL @ ( hAPP @ SV137 @ SY2332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1804,plain,
! [SV138: $i] :
( ( ! [SY2333: $i,SY2334: $i,SY2335: $i,SY2336: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 @ SY2333 @ ( tc_fun @ SY2334 @ tc_bool ) ) @ ( c_COMBK @ SY2335 @ ( tc_fun @ SY2336 @ tc_bool ) @ SY2334 ) @ SY2334 @ SY2336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV138 @ ( c_COMBK @ SY2335 @ ( tc_fun @ SY2336 @ tc_bool ) @ SY2334 ) @ SY2334 @ SY2336 ) @ ( c_Product__Type_OSigma @ SY2333 @ ( c_COMBK @ SY2335 @ ( tc_fun @ SY2336 @ tc_bool ) @ SY2334 ) @ SY2334 @ SY2336 ) @ ( tc_fun @ ( tc_prod @ SY2334 @ SY2336 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1805,plain,
! [SV139: $i] :
( ( ! [SY2337: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV139 @ SV139 @ SY2337 @ SY2337 @ SY2337 ) @ SV139 @ ( tc_fun @ ( tc_prod @ SY2337 @ SY2337 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV139 @ SY2337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1806,plain,
! [SV140: $i] :
( ( ! [SY2338: $i,SY2339: $i,SY2340: $i,SY2341: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SY2338 @ ( tc_fun @ SY2339 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2340 @ SY2341 @ ( tc_fun @ ( tc_prod @ SY2339 @ SY2339 ) @ tc_bool ) ) @ SY2339 )
| ~ ( c_Relation_Orefl__on @ SY2338 @ SY2341 @ SY2339 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SY2340 @ SY2339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1807,plain,
! [SV141: $i] :
( ( ! [SY2342: $i,SY2343: $i,SY2344: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2342 @ SY2343 @ SV141 ) @ SY2344 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2342 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2343 @ SY2344 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1808,plain,
! [SV142: $i] :
( ( ! [SY2345: $i,SY2346: $i,SY2347: $i] :
( ~ ( class_Lattices_Olattice @ SV142 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2345 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2346 @ SY2347 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2346 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2345 @ SY2347 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1809,plain,
! [SV143: $i] :
( ( ! [SY2348: $i,SY2349: $i,SY2350: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2348 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2349 @ SY2350 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2349 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2348 @ SY2350 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1810,plain,
! [SV144: $i] :
( ( ! [SY2351: $i,SY2352: $i,SY2353: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2351 @ SY2352 @ SV144 ) @ SY2353 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2351 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2352 @ SY2353 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1811,plain,
! [SV145: $i] :
( ( ! [SY2354: $i,SY2355: $i,SY2356: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ SY2354 @ ( tc_fun @ SY2355 @ tc_bool ) ) @ SY2356 @ ( tc_fun @ SY2355 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2354 @ SY2356 @ ( tc_fun @ SY2355 @ tc_bool ) ) @ ( tc_fun @ SY2355 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1812,plain,
! [SV146: $i] :
( ( ! [SY2357: $i,SY2358: $i,SY2359: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2357 @ SY2358 @ ( tc_fun @ SY2359 @ tc_bool ) ) @ ( tc_fun @ SY2359 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2357 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SY2358 @ ( tc_fun @ SY2359 @ tc_bool ) ) @ ( tc_fun @ SY2359 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1813,plain,
! [SV147: $i] :
( ( ! [SY2360: $i,SY2361: $i] :
( ( c_Finite__Set_Ofinite @ SV147 @ SY2360 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV147 @ SY2361 @ ( tc_fun @ SY2360 @ tc_bool ) ) @ SY2360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1814,plain,
! [SV148: $i] :
( ( ! [SY2362: $i,SY2363: $i] :
( ( c_Finite__Set_Ofinite @ SV148 @ SY2362 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2363 @ SV148 @ ( tc_fun @ SY2362 @ tc_bool ) ) @ SY2362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1815,plain,
! [SV149: $i] :
( ( c_Relation_Otrans @ ( c_Relation_OId @ SV149 ) @ SV149 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1816,plain,
! [SV150: $i] :
( ( ! [SY2364: $i,SY2365: $i,SY2366: $i,SY2367: $i,SY2368: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SY2364 @ SY2365 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY2366 @ SY2367 @ SY2368 ) @ ( tc_fun @ SY2368 @ tc_bool ) @ SY2365 ) @ SY2365 @ SY2368 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SY2366 @ SY2365 @ SY2368 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SY2364 @ ( c_COMBK @ ( c_Set_Oinsert @ SY2366 @ SY2367 @ SY2368 ) @ ( tc_fun @ SY2368 @ tc_bool ) @ SY2365 ) @ SY2365 @ SY2368 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SY2364 @ SY2365 ) @ ( c_COMBK @ SY2367 @ ( tc_fun @ SY2368 @ tc_bool ) @ SY2365 ) @ SY2365 @ SY2368 ) @ ( tc_fun @ ( tc_prod @ SY2365 @ SY2368 ) @ tc_bool ) ) @ ( tc_prod @ SY2365 @ SY2368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1817,plain,
! [SV151: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SY2369 @ ( tc_fun @ ( tc_prod @ SY2370 @ SY2370 ) @ tc_bool ) ) @ SY2370 )
| ~ ( c_Relation_Otrans @ SY2369 @ SY2370 )
| ~ ( c_Relation_Otrans @ SV151 @ SY2370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1818,plain,
! [SV152: $i] :
( ( ! [SY2371: $i,SY2372: $i,SY2373: $i] :
( ~ ( class_Lattices_Olattice @ SV152 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2371 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2372 @ SY2373 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2371 @ SY2372 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2371 @ SY2373 @ SV152 ) @ SV152 ) @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1819,plain,
! [SV153: $i] :
( ( ! [SY2374: $i,SY2375: $i] :
( ~ ( class_Lattices_Olattice @ SV153 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2374 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2374 @ SY2375 @ SV153 ) @ SV153 )
= SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1820,plain,
! [SV154: $i] :
( ( ! [SY2376: $i,SY2377: $i] :
( ~ ( class_Lattices_Olattice @ SV154 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2376 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2376 @ SY2377 @ SV154 ) @ SV154 )
= SY2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1821,plain,
! [SV155: $i] :
( ( ! [SY2378: $i,SY2379: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV155 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2378 @ SY2379 @ SV155 )
= SY2378 )
| ~ ( c_lessequals @ SY2379 @ SY2378 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1822,plain,
! [SV156: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV156 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2380 @ SY2381 @ SV156 )
= SY2381 )
| ~ ( c_lessequals @ SY2380 @ SY2381 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1823,plain,
! [SV157: $i] :
( ( ! [SY2382: $i,SY2383: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) )
= SY2382 )
| ~ ( c_lessequals @ SV157 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1824,plain,
! [SV158: $i] :
( ( ! [SY2384: $i,SY2385: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SY2384 @ ( tc_fun @ SY2385 @ tc_bool ) )
= SV158 )
| ~ ( c_lessequals @ SY2384 @ SV158 @ ( tc_fun @ SY2385 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1825,plain,
! [SV159: $i] :
( ( ! [SY2386: $i,SY2387: $i,SY2388: $i,SY2389: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SY2386 @ ( tc_fun @ SY2387 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2388 @ SY2389 @ ( tc_fun @ ( tc_prod @ SY2387 @ SY2387 ) @ tc_bool ) ) @ SY2387 )
| ~ ( c_Relation_Orefl__on @ SY2386 @ SY2389 @ SY2387 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SY2388 @ SY2387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1826,plain,
! [SV160: $i] :
( ( ! [SY2390: $i,SY2391: $i,SY2392: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SY2390 @ SY2391 @ SY2392 ) @ SY2392 )
| ~ ( c_Finite__Set_Ofinite @ SY2390 @ SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1827,plain,
! [SV161: $i] :
( ( ! [SY2393: $i,SY2394: $i,SY2395: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SY2393 @ SY2394 ) @ SY2395 @ ( tc_fun @ SY2394 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2393 @ SY2395 @ ( tc_fun @ SY2394 @ tc_bool ) ) @ SY2394 ) )
| ~ ( c_in @ SV161 @ SY2395 @ SY2394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1828,plain,
! [SV162: $i] :
( ( ! [SY2396: $i,SY2397: $i,SY2398: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SY2396 @ SY2397 @ SY2398 ) @ ( tc_fun @ SY2398 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2396 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SY2397 @ ( tc_fun @ SY2398 @ tc_bool ) ) @ SY2398 ) )
| ~ ( c_in @ SY2396 @ SV162 @ SY2398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1829,plain,
! [SV163: $i] :
( ( ! [SY2399: $i,SY2400: $i,SY2401: $i,SY2402: $i] :
( ( c_Set_Oimage @ SV163 @ ( c_Set_Oinsert @ SY2399 @ SY2400 @ SY2401 ) @ SY2401 @ SY2402 )
= ( c_Set_Oinsert @ ( hAPP @ SV163 @ SY2399 ) @ ( c_Set_Oimage @ SV163 @ SY2400 @ SY2401 @ SY2402 ) @ SY2402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1830,plain,
! [SV164: $i] :
( ( ! [SY2403: $i,SY2404: $i,SY2405: $i,SY2406: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SY2403 @ ( tc_fun @ SY2404 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2405 @ SY2406 @ ( tc_fun @ SY2404 @ tc_bool ) ) @ ( tc_fun @ SY2404 @ tc_bool ) )
| ~ ( c_lessequals @ SY2403 @ SY2406 @ ( tc_fun @ SY2404 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SY2405 @ ( tc_fun @ SY2404 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1831,plain,
! [SV165: $i] :
( ( ! [SY2407: $i,SY2408: $i,SY2409: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV165 @ SY2407 @ ( tc_fun @ ( tc_prod @ SY2408 @ SY2409 ) @ tc_bool ) ) @ SY2408 @ SY2409 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV165 @ SY2408 @ SY2409 ) @ ( c_Relation_Oconverse @ SY2407 @ SY2408 @ SY2409 ) @ ( tc_fun @ ( tc_prod @ SY2409 @ SY2408 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1832,plain,
! [SV166: $i] :
( ( ! [SY2410: $i,SY2411: $i] :
( ~ ( class_Lattices_Olattice @ SV166 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2410 @ SY2411 @ SV166 ) @ SY2410 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1833,plain,
! [SV167: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ~ ( class_Lattices_Olattice @ SV167 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2412 @ SY2413 @ SV167 ) @ SY2413 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1834,plain,
! [SV168: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV168 )
| ( c_lessequals @ SY2414 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2415 @ SY2416 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SY2414 @ SY2416 @ SV168 )
| ~ ( c_lessequals @ SY2414 @ SY2415 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1835,plain,
! [SV169: $i] :
( ( ! [SY2417: $i,SY2418: $i,SY2419: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV169 )
| ( c_lessequals @ SY2417 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2418 @ SY2419 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SY2417 @ SY2419 @ SV169 )
| ~ ( c_lessequals @ SY2417 @ SY2418 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1836,plain,
! [SV170: $i] :
( ( ! [SY2420: $i,SY2421: $i,SY2422: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV170 )
| ( c_lessequals @ SY2420 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2421 @ SY2422 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SY2420 @ SY2422 @ SV170 )
| ~ ( c_lessequals @ SY2420 @ SY2421 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1837,plain,
! [SV171: $i] :
( ( ! [SY2423: $i,SY2424: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV171 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2423 @ SY2424 @ SV171 ) @ SY2424 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1838,plain,
! [SV172: $i] :
( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV172 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2425 @ SY2426 @ SV172 ) @ SY2425 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1839,plain,
! [SV173: $i] :
( ( ! [SY2427: $i,SY2428: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV173 @ SY2427 @ ( tc_fun @ SY2428 @ tc_bool ) ) @ SV173 @ ( tc_fun @ SY2428 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1840,plain,
! [SV174: $i] :
( ( ! [SY2429: $i,SY2430: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV174 @ SY2429 @ ( tc_fun @ SY2430 @ tc_bool ) ) @ SY2429 @ ( tc_fun @ SY2430 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1841,plain,
! [SV175: $i] :
( ( ! [SY2431: $i,SY2432: $i,SY2433: $i] :
( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2431 @ SY2432 @ ( tc_fun @ SY2433 @ tc_bool ) ) @ ( tc_fun @ SY2433 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SY2432 @ ( tc_fun @ SY2433 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SY2431 @ ( tc_fun @ SY2433 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1842,plain,
! [SV176: $i] :
( ( ! [SY2434: $i,SY2435: $i,SY2436: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2434 @ SY2435 @ ( tc_fun @ SY2436 @ tc_bool ) ) @ ( tc_fun @ SY2436 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SY2435 @ ( tc_fun @ SY2436 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SY2434 @ ( tc_fun @ SY2436 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1843,plain,
! [SV177: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i,SY2440: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV177 @ SY2437 @ ( tc_fun @ SY2438 @ tc_bool ) ) @ ( c_COMBK @ SY2439 @ ( tc_fun @ SY2440 @ tc_bool ) @ SY2438 ) @ SY2438 @ SY2440 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV177 @ ( c_COMBK @ SY2439 @ ( tc_fun @ SY2440 @ tc_bool ) @ SY2438 ) @ SY2438 @ SY2440 ) @ ( c_Product__Type_OSigma @ SY2437 @ ( c_COMBK @ SY2439 @ ( tc_fun @ SY2440 @ tc_bool ) @ SY2438 ) @ SY2438 @ SY2440 ) @ ( tc_fun @ ( tc_prod @ SY2438 @ SY2440 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1844,plain,
! [SV178: $i] :
( ( ! [SY2441: $i,SY2442: $i,SY2443: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV178 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2441 @ SY2442 @ SV178 ) @ SY2443 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2441 @ SY2443 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2442 @ SY2443 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1845,plain,
! [SV179: $i] :
( ( ! [SY2444: $i,SY2445: $i,SY2446: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV179 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2444 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2445 @ SY2446 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2444 @ SY2445 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2444 @ SY2446 @ SV179 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1846,plain,
! [SV180: $i] :
( ( ! [SY2447: $i,SY2448: $i,SY2449: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2447 @ SY2448 @ ( tc_fun @ SY2449 @ tc_bool ) ) @ ( tc_fun @ SY2449 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SY2447 @ ( tc_fun @ SY2449 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SY2448 @ ( tc_fun @ SY2449 @ tc_bool ) ) @ ( tc_fun @ SY2449 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1847,plain,
! [SV181: $i] :
( ( ! [SY2450: $i,SY2451: $i,SY2452: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV181 @ SY2450 @ ( tc_fun @ SY2451 @ tc_bool ) ) @ SY2452 @ ( tc_fun @ SY2451 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV181 @ SY2452 @ ( tc_fun @ SY2451 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2450 @ SY2452 @ ( tc_fun @ SY2451 @ tc_bool ) ) @ ( tc_fun @ SY2451 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1848,plain,
! [SV182: $i] :
( ( ! [SY2453: $i,SY2454: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV182 @ SY2453 @ SY2454 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1849,plain,
! [SV183: $i] :
( ( ! [SY2455: $i,SY2456: $i,SY2457: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SY2455 @ SY2456 ) @ SY2457 @ ( tc_fun @ SY2456 @ tc_bool ) )
| ~ ( c_lessequals @ SY2455 @ SY2457 @ ( tc_fun @ SY2456 @ tc_bool ) )
| ~ ( c_in @ SV183 @ SY2457 @ SY2456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1850,plain,
! [SV184: $i] :
( ( ! [SY2458: $i,SY2459: $i] :
( ~ ( class_Lattices_Olattice @ SV184 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2458 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2458 @ SY2459 @ SV184 ) @ SV184 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2458 @ SY2459 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1851,plain,
! [SV185: $i] :
( ( ! [SY2460: $i,SY2461: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV185 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2460 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2460 @ SY2461 @ SV185 ) @ SV185 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2460 @ SY2461 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1852,plain,
! [SV186: $i] :
( ( ! [SY2462: $i,SY2463: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SY2462 @ ( tc_fun @ SY2463 @ tc_bool ) ) @ ( tc_fun @ SY2463 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SY2462 @ ( tc_fun @ SY2463 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1853,plain,
! [SV187: $i] :
( ( ! [SY2464: $i,SY2465: $i] :
( ( c_lessequals @ ( c_Relation_OField @ SV187 @ SY2464 ) @ ( c_Relation_OField @ SY2465 @ SY2464 ) @ ( tc_fun @ SY2464 @ tc_bool ) )
| ~ ( c_lessequals @ SV187 @ SY2465 @ ( tc_fun @ ( tc_prod @ SY2464 @ SY2464 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1854,plain,
! [SV188: $i] :
( ( ! [SY2466: $i,SY2467: $i,SY2468: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV188 @ SY2466 @ ( tc_fun @ ( tc_prod @ SY2467 @ SY2468 ) @ tc_bool ) ) @ SY2467 @ SY2468 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV188 @ SY2467 @ SY2468 ) @ ( c_Relation_ORange @ SY2466 @ SY2467 @ SY2468 ) @ ( tc_fun @ SY2468 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1855,plain,
! [SV189: $i] :
( ( ! [SY2469: $i,SY2470: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SY2469 @ ( tc_fun @ ( tc_prod @ SY2470 @ SY2470 ) @ tc_bool ) ) @ SY2470 )
| ~ ( c_Wellfounded_Owf @ SV189 @ SY2470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1856,plain,
! [SV190: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV190 @ SY2471 @ ( tc_fun @ ( tc_prod @ SY2472 @ SY2472 ) @ tc_bool ) ) @ SY2472 )
| ~ ( c_Wellfounded_Owf @ SY2471 @ SY2472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1857,plain,
! [SV191: $i] :
( ( ! [SY2473: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV191 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2473 @ SY2473 @ SV191 )
= SY2473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1858,plain,
! [SV192: $i] :
( ( ! [SY2474: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV192 @ ( tc_fun @ SY2474 @ tc_bool ) )
= SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1859,plain,
! [SV193: $i] :
( ( ! [SY2475: $i] :
( ( c_Relation_OField @ SV193 @ SY2475 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV193 @ SY2475 @ SY2475 ) @ ( c_Relation_ORange @ SV193 @ SY2475 @ SY2475 ) @ ( tc_fun @ SY2475 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1860,plain,
! [SV194: $i] :
( ( ! [SY2476: $i,SY2477: $i,SY2478: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV194 )
| ( c_lessequals @ SY2476 @ SY2477 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2478 @ SY2476 @ SV194 ) @ SY2477 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1861,plain,
! [SV195: $i] :
( ( ! [SY2479: $i,SY2480: $i,SY2481: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV195 )
| ( c_lessequals @ SY2479 @ SY2480 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2479 @ SY2481 @ SV195 ) @ SY2480 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1862,plain,
! [SV196: $i] :
( ( ! [SY2482: $i,SY2483: $i,SY2484: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV196 )
| ( c_lessequals @ SY2482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2483 @ SY2484 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SY2482 @ SY2484 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1863,plain,
! [SV197: $i] :
( ( ! [SY2485: $i,SY2486: $i,SY2487: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV197 )
| ( c_lessequals @ SY2485 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2486 @ SY2487 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SY2485 @ SY2486 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1864,plain,
! [SV198: $i] :
( ( ! [SY2488: $i,SY2489: $i,SY2490: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV198 )
| ( c_lessequals @ SY2488 @ SY2489 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2490 @ SY2488 @ SV198 ) @ SY2489 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1865,plain,
! [SV199: $i] :
( ( ! [SY2491: $i,SY2492: $i,SY2493: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV199 )
| ( c_lessequals @ SY2491 @ SY2492 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2491 @ SY2493 @ SV199 ) @ SY2492 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1866,plain,
! [SV200: $i] :
( ( ! [SY2494: $i,SY2495: $i,SY2496: $i] :
( ( c_lessequals @ SV200 @ SY2494 @ ( tc_fun @ SY2495 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY2496 @ ( tc_fun @ SY2495 @ tc_bool ) ) @ SY2494 @ ( tc_fun @ SY2495 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1867,plain,
! [SV201: $i] :
( ( ! [SY2497: $i,SY2498: $i,SY2499: $i] :
( ( c_lessequals @ SV201 @ SY2497 @ ( tc_fun @ SY2498 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2499 @ SV201 @ ( tc_fun @ SY2498 @ tc_bool ) ) @ SY2497 @ ( tc_fun @ SY2498 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1868,plain,
! [SV202: $i] :
( ( ! [SY2500: $i,SY2501: $i] :
( ( c_Finite__Set_Ofinite @ SV202 @ SY2500 )
| ~ ( c_Finite__Set_Ofinite @ SY2501 @ SY2500 )
| ~ ( c_lessequals @ SV202 @ SY2501 @ ( tc_fun @ SY2500 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1869,plain,
! [SV203: $i] :
( ( ! [SY2502: $i,SY2503: $i] :
( ( c_Finite__Set_Ofinite @ SV203 @ SY2502 )
| ~ ( c_lessequals @ SV203 @ SY2503 @ ( tc_fun @ SY2502 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY2503 @ SY2502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1870,plain,
! [SV204: $i] :
( ( ! [SY2504: $i,SY2505: $i,SY2506: $i,SY2507: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SY2504 @ ( tc_fun @ SY2505 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2506 @ SY2507 @ ( tc_fun @ SY2505 @ tc_bool ) ) @ ( tc_fun @ SY2505 @ tc_bool ) )
| ~ ( c_lessequals @ SY2504 @ SY2507 @ ( tc_fun @ SY2505 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SY2506 @ ( tc_fun @ SY2505 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1871,plain,
! [SV205: $i] :
( ( ! [SY2508: $i,SY2509: $i,SY2510: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SY2508 @ ( tc_fun @ SY2509 @ tc_bool ) ) @ SY2510 ) )
| ~ ( hBOOL @ ( hAPP @ SY2508 @ SY2510 ) )
| ~ ( hBOOL @ ( hAPP @ SV205 @ SY2510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1872,plain,
! [SV206: $i] :
( ( ! [SY2511: $i,SY2512: $i,SY2513: $i,SY2514: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SY2511 @ SY2512 @ SY2513 ) @ ( c_Set_Oimage @ SV206 @ SY2514 @ SY2512 @ SY2513 ) @ ( tc_fun @ SY2513 @ tc_bool ) )
| ~ ( c_lessequals @ SY2511 @ SY2514 @ ( tc_fun @ SY2512 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1873,plain,
! [SV207: $i] :
( ( ! [SY2515: $i,SY2516: $i,SY2517: $i,SY2518: $i] :
( ~ ( c_lessequals @ SV207 @ SY2515 @ ( tc_fun @ SY2516 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY2517 @ SV207 @ SY2516 @ SY2518 ) @ ( c_Set_Oimage @ SY2517 @ SY2515 @ SY2516 @ SY2518 ) @ ( tc_fun @ SY2518 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1874,plain,
! [SV208: $i] :
( ( ! [SY2519: $i,SY2520: $i,SY2521: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SY2519 @ SY2520 ) @ ( c_Set_Oinsert @ SV208 @ SY2521 @ SY2520 ) @ ( tc_fun @ SY2520 @ tc_bool ) )
| ~ ( c_lessequals @ SY2519 @ SY2521 @ ( tc_fun @ SY2520 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1875,plain,
! [SV209: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ( c_Relation_Otrans @ SV209 @ SY2522 )
| ~ ( c_Equiv__Relations_Oequiv @ SY2523 @ SV209 @ SY2522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1876,plain,
! [SV210: $i] :
( ( ! [SY2524: $i,SY2525: $i,SY2526: $i,SY2527: $i] :
( ( c_Set_Oimage @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2524 @ SY2525 @ ( tc_fun @ SY2526 @ tc_bool ) ) @ SY2526 @ SY2527 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV210 @ SY2524 @ SY2526 @ SY2527 ) @ ( c_Set_Oimage @ SV210 @ SY2525 @ SY2526 @ SY2527 ) @ ( tc_fun @ SY2527 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1877,plain,
! [SV211: $i] :
( ( ! [SY2528: $i,SY2529: $i,SY2530: $i,SY2531: $i] :
( ( c_in @ ( c_Pair @ SV211 @ SY2528 @ SY2529 @ SY2529 ) @ SY2530 @ ( tc_prod @ SY2529 @ SY2529 ) )
| ~ ( c_in @ ( c_Pair @ SY2531 @ SY2528 @ SY2529 @ SY2529 ) @ SY2530 @ ( tc_prod @ SY2529 @ SY2529 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SY2531 @ SY2529 @ SY2529 ) @ SY2530 @ ( tc_prod @ SY2529 @ SY2529 ) )
| ~ ( c_Relation_Otrans @ SY2530 @ SY2529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1878,plain,
! [SV212: $i] :
( ( ! [SY2532: $i,SY2533: $i,SY2534: $i,SY2535: $i] :
( ( c_in @ ( c_Pair @ SV212 @ SY2532 @ SY2533 @ SY2533 ) @ SY2534 @ ( tc_prod @ SY2533 @ SY2533 ) )
| ~ ( c_in @ ( c_Pair @ SY2535 @ SY2532 @ SY2533 @ SY2533 ) @ SY2534 @ ( tc_prod @ SY2533 @ SY2533 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SY2535 @ SY2533 @ SY2533 ) @ SY2534 @ ( tc_prod @ SY2533 @ SY2533 ) )
| ~ ( c_Relation_Otrans @ SY2534 @ SY2533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1879,plain,
! [SV213: $i] :
( ( ! [SY2536: $i,SY2537: $i,SY2538: $i] :
( ( c_Wellfounded_Owf @ SV213 @ SY2536 )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY2537 @ SY2538 @ SY2536 @ SY2536 ) @ SV213 @ ( tc_prod @ SY2536 @ SY2536 ) ) @ SY2536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1880,plain,
! [SV214: $i] :
( ( ! [SY2539: $i,SY2540: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV214 @ SV214 @ SY2539 @ SY2539 @ SY2539 ) @ ( c_Relation_Orel__comp @ SY2540 @ SV214 @ SY2539 @ SY2539 @ SY2539 ) @ ( tc_fun @ ( tc_prod @ SY2539 @ SY2539 ) @ tc_bool ) ) @ SY2540 @ ( tc_fun @ ( tc_prod @ SY2539 @ SY2539 ) @ tc_bool ) ) @ SY2539 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV214 @ SY2540 @ ( tc_fun @ ( tc_prod @ SY2539 @ SY2539 ) @ tc_bool ) ) @ SY2539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1881,plain,
! [SV215: $i] :
( ( ! [SY2541: $i,SY2542: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SY2541 @ ( tc_fun @ ( tc_prod @ SY2542 @ SY2542 ) @ tc_bool ) ) @ SY2542 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV215 @ SV215 @ SY2542 @ SY2542 @ SY2542 ) @ ( c_Relation_Orel__comp @ SY2541 @ SV215 @ SY2542 @ SY2542 @ SY2542 ) @ ( tc_fun @ ( tc_prod @ SY2542 @ SY2542 ) @ tc_bool ) ) @ SY2541 @ ( tc_fun @ ( tc_prod @ SY2542 @ SY2542 ) @ tc_bool ) ) @ SY2542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1882,plain,
! [SV216: $i] :
( ( ! [SY2543: $i] :
( ( c_Transitive__Closure_Otrancl @ SV216 @ SY2543 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV216 @ SY2543 ) @ SV216 @ SY2543 @ SY2543 @ SY2543 ) @ ( tc_fun @ ( tc_prod @ SY2543 @ SY2543 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1883,plain,
! [SV217: $i] :
( ( ! [SY2544: $i,SY2545: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SY2544 @ tc_bool ) ) @ SY2544 )
| ~ ( c_Finite__Set_Ofinite @ SY2545 @ SY2544 )
| ~ ( c_in @ SY2545 @ SV217 @ ( tc_fun @ SY2544 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1884,plain,
! [SV218: $i] :
( ( ! [SY2546: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV218 @ ( c_Relation_Oconverse @ SV218 @ SY2546 @ SY2546 ) @ ( tc_fun @ ( tc_prod @ SY2546 @ SY2546 ) @ tc_bool ) ) @ SY2546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1885,plain,
! [SV219: $i] :
( ( ! [SY2547: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV219 @ ( c_Relation_Oconverse @ SV219 @ SY2547 @ SY2547 ) @ ( tc_fun @ ( tc_prod @ SY2547 @ SY2547 ) @ tc_bool ) ) @ SY2547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1886,plain,
! [SV220: $i] :
( ( ! [SY2548: $i,SY2549: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV220 @ SY2548 ) @ SY2549 @ SY2548 @ SY2548 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV220 @ SY2549 @ ( tc_fun @ SY2548 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1887,plain,
! [SV221: $i] :
( ( ! [SY2550: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV221 @ SY2550 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV221 @ SY2550 ) @ ( c_Relation_OId @ SY2550 ) @ ( tc_fun @ ( tc_prod @ SY2550 @ SY2550 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1888,plain,
! [SV222: $i] :
( ( ! [SY2551: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV222 @ SY2551 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SY2551 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV222 @ SY2551 ) @ SV222 @ SY2551 @ SY2551 @ SY2551 ) @ ( tc_fun @ ( tc_prod @ SY2551 @ SY2551 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1889,plain,
! [SV223: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i] :
( ~ ( c_in @ ( c_Pair @ SV223 @ SY2552 @ SY2553 @ SY2553 ) @ ( c_Transitive__Closure_Ortrancl @ SY2554 @ SY2553 ) @ ( tc_prod @ SY2553 @ SY2553 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY2552 @ SV223 @ SY2553 @ SY2553 ) @ SY2554 @ ( tc_prod @ SY2553 @ SY2553 ) ) @ SY2553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1890,plain,
! [SV224: $i] :
( ( ! [SY2555: $i,SY2556: $i,SY2557: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SY2555 @ SY2556 @ SY2556 ) @ SY2557 @ ( tc_prod @ SY2556 @ SY2556 ) ) @ SY2556 )
| ( c_in @ ( c_Pair @ SY2555 @ SV224 @ SY2556 @ SY2556 ) @ ( c_Transitive__Closure_Ortrancl @ SY2557 @ SY2556 ) @ ( tc_prod @ SY2556 @ SY2556 ) )
| ~ ( c_Wellfounded_Owf @ SY2557 @ SY2556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1891,plain,
! [SV225: $i] :
( ( ! [SY2558: $i,SY2559: $i,SY2560: $i] :
( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SY2558 @ SV225 @ SY2559 @ SY2560 ) @ SY2560 @ SY2560 ) @ ( c_Transitive__Closure_Ortrancl @ SY2558 @ SY2560 ) @ ( tc_prod @ SY2560 @ SY2560 ) )
| ~ ( c_in @ ( c_Pair @ SV225 @ SY2559 @ SY2560 @ SY2560 ) @ ( c_Transitive__Closure_Otrancl @ SY2558 @ SY2560 ) @ ( tc_prod @ SY2560 @ SY2560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1892,plain,
! [SV226: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i,SY2564: $i,SY2565: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SY2561 @ SY2562 @ SY2563 ) @ ( c_Product__Type_OSigma @ SY2564 @ SY2565 @ SY2562 @ SY2563 ) @ ( tc_fun @ ( tc_prod @ SY2562 @ SY2563 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SY2561 @ SY2565 @ SY2562 @ SY2563 ) @ SV226 @ SY2562 )
| ~ ( c_lessequals @ SV226 @ SY2564 @ ( tc_fun @ SY2562 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1893,plain,
! [SV227: $i] :
( ( ! [SY2566: $i,SY2567: $i,SY2568: $i,SY2569: $i] :
( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SY2566 @ ( c_COMBK @ SY2567 @ ( tc_fun @ SY2568 @ tc_bool ) @ SY2569 ) @ SY2569 @ SY2568 ) @ ( tc_fun @ SY2569 @ SY2568 ) )
| ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SY2566 @ SY2567 @ SV227 @ SY2569 @ SY2568 ) ) @ SY2567 @ SY2568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1894,plain,
! [SV228: $i] :
( ( ! [SY2570: $i,SY2571: $i,SY2572: $i,SY2573: $i] :
( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SY2570 @ ( c_COMBK @ SY2571 @ ( tc_fun @ SY2572 @ tc_bool ) @ SY2573 ) @ SY2573 @ SY2572 ) @ ( tc_fun @ SY2573 @ SY2572 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SY2570 @ SY2571 @ SV228 @ SY2573 @ SY2572 ) @ SY2570 @ SY2573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1895,plain,
! [SV229: $i] :
( ( ! [SY2574: $i,SY2575: $i,SY2576: $i,SY2577: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SY2574 @ SY2575 @ SY2576 ) @ SY2577 @ ( tc_fun @ SY2576 @ tc_bool ) )
| ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SY2574 @ ( c_COMBK @ SY2577 @ ( tc_fun @ SY2576 @ tc_bool ) @ SY2575 ) @ SY2575 @ SY2576 ) @ ( tc_fun @ SY2575 @ SY2576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1896,plain,
! [SV230: $i] :
( ( ! [SY2578: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV230 @ SY2578 ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ SV230 @ SY2578 ) @ ( c_COMBK @ ( c_Relation_OField @ SV230 @ SY2578 ) @ ( tc_fun @ SY2578 @ tc_bool ) @ SY2578 ) @ SY2578 @ SY2578 ) @ ( tc_fun @ ( tc_prod @ SY2578 @ SY2578 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1897,plain,
! [SV231: $i] :
( ( ! [SY2579: $i,SY2580: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SY2579 ) @ SY2580 @ ( tc_fun @ ( tc_prod @ SY2579 @ SY2579 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SY2579 ) @ SY2580 @ ( tc_fun @ ( tc_prod @ SY2579 @ SY2579 ) @ tc_bool ) ) @ SV231 @ SY2579 @ SY2579 @ SY2579 ) @ SY2580 @ ( tc_fun @ ( tc_prod @ SY2579 @ SY2579 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SY2579 ) @ SY2580 @ ( tc_fun @ ( tc_prod @ SY2579 @ SY2579 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1898,plain,
! [SV232: $i] :
( ( ! [SY2581: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SY2581 @ SY2581 ) @ SV232 @ SY2581 @ SY2581 @ SY2581 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SY2581 @ SY2581 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV232 @ SY2581 )
| ~ ( c_Relation_Osym @ SV232 @ SY2581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1899,plain,
! [SV233: $i] :
( ( ! [SY2582: $i,SY2583: $i,SY2584: $i] :
( ( c_Wellfounded_Owf @ SV233 @ SY2582 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SY2583 @ SY2584 @ SV233 @ SY2582 ) @ SY2584 @ SY2582 )
| ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SY2583 @ ( c_COMBK @ SY2584 @ ( tc_fun @ SY2582 @ tc_bool ) @ SY2582 ) @ SY2582 @ SY2582 ) @ ( tc_fun @ ( tc_prod @ SY2582 @ SY2582 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1900,plain,
! [SV234: $i] :
( ( ! [SY2585: $i,SY2586: $i,SY2587: $i] :
( ( c_Wellfounded_Owf @ SV234 @ SY2585 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SY2586 @ SY2587 @ SV234 @ SY2585 ) @ SY2586 @ SY2585 )
| ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SY2586 @ ( c_COMBK @ SY2587 @ ( tc_fun @ SY2585 @ tc_bool ) @ SY2585 ) @ SY2585 @ SY2585 ) @ ( tc_fun @ ( tc_prod @ SY2585 @ SY2585 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1901,plain,
! [SV235: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ( c_Relation_Orefl__on @ SV235 @ SY2588 @ SY2589 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SY2588 @ SY2589 ) @ SV235 @ SY2589 )
| ~ ( c_lessequals @ SY2588 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SY2589 @ tc_bool ) @ SY2589 ) @ SY2589 @ SY2589 ) @ ( tc_fun @ ( tc_prod @ SY2589 @ SY2589 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1902,plain,
! [SV236: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ( c_Relation_Orefl__on @ SV236 @ SY2590 @ SY2591 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SY2590 @ SY2591 ) @ SV236 @ SY2591 )
| ~ ( c_lessequals @ SY2590 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SY2591 @ tc_bool ) @ SY2591 ) @ SY2591 @ SY2591 ) @ ( tc_fun @ ( tc_prod @ SY2591 @ SY2591 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1903,plain,
! [SV237: $i] :
( ( ! [SY2592: $i,SY2593: $i,SY2594: $i] :
( ( c_Finite__Set_Ofinite @ SV237 @ SY2592 )
| ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SY2593 @ SY2594 @ SY2592 ) @ ( tc_fun @ SY2592 @ tc_bool ) )
| ~ ( c_lessequals @ SY2594 @ ( c_Product__Type_OSigma @ SY2593 @ ( c_COMBK @ SY2593 @ ( tc_fun @ SY2592 @ tc_bool ) @ SY2592 ) @ SY2592 @ SY2592 ) @ ( tc_fun @ ( tc_prod @ SY2592 @ SY2592 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY2593 @ SY2592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1904,plain,
! [SV238: $i] :
( ( ! [SY2595: $i,SY2596: $i] :
( ( c_Relation_Orefl__on @ SV238 @ SY2595 @ SY2596 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SY2595 @ SY2596 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SY2595 @ SY2596 ) @ SY2596 @ SY2596 ) @ SY2595 @ ( tc_prod @ SY2596 @ SY2596 ) )
| ~ ( c_lessequals @ SY2595 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SY2596 @ tc_bool ) @ SY2596 ) @ SY2596 @ SY2596 ) @ ( tc_fun @ ( tc_prod @ SY2596 @ SY2596 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1905,plain,
! [SV239: $i] :
( ( ! [SY2597: $i,SY2598: $i] :
( ( c_Relation_Orefl__on @ SV239 @ SY2597 @ SY2598 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SY2597 @ SY2598 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SY2597 @ SY2598 ) @ SY2598 @ SY2598 ) @ SY2597 @ ( tc_prod @ SY2598 @ SY2598 ) )
| ~ ( c_lessequals @ SY2597 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SY2598 @ tc_bool ) @ SY2598 ) @ SY2598 @ SY2598 ) @ ( tc_fun @ ( tc_prod @ SY2598 @ SY2598 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1906,plain,
! [SV240: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i] :
( ( c_in @ ( c_Pair @ SV240 @ SY2599 @ SY2600 @ SY2600 ) @ ( c_Transitive__Closure_Otrancl @ SY2601 @ SY2600 ) @ ( tc_prod @ SY2600 @ SY2600 ) )
| ( SV240 = SY2599 )
| ~ ( c_in @ ( c_Pair @ SV240 @ SY2599 @ SY2600 @ SY2600 ) @ ( c_Transitive__Closure_Ortrancl @ SY2601 @ SY2600 ) @ ( tc_prod @ SY2600 @ SY2600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1907,plain,
! [SV241: $i] :
( ( ! [SY2602: $i,SY2603: $i,SY2604: $i] :
( ( c_in @ ( c_Pair @ SV241 @ SY2602 @ SY2603 @ SY2603 ) @ ( c_Transitive__Closure_Otrancl @ SY2604 @ SY2603 ) @ ( tc_prod @ SY2603 @ SY2603 ) )
| ( SV241 = SY2602 )
| ~ ( c_in @ ( c_Pair @ SV241 @ SY2602 @ SY2603 @ SY2603 ) @ ( c_Transitive__Closure_Ortrancl @ SY2604 @ SY2603 ) @ ( tc_prod @ SY2603 @ SY2603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1908,plain,
! [SV242: $i] :
( ( ! [SY2605: $i,SY2606: $i,SY2607: $i] :
( ( c_in @ ( c_Pair @ SV242 @ SY2605 @ SY2606 @ SY2606 ) @ ( c_Transitive__Closure_Ortrancl @ SY2607 @ SY2606 ) @ ( tc_prod @ SY2606 @ SY2606 ) )
| ~ ( c_in @ ( c_Pair @ SV242 @ SY2605 @ SY2606 @ SY2606 ) @ ( c_Transitive__Closure_Otrancl @ SY2607 @ SY2606 ) @ ( tc_prod @ SY2606 @ SY2606 ) )
| ( SV242 = SY2605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1909,plain,
! [SV243: $i] :
( ( ! [SY2608: $i,SY2609: $i,SY2610: $i] :
( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SY2608 @ SV243 @ SY2609 @ SY2610 ) @ SY2610 @ SY2610 ) @ SY2608 @ ( tc_prod @ SY2610 @ SY2610 ) )
| ( c_in @ ( c_Pair @ SV243 @ SY2609 @ SY2610 @ SY2610 ) @ SY2608 @ ( tc_prod @ SY2610 @ SY2610 ) )
| ~ ( c_in @ ( c_Pair @ SV243 @ SY2609 @ SY2610 @ SY2610 ) @ ( c_Transitive__Closure_Otrancl @ SY2608 @ SY2610 ) @ ( tc_prod @ SY2610 @ SY2610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1910,plain,
! [SV244: $i] :
( ( ! [SY2611: $i,SY2612: $i,SY2613: $i,SY2614: $i] :
( ( c_in @ ( c_Pair @ SV244 @ SY2611 @ SY2612 @ SY2612 ) @ ( c_Transitive__Closure_Otrancl @ SY2613 @ SY2612 ) @ ( tc_prod @ SY2612 @ SY2612 ) )
| ~ ( c_in @ ( c_Pair @ SY2614 @ SY2611 @ SY2612 @ SY2612 ) @ SY2613 @ ( tc_prod @ SY2612 @ SY2612 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SY2614 @ SY2612 @ SY2612 ) @ ( c_Transitive__Closure_Ortrancl @ SY2613 @ SY2612 ) @ ( tc_prod @ SY2612 @ SY2612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1911,plain,
! [SV245: $i] :
( ( ! [SY2615: $i,SY2616: $i,SY2617: $i,SY2618: $i] :
( ( c_in @ ( c_Pair @ SV245 @ SY2615 @ SY2616 @ SY2616 ) @ ( c_Transitive__Closure_Otrancl @ SY2617 @ SY2616 ) @ ( tc_prod @ SY2616 @ SY2616 ) )
| ~ ( c_in @ ( c_Pair @ SY2618 @ SY2615 @ SY2616 @ SY2616 ) @ ( c_Transitive__Closure_Ortrancl @ SY2617 @ SY2616 ) @ ( tc_prod @ SY2616 @ SY2616 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SY2618 @ SY2616 @ SY2616 ) @ SY2617 @ ( tc_prod @ SY2616 @ SY2616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1912,plain,
! [SV246: $i] :
( ( ! [SY2619: $i,SY2620: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV246 @ ( tc_fun @ SY2619 @ tc_bool ) ) @ SY2620 @ ( tc_fun @ SY2619 @ tc_bool ) )
| ~ ( c_in @ SY2620 @ SV246 @ ( tc_fun @ SY2619 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1913,plain,
! [SV247: $i] :
( ( ! [SY2621: $i] :
( ( c_Transitive__Closure_Otrancl @ SV247 @ SY2621 )
= ( c_Relation_Orel__comp @ SV247 @ ( c_Transitive__Closure_Ortrancl @ SV247 @ SY2621 ) @ SY2621 @ SY2621 @ SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1914,plain,
! [SV248: $i] :
( ( ! [SY2622: $i] :
( ( c_Transitive__Closure_Otrancl @ SV248 @ SY2622 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV248 @ SY2622 ) @ SV248 @ SY2622 @ SY2622 @ SY2622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1915,plain,
! [SV249: $i] :
( ( ! [SY2623: $i,SY2624: $i] :
( ( c_in @ SV249 @ ( c_Complete__Lattice_OInf__class_OInf @ SY2623 @ ( tc_fun @ SY2624 @ tc_bool ) ) @ SY2624 )
| ~ ( c_in @ SV249 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV249 @ SY2623 @ SY2624 ) @ SY2624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1916,plain,
! [SV250: $i] :
( ( ! [SY2625: $i,SY2626: $i,SY2627: $i] :
( ( hBOOL @ ( hAPP @ SV250 @ SY2625 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SY2626 @ SY2627 ) @ ( c_Wellfounded_Oacc @ SY2626 @ SY2627 ) @ SY2627 )
| ~ ( c_in @ SY2625 @ ( c_Wellfounded_Oacc @ SY2626 @ SY2627 ) @ SY2627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1917,plain,
! [SV251: $i] :
( ( ! [SY2628: $i,SY2629: $i] :
( ( c_in @ SV251 @ ( c_Wellfounded_Oacc @ SY2628 @ SY2629 ) @ SY2629 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY2628 @ SV251 @ SY2629 ) @ ( c_Wellfounded_Oacc @ SY2628 @ SY2629 ) @ SY2629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1918,plain,
! [SV252: $i] :
( ( ! [SY2630: $i,SY2631: $i] :
( ( hBOOL @ ( hAPP @ SV252 @ SY2630 ) )
| ~ ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SY2631 ) ) )
| ~ ( c_in @ SY2630 @ ( c_Wellfounded_Oacc @ SY2631 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1919,plain,
! [SV253: $i] :
( ( ! [SY2632: $i,SY2633: $i,SY2634: $i] :
( ( hBOOL @ ( hAPP @ SV253 @ SY2632 ) )
| ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SY2633 @ SY2634 ) ) )
| ~ ( c_in @ SY2632 @ ( c_Wellfounded_Oacc @ SY2633 @ SY2634 ) @ SY2634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1920,plain,
! [SV254: $i] :
( ( ! [SY2635: $i,SY2636: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV254 @ SY2635 @ SY2636 ) @ ( c_Wellfounded_Oacc @ SV254 @ SY2636 ) @ SY2636 )
| ( c_in @ SY2635 @ ( c_Wellfounded_Oacc @ SV254 @ SY2636 ) @ SY2636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1921,plain,
! [SV255: $i] :
( ( ! [SY2637: $i,SY2638: $i,SY2639: $i] :
( ( hBOOL @ ( hAPP @ SV255 @ SY2637 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SY2638 @ SY2639 ) @ ( c_Wellfounded_Oacc @ SY2638 @ SY2639 ) @ SY2639 )
| ~ ( c_in @ SY2637 @ ( c_Wellfounded_Oacc @ SY2638 @ SY2639 ) @ SY2639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1922,plain,
! [SV256: $i] :
( ( ! [SY2640: $i,SY2641: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SY2640 ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SY2641 ) ) )
| ~ ( c_in @ SY2640 @ ( c_Wellfounded_Oacc @ SY2641 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1923,plain,
! [SV257: $i] :
( ( ! [SY2642: $i,SY2643: $i,SY2644: $i] :
( ( hBOOL @ ( hAPP @ SV257 @ SY2642 ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SY2643 @ SY2644 ) ) )
| ~ ( c_in @ SY2642 @ ( c_Wellfounded_Oacc @ SY2643 @ SY2644 ) @ SY2644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1924,plain,
! [SV258: $i] :
( ( ! [SY2645: $i,SY2646: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SY2645 @ SV258 ) @ SY2646 @ SV258 )
| ~ ( c_in @ SY2646 @ SY2645 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1925,plain,
! [SV259: $i] :
( ( ! [SY2647: $i,SY2648: $i] :
( ( c_lessequals @ SV259 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2647 @ ( tc_fun @ SY2648 @ tc_bool ) ) @ ( tc_fun @ SY2648 @ tc_bool ) )
| ~ ( c_in @ SV259 @ SY2647 @ ( tc_fun @ SY2648 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1926,plain,
! [SV260: $i] :
( ( ! [SY2649: $i,SY2650: $i,SY2651: $i] :
( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SY2649 @ SY2650 ) @ ( tc_prod @ SY2650 @ SY2650 ) )
| ~ ( c_lessequals @ SY2651 @ SY2649 @ ( tc_fun @ ( tc_prod @ SY2650 @ SY2650 ) @ tc_bool ) )
| ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SY2651 @ SY2650 ) @ ( tc_prod @ SY2650 @ SY2650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1927,plain,
! [SV261: $i] :
( ( ! [SY2652: $i,SY2653: $i,SY2654: $i,SY2655: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SY2652 @ SY2653 @ SY2654 @ SY2655 ) @ SV261 @ SY2654 )
| ~ ( c_in @ SY2652 @ ( c_Relation_OImage @ SY2653 @ SV261 @ SY2654 @ SY2655 ) @ SY2655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1928,plain,
! [SV262: $i] :
( ( ! [SY2656: $i,SY2657: $i,SY2658: $i,SY2659: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SY2656 @ SY2657 @ SY2658 @ SY2659 ) @ SV262 @ SY2658 )
| ~ ( c_in @ SY2656 @ ( c_Relation_OImage @ SY2657 @ SV262 @ SY2658 @ SY2659 ) @ SY2659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1929,plain,
! [SV263: $i] :
( ( ! [SY2660: $i,SY2661: $i,SY2662: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SY2660 @ SY2661 ) @ SV263 @ SY2661 )
| ~ ( c_in @ SY2662 @ SV263 @ SY2661 )
| ~ ( c_Wellfounded_Owf @ SY2660 @ SY2661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1930,plain,
! [SV264: $i] :
( ( ! [SY2663: $i,SY2664: $i,SY2665: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SY2663 @ SY2664 ) @ SV264 @ SY2664 )
| ~ ( c_in @ SY2665 @ SV264 @ SY2664 )
| ~ ( c_Wellfounded_Owf @ SY2663 @ SY2664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1931,plain,
! [SV265: $i] :
( ( ! [SY2666: $i,SY2667: $i] :
( ( c_in @ SV265 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV265 @ SY2666 @ SY2667 ) @ SY2667 )
| ~ ( c_in @ SV265 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2666 @ ( tc_fun @ SY2667 @ tc_bool ) ) @ SY2667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1932,plain,
! [SV266: $i] :
( ( ! [SY2668: $i,SY2669: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
| ( c_lessequals @ SY2668 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2669 @ SV266 ) @ SV266 )
| ~ ( c_in @ SY2668 @ SY2669 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1933,plain,
! [SV267: $i] :
( ( ! [SY2670: $i,SY2671: $i,SY2672: $i,SY2673: $i] :
( ( c_in @ ( c_Pair @ SV267 @ SY2670 @ SY2671 @ SY2671 ) @ ( c_Transitive__Closure_Ortrancl @ SY2672 @ SY2671 ) @ ( tc_prod @ SY2671 @ SY2671 ) )
| ~ ( c_in @ ( c_Pair @ SY2673 @ SY2670 @ SY2671 @ SY2671 ) @ SY2672 @ ( tc_prod @ SY2671 @ SY2671 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SY2673 @ SY2671 @ SY2671 ) @ ( c_Transitive__Closure_Ortrancl @ SY2672 @ SY2671 ) @ ( tc_prod @ SY2671 @ SY2671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1934,plain,
! [SV268: $i] :
( ( ! [SY2674: $i,SY2675: $i,SY2676: $i,SY2677: $i] :
( ( c_in @ ( c_Pair @ SV268 @ SY2674 @ SY2675 @ SY2675 ) @ ( c_Transitive__Closure_Ortrancl @ SY2676 @ SY2675 ) @ ( tc_prod @ SY2675 @ SY2675 ) )
| ~ ( c_in @ ( c_Pair @ SY2677 @ SY2674 @ SY2675 @ SY2675 ) @ ( c_Transitive__Closure_Ortrancl @ SY2676 @ SY2675 ) @ ( tc_prod @ SY2675 @ SY2675 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SY2677 @ SY2675 @ SY2675 ) @ SY2676 @ ( tc_prod @ SY2675 @ SY2675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1935,plain,
! [SV269: $i] :
( ( ! [SY2678: $i,SY2679: $i,SY2680: $i,SY2681: $i] :
( ( c_in @ ( c_Pair @ SV269 @ SY2678 @ SY2679 @ SY2679 ) @ ( c_Transitive__Closure_Ortrancl @ SY2680 @ SY2679 ) @ ( tc_prod @ SY2679 @ SY2679 ) )
| ~ ( c_in @ ( c_Pair @ SY2681 @ SY2678 @ SY2679 @ SY2679 ) @ ( c_Transitive__Closure_Ortrancl @ SY2680 @ SY2679 ) @ ( tc_prod @ SY2679 @ SY2679 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SY2681 @ SY2679 @ SY2679 ) @ ( c_Transitive__Closure_Ortrancl @ SY2680 @ SY2679 ) @ ( tc_prod @ SY2679 @ SY2679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1936,plain,
! [SV270: $i] :
( ( ! [SY2682: $i,SY2683: $i] : ( c_in @ ( c_Pair @ SV270 @ SV270 @ SY2682 @ SY2682 ) @ ( c_Transitive__Closure_Ortrancl @ SY2683 @ SY2682 ) @ ( tc_prod @ SY2682 @ SY2682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1937,plain,
! [SV271: $i] :
( ( ! [SY2684: $i,SY2685: $i] : ( c_in @ ( c_Pair @ SV271 @ SV271 @ SY2684 @ SY2684 ) @ ( c_Transitive__Closure_Ortrancl @ SY2685 @ SY2684 ) @ ( tc_prod @ SY2684 @ SY2684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1938,plain,
! [SV272: $i] :
( ( ! [SY2686: $i,SY2687: $i,SY2688: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SY2686 @ SY2687 @ SY2688 ) @ SY2687 @ SY2688 @ SY2688 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SY2688 ) @ ( tc_prod @ SY2688 @ SY2688 ) )
| ~ ( c_in @ ( c_Pair @ SY2686 @ SY2687 @ SY2688 @ SY2688 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SY2688 ) @ ( tc_prod @ SY2688 @ SY2688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1939,plain,
! [SV273: $i] :
( ( ! [SY2689: $i,SY2690: $i] :
( ~ ( class_Orderings_Olinorder @ SV273 )
| ( c_lessequals @ SY2689 @ SY2690 @ SV273 )
| ( c_lessequals @ SY2690 @ SY2689 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1940,plain,
! [SV274: $i] :
( ( ! [SY2691: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV274 @ SY2691 ) @ SY2691 )
= ( c_Transitive__Closure_Ortrancl @ SV274 @ SY2691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1941,plain,
! [SV275: $i] :
( ( ! [SY2692: $i,SY2693: $i] :
( ( c_lessequals @ SV275 @ ( c_Product__Type_OSigma @ SY2692 @ ( c_COMBK @ SY2692 @ ( tc_fun @ SY2693 @ tc_bool ) @ SY2693 ) @ SY2693 @ SY2693 ) @ ( tc_fun @ ( tc_prod @ SY2693 @ SY2693 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY2692 @ SV275 @ SY2693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1942,plain,
! [SV276: $i] :
( ( ! [SY2694: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV276 @ SY2694 ) @ SY2694 )
= ( c_Transitive__Closure_Ortrancl @ SV276 @ SY2694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1943,plain,
! [SV277: $i] :
( ( ! [SY2695: $i,SY2696: $i,SY2697: $i,SY2698: $i,SY2699: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SY2695 @ SY2696 @ SY2697 ) @ ( c_Relation_OImage @ SY2698 @ SY2699 @ SY2696 @ SY2697 ) @ ( tc_fun @ SY2697 @ tc_bool ) )
| ~ ( c_lessequals @ SY2695 @ SY2699 @ ( tc_fun @ SY2696 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SY2698 @ ( tc_fun @ ( tc_prod @ SY2696 @ SY2697 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1944,plain,
! [SV278: $i] :
( ( ! [SY2700: $i,SY2701: $i,SY2702: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SY2700 @ SY2701 ) @ ( c_Relation_ODomain @ SY2702 @ SY2700 @ SY2701 ) @ ( tc_fun @ SY2700 @ tc_bool ) )
| ~ ( c_lessequals @ SV278 @ SY2702 @ ( tc_fun @ ( tc_prod @ SY2700 @ SY2701 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1945,plain,
! [SV279: $i] :
( ( ! [SY2703: $i,SY2704: $i,SY2705: $i] :
( ( hBOOL @ ( hAPP @ SV279 @ SY2703 ) )
| ~ ( c_lessequals @ SY2704 @ SV279 @ ( tc_fun @ SY2705 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY2704 @ SY2703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1946,plain,
! [SV280: $i] :
( ( ! [SY2706: $i] :
( ~ ( class_Orderings_Opreorder @ SV280 )
| ( c_lessequals @ SY2706 @ SY2706 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1947,plain,
! [SV281: $i] :
( ( ! [SY2707: $i] :
( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_lessequals @ SY2707 @ SY2707 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1948,plain,
! [SV282: $i] :
( ( ! [SY2708: $i,SY2709: $i] :
( ( c_Wellfounded_Owf @ SV282 @ SY2708 )
| ~ ( c_lessequals @ SV282 @ SY2709 @ ( tc_fun @ ( tc_prod @ SY2708 @ SY2708 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2709 @ SY2708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1949,plain,
! [SV283: $i] :
( ( ! [SY2710: $i,SY2711: $i,SY2712: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ SY2710 ) )
| ~ ( hBOOL @ ( hAPP @ SY2711 @ SY2710 ) )
| ~ ( c_lessequals @ SY2711 @ SV283 @ ( tc_fun @ SY2712 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1950,plain,
! [SV284: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i] :
( ( c_lessequals @ SV284 @ SY2713 @ ( tc_fun @ SY2714 @ tc_bool ) )
| ~ ( c_lessequals @ SY2715 @ SY2713 @ ( tc_fun @ SY2714 @ tc_bool ) )
| ~ ( c_lessequals @ SV284 @ SY2715 @ ( tc_fun @ SY2714 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1951,plain,
! [SV285: $i] :
( ( ! [SY2716: $i] : ( c_lessequals @ SV285 @ SV285 @ ( tc_fun @ SY2716 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1952,plain,
! [SV286: $i] :
( ( ! [SY2717: $i] : ( c_lessequals @ SV286 @ SV286 @ ( tc_fun @ SY2717 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1953,plain,
! [SV287: $i] :
( ( ! [SY2718: $i,SY2719: $i,SY2720: $i] :
( ~ ( class_Orderings_Opreorder @ SV287 )
| ( c_lessequals @ SY2718 @ SY2719 @ SV287 )
| ~ ( c_lessequals @ SY2720 @ SY2719 @ SV287 )
| ~ ( c_lessequals @ SY2718 @ SY2720 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1954,plain,
! [SV288: $i] :
( ( ! [SY2721: $i,SY2722: $i,SY2723: $i] :
( ~ ( class_Orderings_Oorder @ SV288 )
| ( c_lessequals @ SY2721 @ SY2722 @ SV288 )
| ~ ( c_lessequals @ SY2721 @ SY2723 @ SV288 )
| ~ ( c_lessequals @ SY2723 @ SY2722 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1955,plain,
! [SV289: $i] :
( ( ! [SY2724: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV289 @ SY2724 @ SY2724 ) @ SY2724 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ SV289 @ SY2724 ) @ SY2724 @ SY2724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1956,plain,
! [SV290: $i] :
( ( ! [SY2725: $i,SY2726: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV290 @ SY2725 ) @ ( c_Transitive__Closure_Ortrancl @ SY2726 @ SY2725 ) @ ( tc_fun @ ( tc_prod @ SY2725 @ SY2725 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ ( c_Transitive__Closure_Ortrancl @ SY2726 @ SY2725 ) @ ( tc_fun @ ( tc_prod @ SY2725 @ SY2725 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1957,plain,
! [SV291: $i] :
( ( ! [SY2727: $i,SY2728: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV291 @ SY2727 ) @ ( c_Product__Type_OSigma @ SY2728 @ ( c_COMBK @ SY2728 @ ( tc_fun @ SY2727 @ tc_bool ) @ SY2727 ) @ SY2727 @ SY2727 ) @ ( tc_fun @ ( tc_prod @ SY2727 @ SY2727 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV291 @ ( c_Product__Type_OSigma @ SY2728 @ ( c_COMBK @ SY2728 @ ( tc_fun @ SY2727 @ tc_bool ) @ SY2727 ) @ SY2727 @ SY2727 ) @ ( tc_fun @ ( tc_prod @ SY2727 @ SY2727 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1958,plain,
! [SV292: $i] :
( ( ! [SY2729: $i,SY2730: $i] :
( ~ ( class_Orderings_Oorder @ SV292 )
| ( SY2729 = SY2730 )
| ~ ( c_lessequals @ SY2729 @ SY2730 @ SV292 )
| ~ ( c_lessequals @ SY2730 @ SY2729 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1959,plain,
! [SV293: $i] :
( ( ! [SY2731: $i,SY2732: $i] :
( ~ ( class_Orderings_Oorder @ SV293 )
| ( SY2731 = SY2732 )
| ~ ( c_lessequals @ SY2732 @ SY2731 @ SV293 )
| ~ ( c_lessequals @ SY2731 @ SY2732 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1960,plain,
! [SV294: $i] :
( ( ! [SY2733: $i,SY2734: $i] :
( ~ ( class_Orderings_Oorder @ SV294 )
| ( SY2733 = SY2734 )
| ~ ( c_lessequals @ SY2734 @ SY2733 @ SV294 )
| ~ ( c_lessequals @ SY2733 @ SY2734 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1961,plain,
! [SV295: $i] :
( ( ! [SY2735: $i,SY2736: $i] :
( ( SV295 = SY2735 )
| ~ ( c_lessequals @ SY2735 @ SV295 @ ( tc_fun @ SY2736 @ tc_bool ) )
| ~ ( c_lessequals @ SV295 @ SY2735 @ ( tc_fun @ SY2736 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1962,plain,
! [SV296: $i] :
( ( ! [SY2737: $i,SY2738: $i] :
( ( SV296 = SY2737 )
| ~ ( c_lessequals @ SY2737 @ SV296 @ ( tc_fun @ SY2738 @ tc_bool ) )
| ~ ( c_lessequals @ SV296 @ SY2737 @ ( tc_fun @ SY2738 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1963,plain,
! [SV297: $i] :
( ( ! [SY2739: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV297 @ SY2739 ) @ ( c_Transitive__Closure_Ortrancl @ SV297 @ SY2739 ) @ SY2739 @ SY2739 @ SY2739 )
= ( c_Transitive__Closure_Ortrancl @ SV297 @ SY2739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1964,plain,
! [SV298: $i] :
( ( ! [SY2740: $i,SY2741: $i,SY2742: $i,SY2743: $i,SY2744: $i,SY2745: $i,SY2746: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SY2740 @ SY2741 @ SY2742 @ SY2743 ) @ ( c_Product__Type_OSigma @ SY2744 @ ( c_COMBK @ SY2745 @ ( tc_fun @ SY2743 @ tc_bool ) @ SY2741 ) @ SY2741 @ SY2743 ) @ ( tc_fun @ ( tc_prod @ SY2741 @ SY2743 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2740 @ ( c_Product__Type_OSigma @ SY2746 @ ( c_COMBK @ SY2745 @ ( tc_fun @ SY2743 @ tc_bool ) @ SY2742 ) @ SY2742 @ SY2743 ) @ ( tc_fun @ ( tc_prod @ SY2742 @ SY2743 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SY2744 @ ( c_COMBK @ SY2746 @ ( tc_fun @ SY2742 @ tc_bool ) @ SY2741 ) @ SY2741 @ SY2742 ) @ ( tc_fun @ ( tc_prod @ SY2741 @ SY2742 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1965,plain,
! [SV299: $i] :
( ( ! [SY2747: $i,SY2748: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV299 @ SY2747 ) @ ( c_Transitive__Closure_Ortrancl @ SY2748 @ SY2747 ) @ ( tc_fun @ ( tc_prod @ SY2747 @ SY2747 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ SY2748 @ ( tc_fun @ ( tc_prod @ SY2747 @ SY2747 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1966,plain,
! [SV300: $i] :
( ( ! [SY2749: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV300 @ SY2749 ) @ SY2749 )
= ( c_Transitive__Closure_Ortrancl @ SV300 @ SY2749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1967,plain,
! [SV301: $i] :
( ( ! [SY2750: $i] :
( ( c_Relation_Orel__comp @ SV301 @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY2750 ) @ SY2750 @ SY2750 @ SY2750 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SY2750 ) @ SV301 @ SY2750 @ SY2750 @ SY2750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1968,plain,
! [SV302: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i,SY2754: $i,SY2755: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SY2751 @ ( tc_fun @ SY2752 @ tc_bool ) @ SY2753 ) @ SY2753 @ SY2752 ) @ ( c_Product__Type_OSigma @ SY2754 @ ( c_COMBK @ SY2751 @ ( tc_fun @ SY2752 @ tc_bool ) @ SY2753 ) @ SY2753 @ SY2752 ) @ ( tc_fun @ ( tc_prod @ SY2753 @ SY2752 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SY2754 @ ( tc_fun @ SY2753 @ tc_bool ) )
| ~ ( c_in @ SY2755 @ SY2751 @ SY2752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1969,plain,
! [SV303: $i] :
( ( ! [SY2756: $i,SY2757: $i,SY2758: $i,SY2759: $i,SY2760: $i] :
( ( c_lessequals @ SV303 @ SY2756 @ ( tc_fun @ SY2757 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SY2758 @ ( tc_fun @ SY2759 @ tc_bool ) @ SY2757 ) @ SY2757 @ SY2759 ) @ ( c_Product__Type_OSigma @ SY2756 @ ( c_COMBK @ SY2758 @ ( tc_fun @ SY2759 @ tc_bool ) @ SY2757 ) @ SY2757 @ SY2759 ) @ ( tc_fun @ ( tc_prod @ SY2757 @ SY2759 ) @ tc_bool ) )
| ~ ( c_in @ SY2760 @ SY2758 @ SY2759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1970,plain,
! [SV304: $i] :
( ( ! [SY2761: $i] : ( c_lessequals @ ( c_Relation_OId__on @ SV304 @ SY2761 ) @ ( c_Product__Type_OSigma @ SV304 @ ( c_COMBK @ SV304 @ ( tc_fun @ SY2761 @ tc_bool ) @ SY2761 ) @ SY2761 @ SY2761 ) @ ( tc_fun @ ( tc_prod @ SY2761 @ SY2761 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1971,plain,
! [SV305: $i] :
( ( ! [SY2762: $i,SY2763: $i] :
( ( c_lessequals @ SV305 @ ( c_Product__Type_OSigma @ SY2762 @ ( c_COMBK @ SY2762 @ ( tc_fun @ SY2763 @ tc_bool ) @ SY2763 ) @ SY2763 @ SY2763 ) @ ( tc_fun @ ( tc_prod @ SY2763 @ SY2763 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SY2762 @ SV305 @ SY2763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1972,plain,
! [SV306: $i] :
( ( ! [SY2764: $i,SY2765: $i,SY2766: $i,SY2767: $i,SY2768: $i,SY2769: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SY2764 @ SY2765 @ SY2766 @ SY2767 ) @ ( c_Relation_Orel__comp @ SY2768 @ SY2769 @ SY2765 @ SY2766 @ SY2767 ) @ ( tc_fun @ ( tc_prod @ SY2765 @ SY2767 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2764 @ SY2769 @ ( tc_fun @ ( tc_prod @ SY2766 @ SY2767 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SY2768 @ ( tc_fun @ ( tc_prod @ SY2765 @ SY2766 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1973,plain,
! [SV307: $i] :
( ( ! [SY2770: $i,SY2771: $i,SY2772: $i] :
( ( hAPP @ ( c_COMBK @ SV307 @ SY2770 @ SY2771 ) @ SY2772 )
= SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1974,plain,
! [SV308: $i] :
( ( ! [SY2773: $i,SY2774: $i,SY2775: $i,SY2776: $i,SY2777: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SY2773 @ SY2774 @ SY2775 ) @ SY2776 @ ( tc_fun @ SY2775 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SY2777 @ ( c_COMBK @ SY2776 @ ( tc_fun @ SY2775 @ tc_bool ) @ SY2774 ) @ SY2774 @ SY2775 ) @ ( tc_fun @ ( tc_prod @ SY2774 @ SY2775 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1975,plain,
! [SV309: $i] :
( ( ! [SY2778: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV309 @ SY2778 ) @ SY2778 )
| ~ ( c_Relation_Osym @ SV309 @ SY2778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1976,plain,
! [SV310: $i] :
( ( ! [SY2779: $i,SY2780: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SY2779 )
= ( c_Transitive__Closure_Ortrancl @ SY2780 @ SY2779 ) )
| ~ ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SY2780 @ SY2779 ) @ ( tc_fun @ ( tc_prod @ SY2779 @ SY2779 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2780 @ SV310 @ ( tc_fun @ ( tc_prod @ SY2779 @ SY2779 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1977,plain,
! [SV311: $i] :
( ( ! [SY2781: $i,SY2782: $i,SY2783: $i,SY2784: $i] :
( ( c_in @ SV311 @ SY2781 @ SY2782 )
| ( SV311 = SY2783 )
| ~ ( c_lessequals @ SY2784 @ ( c_Product__Type_OSigma @ SY2781 @ ( c_COMBK @ SY2781 @ ( tc_fun @ SY2782 @ tc_bool ) @ SY2782 ) @ SY2782 @ SY2782 ) @ ( tc_fun @ ( tc_prod @ SY2782 @ SY2782 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SY2783 @ SY2782 @ SY2782 ) @ ( c_Transitive__Closure_Ortrancl @ SY2784 @ SY2782 ) @ ( tc_prod @ SY2782 @ SY2782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1978,plain,
! [SV312: $i] :
( ( ! [SY2785: $i,SY2786: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV312 @ SY2785 ) @ ( c_Wellfounded_Oacc @ SY2786 @ SY2785 ) @ ( tc_fun @ SY2785 @ tc_bool ) )
| ~ ( c_lessequals @ SY2786 @ SV312 @ ( tc_fun @ ( tc_prod @ SY2785 @ SY2785 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1979,plain,
! [SV313: $i] :
( ( ! [SY2787: $i,SY2788: $i,SY2789: $i,SY2790: $i] :
( ~ ( class_HOL_Oord @ SV313 )
| ( c_lessequals @ ( hAPP @ SY2787 @ SY2788 ) @ ( hAPP @ SY2789 @ SY2788 ) @ SV313 )
| ~ ( c_lessequals @ SY2787 @ SY2789 @ ( tc_fun @ SY2790 @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1980,plain,
! [SV314: $i] :
( ( ! [SY2791: $i,SY2792: $i,SY2793: $i] :
( ( c_in @ SV314 @ SY2791 @ SY2792 )
| ~ ( c_in @ SV314 @ SY2793 @ SY2792 )
| ~ ( c_lessequals @ SY2793 @ SY2791 @ ( tc_fun @ SY2792 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1981,plain,
! [SV315: $i] :
( ( ! [SY2794: $i,SY2795: $i,SY2796: $i] :
( ( c_in @ SV315 @ SY2794 @ SY2795 )
| ~ ( c_lessequals @ SY2796 @ SY2794 @ ( tc_fun @ SY2795 @ tc_bool ) )
| ~ ( c_in @ SV315 @ SY2796 @ SY2795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1982,plain,
! [SV316: $i] :
( ( ! [SY2797: $i,SY2798: $i,SY2799: $i] :
( ( c_in @ SV316 @ SY2797 @ SY2798 )
| ~ ( c_in @ SV316 @ SY2799 @ SY2798 )
| ~ ( c_lessequals @ SY2799 @ SY2797 @ ( tc_fun @ SY2798 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1983,plain,
! [SV317: $i] :
( ( ! [SY2800: $i,SY2801: $i,SY2802: $i] :
( ( c_in @ SV317 @ SY2800 @ SY2801 )
| ~ ( c_in @ SV317 @ SY2802 @ SY2801 )
| ~ ( c_lessequals @ SY2802 @ SY2800 @ ( tc_fun @ SY2801 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1984,plain,
! [SV318: $i] :
( ( ! [SY2803: $i,SY2804: $i] :
( ( c_in @ SV318 @ ( c_Transitive__Closure_Ortrancl @ SY2803 @ SY2804 ) @ ( tc_prod @ SY2804 @ SY2804 ) )
| ~ ( c_in @ SV318 @ SY2803 @ ( tc_prod @ SY2804 @ SY2804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1985,plain,
! [SV319: $i] :
( ( ! [SY2805: $i,SY2806: $i,SY2807: $i] :
( ( c_in @ ( c_Pair @ SV319 @ SY2805 @ SY2806 @ SY2806 ) @ ( c_Transitive__Closure_Ortrancl @ SY2807 @ SY2806 ) @ ( tc_prod @ SY2806 @ SY2806 ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SY2805 @ SY2806 @ SY2806 ) @ ( c_Transitive__Closure_Otrancl @ SY2807 @ SY2806 ) @ ( tc_prod @ SY2806 @ SY2806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1986,plain,
! [SV320: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i,SY2811: $i] :
( ( c_in @ ( c_Pair @ SV320 @ SY2808 @ SY2809 @ SY2809 ) @ ( c_Transitive__Closure_Otrancl @ SY2810 @ SY2809 ) @ ( tc_prod @ SY2809 @ SY2809 ) )
| ~ ( c_in @ ( c_Pair @ SY2811 @ SY2808 @ SY2809 @ SY2809 ) @ ( c_Transitive__Closure_Ortrancl @ SY2810 @ SY2809 ) @ ( tc_prod @ SY2809 @ SY2809 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SY2811 @ SY2809 @ SY2809 ) @ ( c_Transitive__Closure_Otrancl @ SY2810 @ SY2809 ) @ ( tc_prod @ SY2809 @ SY2809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1987,plain,
! [SV321: $i] :
( ( ! [SY2812: $i,SY2813: $i,SY2814: $i,SY2815: $i] :
( ( c_in @ ( c_Pair @ SV321 @ SY2812 @ SY2813 @ SY2813 ) @ ( c_Transitive__Closure_Otrancl @ SY2814 @ SY2813 ) @ ( tc_prod @ SY2813 @ SY2813 ) )
| ~ ( c_in @ ( c_Pair @ SY2815 @ SY2812 @ SY2813 @ SY2813 ) @ ( c_Transitive__Closure_Otrancl @ SY2814 @ SY2813 ) @ ( tc_prod @ SY2813 @ SY2813 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SY2815 @ SY2813 @ SY2813 ) @ ( c_Transitive__Closure_Ortrancl @ SY2814 @ SY2813 ) @ ( tc_prod @ SY2813 @ SY2813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1988,plain,
! [SV322: $i] :
( ( ! [SY2816: $i,SY2817: $i,SY2818: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SY2816 @ SV322 @ SY2817 @ SY2818 ) @ SY2818 @ SY2818 ) @ SY2816 @ ( tc_prod @ SY2818 @ SY2818 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SY2817 @ SY2818 @ SY2818 ) @ ( c_Transitive__Closure_Otrancl @ SY2816 @ SY2818 ) @ ( tc_prod @ SY2818 @ SY2818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1989,plain,
! [SV323: $i] :
( ( ! [SY2819: $i,SY2820: $i,SY2821: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SY2819 @ SY2820 @ SY2821 ) @ SY2820 @ SY2821 @ SY2821 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY2821 ) @ ( tc_prod @ SY2821 @ SY2821 ) )
| ( c_in @ ( c_Pair @ SY2819 @ SY2820 @ SY2821 @ SY2821 ) @ SV323 @ ( tc_prod @ SY2821 @ SY2821 ) )
| ~ ( c_in @ ( c_Pair @ SY2819 @ SY2820 @ SY2821 @ SY2821 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY2821 ) @ ( tc_prod @ SY2821 @ SY2821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1990,plain,
! [SV324: $i] :
( ( ! [SY2822: $i,SY2823: $i] :
( ~ ( c_in @ ( c_Pair @ SV324 @ SV324 @ SY2822 @ SY2822 ) @ SY2823 @ ( tc_prod @ SY2822 @ SY2822 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY2823 @ SY2822 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY2823 @ SY2822 ) @ SY2822 @ SY2822 ) @ ( c_Transitive__Closure_Otrancl @ SY2823 @ SY2822 ) @ ( tc_prod @ SY2822 @ SY2822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1991,plain,
! [SV325: $i] :
( ( ! [SY2824: $i,SY2825: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV325 @ SY2824 @ SY2825 ) @ SY2824 @ ( tc_fun @ SY2825 @ tc_bool ) )
| ~ ( c_in @ SV325 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2824 @ ( tc_fun @ SY2825 @ tc_bool ) ) @ SY2825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1992,plain,
! [SV326: $i] :
( ( ! [SY2826: $i,SY2827: $i,SY2828: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SY2826 @ SY2827 @ SY2827 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY2828 @ SY2827 @ SY2827 ) @ SY2827 ) @ ( tc_prod @ SY2827 @ SY2827 ) )
| ~ ( c_in @ ( c_Pair @ SY2826 @ SV326 @ SY2827 @ SY2827 ) @ ( c_Transitive__Closure_Ortrancl @ SY2828 @ SY2827 ) @ ( tc_prod @ SY2827 @ SY2827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1993,plain,
! [SV327: $i] :
( ( ! [SY2829: $i,SY2830: $i,SY2831: $i] :
( ( c_in @ ( c_Pair @ SV327 @ SY2829 @ SY2830 @ SY2830 ) @ ( c_Transitive__Closure_Ortrancl @ SY2831 @ SY2830 ) @ ( tc_prod @ SY2830 @ SY2830 ) )
| ~ ( c_in @ ( c_Pair @ SY2829 @ SV327 @ SY2830 @ SY2830 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY2831 @ SY2830 @ SY2830 ) @ SY2830 ) @ ( tc_prod @ SY2830 @ SY2830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1994,plain,
! [SV328: $i] :
( ( ! [SY2832: $i,SY2833: $i,SY2834: $i,SY2835: $i,SY2836: $i,SY2837: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SY2832 @ SY2833 @ SY2834 @ SY2835 @ SY2836 @ SY2837 ) @ SY2835 @ SY2837 ) @ SY2833 @ ( tc_prod @ SY2835 @ SY2837 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SY2832 @ SY2835 @ SY2836 ) @ ( c_Relation_Orel__comp @ SY2833 @ SY2834 @ SY2835 @ SY2837 @ SY2836 ) @ ( tc_prod @ SY2835 @ SY2836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1995,plain,
! [SV329: $i] :
( ( ! [SY2838: $i,SY2839: $i,SY2840: $i,SY2841: $i,SY2842: $i,SY2843: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SY2838 @ SY2839 @ SY2840 @ SY2841 @ SY2842 @ SY2843 ) @ SY2838 @ SY2843 @ SY2842 ) @ SY2840 @ ( tc_prod @ SY2843 @ SY2842 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SY2838 @ SY2841 @ SY2842 ) @ ( c_Relation_Orel__comp @ SY2839 @ SY2840 @ SY2841 @ SY2843 @ SY2842 ) @ ( tc_prod @ SY2841 @ SY2842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1996,plain,
! [SV330: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i,SY2847: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SY2844 @ SY2845 @ SY2846 @ SY2847 ) @ ( tc_fun @ SY2846 @ SY2847 ) )
| ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY2844 @ SY2845 @ SV330 @ SY2846 @ SY2847 ) ) @ ( hAPP @ SY2845 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY2844 @ SY2845 @ SV330 @ SY2846 @ SY2847 ) ) @ SY2847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1997,plain,
! [SV331: $i] :
( ( ! [SY2848: $i,SY2849: $i,SY2850: $i,SY2851: $i,SY2852: $i] :
( ( c_in @ ( hAPP @ SV331 @ SY2848 ) @ SY2849 @ SY2850 )
| ~ ( c_in @ SY2848 @ SY2851 @ SY2852 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SY2851 @ ( c_COMBK @ SY2849 @ ( tc_fun @ SY2850 @ tc_bool ) @ SY2852 ) @ SY2852 @ SY2850 ) @ ( tc_fun @ SY2852 @ SY2850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1998,plain,
! [SV332: $i] :
( ( ! [SY2853: $i,SY2854: $i,SY2855: $i,SY2856: $i] :
( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SY2853 @ SY2854 @ SY2855 @ SY2856 ) @ ( tc_fun @ SY2855 @ SY2856 ) )
| ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2853 @ SY2854 @ SV332 @ SY2855 @ SY2856 ) ) @ ( hAPP @ SY2854 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2853 @ SY2854 @ SV332 @ SY2855 @ SY2856 ) ) @ SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1999,plain,
! [SV333: $i] :
( ( ! [SY2857: $i,SY2858: $i,SY2859: $i,SY2860: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SY2857 @ SY2858 @ SY2859 @ SY2860 ) @ ( tc_fun @ SY2859 @ SY2860 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SY2857 @ SY2858 @ SV333 @ SY2859 @ SY2860 ) @ SY2857 @ SY2859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(2000,plain,
! [SV334: $i] :
( ( ! [SY2861: $i,SY2862: $i,SY2863: $i,SY2864: $i] :
( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SY2861 @ SY2862 @ SY2863 @ SY2864 ) @ ( tc_fun @ SY2863 @ SY2864 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SY2861 @ SY2862 @ SV334 @ SY2863 @ SY2864 ) @ SY2861 @ SY2863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(2001,plain,
! [SV335: $i] :
( ( ! [SY2865: $i,SY2866: $i,SY2867: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SY2865 @ SY2866 @ SY2867 ) @ SV335 @ SY2867 )
| ~ ( c_in @ SY2865 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SY2866 @ SY2867 ) @ ( tc_fun @ SY2867 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(2002,plain,
! [SV336: $i] :
( ( ! [SY2868: $i] :
( ( SV336
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SY2868 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SY2868 ) @ SY2868 @ SY2868 ) )
| ~ ( c_in @ SV336 @ ( c_Relation_OId @ SY2868 ) @ ( tc_prod @ SY2868 @ SY2868 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(2003,plain,
! [SV337: $i] :
( ( ! [SY2869: $i,SY2870: $i] :
( ( c_in @ SV337 @ ( c_Complete__Lattice_OInf__class_OInf @ SY2869 @ ( tc_fun @ SY2870 @ tc_bool ) ) @ SY2870 )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV337 @ SY2869 @ SY2870 ) @ SY2869 @ ( tc_fun @ SY2870 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(2004,plain,
! [SV338: $i] :
( ( ! [SY2871: $i] :
( ( c_Wellfounded_Owf @ SV338 @ SY2871 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV338 @ SY2871 ) @ ( c_Wellfounded_Oacc @ SV338 @ SY2871 ) @ SY2871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(2005,plain,
! [SV339: $i] :
( ( ! [SY2872: $i] :
( ( c_Wellfounded_Owf @ SV339 @ SY2872 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV339 @ SY2872 ) @ ( c_Wellfounded_Oacc @ SV339 @ SY2872 ) @ SY2872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(2006,plain,
! [SV340: $i] :
( ( ! [SY2873: $i,SY2874: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV340 @ SY2873 @ SY2874 ) @ SV340 @ SY2874 )
| ~ ( c_in @ SY2873 @ ( c_Relation_OId__on @ SV340 @ SY2874 ) @ ( tc_prod @ SY2874 @ SY2874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(2007,plain,
! [SV341: $i] :
( ( ! [SY2875: $i,SY2876: $i] :
( ( SV341
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY2875 @ SV341 @ SY2876 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY2875 @ SV341 @ SY2876 ) @ SY2876 @ SY2876 ) )
| ~ ( c_in @ SV341 @ ( c_Relation_OId__on @ SY2875 @ SY2876 ) @ ( tc_prod @ SY2876 @ SY2876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(2008,plain,
! [SV342: $i] :
( ( ! [SY2877: $i,SY2878: $i,SY2879: $i,SY2880: $i,SY2881: $i] :
( ( ( c_Recdef_Ocut @ SV342 @ SY2877 @ SY2878 @ SY2879 @ SY2880 )
= ( c_Recdef_Ocut @ SY2881 @ SY2877 @ SY2878 @ SY2879 @ SY2880 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SY2881 @ SY2877 @ SY2878 @ SY2879 @ SY2880 ) @ SY2878 @ SY2879 @ SY2879 ) @ SY2877 @ ( tc_prod @ SY2879 @ SY2879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(2009,plain,
! [SV343: $i] :
( ( ! [SY2882: $i,SY2883: $i] :
( ( c_lessequals @ SV343 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV343 @ SY2882 @ SY2882 ) @ SV343 @ SY2882 @ SY2882 @ SY2882 ) @ ( tc_fun @ ( tc_prod @ SY2882 @ SY2882 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SY2883 @ SV343 @ SY2882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(2010,plain,
! [SV344: $i] :
( ( ! [SY2884: $i] :
( ( c_Nitpick_Orefl_H @ SV344 @ SY2884 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SY2884 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SY2884 ) @ SY2884 @ SY2884 ) @ SV344 @ ( tc_prod @ SY2884 @ SY2884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(2011,plain,
! [SV345: $i] :
( ( ! [SY2885: $i,SY2886: $i,SY2887: $i,SY2888: $i] :
( ~ ( c_in @ SV345 @ SY2885 @ SY2886 )
| ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SY2885 @ SY2887 @ SY2886 ) @ SY2886 @ SY2886 ) @ SY2887 @ ( tc_prod @ SY2886 @ SY2886 ) )
| ~ ( c_in @ SY2888 @ SY2885 @ SY2886 )
| ~ ( c_Wellfounded_Owf @ SY2887 @ SY2886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(2012,plain,
! [SV346: $i] :
( ( ! [SY2889: $i,SY2890: $i,SY2891: $i,SY2892: $i] :
( ~ ( c_in @ SV346 @ SY2889 @ SY2890 )
| ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SY2889 @ SY2891 @ SY2890 ) @ SY2890 @ SY2890 ) @ SY2891 @ ( tc_prod @ SY2890 @ SY2890 ) )
| ~ ( c_in @ SY2892 @ SY2889 @ SY2890 )
| ~ ( c_Wellfounded_Owf @ SY2891 @ SY2890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(2013,plain,
! [SV347: $i] :
( ( ! [SY2893: $i,SY2894: $i,SY2895: $i,SY2896: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SY2893 @ SY2894 @ SY2895 @ SY2896 ) @ SY2893 @ SY2895 @ SY2896 ) @ SY2894 @ ( tc_prod @ SY2895 @ SY2896 ) )
| ~ ( c_in @ SY2893 @ ( c_Relation_OImage @ SY2894 @ SV347 @ SY2895 @ SY2896 ) @ SY2896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(2014,plain,
! [SV348: $i] :
( ( ! [SY2897: $i,SY2898: $i,SY2899: $i,SY2900: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SY2897 @ SY2898 @ SY2899 @ SY2900 ) @ SY2897 @ SY2899 @ SY2900 ) @ SY2898 @ ( tc_prod @ SY2899 @ SY2900 ) )
| ~ ( c_in @ SY2897 @ ( c_Relation_OImage @ SY2898 @ SV348 @ SY2899 @ SY2900 ) @ SY2900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(2015,plain,
! [SV349: $i] :
( ( ! [SY2901: $i,SY2902: $i,SY2903: $i] :
( ( SV349 = SY2901 )
| ~ ( c_in @ ( c_Pair @ SV349 @ SY2901 @ SY2902 @ SY2902 ) @ ( c_Transitive__Closure_Ortrancl @ SY2903 @ SY2902 ) @ ( tc_prod @ SY2902 @ SY2902 ) )
| ( c_in @ SV349 @ ( c_Relation_ODomain @ SY2903 @ SY2902 @ SY2902 ) @ SY2902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(2016,plain,
! [SV350: $i] :
( ( ! [SY2904: $i,SY2905: $i,SY2906: $i] :
( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SY2904 @ SY2905 @ SY2906 ) @ SY2905 @ SY2906 ) @ SY2904 @ ( tc_prod @ SY2905 @ SY2906 ) )
| ~ ( c_in @ SV350 @ ( c_Relation_ODomain @ SY2904 @ SY2905 @ SY2906 ) @ SY2905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(2017,plain,
! [SV351: $i] :
( ( ! [SY2907: $i,SY2908: $i,SY2909: $i] :
( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SY2907 @ SY2908 @ SY2909 ) @ SY2908 @ SY2909 ) @ SY2907 @ ( tc_prod @ SY2908 @ SY2909 ) )
| ~ ( c_in @ SV351 @ ( c_Relation_ODomain @ SY2907 @ SY2908 @ SY2909 ) @ SY2908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(2018,plain,
! [SV352: $i] :
( ( ! [SY2910: $i,SY2911: $i] :
( ( c_in @ SV352 @ ( c_Relation_ODomain @ SY2910 @ SY2911 @ SY2911 ) @ SY2911 )
| ( c_in @ ( c_Pair @ SV352 @ SV352 @ SY2911 @ SY2911 ) @ ( c_Transitive__Closure_Ortrancl @ SY2910 @ SY2911 ) @ ( tc_prod @ SY2911 @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(2019,plain,
! [SV353: $i] :
( ( ! [SY2912: $i,SY2913: $i,SY2914: $i,SY2915: $i] :
( ( hBOOL @ ( hAPP @ SV353 @ SY2912 ) )
| ( hBOOL @ ( hAPP @ SV353 @ SY2913 ) )
| ~ ( c_in @ ( c_Pair @ SY2913 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SY2914 @ SY2915 ) @ SY2915 @ SY2915 ) @ SY2914 @ ( tc_prod @ SY2915 @ SY2915 ) )
| ~ ( c_in @ SY2912 @ ( c_Wellfounded_Oacc @ SY2914 @ SY2915 ) @ SY2915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(2020,plain,
! [SV354: $i] :
( ( ! [SY2916: $i,SY2917: $i,SY2918: $i] :
( ( hBOOL @ ( hAPP @ SV354 @ SY2916 ) )
| ( c_in @ SY2917 @ ( c_Wellfounded_Oacc @ SY2918 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY2917 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SY2918 ) @ t_a @ t_a ) @ SY2918 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY2916 @ ( c_Wellfounded_Oacc @ SY2918 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(2021,plain,
! [SV355: $i] :
( ( ! [SY2919: $i,SY2920: $i,SY2921: $i] :
( ( hBOOL @ ( hAPP @ SV355 @ SY2919 ) )
| ( hBOOL @ ( hAPP @ SV355 @ SY2920 ) )
| ~ ( c_in @ ( c_Pair @ SY2920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SY2921 ) @ t_a @ t_a ) @ SY2921 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY2919 @ ( c_Wellfounded_Oacc @ SY2921 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(2022,plain,
! [SV356: $i] :
( ( ! [SY2922: $i,SY2923: $i,SY2924: $i] :
( ( hBOOL @ ( hAPP @ SV356 @ SY2922 ) )
| ( c_in @ SY2923 @ ( c_Wellfounded_Oacc @ SY2924 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY2923 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SY2924 ) @ t_a @ t_a ) @ SY2924 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY2922 @ ( c_Wellfounded_Oacc @ SY2924 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(2023,plain,
! [SV357: $i] :
( ( ! [SY2925: $i,SY2926: $i,SY2927: $i] :
( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SY2925 @ SY2926 ) @ SY2926 )
| ~ ( c_in @ ( c_Pair @ SV357 @ SY2927 @ SY2926 @ SY2926 ) @ ( c_Transitive__Closure_Ortrancl @ SY2925 @ SY2926 ) @ ( tc_prod @ SY2926 @ SY2926 ) )
| ~ ( c_in @ SY2927 @ ( c_Wellfounded_Oacc @ SY2925 @ SY2926 ) @ SY2926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(2024,plain,
! [SV358: $i] :
( ( ! [SY2928: $i,SY2929: $i,SY2930: $i] :
( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SY2928 @ SY2929 ) @ SY2929 )
| ~ ( c_in @ SY2930 @ ( c_Wellfounded_Oacc @ SY2928 @ SY2929 ) @ SY2929 )
| ~ ( c_in @ ( c_Pair @ SV358 @ SY2930 @ SY2929 @ SY2929 ) @ ( c_Transitive__Closure_Ortrancl @ SY2928 @ SY2929 ) @ ( tc_prod @ SY2929 @ SY2929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(2025,plain,
! [SV359: $i] :
( ( ! [SY2931: $i,SY2932: $i] :
( ( c_in @ SV359 @ ( c_Wellfounded_Oacc @ SY2931 @ SY2932 ) @ SY2932 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY2931 @ SV359 @ SY2932 ) @ SV359 @ SY2932 @ SY2932 ) @ SY2931 @ ( tc_prod @ SY2932 @ SY2932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(2026,plain,
! [SV360: $i] :
( ( ! [SY2933: $i,SY2934: $i,SY2935: $i] :
( ( hBOOL @ ( hAPP @ SV360 @ SY2933 ) )
| ( hBOOL @ ( hAPP @ SV360 @ SY2934 ) )
| ~ ( c_in @ ( c_Pair @ SY2934 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SY2935 ) @ t_a @ t_a ) @ SY2935 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY2933 @ ( c_Wellfounded_Oacc @ SY2935 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(2027,plain,
! [SV361: $i] :
( ( ! [SY2936: $i,SY2937: $i,SY2938: $i,SY2939: $i] :
( ( hBOOL @ ( hAPP @ SV361 @ SY2936 ) )
| ( hBOOL @ ( hAPP @ SV361 @ SY2937 ) )
| ~ ( c_in @ ( c_Pair @ SY2937 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SY2938 @ SY2939 ) @ SY2939 @ SY2939 ) @ SY2938 @ ( tc_prod @ SY2939 @ SY2939 ) )
| ~ ( c_in @ SY2936 @ ( c_Wellfounded_Oacc @ SY2938 @ SY2939 ) @ SY2939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(2028,plain,
! [SV362: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV362 @ SY2940 @ SY2941 ) @ SY2940 @ SY2941 @ SY2941 ) @ SV362 @ ( tc_prod @ SY2941 @ SY2941 ) )
| ( c_in @ SY2940 @ ( c_Wellfounded_Oacc @ SV362 @ SY2941 ) @ SY2941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(2029,plain,
! [SV363: $i] :
( ( ! [SY2942: $i,SY2943: $i,SY2944: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SY2942 @ SY2943 @ SY2944 ) @ SV363 @ SY2944 @ SY2943 ) @ SY2942 @ ( tc_prod @ SY2944 @ SY2943 ) )
| ~ ( c_in @ SV363 @ ( c_Relation_ORange @ SY2942 @ SY2944 @ SY2943 ) @ SY2943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(2030,plain,
! [SV364: $i] :
( ( ! [SY2945: $i,SY2946: $i,SY2947: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SY2945 @ SY2946 @ SY2947 ) @ SV364 @ SY2947 @ SY2946 ) @ SY2945 @ ( tc_prod @ SY2947 @ SY2946 ) )
| ~ ( c_in @ SV364 @ ( c_Relation_ORange @ SY2945 @ SY2947 @ SY2946 ) @ SY2946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(2031,plain,
! [SV365: $i] :
( ( ! [SY2948: $i,SY2949: $i,SY2950: $i] :
( ~ ( c_in @ ( c_Pair @ SV365 @ SY2948 @ SY2949 @ SY2949 ) @ SY2950 @ ( tc_prod @ SY2949 @ SY2949 ) )
| ~ ( c_in @ ( c_Pair @ SY2948 @ SV365 @ SY2949 @ SY2949 ) @ SY2950 @ ( tc_prod @ SY2949 @ SY2949 ) )
| ~ ( c_Wellfounded_Owf @ SY2950 @ SY2949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(2032,plain,
! [SV366: $i] :
( ( ! [SY2951: $i,SY2952: $i,SY2953: $i] :
( ( c_in @ ( c_Pair @ SV366 @ SY2951 @ SY2952 @ SY2952 ) @ ( c_Transitive__Closure_Otrancl @ SY2953 @ SY2952 ) @ ( tc_prod @ SY2952 @ SY2952 ) )
| ~ ( c_in @ ( c_Pair @ SV366 @ SY2951 @ SY2952 @ SY2952 ) @ SY2953 @ ( tc_prod @ SY2952 @ SY2952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(2033,plain,
! [SV367: $i] :
( ( ! [SY2954: $i,SY2955: $i,SY2956: $i,SY2957: $i] :
( ( c_in @ ( c_Pair @ SV367 @ SY2954 @ SY2955 @ SY2955 ) @ ( c_Transitive__Closure_Otrancl @ SY2956 @ SY2955 ) @ ( tc_prod @ SY2955 @ SY2955 ) )
| ~ ( c_in @ ( c_Pair @ SY2957 @ SY2954 @ SY2955 @ SY2955 ) @ ( c_Transitive__Closure_Otrancl @ SY2956 @ SY2955 ) @ ( tc_prod @ SY2955 @ SY2955 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SY2957 @ SY2955 @ SY2955 ) @ SY2956 @ ( tc_prod @ SY2955 @ SY2955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(2034,plain,
! [SV368: $i] :
( ( ! [SY2958: $i,SY2959: $i,SY2960: $i,SY2961: $i] :
( ( c_in @ ( c_Pair @ SV368 @ SY2958 @ SY2959 @ SY2959 ) @ ( c_Transitive__Closure_Otrancl @ SY2960 @ SY2959 ) @ ( tc_prod @ SY2959 @ SY2959 ) )
| ~ ( c_in @ ( c_Pair @ SY2961 @ SY2958 @ SY2959 @ SY2959 ) @ SY2960 @ ( tc_prod @ SY2959 @ SY2959 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SY2961 @ SY2959 @ SY2959 ) @ ( c_Transitive__Closure_Otrancl @ SY2960 @ SY2959 ) @ ( tc_prod @ SY2959 @ SY2959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(2035,plain,
! [SV369: $i] :
( ( ! [SY2962: $i,SY2963: $i,SY2964: $i,SY2965: $i] :
( ( c_in @ ( c_Pair @ SV369 @ SY2962 @ SY2963 @ SY2964 ) @ SY2965 @ ( tc_prod @ SY2963 @ SY2964 ) )
| ~ ( c_in @ ( c_Pair @ SY2962 @ SV369 @ SY2964 @ SY2963 ) @ ( c_Relation_Oconverse @ SY2965 @ SY2963 @ SY2964 ) @ ( tc_prod @ SY2964 @ SY2963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(2036,plain,
! [SV370: $i] :
( ( ! [SY2966: $i,SY2967: $i,SY2968: $i,SY2969: $i] :
( ( c_in @ ( c_Pair @ SV370 @ SY2966 @ SY2967 @ SY2968 ) @ ( c_Relation_Oconverse @ SY2969 @ SY2968 @ SY2967 ) @ ( tc_prod @ SY2967 @ SY2968 ) )
| ~ ( c_in @ ( c_Pair @ SY2966 @ SV370 @ SY2968 @ SY2967 ) @ SY2969 @ ( tc_prod @ SY2968 @ SY2967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(2037,plain,
! [SV371: $i] :
( ( ! [SY2970: $i,SY2971: $i,SY2972: $i,SY2973: $i] :
( ( c_in @ ( c_Pair @ SV371 @ SY2970 @ SY2971 @ SY2972 ) @ ( c_Relation_Oconverse @ SY2973 @ SY2972 @ SY2971 ) @ ( tc_prod @ SY2971 @ SY2972 ) )
| ~ ( c_in @ ( c_Pair @ SY2970 @ SV371 @ SY2972 @ SY2971 ) @ SY2973 @ ( tc_prod @ SY2972 @ SY2971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(2038,plain,
! [SV372: $i] :
( ( ! [SY2974: $i,SY2975: $i,SY2976: $i,SY2977: $i,SY2978: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SY2974 @ SY2975 @ SY2976 @ SY2977 ) @ SY2978 )
= ( hAPP @ SV372 @ SY2978 ) )
| ~ ( c_in @ ( c_Pair @ SY2978 @ SY2975 @ SY2976 @ SY2976 ) @ SY2974 @ ( tc_prod @ SY2976 @ SY2976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(2039,plain,
! [SV373: $i] :
( ( ! [SY2979: $i,SY2980: $i,SY2981: $i,SY2982: $i,SY2983: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SY2979 @ SY2980 @ SY2981 @ SY2982 ) @ SY2983 )
= ( hAPP @ SV373 @ SY2983 ) )
| ~ ( c_in @ ( c_Pair @ SY2983 @ SY2980 @ SY2981 @ SY2981 ) @ SY2979 @ ( tc_prod @ SY2981 @ SY2981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(2040,plain,
! [SV374: $i] :
( ( ! [SY2984: $i,SY2985: $i] :
( ( c_in @ SV374 @ ( c_Transitive__Closure_Otrancl @ SY2984 @ SY2985 ) @ ( tc_prod @ SY2985 @ SY2985 ) )
| ~ ( c_in @ SV374 @ SY2984 @ ( tc_prod @ SY2985 @ SY2985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(2041,plain,
! [SV375: $i] :
( ( ! [SY2986: $i,SY2987: $i,SY2988: $i] :
( ( c_in @ ( c_Pair @ SV375 @ SY2986 @ SY2987 @ SY2987 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY2988 @ SY2987 ) @ SY2987 @ SY2987 ) @ ( tc_prod @ SY2987 @ SY2987 ) )
| ~ ( c_in @ ( c_Pair @ SV375 @ SY2986 @ SY2987 @ SY2987 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY2988 @ SY2987 @ SY2987 ) @ SY2987 ) @ ( tc_prod @ SY2987 @ SY2987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(2042,plain,
! [SV376: $i] :
( ( ! [SY2989: $i,SY2990: $i,SY2991: $i] :
( ( c_in @ ( c_Pair @ SV376 @ SY2989 @ SY2990 @ SY2990 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY2991 @ SY2990 @ SY2990 ) @ SY2990 ) @ ( tc_prod @ SY2990 @ SY2990 ) )
| ~ ( c_in @ ( c_Pair @ SV376 @ SY2989 @ SY2990 @ SY2990 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY2991 @ SY2990 ) @ SY2990 @ SY2990 ) @ ( tc_prod @ SY2990 @ SY2990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(2043,plain,
! [SV377: $i] :
( ( ! [SY2992: $i,SY2993: $i] :
( ( c_in @ SV377 @ ( c_Wellfounded_Oacc @ SY2992 @ SY2993 ) @ SY2993 )
| ~ ( c_Wellfounded_Owf @ SY2992 @ SY2993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(2044,plain,
! [SV378: $i] :
( ( ! [SY2994: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV378 @ SY2994 ) @ SY2994 )
| ~ ( c_Relation_Osym @ SV378 @ SY2994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(2045,plain,
! [SV379: $i] :
( ( ! [SY2995: $i] :
( ( c_Relation_Osym @ SV379 @ SY2995 )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV379 @ SY2995 @ SY2995 ) @ SY2995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(2046,plain,
! [SV380: $i] :
( ( ! [SY2996: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV380 @ SY2996 @ SY2996 ) @ SY2996 )
| ~ ( c_Relation_Osym @ SV380 @ SY2996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(2047,plain,
! [SV381: $i] :
( ( ! [SY2997: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV381 @ SY2997 ) @ SY2997 @ SY2997 )
= ( c_Relation_ODomain @ SV381 @ SY2997 @ SY2997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(2048,plain,
! [SV382: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId @ SV382 ) @ SV382 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(2049,plain,
! [SV383: $i] :
( ( ! [SY2998: $i,SY2999: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV383 ) @ SY2998 @ SV383 @ SV383 @ SY2999 )
= SY2998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(2050,plain,
! [SV384: $i] :
( ( ! [SY3000: $i,SY3001: $i] :
( ( c_Relation_Orel__comp @ SV384 @ ( c_Relation_OId @ SY3000 ) @ SY3001 @ SY3000 @ SY3000 )
= SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(2051,plain,
! [SV385: $i] :
( ( ! [SY3002: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV385 @ SY3002 ) @ SY3002 @ SY3002 ) @ SY3002 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV385 @ SY3002 @ SY3002 ) @ SY3002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(2052,plain,
! [SV386: $i] :
( ( ! [SY3003: $i,SY3004: $i] :
( ( c_Relation_Orefl__on @ SV386 @ SY3003 @ SY3004 )
| ~ ( c_Relation_Orefl__on @ SV386 @ ( c_Relation_Oconverse @ SY3003 @ SY3004 @ SY3004 ) @ SY3004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(2053,plain,
! [SV387: $i] :
( ( ! [SY3005: $i,SY3006: $i] :
( ( c_Relation_Orefl__on @ SV387 @ ( c_Relation_Oconverse @ SY3005 @ SY3006 @ SY3006 ) @ SY3006 )
| ~ ( c_Relation_Orefl__on @ SV387 @ SY3005 @ SY3006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(2054,plain,
! [SV388: $i] :
( ( ! [SY3007: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV388 @ SV388 @ SY3007 @ SY3007 @ SY3007 ) @ SY3007 )
| ~ ( c_Wellfounded_Owf @ SV388 @ SY3007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(2055,plain,
! [SV389: $i] :
( ( ! [SY3008: $i] :
( ( c_Wellfounded_Owf @ SV389 @ SY3008 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV389 @ SV389 @ SY3008 @ SY3008 @ SY3008 ) @ SY3008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(2056,plain,
! [SV390: $i] :
( ( ! [SY3009: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ SV390 ) @ SY3009 @ SV390 @ SV390 )
= SY3009 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2057,plain,
! [SV391: $i] :
( ( ! [SY3010: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV391 @ SY3010 ) @ SY3010 @ SY3010 )
= SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(2058,plain,
! [SV392: $i] :
( ( ! [SY3011: $i] :
( ( ( c_Relation_Oconverse @ SV392 @ SY3011 @ SY3011 )
= SV392 )
| ~ ( c_Relation_Osym @ SV392 @ SY3011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(2059,plain,
! [SV393: $i] :
( ( ! [SY3012: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV393 @ SY3012 ) @ SY3012 @ SY3012 )
= ( c_Relation_ORange @ SV393 @ SY3012 @ SY3012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2060,plain,
! [SV394: $i] :
( ( ! [SY3013: $i,SY3014: $i,SY3015: $i,SY3016: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV394 @ SY3013 @ SY3014 @ SY3015 @ SY3016 ) @ SY3014 @ SY3016 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SY3013 @ SY3015 @ SY3016 ) @ ( c_Relation_Oconverse @ SV394 @ SY3014 @ SY3015 ) @ SY3016 @ SY3015 @ SY3014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(2061,plain,
! [SV395: $i] :
( ( ! [SY3017: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ SV395 @ SY3017 ) @ SY3017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(2062,plain,
! [SV396: $i] :
( ( ! [SY3018: $i] : ( c_Relation_Orefl__on @ SV396 @ ( c_Relation_OId__on @ SV396 @ SY3018 ) @ SY3018 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2063,plain,
! [SV397: $i] :
( ( ! [SY3019: $i,SY3020: $i,SY3021: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SY3019 @ SY3020 @ SY3021 ) @ SY3021 )
| ~ ( c_Wellfounded_Owf @ SV397 @ SY3020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2064,plain,
! [SV398: $i] :
( ( ! [SY3022: $i,SY3023: $i,SY3024: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SY3022 @ SY3023 @ SY3024 ) @ SY3024 )
| ~ ( c_Relation_Osym @ SV398 @ SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2065,plain,
! [SV399: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_OId @ SV399 ) @ SV399 @ SV399 )
= ( c_Relation_OId @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2066,plain,
! [SV400: $i] :
( ( ! [SY3025: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV400 @ SY3025 ) @ SY3025 )
| ~ ( c_Wellfounded_Owf @ SV400 @ SY3025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2067,plain,
! [SV401: $i] :
( ( ! [SY3026: $i,SY3027: $i,SY3028: $i,SY3029: $i,SY3030: $i,SY3031: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SY3026 @ SY3027 @ SY3028 @ SY3029 ) @ SY3030 @ SY3027 @ SY3029 @ SY3031 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SY3026 @ SY3030 @ SY3028 @ SY3029 @ SY3031 ) @ SY3027 @ SY3028 @ SY3031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(2068,plain,
! [SV402: $i] :
( ( ! [SY3032: $i,SY3033: $i,SY3034: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV402 @ SY3032 @ SY3033 @ SY3034 ) @ SY3034 @ SY3034 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV402 @ SY3033 @ SY3033 ) @ SY3032 @ SY3033 @ SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2069,plain,
! [SV403: $i] :
( ( ! [SY3035: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV403 @ SY3035 @ SY3035 ) @ SY3035 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV403 @ SY3035 ) @ SY3035 @ SY3035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(2070,plain,
! [SV404: $i] :
( ( ! [SY3036: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ SV404 @ SY3036 ) @ SY3036 @ SY3036 )
= ( c_Relation_OId__on @ SV404 @ SY3036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(2071,plain,
! [SV405: $i] :
( ( ! [SY3037: $i,SY3038: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV405 @ SY3037 @ SY3038 ) @ SY3038 @ SY3037 )
= ( c_Relation_ODomain @ SV405 @ SY3037 @ SY3038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2072,plain,
! [SV406: $i] :
( ( ! [SY3039: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV406 @ SY3039 ) @ SY3039 @ SY3039 )
= SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2073,plain,
! [SV407: $i] :
( ( ! [SY3040: $i,SY3041: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV407 @ SY3040 @ SY3041 ) @ SY3041 @ SY3040 )
= SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2074,plain,
! [SV408: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV408 @ SY3042 @ SY3042 ) @ SV408 @ SY3042 @ SY3042 @ SY3042 )
= SV408 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3043 @ SV408 @ SY3042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2075,plain,
! [SV409: $i] :
( ( ! [SY3044: $i,SY3045: $i] :
( ( c_Relation_Orefl__on @ SV409 @ SY3044 @ SY3045 )
| ~ ( c_Equiv__Relations_Oequiv @ SV409 @ SY3044 @ SY3045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2076,plain,
! [SV410: $i] :
( ( ! [SY3046: $i,SY3047: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ SV410 @ SY3046 @ SY3047 ) @ ( tc_fun @ SY3047 @ tc_bool ) )
= SV410 )
| ~ ( c_Equiv__Relations_Oequiv @ SV410 @ SY3046 @ SY3047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2077,plain,
! [SV411: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( c_Relation_Osym @ SV411 @ SY3048 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3049 @ SV411 @ SY3048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(2078,plain,
! [SV412: $i] :
( ( ! [SY3050: $i,SY3051: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV412 @ SY3050 @ SY3051 ) @ SY3051 @ SY3050 )
= ( c_Relation_ORange @ SV412 @ SY3050 @ SY3051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2079,plain,
! [SV413: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( c_Relation_ORange @ SV413 @ SY3052 @ SY3053 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV413 @ SY3052 @ SY3053 ) @ SY3053 @ SY3052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(2080,plain,
! [SV414: $i] :
( ( ! [SY3054: $i,SY3055: $i] :
( ( c_Relation_Ototal__on @ SV414 @ SY3054 @ SY3055 )
| ~ ( c_Relation_Ototal__on @ SV414 @ ( c_Relation_Oconverse @ SY3054 @ SY3055 @ SY3055 ) @ SY3055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2081,plain,
! [SV415: $i] :
( ( ! [SY3056: $i,SY3057: $i] :
( ( c_Relation_Ototal__on @ SV415 @ ( c_Relation_Oconverse @ SY3056 @ SY3057 @ SY3057 ) @ SY3057 )
| ~ ( c_Relation_Ototal__on @ SV415 @ SY3056 @ SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2082,plain,
! [SV416: $i] :
( ( ! [SY3058: $i,SY3059: $i,SY3060: $i] :
( ( SV416 = SY3058 )
| ~ ( c_in @ ( c_Pair @ SV416 @ SY3058 @ SY3059 @ SY3059 ) @ ( c_Relation_OId__on @ SY3060 @ SY3059 ) @ ( tc_prod @ SY3059 @ SY3059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2083,plain,
! [SV417: $i] :
( ( ! [SY3061: $i,SY3062: $i] :
( ( SV417 = SY3061 )
| ~ ( c_in @ ( c_Pair @ SV417 @ SY3061 @ SY3062 @ SY3062 ) @ ( c_Relation_OId @ SY3062 ) @ ( tc_prod @ SY3062 @ SY3062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2084,plain,
! [SV418: $i] :
( ( ! [SY3063: $i,SY3064: $i] :
( ( c_in @ ( c_Pair @ SV418 @ SV418 @ SY3063 @ SY3063 ) @ SY3064 @ ( tc_prod @ SY3063 @ SY3063 ) )
| ~ ( c_Nitpick_Orefl_H @ SY3064 @ SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2085,plain,
! [SV419: $i] :
( ( ! [SY3065: $i,SY3066: $i] :
( ~ ( c_in @ ( c_Pair @ SV419 @ SV419 @ SY3065 @ SY3065 ) @ SY3066 @ ( tc_prod @ SY3065 @ SY3065 ) )
| ~ ( c_Wellfounded_Owf @ SY3066 @ SY3065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2086,plain,
! [SV420: $i] :
( ( ! [SY3067: $i,SY3068: $i,SY3069: $i,SY3070: $i,SY3071: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SY3067 @ SY3068 @ SY3068 ) @ ( c_Relation_Oinv__image @ SY3069 @ SY3070 @ SY3071 @ SY3068 ) @ ( tc_prod @ SY3068 @ SY3068 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY3070 @ SV420 ) @ ( hAPP @ SY3070 @ SY3067 ) @ SY3071 @ SY3071 ) @ SY3069 @ ( tc_prod @ SY3071 @ SY3071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2087,plain,
! [SV421: $i] :
( ( ! [SY3072: $i,SY3073: $i,SY3074: $i,SY3075: $i,SY3076: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SY3072 ) @ ( hAPP @ SV421 @ SY3073 ) @ SY3074 @ SY3074 ) @ SY3075 @ ( tc_prod @ SY3074 @ SY3074 ) )
| ~ ( c_in @ ( c_Pair @ SY3072 @ SY3073 @ SY3076 @ SY3076 ) @ ( c_Relation_Oinv__image @ SY3075 @ SV421 @ SY3074 @ SY3076 ) @ ( tc_prod @ SY3076 @ SY3076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2088,plain,
! [SV422: $i] :
( ( ! [SY3077: $i,SY3078: $i,SY3079: $i] :
( ( c_in @ ( c_Pair @ SV422 @ SY3077 @ SY3078 @ SY3078 ) @ SY3079 @ ( tc_prod @ SY3078 @ SY3078 ) )
| ~ ( c_in @ ( c_Pair @ SY3077 @ SV422 @ SY3078 @ SY3078 ) @ SY3079 @ ( tc_prod @ SY3078 @ SY3078 ) )
| ~ ( c_Relation_Osym @ SY3079 @ SY3078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2089,plain,
! [SV423: $i] :
( ( ! [SY3080: $i,SY3081: $i,SY3082: $i] :
( ( c_in @ ( c_Pair @ SV423 @ SY3080 @ SY3081 @ SY3081 ) @ SY3082 @ ( tc_prod @ SY3081 @ SY3081 ) )
| ~ ( c_in @ ( c_Pair @ SY3080 @ SV423 @ SY3081 @ SY3081 ) @ SY3082 @ ( tc_prod @ SY3081 @ SY3081 ) )
| ~ ( c_Relation_Osym @ SY3082 @ SY3081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2090,plain,
! [SV424: $i] :
( ( ! [SY3083: $i,SY3084: $i,SY3085: $i,SY3086: $i,SY3087: $i,SY3088: $i,SY3089: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SY3083 @ SY3084 @ SY3085 ) @ ( c_Relation_Orel__comp @ SY3086 @ SY3087 @ SY3084 @ SY3088 @ SY3085 ) @ ( tc_prod @ SY3084 @ SY3085 ) )
| ~ ( c_in @ ( c_Pair @ SY3089 @ SY3083 @ SY3088 @ SY3085 ) @ SY3087 @ ( tc_prod @ SY3088 @ SY3085 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY3089 @ SY3084 @ SY3088 ) @ SY3086 @ ( tc_prod @ SY3084 @ SY3088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2091,plain,
! [SV425: $i] :
( ( ! [SY3090: $i,SY3091: $i,SY3092: $i,SY3093: $i] :
( ( c_in @ ( c_Pair @ SV425 @ SY3090 @ SY3091 @ SY3091 ) @ ( c_Transitive__Closure_Otrancl @ SY3092 @ SY3091 ) @ ( tc_prod @ SY3091 @ SY3091 ) )
| ~ ( c_in @ ( c_Pair @ SY3093 @ SY3090 @ SY3091 @ SY3091 ) @ SY3092 @ ( tc_prod @ SY3091 @ SY3091 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SY3093 @ SY3091 @ SY3091 ) @ SY3092 @ ( tc_prod @ SY3091 @ SY3091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2092,plain,
! [SV426: $i] :
( ( ! [SY3094: $i,SY3095: $i,SY3096: $i,SY3097: $i] :
( ( c_in @ ( c_Pair @ SV426 @ SY3094 @ SY3095 @ SY3095 ) @ ( c_Transitive__Closure_Otrancl @ SY3096 @ SY3095 ) @ ( tc_prod @ SY3095 @ SY3095 ) )
| ~ ( c_in @ ( c_Pair @ SY3097 @ SY3094 @ SY3095 @ SY3095 ) @ ( c_Transitive__Closure_Otrancl @ SY3096 @ SY3095 ) @ ( tc_prod @ SY3095 @ SY3095 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY3097 @ SY3095 @ SY3095 ) @ ( c_Transitive__Closure_Otrancl @ SY3096 @ SY3095 ) @ ( tc_prod @ SY3095 @ SY3095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2093,plain,
! [SV427: $i] :
( ( ! [SY3098: $i] : ( c_in @ ( c_Pair @ SV427 @ SV427 @ SY3098 @ SY3098 ) @ ( c_Relation_OId @ SY3098 ) @ ( tc_prod @ SY3098 @ SY3098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2094,plain,
! [SV428: $i] :
( ( ! [SY3099: $i] : ( c_in @ ( c_Pair @ SV428 @ SV428 @ SY3099 @ SY3099 ) @ ( c_Relation_OId @ SY3099 ) @ ( tc_prod @ SY3099 @ SY3099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2095,plain,
! [SV429: $i] :
( ( ! [SY3100: $i,SY3101: $i,SY3102: $i,SY3103: $i,SY3104: $i] :
( ( c_in @ ( hAPP @ SV429 @ SY3100 ) @ ( hAPP @ SY3101 @ SY3100 ) @ SY3102 )
| ~ ( c_in @ SY3100 @ SY3103 @ SY3104 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SY3103 @ SY3101 @ SY3104 @ SY3102 ) @ ( tc_fun @ SY3104 @ SY3102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2096,plain,
! [SV430: $i] :
( ( ! [SY3105: $i,SY3106: $i,SY3107: $i,SY3108: $i,SY3109: $i] :
( ~ ( c_in @ SV430 @ SY3105 @ SY3106 )
| ( c_in @ ( hAPP @ SY3107 @ SV430 ) @ ( hAPP @ SY3108 @ SV430 ) @ SY3109 )
| ~ ( c_in @ SY3107 @ ( c_FuncSet_OPi @ SY3105 @ SY3108 @ SY3106 @ SY3109 ) @ ( tc_fun @ SY3106 @ SY3109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2097,plain,
! [SV431: $i] :
( ( ! [SY3110: $i,SY3111: $i,SY3112: $i,SY3113: $i,SY3114: $i,SY3115: $i] :
( ( SV431 = SY3110 )
| ~ ( c_in @ ( c_Pair @ SY3111 @ SY3112 @ SY3113 @ SY3113 ) @ SY3114 @ ( tc_prod @ SY3113 @ SY3113 ) )
| ~ ( c_in @ SY3112 @ SY3110 @ SY3113 )
| ~ ( c_in @ SY3111 @ SV431 @ SY3113 )
| ~ ( c_in @ SY3110 @ ( c_Equiv__Relations_Oquotient @ SY3115 @ SY3114 @ SY3113 ) @ ( tc_fun @ SY3113 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY3115 @ SY3114 @ SY3113 ) @ ( tc_fun @ SY3113 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3115 @ SY3114 @ SY3113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2098,plain,
! [SV432: $i] :
( ( ! [SY3116: $i,SY3117: $i,SY3118: $i,SY3119: $i,SY3120: $i] :
( ~ ( c_in @ SV432 @ SY3116 @ SY3117 )
| ~ ( c_in @ SY3118 @ SY3116 @ SY3117 )
| ~ ( c_in @ SY3116 @ ( c_Equiv__Relations_Oquotient @ SY3119 @ SY3120 @ SY3117 ) @ ( tc_fun @ SY3117 @ tc_bool ) )
| ~ ( c_in @ SY3116 @ ( c_Equiv__Relations_Oquotient @ SY3119 @ SY3120 @ SY3117 ) @ ( tc_fun @ SY3117 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3119 @ SY3120 @ SY3117 )
| ( c_in @ ( c_Pair @ SY3118 @ SV432 @ SY3117 @ SY3117 ) @ SY3120 @ ( tc_prod @ SY3117 @ SY3117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2099,plain,
! [SV433: $i] :
( ( ! [SY3121: $i,SY3122: $i,SY3123: $i] :
( ( c_in @ SV433 @ SY3121 @ SY3122 )
| ~ ( c_in @ SY3121 @ SY3123 @ ( tc_fun @ SY3122 @ tc_bool ) )
| ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SY3123 @ ( tc_fun @ SY3122 @ tc_bool ) ) @ SY3122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2100,plain,
! [SV434: $i] :
( ( ! [SY3124: $i,SY3125: $i,SY3126: $i] :
( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SY3124 @ ( tc_fun @ SY3125 @ tc_bool ) ) @ SY3125 )
| ~ ( c_in @ SV434 @ SY3126 @ SY3125 )
| ~ ( c_in @ SY3126 @ SY3124 @ ( tc_fun @ SY3125 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2101,plain,
! [SV435: $i] :
( ( ! [SY3127: $i,SY3128: $i,SY3129: $i] :
( ( c_in @ ( c_Pair @ SV435 @ SY3127 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3128 @ SY3129 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV435 @ SY3127 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3128 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV435 = SY3127 )
| ( SV435 = SY3129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2102,plain,
! [SV436: $i] :
( ( ! [SY3130: $i,SY3131: $i,SY3132: $i] :
( ( c_in @ ( c_Pair @ SV436 @ SY3130 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3131 @ SY3132 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV436 @ SY3130 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3131 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3130 = SY3132 )
| ( SV436 = SY3132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2103,plain,
! [SV437: $i] :
( ( ! [SY3133: $i] :
~ ( c_in @ ( c_Pair @ SV437 @ SV437 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3133 @ SV437 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2104,plain,
! [SV438: $i] :
( ( ! [SY3134: $i,SY3135: $i] :
~ ( c_in @ ( c_Pair @ SV438 @ SY3134 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3135 @ SV438 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2105,plain,
! [SV439: $i] :
( ( ! [SY3136: $i,SY3137: $i,SY3138: $i] :
( ( c_in @ ( c_Pair @ SV439 @ SY3136 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3137 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3136 = SY3138 )
| ~ ( c_in @ ( c_Pair @ SV439 @ SY3136 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3137 @ SY3138 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2106,plain,
! [SV440: $i] :
( ( ! [SY3139: $i,SY3140: $i] :
( ( SV440 = SY3139 )
| ( SY3139 = SV440 )
| ( c_in @ ( c_Pair @ SV440 @ SY3139 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3140 @ SV440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2107,plain,
! [SV441: $i] :
( ( ! [SY3141: $i] :
~ ( c_in @ ( c_Pair @ SV441 @ SV441 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3141 @ SV441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2108,plain,
! [SV442: $i] :
( ( ! [SY3142: $i,SY3143: $i] :
~ ( c_in @ ( c_Pair @ SV442 @ SY3142 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3143 @ SY3142 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2109,plain,
! [SV443: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i] :
( ( c_in @ ( c_Pair @ SV443 @ SY3144 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3145 @ SY3146 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV443 @ SY3144 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3145 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV443 = SY3144 )
| ( SY3144 = SY3146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2110,plain,
! [SV444: $i] :
( ( ! [SY3147: $i,SY3148: $i,SY3149: $i] :
( ( c_in @ ( c_Pair @ SV444 @ SY3147 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3148 @ SY3149 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV444 @ SY3147 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3148 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV444 = SY3149 )
| ( SY3147 = SY3149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2111,plain,
! [SV445: $i] :
( ( ! [SY3150: $i,SY3151: $i] :
( ( SV445 = SY3150 )
| ( SV445 = SY3150 )
| ( c_in @ ( c_Pair @ SV445 @ SY3150 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY3151 @ SY3150 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2112,plain,
! [SV446: $i] :
( ( ! [SY3152: $i,SY3153: $i,SY3154: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SY3152 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3153 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV446 = SY3154 )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY3152 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY3153 @ SY3154 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2113,plain,
! [SV447: $i] :
( ( ! [SY3155: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SY3155 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV447 @ SY3155 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV447 = SY3155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2114,plain,
! [SV448: $i] :
( ( ! [SY3156: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV448 @ SY3156 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV448 = SY3156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2115,plain,
! [SV449: $i] :
( ( ! [SY3157: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ SV449 @ SY3157 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV449 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2116,plain,
! [SV450: $i] :
( ( ! [SY3158: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV450 @ SY3158 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV450 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2117,plain,
! [SV451: $i] :
( ( ! [SY3159: $i,SY3160: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SY3159 @ SY3160 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3159 = SY3160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2118,plain,
! [SV452: $i] :
( ( ( c_in @ SV452 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ SV452 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2119,plain,
! [SV453: $i] :
( ( ( c_in @ ( c_Relation_Oconverse @ SV453 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV453 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2120,plain,
! [SV454: $i] :
( ( ! [SY3161: $i,SY3162: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SY3161 @ SY3162 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3161 = SY3162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2121,plain,
! [SV455: $i] :
( ( ! [SY3163: $i,SY3164: $i,SY3165: $i,SY3166: $i,SY3167: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SY3163 @ SY3164 @ SY3165 ) @ ( c_Product__Type_OSigma @ SY3166 @ SY3167 @ SY3164 @ SY3165 ) @ ( tc_prod @ SY3164 @ SY3165 ) )
| ~ ( c_in @ SY3163 @ ( hAPP @ SY3167 @ SV455 ) @ SY3165 )
| ~ ( c_in @ SV455 @ SY3166 @ SY3164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2122,plain,
! [SV456: $i] :
( ( ! [SY3168: $i,SY3169: $i,SY3170: $i,SY3171: $i,SY3172: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SY3168 @ SY3169 @ SY3170 ) @ ( c_Product__Type_OSigma @ SY3171 @ SY3172 @ SY3169 @ SY3170 ) @ ( tc_prod @ SY3169 @ SY3170 ) )
| ~ ( c_in @ SY3168 @ ( hAPP @ SY3172 @ SV456 ) @ SY3170 )
| ~ ( c_in @ SV456 @ SY3171 @ SY3169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2123,plain,
! [SV457: $i] :
( ( ! [SY3173: $i,SY3174: $i,SY3175: $i] :
( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SY3173 @ SY3174 ) @ SY3174 )
| ~ ( c_in @ ( c_Pair @ SV457 @ SY3175 @ SY3174 @ SY3174 ) @ SY3173 @ ( tc_prod @ SY3174 @ SY3174 ) )
| ~ ( c_in @ SY3175 @ ( c_Wellfounded_Oacc @ SY3173 @ SY3174 ) @ SY3174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2124,plain,
! [SV458: $i] :
( ( ! [SY3176: $i,SY3177: $i,SY3178: $i] :
( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SY3176 @ SY3177 ) @ SY3177 )
| ~ ( c_in @ ( c_Pair @ SV458 @ SY3178 @ SY3177 @ SY3177 ) @ SY3176 @ ( tc_prod @ SY3177 @ SY3177 ) )
| ~ ( c_in @ SY3178 @ ( c_Wellfounded_Oacc @ SY3176 @ SY3177 ) @ SY3177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2125,plain,
! [SV459: $i] :
( ( ! [SY3179: $i,SY3180: $i,SY3181: $i,SY3182: $i,SY3183: $i] :
( ( c_in @ SV459 @ ( c_Relation_OImage @ SY3179 @ SY3180 @ SY3181 @ SY3182 ) @ SY3182 )
| ~ ( c_in @ ( c_Pair @ SY3183 @ SV459 @ SY3181 @ SY3182 ) @ SY3179 @ ( tc_prod @ SY3181 @ SY3182 ) )
| ~ ( c_in @ SY3183 @ SY3180 @ SY3181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2126,plain,
! [SV460: $i] :
( ( ! [SY3184: $i,SY3185: $i,SY3186: $i,SY3187: $i,SY3188: $i] :
( ( c_in @ SV460 @ ( c_Relation_OImage @ SY3184 @ SY3185 @ SY3186 @ SY3187 ) @ SY3187 )
| ~ ( c_in @ ( c_Pair @ SY3188 @ SV460 @ SY3186 @ SY3187 ) @ SY3184 @ ( tc_prod @ SY3186 @ SY3187 ) )
| ~ ( c_in @ SY3188 @ SY3185 @ SY3186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2127,plain,
! [SV461: $i] :
( ( ! [SY3189: $i,SY3190: $i,SY3191: $i] :
( ( c_in @ SV461 @ SY3189 @ SY3190 )
| ~ ( c_in @ ( c_Pair @ SV461 @ SY3191 @ SY3190 @ SY3190 ) @ ( c_Relation_OId__on @ SY3189 @ SY3190 ) @ ( tc_prod @ SY3190 @ SY3190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2128,plain,
! [SV462: $i] :
( ( ! [SY3192: $i,SY3193: $i] :
( ( c_in @ ( c_Pair @ SV462 @ SV462 @ SY3192 @ SY3192 ) @ ( c_Relation_OId__on @ SY3193 @ SY3192 ) @ ( tc_prod @ SY3192 @ SY3192 ) )
| ~ ( c_in @ SV462 @ SY3193 @ SY3192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2129,plain,
! [SV463: $i] :
( ( ! [SY3194: $i,SY3195: $i,SY3196: $i,SY3197: $i] :
( ( c_in @ SV463 @ SY3194 @ SY3195 )
| ~ ( c_in @ ( c_Pair @ SY3196 @ SV463 @ SY3195 @ SY3195 ) @ SY3197 @ ( tc_prod @ SY3195 @ SY3195 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3194 @ SY3197 @ SY3195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2130,plain,
! [SV464: $i] :
( ( ! [SY3198: $i,SY3199: $i,SY3200: $i,SY3201: $i] :
( ( c_in @ SV464 @ SY3198 @ SY3199 )
| ~ ( c_in @ ( c_Pair @ SV464 @ SY3200 @ SY3199 @ SY3199 ) @ SY3201 @ ( tc_prod @ SY3199 @ SY3199 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3198 @ SY3201 @ SY3199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2131,plain,
! [SV465: $i] :
( ( ! [SY3202: $i,SY3203: $i,SY3204: $i,SY3205: $i] :
( ( c_in @ SV465 @ ( c_Relation_ORange @ SY3202 @ SY3203 @ SY3204 ) @ SY3204 )
| ~ ( c_in @ ( c_Pair @ SY3205 @ SV465 @ SY3203 @ SY3204 ) @ SY3202 @ ( tc_prod @ SY3203 @ SY3204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2132,plain,
! [SV466: $i] :
( ( ! [SY3206: $i,SY3207: $i,SY3208: $i,SY3209: $i] :
( ( c_in @ SV466 @ ( c_Relation_ORange @ SY3206 @ SY3207 @ SY3208 ) @ SY3208 )
| ~ ( c_in @ ( c_Pair @ SY3209 @ SV466 @ SY3207 @ SY3208 ) @ SY3206 @ ( tc_prod @ SY3207 @ SY3208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2133,plain,
! [SV467: $i] :
( ( ! [SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i] :
( ( c_in @ SV467 @ ( c_Relation_ODomain @ SY3210 @ SY3211 @ SY3212 ) @ SY3211 )
| ~ ( c_in @ ( c_Pair @ SV467 @ SY3213 @ SY3211 @ SY3212 ) @ SY3210 @ ( tc_prod @ SY3211 @ SY3212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2134,plain,
! [SV468: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i,SY3217: $i] :
( ( c_in @ SV468 @ ( c_Relation_ODomain @ SY3214 @ SY3215 @ SY3216 ) @ SY3215 )
| ~ ( c_in @ ( c_Pair @ SV468 @ SY3217 @ SY3215 @ SY3216 ) @ SY3214 @ ( tc_prod @ SY3215 @ SY3216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2135,plain,
! [SV469: $i] :
( ( ! [SY3218: $i,SY3219: $i,SY3220: $i,SY3221: $i,SY3222: $i] :
( ( c_in @ SV469 @ ( hAPP @ SY3218 @ SY3219 ) @ SY3220 )
| ~ ( c_in @ ( c_Pair @ SY3219 @ SV469 @ SY3221 @ SY3220 ) @ ( c_Product__Type_OSigma @ SY3222 @ SY3218 @ SY3221 @ SY3220 ) @ ( tc_prod @ SY3221 @ SY3220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2136,plain,
! [SV470: $i] :
( ( ! [SY3223: $i,SY3224: $i,SY3225: $i,SY3226: $i,SY3227: $i] :
( ( c_in @ SV470 @ SY3223 @ SY3224 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SY3225 @ SY3224 @ SY3226 ) @ ( c_Product__Type_OSigma @ SY3223 @ SY3227 @ SY3224 @ SY3226 ) @ ( tc_prod @ SY3224 @ SY3226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2137,plain,
! [SV471: $i] :
( ( ! [SY3228: $i,SY3229: $i,SY3230: $i,SY3231: $i] :
( ( c_in @ ( c_Pair @ SV471 @ SY3228 @ SY3229 @ SY3229 ) @ SY3230 @ ( tc_prod @ SY3229 @ SY3229 ) )
| ( c_in @ ( c_Pair @ SY3228 @ SV471 @ SY3229 @ SY3229 ) @ SY3230 @ ( tc_prod @ SY3229 @ SY3229 ) )
| ( SY3228 = SV471 )
| ~ ( c_in @ SV471 @ SY3231 @ SY3229 )
| ~ ( c_in @ SY3228 @ SY3231 @ SY3229 )
| ~ ( c_Relation_Ototal__on @ SY3231 @ SY3230 @ SY3229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2138,plain,
! [SV472: $i] :
( ( ! [SY3232: $i,SY3233: $i,SY3234: $i] :
( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SY3232 @ SY3232 ) @ SY3233 @ ( tc_prod @ SY3232 @ SY3232 ) )
| ~ ( c_in @ SV472 @ SY3234 @ SY3232 )
| ~ ( c_Relation_Orefl__on @ SY3234 @ SY3233 @ SY3232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2139,plain,
! [SV473: $i] :
( ( ! [SY3235: $i,SY3236: $i,SY3237: $i,SY3238: $i] :
( ( c_in @ SV473 @ SY3235 @ SY3236 )
| ~ ( c_in @ ( c_Pair @ SY3237 @ SV473 @ SY3236 @ SY3236 ) @ SY3238 @ ( tc_prod @ SY3236 @ SY3236 ) )
| ~ ( c_Relation_Orefl__on @ SY3235 @ SY3238 @ SY3236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2140,plain,
! [SV474: $i] :
( ( ! [SY3239: $i,SY3240: $i,SY3241: $i,SY3242: $i] :
( ( c_in @ SV474 @ SY3239 @ SY3240 )
| ~ ( c_in @ ( c_Pair @ SV474 @ SY3241 @ SY3240 @ SY3240 ) @ SY3242 @ ( tc_prod @ SY3240 @ SY3240 ) )
| ~ ( c_Relation_Orefl__on @ SY3239 @ SY3242 @ SY3240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2141,plain,
! [SV475: $i] :
( ( ! [SY3243: $i,SY3244: $i,SY3245: $i] :
( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SY3243 @ SY3243 ) @ SY3244 @ ( tc_prod @ SY3243 @ SY3243 ) )
| ~ ( c_in @ SV475 @ SY3245 @ SY3243 )
| ~ ( c_Relation_Orefl__on @ SY3245 @ SY3244 @ SY3243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2142,plain,
! [SV476: $i] :
( ( ! [SY3246: $i,SY3247: $i,SY3248: $i] :
( ~ ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3246 @ SY3247 @ SY3248 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3246 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3247 = SY3248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2143,plain,
! [SV477: $i] :
( ( ! [SY3249: $i,SY3250: $i,SY3251: $i] :
( ~ ( c_in @ ( c_Pair @ SV477 @ SY3249 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3250 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV477 = SY3251 )
| ( SV477 = SY3251 )
| ~ ( c_in @ SY3250 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3249 = SY3251 )
| ( c_in @ ( c_Pair @ SV477 @ SY3251 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3250 @ SY3249 @ SY3251 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2144,plain,
! [SV478: $i] :
( ( ! [SY3252: $i,SY3253: $i,SY3254: $i] :
( ( SV478 = SY3252 )
| ( SV478 = SY3253 )
| ~ ( c_in @ SY3254 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SY3252 )
| ( c_in @ ( c_Pair @ SV478 @ SY3253 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3254 @ SV478 @ SY3252 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SY3253 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3254 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2145,plain,
! [SV479: $i] :
( ( ! [SY3255: $i,SY3256: $i,SY3257: $i,SY3258: $i] :
( ( c_in @ ( c_Pair @ SV479 @ SY3255 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3256 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3255 = SY3257 )
| ( SV479 = SY3257 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SY3255 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3256 @ SY3258 @ SY3257 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3256 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3258 = SY3257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2146,plain,
! [SV480: $i] :
( ( ! [SY3259: $i,SY3260: $i,SY3261: $i] :
( ( SV480 = SY3259 )
| ~ ( c_in @ ( c_Pair @ SV480 @ SY3259 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3260 @ SY3261 @ SY3259 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3260 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3261 = SY3259 )
| ( c_in @ ( c_Pair @ SV480 @ SY3261 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3260 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SY3261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2147,plain,
! [SV481: $i] :
( ( ! [SY3262: $i,SY3263: $i,SY3264: $i] :
( ~ ( c_in @ ( c_Pair @ SV481 @ SY3262 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3263 @ SY3264 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3263 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3264 = SV481 )
| ( c_in @ ( c_Pair @ SY3264 @ SY3262 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3263 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2148,plain,
! [SV482: $i] :
( ( ! [SY3265: $i,SY3266: $i,SY3267: $i] :
( ~ ( c_in @ ( c_Pair @ SV482 @ SY3265 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3266 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3267 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3266 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3267 = SY3265 )
| ~ ( c_in @ SY3266 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3267 = SV482 )
| ( c_in @ ( c_Pair @ SY3267 @ SY3265 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3266 @ SY3267 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2149,plain,
! [SV483: $i] :
( ( ! [SY3268: $i,SY3269: $i,SY3270: $i] :
( ~ ( c_in @ ( c_Pair @ SV483 @ SY3268 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3269 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV483 = SY3268 )
| ~ ( c_in @ SY3269 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3270 = SY3268 )
| ( c_in @ ( c_Pair @ SV483 @ SY3268 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3269 @ SY3270 @ SY3268 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SY3268 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3269 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2150,plain,
! [SV484: $i] :
( ( ! [SY3271: $i,SY3272: $i,SY3273: $i,SY3274: $i] :
( ( c_in @ ( c_Pair @ SV484 @ SY3271 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3272 @ SY3273 @ SY3274 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV484 @ SY3271 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3272 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SY3273 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SY3274 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3272 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SY3271 )
| ~ ( c_in @ SY3272 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3273 = SY3274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2151,plain,
! [SV485: $i] :
( ( ! [SY3275: $i,SY3276: $i,SY3277: $i,SY3278: $i] :
( ( c_in @ ( c_Pair @ SV485 @ SY3275 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3276 @ SY3277 @ SY3278 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV485 @ SY3275 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3276 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3278 @ SY3275 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3276 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3275 = SY3277 )
| ( SV485 = SY3275 )
| ~ ( c_in @ SY3276 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3277 = SY3278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2152,plain,
! [SV486: $i] :
( ( ! [SY3279: $i,SY3280: $i] :
( ( SV486 = SY3279 )
| ( SY3279 = SV486 )
| ~ ( c_in @ SY3280 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3279 = SV486 )
| ( c_in @ ( c_Pair @ SY3279 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3280 @ SY3279 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2153,plain,
! [SV487: $i] :
( ( ! [SY3281: $i,SY3282: $i,SY3283: $i,SY3284: $i] :
( ( c_in @ ( c_Pair @ SV487 @ SY3281 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3282 @ SY3283 @ SY3284 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SY3281 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3282 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SY3283 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3282 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3283 @ SY3281 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3282 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SY3281 )
| ~ ( c_in @ SY3282 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3283 = SY3284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2154,plain,
! [SV488: $i] :
( ( ! [SY3285: $i,SY3286: $i] :
( ~ ( c_in @ ( c_Pair @ SV488 @ SY3285 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3286 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV488 = SY3285 )
| ~ ( c_in @ SY3286 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SY3285 )
| ( c_in @ ( c_Pair @ SV488 @ SY3285 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3286 @ SV488 @ SY3285 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2155,plain,
! [SV489: $i] :
( ( ! [SY3287: $i,SY3288: $i,SY3289: $i] :
( ~ ( c_in @ ( c_Pair @ SV489 @ SY3287 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3288 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3289 = SY3287 )
| ~ ( c_in @ SY3288 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SY3289 )
| ( c_in @ ( c_Pair @ SY3289 @ SY3287 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3288 @ SV489 @ SY3289 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2156,plain,
! [SV490: $i] :
( ( ! [SY3290: $i,SY3291: $i,SY3292: $i,SY3293: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SY3290 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3291 @ SY3292 @ SY3293 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SY3290 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3291 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3290 = SY3293 )
| ( SV490 = SY3293 )
| ( SV490 = SY3290 )
| ~ ( c_in @ SY3291 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3292 = SY3293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2157,plain,
! [SV491: $i] :
( ( ! [SY3294: $i,SY3295: $i,SY3296: $i] :
( ~ ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3294 @ SY3295 @ SY3296 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3294 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3295 = SY3296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2158,plain,
! [SV492: $i] :
( ( ! [SY3297: $i,SY3298: $i,SY3299: $i] :
( ~ ( c_in @ ( c_Pair @ SV492 @ SY3297 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3298 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3297 = SY3299 )
| ( SY3299 = SY3297 )
| ~ ( c_in @ SY3298 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3299 = SV492 )
| ( c_in @ ( c_Pair @ SY3299 @ SY3297 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3298 @ SY3299 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2159,plain,
! [SV493: $i] :
( ( ! [SY3300: $i,SY3301: $i,SY3302: $i] :
( ( SV493 = SY3300 )
| ( SY3301 = SV493 )
| ~ ( c_in @ SY3302 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3300 = SV493 )
| ( c_in @ ( c_Pair @ SY3301 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3302 @ SY3300 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3301 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3302 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2160,plain,
! [SV494: $i] :
( ( ! [SY3303: $i,SY3304: $i,SY3305: $i,SY3306: $i] :
( ( c_in @ ( c_Pair @ SV494 @ SY3303 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3304 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV494 = SY3305 )
| ( SY3303 = SY3305 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SY3303 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3304 @ SY3305 @ SY3306 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3304 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3305 = SY3306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2161,plain,
! [SV495: $i] :
( ( ! [SY3307: $i,SY3308: $i,SY3309: $i] :
( ( SV495 = SY3307 )
| ~ ( c_in @ ( c_Pair @ SY3307 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3308 @ SY3307 @ SY3309 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3308 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3307 = SY3309 )
| ( c_in @ ( c_Pair @ SY3309 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3308 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SY3309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2162,plain,
! [SV496: $i] :
( ( ! [SY3310: $i,SY3311: $i,SY3312: $i] :
( ~ ( c_in @ ( c_Pair @ SV496 @ SY3310 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3311 @ SY3310 @ SY3312 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3311 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3310 = SY3312 )
| ( c_in @ ( c_Pair @ SV496 @ SY3312 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3311 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2163,plain,
! [SV497: $i] :
( ( ! [SY3313: $i,SY3314: $i,SY3315: $i] :
( ~ ( c_in @ ( c_Pair @ SV497 @ SY3313 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3314 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3313 @ SY3315 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3314 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SY3315 )
| ~ ( c_in @ SY3314 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3313 = SY3315 )
| ( c_in @ ( c_Pair @ SV497 @ SY3315 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3314 @ SY3313 @ SY3315 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2164,plain,
! [SV498: $i] :
( ( ! [SY3316: $i,SY3317: $i,SY3318: $i] :
( ~ ( c_in @ ( c_Pair @ SV498 @ SY3316 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3317 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV498 = SY3316 )
| ~ ( c_in @ SY3317 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SY3318 )
| ( c_in @ ( c_Pair @ SV498 @ SY3316 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3317 @ SV498 @ SY3318 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SY3316 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3317 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2165,plain,
! [SV499: $i] :
( ( ! [SY3319: $i,SY3320: $i,SY3321: $i,SY3322: $i] :
( ( c_in @ ( c_Pair @ SV499 @ SY3319 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3320 @ SY3321 @ SY3322 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV499 @ SY3319 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3320 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3319 = SY3322 )
| ~ ( c_in @ ( c_Pair @ SY3321 @ SY3319 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3320 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SY3319 )
| ~ ( c_in @ SY3320 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3321 = SY3322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2166,plain,
! [SV500: $i] :
( ( ! [SY3323: $i,SY3324: $i,SY3325: $i,SY3326: $i] :
( ( c_in @ ( c_Pair @ SV500 @ SY3323 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3324 @ SY3325 @ SY3326 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SY3323 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3324 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SY3325 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3324 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SY3326 )
| ( SV500 = SY3323 )
| ~ ( c_in @ SY3324 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3325 = SY3326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2167,plain,
! [SV501: $i] :
( ( ! [SY3327: $i,SY3328: $i] :
( ( SV501 = SY3327 )
| ( SV501 = SY3327 )
| ~ ( c_in @ SY3328 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV501 = SY3327 )
| ( c_in @ ( c_Pair @ SV501 @ SY3327 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY3328 @ SV501 @ SY3327 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2168,plain,
! [SV502: $i] :
( ( ! [SY3329: $i,SY3330: $i,SY3331: $i,SY3332: $i] :
( ( c_in @ ( c_Pair @ SV502 @ SY3329 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3330 @ SY3331 @ SY3332 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SY3329 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3330 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3332 @ SY3329 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3330 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SY3332 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3330 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SY3329 )
| ~ ( c_in @ SY3330 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3331 = SY3332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2169,plain,
! [SV503: $i] :
( ( ! [SY3333: $i,SY3334: $i] :
( ~ ( c_in @ ( c_Pair @ SV503 @ SY3333 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3334 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV503 = SY3333 )
| ~ ( c_in @ SY3334 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SY3333 )
| ( c_in @ ( c_Pair @ SV503 @ SY3333 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3334 @ SV503 @ SY3333 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2170,plain,
! [SV504: $i] :
( ( ! [SY3335: $i,SY3336: $i,SY3337: $i] :
( ~ ( c_in @ ( c_Pair @ SV504 @ SY3335 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3336 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV504 = SY3337 )
| ~ ( c_in @ SY3336 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3337 = SY3335 )
| ( c_in @ ( c_Pair @ SV504 @ SY3337 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3336 @ SY3337 @ SY3335 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2171,plain,
! [SV505: $i] :
( ( ! [SY3338: $i,SY3339: $i,SY3340: $i,SY3341: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SY3338 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY3339 @ SY3340 @ SY3341 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV505 @ SY3338 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3339 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SY3340 )
| ( SY3338 = SY3340 )
| ( SV505 = SY3338 )
| ~ ( c_in @ SY3339 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY3340 = SY3341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2172,plain,
! [SV506: $i] :
( ( ! [SY3342: $i,SY3343: $i] :
( ~ ( c_in @ ( c_Pair @ SV506 @ SY3342 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3343 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3342 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3343 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV506 = SY3342 )
| ~ ( c_in @ SY3343 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2173,plain,
! [SV507: $i] :
( ( ! [SY3344: $i,SY3345: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SY3344 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3345 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SY3344 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3345 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3344 = SV507 )
| ~ ( c_in @ SY3345 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2174,plain,
! [SV508: $i] :
( ( ! [SY3346: $i,SY3347: $i] :
( ( c_in @ SV508 @ SY3346 @ SY3347 )
| ~ ( hBOOL @ ( hAPP @ SY3346 @ SV508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2175,plain,
! [SV509: $i] :
( ( ! [SY3348: $i,SY3349: $i] :
( ( hBOOL @ ( hAPP @ SV509 @ SY3348 ) )
| ~ ( c_in @ SY3348 @ SV509 @ SY3349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2176,plain,
! [SV510: $i] :
( ( v_thesis____
| ~ ( c_in @ SV510 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV510 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2177,plain,
! [SV511: $i] :
( ( ! [SY3350: $i,SY3351: $i] :
( ~ ( c_in @ ( c_Pair @ SV511 @ SY3350 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3351 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY3350 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3351 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY3351 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2178,plain,
! [SV512: $i] :
( ( ! [SY3352: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SY3352 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SY3352 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2179,plain,
! [SV513: $i] :
( ( ! [SY3353: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV513 @ SY3353 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2180,plain,
! [SV514: $i] :
( ( ! [SY3354: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV514 @ SY3354 ) )
| ~ ( class_Lattices_Olattice @ SY3354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2181,plain,
! [SV515: $i] :
( ( ! [SY3355: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV515 @ SY3355 ) )
| ~ ( class_Lattices_Olattice @ SY3355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2182,plain,
! [SV516: $i] :
( ( ! [SY3356: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV516 @ SY3356 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY3356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2183,plain,
! [SV517: $i] :
( ( ! [SY3357: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SY3357 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SY3357 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2184,plain,
! [SV518: $i] :
( ( ! [SY3358: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV518 @ SY3358 ) )
| ~ ( class_Orderings_Opreorder @ SY3358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2185,plain,
! [SV519: $i] :
( ( ! [SY3359: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV519 @ SY3359 ) )
| ~ ( class_Lattices_Olattice @ SY3359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2186,plain,
! [SV520: $i] :
( ( ! [SY3360: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV520 @ SY3360 ) )
| ~ ( class_Orderings_Oorder @ SY3360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2187,plain,
! [SV521: $i] :
( ( ! [SY3361: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV521 @ SY3361 ) )
| ~ ( class_HOL_Oord @ SY3361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2188,plain,
! [SV522: $i] :
( ( ! [SY3362: $i] : ( c_fequal @ SV522 @ SV522 @ SY3362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2189,plain,
! [SV523: $i] :
( ( ! [SY3363: $i,SY3364: $i] :
( ( SV523 = SY3363 )
| ~ ( c_fequal @ SV523 @ SY3363 @ SY3364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2190,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(2191,plain,
! [SV524: $i] :
( ( ! [SY3365: $i,SY3366: $i,SY3367: $i,SY3368: $i,SY3369: $i,SY3370: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SY3365 @ SY3366 @ SY3367 @ SY3368 )
!= ( c_Recdef_Ocut @ SY3369 @ SY3365 @ SY3366 @ SY3367 @ SY3368 ) )
| ( ( hAPP @ SV524 @ SY3370 )
= ( hAPP @ SY3369 @ SY3370 ) )
| ~ ( c_in @ ( c_Pair @ SY3370 @ SY3366 @ SY3367 @ SY3367 ) @ SY3365 @ ( tc_prod @ SY3367 @ SY3367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2192,plain,
( ( v_a____ = v_b____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(2193,plain,
! [SV525: $i] :
( ( ! [SY3371: $i,SY3372: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV525 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3371 @ SY3372 @ SV525 )
!= SY3372 )
| ( c_lessequals @ SY3371 @ SY3372 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2194,plain,
! [SV526: $i] :
( ( ! [SY3373: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV526 @ SY3373 @ SY3373 ) @ SV526 @ SY3373 @ SY3373 @ SY3373 )
!= SV526 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV526 @ SY3373 @ SY3373 ) @ SV526 @ SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2195,plain,
! [SV527: $i] :
( ( ! [SY3374: $i,SY3375: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV527 @ SY3374 @ ( tc_fun @ SY3375 @ tc_bool ) )
!= SY3374 )
| ( c_lessequals @ SV527 @ SY3374 @ ( tc_fun @ SY3375 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2196,plain,
! [SV528: $i] :
( ( ! [SY3376: $i,SY3377: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV528 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3376 @ SY3377 @ SV528 )
!= SY3376 )
| ( c_lessequals @ SY3376 @ SY3377 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2197,plain,
! [SV529: $i] :
( ( ! [SY3378: $i,SY3379: $i,SY3380: $i,SY3381: $i,SY3382: $i] :
( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SY3378 @ ( tc_fun @ SY3379 @ tc_bool ) @ SY3380 ) @ SY3380 @ SY3379 )
!= ( c_Product__Type_OSigma @ SY3381 @ ( c_COMBK @ SY3378 @ ( tc_fun @ SY3379 @ tc_bool ) @ SY3380 ) @ SY3380 @ SY3379 ) )
| ~ ( c_in @ SY3382 @ SY3378 @ SY3379 )
| ( SV529 = SY3381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2198,plain,
! [SV530: $i] :
( ( ! [SY3383: $i,SY3384: $i,SY3385: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SY3383 @ ( tc_fun @ SY3384 @ tc_bool ) ) @ SY3385 @ ( tc_fun @ SY3384 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3383 @ SY3385 @ ( tc_fun @ SY3384 @ tc_bool ) ) @ ( tc_fun @ SY3384 @ tc_bool ) ) )
| ( c_lessequals @ SY3385 @ SV530 @ ( tc_fun @ SY3384 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2199,plain,
! [SV531: $i] :
( ( ! [SY3386: $i,SY3387: $i,SY3388: $i,SY3389: $i,SY3390: $i] :
( ( ( c_Pair @ SV531 @ SY3386 @ SY3387 @ SY3388 )
!= ( c_Pair @ SY3389 @ SY3390 @ SY3387 @ SY3388 ) )
| ( SY3386 = SY3390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2200,plain,
! [SV532: $i] :
( ( ! [SY3391: $i] :
( ( ( c_Relation_Oconverse @ SV532 @ SY3391 @ SY3391 )
!= SV532 )
| ( c_Relation_Osym @ SV532 @ SY3391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2201,plain,
! [SV533: $i] :
( ( ! [SY3392: $i,SY3393: $i,SY3394: $i] :
( ( ( c_Set_Oinsert @ SV533 @ SY3392 @ SY3393 )
!= ( c_Set_Oinsert @ SV533 @ SY3394 @ SY3393 ) )
| ( c_in @ SV533 @ SY3394 @ SY3393 )
| ( c_in @ SV533 @ SY3392 @ SY3393 )
| ( SY3392 = SY3394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2202,plain,
! [SV534: $i] :
( ( ! [SY3395: $i,SY3396: $i,SY3397: $i,SY3398: $i,SY3399: $i] :
( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SY3395 @ SY3396 @ SY3397 @ SY3398 @ SY3399 ) )
!= ( hAPP @ SY3395 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SY3395 @ SY3396 @ SY3397 @ SY3398 @ SY3399 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SY3396 @ SY3397 @ SY3398 @ SY3399 )
= ( c_Recdef_Ocut @ SY3395 @ SY3396 @ SY3397 @ SY3398 @ SY3399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2203,plain,
! [SV535: $i] :
( ( ! [SY3400: $i,SY3401: $i,SY3402: $i,SY3403: $i,SY3404: $i] :
( ( ( c_Pair @ SV535 @ SY3400 @ SY3401 @ SY3402 )
!= ( c_Pair @ SY3403 @ SY3404 @ SY3401 @ SY3402 ) )
| ( SV535 = SY3403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2204,plain,
! [SV536: $i,SV1: $i] :
( ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ SV1 @ SV536 ) @ SV536 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2205,plain,
! [SV537: $i,SV2: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV2 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV537 @ SV537 @ SV2 )
= SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2206,plain,
! [SV538: $i,SV3: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV3 @ SV3 @ ( tc_fun @ SV538 @ tc_bool ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2207,plain,
! [SV539: $i,SV4: $i] :
( ( ! [SY3405: $i,SY3406: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV4 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV539 @ SY3405 @ SV4 ) @ SY3406 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV539 @ SY3406 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3405 @ SY3406 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2208,plain,
! [SV540: $i,SV5: $i] :
( ( ! [SY3407: $i,SY3408: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV5 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3407 @ SY3408 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SY3407 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SY3408 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2209,plain,
! [SV541: $i,SV6: $i] :
( ( ! [SY3409: $i,SY3410: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV541 @ SY3409 @ ( tc_fun @ SY3410 @ tc_bool ) ) @ ( tc_fun @ SY3410 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SV541 @ ( tc_fun @ SY3410 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SY3409 @ ( tc_fun @ SY3410 @ tc_bool ) ) @ ( tc_fun @ SY3410 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2210,plain,
! [SV542: $i,SV7: $i] :
( ( ! [SY3411: $i,SY3412: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV542 @ ( tc_fun @ SY3411 @ tc_bool ) ) @ SY3412 @ ( tc_fun @ SY3411 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV7 @ SY3412 @ ( tc_fun @ SY3411 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV542 @ SY3412 @ ( tc_fun @ SY3411 @ tc_bool ) ) @ ( tc_fun @ SY3411 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2211,plain,
! [SV543: $i,SV8: $i] :
( ( ! [SY3413: $i,SY3414: $i,SY3415: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV8 @ SV543 @ ( tc_fun @ SY3413 @ tc_bool ) ) @ SY3414 @ SY3413 @ SY3415 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV8 @ SY3414 @ SY3413 @ SY3415 ) @ ( c_Product__Type_OSigma @ SV543 @ SY3414 @ SY3413 @ SY3415 ) @ ( tc_fun @ ( tc_prod @ SY3413 @ SY3415 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2212,plain,
! [SV544: $i,SV9: $i] :
( ( ! [SY3416: $i,SY3417: $i,SY3418: $i,SY3419: $i] :
( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SY3416 @ SY3417 )
| ~ ( c_in @ SV544 @ SY3418 @ SY3419 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SY3418 @ SY3419 @ SY3417 ) @ SY3416 @ ( tc_fun @ SY3417 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2213,plain,
! [SV545: $i,SV10: $i] :
( ( ! [SY3420: $i,SY3421: $i,SY3422: $i] :
( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
| ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SY3420 @ SY3421 @ SY3422 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3421 @ SY3422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2214,plain,
! [SV546: $i,SV11: $i] :
( ( ! [SY3423: $i,SY3424: $i] :
( ( c_lessequals @ SV11 @ SV546 @ ( tc_fun @ SY3423 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY3424 @ SV11 @ SY3423 ) @ SV546 @ ( tc_fun @ SY3423 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2215,plain,
! [SV547: $i,SV12: $i] :
( ( ! [SY3425: $i,SY3426: $i] :
( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SV547 @ SY3425 @ SY3426 ) @ ( tc_fun @ SY3426 @ tc_bool ) )
| ~ ( c_lessequals @ SV12 @ SY3425 @ ( tc_fun @ SY3426 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2216,plain,
! [SV548: $i,SV13: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV13 @ ( c_Relation_OId @ SV548 ) @ ( tc_fun @ ( tc_prod @ SV548 @ SV548 ) @ tc_bool ) ) @ SV548 )
= ( c_Transitive__Closure_Ortrancl @ SV13 @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2217,plain,
! [SV549: $i,SV14: $i] :
( ( ! [SY3427: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV14 @ SV549 ) @ ( c_Transitive__Closure_Ortrancl @ SY3427 @ SV549 ) @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV14 @ SY3427 @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) ) @ SV549 ) @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2218,plain,
! [SV550: $i,SV15: $i] :
( ( ! [SY3428: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV15 )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SV550 @ SY3428 @ SV15 ) @ SV15 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV550 @ ( c_Complete__Lattice_OInf__class_OInf @ SY3428 @ SV15 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2219,plain,
! [SV551: $i,SV16: $i] :
( ( ! [SY3429: $i,SY3430: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV16 @ SV551 @ SY3429 ) @ SY3430 @ ( tc_fun @ SY3429 @ tc_bool ) )
= ( c_Set_Oinsert @ SV16 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV551 @ SY3430 @ ( tc_fun @ SY3429 @ tc_bool ) ) @ SY3429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2220,plain,
! [SV552: $i,SV17: $i] :
( ( ! [SY3431: $i,SY3432: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ ( c_Set_Oinsert @ SV552 @ SY3431 @ SY3432 ) @ ( tc_fun @ SY3432 @ tc_bool ) )
= ( c_Set_Oinsert @ SV552 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ SY3431 @ ( tc_fun @ SY3432 @ tc_bool ) ) @ SY3432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2221,plain,
! [SV553: $i,SV18: $i] :
( ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ SV18 @ SV553 ) @ SV553 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2222,plain,
! [SV554: $i,SV19: $i] :
( ( ( c_Relation_Otrans @ SV19 @ SV554 )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV19 @ SV554 @ SV554 ) @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2223,plain,
! [SV555: $i,SV20: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV20 @ SV555 @ SV555 ) @ SV555 )
| ~ ( c_Relation_Otrans @ SV20 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2224,plain,
! [SV556: $i,SV21: $i] :
( ( ! [SY3433: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV21 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV556 @ SY3433 @ SV21 ) @ SV21 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV556 @ ( c_Complete__Lattice_OSup__class_OSup @ SY3433 @ SV21 ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2225,plain,
! [SV557: $i,SV22: $i] :
( ( ! [SY3434: $i,SY3435: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV22 @ SV557 @ SY3434 ) @ ( c_Set_Oinsert @ SV22 @ SY3435 @ SY3434 ) @ ( tc_fun @ SY3434 @ tc_bool ) )
= ( c_Set_Oinsert @ SV22 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV557 @ SY3435 @ ( tc_fun @ SY3434 @ tc_bool ) ) @ SY3434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2226,plain,
! [SV558: $i,SV23: $i] :
( ( ! [SY3436: $i] :
( ( c_Set_Oinsert @ SV23 @ ( c_Set_Oinsert @ SV23 @ SV558 @ SY3436 ) @ SY3436 )
= ( c_Set_Oinsert @ SV23 @ SV558 @ SY3436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2227,plain,
! [SV559: $i,SV24: $i] :
( ( ! [SY3437: $i,SY3438: $i] :
( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
| ( SY3437 = SV559 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3437 @ SV24 @ SY3438 ) @ SV559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2228,plain,
! [SV560: $i,SV25: $i] :
( ( ! [SY3439: $i,SY3440: $i,SY3441: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV25 @ SV560 @ SY3439 @ SY3440 ) @ SY3441 @ ( tc_prod @ SY3439 @ SY3440 ) ) @ SY3439 @ SY3440 )
= ( c_Set_Oinsert @ SV25 @ ( c_Relation_ODomain @ SY3441 @ SY3439 @ SY3440 ) @ SY3439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2229,plain,
! [SV561: $i,SV26: $i] :
( ( ! [SY3442: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SY3442 @ SY3442 ) @ tc_bool ) ) @ SY3442 )
| ~ ( c_Relation_Osym @ SV561 @ SY3442 )
| ~ ( c_Relation_Osym @ SV26 @ SY3442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2230,plain,
! [SV562: $i,SV27: $i] :
( ( ! [SY3443: $i,SY3444: $i,SY3445: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 @ SV562 @ ( tc_fun @ ( tc_prod @ SY3443 @ SY3444 ) @ tc_bool ) ) @ SY3445 @ SY3443 @ SY3444 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV27 @ SY3445 @ SY3443 @ SY3444 ) @ ( c_Relation_OImage @ SV562 @ SY3445 @ SY3443 @ SY3444 ) @ ( tc_fun @ SY3444 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2231,plain,
! [SV563: $i,SV28: $i] :
( ( ! [SY3446: $i,SY3447: $i,SY3448: $i] :
( ( c_Relation_OImage @ SV28 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV563 @ SY3446 @ ( tc_fun @ SY3447 @ tc_bool ) ) @ SY3447 @ SY3448 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV28 @ SV563 @ SY3447 @ SY3448 ) @ ( c_Relation_OImage @ SV28 @ SY3446 @ SY3447 @ SY3448 ) @ ( tc_fun @ SY3448 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2232,plain,
! [SV564: $i,SV29: $i] :
( ( ! [SY3449: $i,SY3450: $i] :
( ( c_Set_Oinsert @ SV29 @ ( c_Set_Oinsert @ SV564 @ SY3449 @ SY3450 ) @ SY3450 )
= ( c_Set_Oinsert @ SV564 @ ( c_Set_Oinsert @ SV29 @ SY3449 @ SY3450 ) @ SY3450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2233,plain,
! [SV565: $i,SV30: $i] :
( ( ! [SY3451: $i,SY3452: $i] :
( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV565 @ SY3451 @ ( tc_fun @ ( tc_prod @ SY3452 @ SY3452 ) @ tc_bool ) ) @ SY3452 ) @ ( tc_prod @ SY3452 @ SY3452 ) )
| ~ ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SY3451 @ SY3452 ) @ ( tc_prod @ SY3452 @ SY3452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2234,plain,
! [SV566: $i,SV31: $i] :
( ( ! [SY3453: $i,SY3454: $i] :
( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 @ SY3453 @ ( tc_fun @ ( tc_prod @ SY3454 @ SY3454 ) @ tc_bool ) ) @ SY3454 ) @ ( tc_prod @ SY3454 @ SY3454 ) )
| ~ ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SV566 @ SY3454 ) @ ( tc_prod @ SY3454 @ SY3454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2235,plain,
! [SV567: $i,SV32: $i] :
( ( ! [SY3455: $i,SY3456: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ SY3455 @ ( tc_fun @ SY3456 @ tc_bool ) ) @ ( tc_fun @ SY3456 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SY3455 @ ( tc_fun @ SY3456 @ tc_bool ) ) @ ( tc_fun @ SY3456 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2236,plain,
! [SV568: $i,SV33: $i] :
( ( ! [SY3457: $i,SY3458: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ SV568 @ ( tc_fun @ SY3457 @ tc_bool ) ) @ SY3458 @ ( tc_fun @ SY3457 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV568 @ SY3458 @ ( tc_fun @ SY3457 @ tc_bool ) ) @ ( tc_fun @ SY3457 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2237,plain,
! [SV569: $i,SV34: $i] :
( ( ! [SY3459: $i,SY3460: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV34 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ SY3459 @ SV34 ) @ SY3460 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3459 @ SY3460 @ SV34 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2238,plain,
! [SV570: $i,SV35: $i] :
( ( ! [SY3461: $i,SY3462: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3461 @ SY3462 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3461 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ SY3462 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2239,plain,
! [SV571: $i,SV36: $i] :
( ( ! [SY3463: $i,SY3464: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3463 @ SY3464 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3463 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ SY3464 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2240,plain,
! [SV572: $i,SV37: $i] :
( ( ! [SY3465: $i,SY3466: $i] :
( ~ ( class_Lattices_Olattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ SY3465 @ SV37 ) @ SY3466 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3465 @ SY3466 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2241,plain,
! [SV573: $i,SV38: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV38 @ SV573 ) @ ( c_Relation_OId @ SV573 ) @ ( tc_fun @ ( tc_prod @ SV573 @ SV573 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV38 @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2242,plain,
! [SV574: $i,SV39: $i] :
( ( ! [SY3467: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV39 @ SV574 @ ( tc_fun @ SY3467 @ tc_bool ) )
= SV39 )
| ~ ( c_lessequals @ SV39 @ SV574 @ ( tc_fun @ SY3467 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2243,plain,
! [SV575: $i,SV40: $i] :
( ( ! [SY3468: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV40 @ SV575 @ ( tc_fun @ SY3468 @ tc_bool ) )
= SV575 )
| ~ ( c_lessequals @ SV575 @ SV40 @ ( tc_fun @ SY3468 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2244,plain,
! [SV576: $i,SV41: $i] :
( ( ! [SY3469: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SY3469 @ SV41 )
= SV576 )
| ~ ( c_lessequals @ SV576 @ SY3469 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2245,plain,
! [SV577: $i,SV42: $i] :
( ( ! [SY3470: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV42 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SY3470 @ SV42 )
= SY3470 )
| ~ ( c_lessequals @ SY3470 @ SV577 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2246,plain,
! [SV578: $i,SV43: $i] :
( ( ! [SY3471: $i,SY3472: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SY3471 @ tc_bool ) ) @ SY3472 @ ( tc_fun @ SY3471 @ tc_bool ) )
| ~ ( c_lessequals @ SV578 @ SY3472 @ ( tc_fun @ SY3471 @ tc_bool ) )
| ~ ( c_lessequals @ SV43 @ SY3472 @ ( tc_fun @ SY3471 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2247,plain,
! [SV579: $i,SV44: $i] :
( ( ! [SY3473: $i] : ( c_lessequals @ SV44 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV579 @ SV44 @ ( tc_fun @ SY3473 @ tc_bool ) ) @ ( tc_fun @ SY3473 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2248,plain,
! [SV580: $i,SV45: $i] :
( ( ! [SY3474: $i] : ( c_lessequals @ SV45 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV45 @ SV580 @ ( tc_fun @ SY3474 @ tc_bool ) ) @ ( tc_fun @ SY3474 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2249,plain,
! [SV581: $i,SV46: $i] :
( ( ! [SY3475: $i,SY3476: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SY3475 @ tc_bool ) ) @ SY3476 @ ( tc_fun @ SY3475 @ tc_bool ) )
| ~ ( c_lessequals @ SV581 @ SY3476 @ ( tc_fun @ SY3475 @ tc_bool ) )
| ~ ( c_lessequals @ SV46 @ SY3476 @ ( tc_fun @ SY3475 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2250,plain,
! [SV582: $i,SV47: $i] :
( ( ! [SY3477: $i,SY3478: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV47 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SY3477 @ SV47 ) @ SY3478 @ SV47 )
| ~ ( c_lessequals @ SY3477 @ SY3478 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SY3478 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2251,plain,
! [SV583: $i,SV48: $i] :
( ( ! [SY3479: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV48 )
| ( c_lessequals @ SV583 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV583 @ SY3479 @ SV48 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2252,plain,
! [SV584: $i,SV49: $i] :
( ( ! [SY3480: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV49 )
| ( c_lessequals @ SV584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3480 @ SV584 @ SV49 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2253,plain,
! [SV585: $i,SV50: $i] :
( ( ! [SY3481: $i,SY3482: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV50 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SY3481 @ SV50 ) @ SY3482 @ SV50 )
| ~ ( c_lessequals @ SY3481 @ SY3482 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SY3482 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2254,plain,
! [SV586: $i,SV51: $i] :
( ( ! [SY3483: $i,SY3484: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV51 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SY3483 @ SV51 ) @ SY3484 @ SV51 )
| ~ ( c_lessequals @ SY3483 @ SY3484 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SY3484 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2255,plain,
! [SV587: $i,SV52: $i] :
( ( ! [SY3485: $i] :
( ~ ( class_Lattices_Olattice @ SV52 )
| ( c_lessequals @ SV587 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3485 @ SV587 @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2256,plain,
! [SV588: $i,SV53: $i] :
( ( ! [SY3486: $i] :
( ~ ( class_Lattices_Olattice @ SV53 )
| ( c_lessequals @ SV588 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV588 @ SY3486 @ SV53 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2257,plain,
! [SV589: $i,SV54: $i] :
( ( ! [SY3487: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV54 @ SV589 @ ( tc_fun @ SY3487 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV589 @ SV54 @ ( tc_fun @ SY3487 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2258,plain,
! [SV590: $i,SV55: $i] :
( ( ! [SY3488: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV590 @ SY3488 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3488 @ SV590 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2259,plain,
! [SV591: $i,SV56: $i] :
( ( ! [SY3489: $i] :
( ~ ( class_Lattices_Olattice @ SV56 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV591 @ SY3489 @ SV56 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3489 @ SV591 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2260,plain,
! [SV592: $i,SV57: $i] :
( ( ! [SY3490: $i,SY3491: $i] :
( ~ ( class_Lattices_Olattice @ SV57 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SY3490 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SY3491 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3490 @ SY3491 @ SV57 ) @ SV57 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2261,plain,
! [SV593: $i,SV58: $i] :
( ( ! [SY3492: $i,SY3493: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV593 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV593 @ SY3493 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3493 @ SV58 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( tc_fun @ SY3492 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV58 @ SV593 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SY3493 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3493 @ SV58 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( tc_fun @ SY3492 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2262,plain,
! [SV594: $i,SV59: $i] :
( ( ( c_Relation_OField @ ( c_Relation_Oconverse @ SV59 @ SV594 @ SV594 ) @ SV594 )
= ( c_Relation_OField @ SV59 @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2263,plain,
! [SV595: $i,SV60: $i] :
( ( ! [SY3494: $i,SY3495: $i] :
( ( c_in @ SV60 @ SV595 @ SY3494 )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SY3495 @ SY3494 ) @ SV595 @ ( tc_fun @ SY3494 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2264,plain,
! [SV596: $i,SV61: $i] :
( ( ! [SY3496: $i,SY3497: $i,SY3498: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV596 @ ( tc_fun @ SY3496 @ tc_bool ) ) @ SY3497 @ SY3496 @ SY3498 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV61 @ SY3497 @ SY3496 @ SY3498 ) @ ( c_Product__Type_OSigma @ SV596 @ SY3497 @ SY3496 @ SY3498 ) @ ( tc_fun @ ( tc_prod @ SY3496 @ SY3498 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2265,plain,
! [SV597: $i,SV62: $i] :
( ( ! [SY3499: $i,SY3500: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SV597 @ SY3499 ) @ SY3500 ) )
| ~ ( hBOOL @ ( hAPP @ SV597 @ SY3500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2266,plain,
! [SV598: $i,SV63: $i] :
( ( ! [SY3501: $i,SY3502: $i,SY3503: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SY3501 @ SY3502 @ SY3503 ) @ SY3503 )
= ( c_Set_Oimage @ SV63 @ SY3501 @ SY3502 @ SY3503 ) )
| ~ ( c_in @ SV598 @ SY3501 @ SY3502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2267,plain,
! [SV599: $i,SV64: $i] :
( ( ! [SY3504: $i,SY3505: $i] :
( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SY3504 @ SY3505 ) @ ( tc_fun @ SY3505 @ tc_bool ) )
| ~ ( c_lessequals @ SV64 @ SY3504 @ ( tc_fun @ SY3505 @ tc_bool ) )
| ( c_in @ SV599 @ SV64 @ SY3505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2268,plain,
! [SV600: $i,SV65: $i] :
( ( ! [SY3506: $i,SY3507: $i] :
( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SY3506 @ tc_bool ) )
| ( c_in @ SY3507 @ SV65 @ SY3506 )
| ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SY3507 @ SV600 @ SY3506 ) @ ( tc_fun @ SY3506 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2269,plain,
! [SV601: $i,SV66: $i] :
( ( ! [SY3508: $i,SY3509: $i] :
( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SY3508 @ SY3509 ) @ ( tc_fun @ SY3509 @ tc_bool ) )
| ~ ( c_lessequals @ SV66 @ SY3508 @ ( tc_fun @ SY3509 @ tc_bool ) )
| ( c_in @ SV601 @ SV66 @ SY3509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2270,plain,
! [SV602: $i,SV67: $i] :
( ( ! [SY3510: $i,SY3511: $i] :
( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SY3510 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SY3511 @ SV602 @ SY3510 ) @ ( tc_fun @ SY3510 @ tc_bool ) )
| ( c_in @ SY3511 @ SV67 @ SY3510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2271,plain,
! [SV603: $i,SV68: $i] :
( ( ! [SY3512: $i,SY3513: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SV603 @ ( tc_fun @ ( tc_prod @ SY3512 @ SY3513 ) @ tc_bool ) ) @ SY3512 @ SY3513 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV68 @ SY3512 @ SY3513 ) @ ( c_Relation_Oconverse @ SV603 @ SY3512 @ SY3513 ) @ ( tc_fun @ ( tc_prod @ SY3513 @ SY3512 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2272,plain,
! [SV604: $i,SV69: $i] :
( ( ! [SY3514: $i,SY3515: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Set_Oinsert @ SV604 @ SY3514 @ SY3515 ) @ ( tc_fun @ SY3515 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SY3514 @ ( tc_fun @ SY3515 @ tc_bool ) ) )
| ( c_in @ SV604 @ SV69 @ SY3515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2273,plain,
! [SV605: $i,SV70: $i] :
( ( ! [SY3516: $i,SY3517: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV70 @ SV605 @ SY3516 ) @ SY3517 @ ( tc_fun @ SY3516 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV605 @ SY3517 @ ( tc_fun @ SY3516 @ tc_bool ) ) )
| ( c_in @ SV70 @ SY3517 @ SY3516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2274,plain,
! [SV606: $i,SV71: $i] :
( ( ! [SY3518: $i,SY3519: $i,SY3520: $i,SY3521: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV606 @ ( tc_fun @ ( tc_prod @ SY3518 @ SY3519 ) @ tc_bool ) ) @ SY3520 @ SY3518 @ SY3519 @ SY3521 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SY3520 @ SY3518 @ SY3519 @ SY3521 ) @ ( c_Relation_Orel__comp @ SV606 @ SY3520 @ SY3518 @ SY3519 @ SY3521 ) @ ( tc_fun @ ( tc_prod @ SY3518 @ SY3521 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2275,plain,
! [SV607: $i,SV72: $i] :
( ( ! [SY3522: $i,SY3523: $i,SY3524: $i,SY3525: $i] :
( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SY3522 @ ( tc_fun @ ( tc_prod @ SY3523 @ SY3524 ) @ tc_bool ) ) @ SY3525 @ SY3523 @ SY3524 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SV607 @ SY3525 @ SY3523 @ SY3524 ) @ ( c_Relation_Orel__comp @ SV72 @ SY3522 @ SY3525 @ SY3523 @ SY3524 ) @ ( tc_fun @ ( tc_prod @ SY3525 @ SY3524 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2276,plain,
! [SV608: $i,SV73: $i] :
( ( c_Relation_Otrans @ ( c_Relation_OId__on @ SV73 @ SV608 ) @ SV608 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2277,plain,
! [SV609: $i,SV74: $i] :
( ( ! [SY3526: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV74 @ SV609 @ ( tc_fun @ ( tc_prod @ SY3526 @ SY3526 ) @ tc_bool ) ) @ SY3526 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV74 @ SY3526 ) @ ( c_Relation_OField @ SV609 @ SY3526 ) @ ( tc_fun @ SY3526 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2278,plain,
! [SV610: $i,SV75: $i] :
( ( ! [SY3527: $i,SY3528: $i] :
( ( c_lessequals @ SV75 @ SV610 @ ( tc_fun @ SY3527 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3528 @ SV610 @ ( tc_fun @ SY3527 @ tc_bool ) ) @ ( tc_fun @ SY3527 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2279,plain,
! [SV611: $i,SV76: $i] :
( ( ! [SY3529: $i,SY3530: $i] :
( ( c_lessequals @ SV76 @ SV611 @ ( tc_fun @ SY3529 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV611 @ SY3530 @ ( tc_fun @ SY3529 @ tc_bool ) ) @ ( tc_fun @ SY3529 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2280,plain,
! [SV612: $i,SV77: $i] :
( ( ! [SY3531: $i,SY3532: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ( c_lessequals @ SV612 @ SY3531 @ SV77 )
| ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3531 @ SY3532 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2281,plain,
! [SV613: $i,SV78: $i] :
( ( ! [SY3533: $i,SY3534: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ( c_lessequals @ SV613 @ SY3533 @ SV78 )
| ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3534 @ SY3533 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2282,plain,
! [SV614: $i,SV79: $i] :
( ( ! [SY3535: $i,SY3536: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV79 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SY3535 @ SV79 ) @ SY3536 @ SV79 )
| ~ ( c_lessequals @ SV614 @ SY3536 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2283,plain,
! [SV615: $i,SV80: $i] :
( ( ! [SY3537: $i,SY3538: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV80 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SY3537 @ SV80 ) @ SY3538 @ SV80 )
| ~ ( c_lessequals @ SY3537 @ SY3538 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2284,plain,
! [SV616: $i,SV81: $i] :
( ( ! [SY3539: $i,SY3540: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV81 )
| ( c_lessequals @ SV616 @ SY3539 @ SV81 )
| ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3539 @ SY3540 @ SV81 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2285,plain,
! [SV617: $i,SV82: $i] :
( ( ! [SY3541: $i,SY3542: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( c_lessequals @ SV617 @ SY3541 @ SV82 )
| ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3542 @ SY3541 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2286,plain,
! [SV618: $i,SV83: $i] :
( ( ! [SY3543: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV83 @ SV618 @ ( tc_fun @ SY3543 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV618 @ SV83 @ ( tc_fun @ SY3543 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2287,plain,
! [SV619: $i,SV84: $i] :
( ( ! [SY3544: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV84 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV619 @ SY3544 @ SV84 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3544 @ SV619 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2288,plain,
! [SV620: $i,SV85: $i] :
( ( ! [SY3545: $i] :
( ~ ( class_Lattices_Olattice @ SV85 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SY3545 @ SV85 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3545 @ SV620 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2289,plain,
! [SV621: $i,SV86: $i] :
( ( ! [SY3546: $i,SY3547: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV86 @ SV621 @ ( tc_fun @ ( tc_prod @ SY3546 @ SY3547 ) @ tc_bool ) ) @ SY3546 @ SY3547 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV86 @ SY3546 @ SY3547 ) @ ( c_Relation_ODomain @ SV621 @ SY3546 @ SY3547 ) @ ( tc_fun @ SY3546 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2290,plain,
! [SV622: $i,SV87: $i] :
( ( ! [SY3548: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SV622 @ ( tc_fun @ SY3548 @ tc_bool ) ) @ ( tc_fun @ SY3548 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SV622 @ ( tc_fun @ SY3548 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2291,plain,
! [SV623: $i,SV88: $i] :
( ( ! [SY3549: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SY3549 @ SV88 ) @ SV88 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SY3549 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2292,plain,
! [SV624: $i,SV89: $i] :
( ( ! [SY3550: $i] :
( ~ ( class_Lattices_Olattice @ SV89 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SY3550 @ SV89 ) @ SV89 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SY3550 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2293,plain,
! [SV625: $i,SV90: $i] :
( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV90 )
| ( c_Finite__Set_Ofinite @ SV625 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2294,plain,
! [SV626: $i,SV91: $i] :
( ( ! [SY3551: $i,SY3552: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV91 @ SV626 @ ( tc_fun @ ( tc_prod @ SY3551 @ SY3552 ) @ tc_bool ) ) @ SY3551 @ SY3552 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV91 @ SY3551 @ SY3552 ) @ ( c_Relation_ORange @ SV626 @ SY3551 @ SY3552 ) @ ( tc_fun @ SY3552 @ tc_bool ) ) @ ( tc_fun @ SY3552 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2295,plain,
! [SV627: $i,SV92: $i] :
( ( ! [SY3553: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV92 @ SV627 ) @ ( c_Transitive__Closure_Ortrancl @ SY3553 @ SV627 ) @ ( tc_fun @ ( tc_prod @ SV627 @ SV627 ) @ tc_bool ) ) @ SV627 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV92 @ SY3553 @ ( tc_fun @ ( tc_prod @ SV627 @ SV627 ) @ tc_bool ) ) @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2296,plain,
! [SV628: $i,SV93: $i] :
( ( ! [SY3554: $i,SY3555: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3554 @ SV93 @ ( tc_fun @ SY3555 @ tc_bool ) ) @ SV628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2297,plain,
! [SV629: $i,SV94: $i] :
( ( ! [SY3556: $i,SY3557: $i] :
( ( hBOOL @ ( hAPP @ SV94 @ SV629 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SY3556 @ ( tc_fun @ SY3557 @ tc_bool ) ) @ SV629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2298,plain,
! [SV630: $i,SV95: $i] :
( ( ! [SY3558: $i,SY3559: $i,SY3560: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV95 @ SV630 @ SY3558 @ SY3559 ) @ SY3560 @ ( tc_prod @ SY3558 @ SY3559 ) ) @ SY3558 @ SY3559 )
= ( c_Set_Oinsert @ SV630 @ ( c_Relation_ORange @ SY3560 @ SY3558 @ SY3559 ) @ SY3559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2299,plain,
! [SV631: $i,SV96: $i] :
( ( ! [SY3561: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SY3561 @ SY3561 ) @ tc_bool ) ) @ SY3561 )
| ~ ( c_Relation_Osym @ SV631 @ SY3561 )
| ~ ( c_Relation_Osym @ SV96 @ SY3561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2300,plain,
! [SV632: $i,SV97: $i] :
( ( ( ( c_Transitive__Closure_Otrancl @ SV97 @ SV632 )
= SV97 )
| ~ ( c_Relation_Otrans @ SV97 @ SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2301,plain,
! [SV633: $i,SV98: $i] :
( ( ! [SY3562: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV633 @ ( tc_fun @ SY3562 @ tc_bool ) ) @ SY3562 )
| ~ ( c_Finite__Set_Ofinite @ SV633 @ SY3562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2302,plain,
! [SV634: $i,SV99: $i] :
( ( ! [SY3563: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV634 @ ( tc_fun @ SY3563 @ tc_bool ) ) @ SY3563 )
| ~ ( c_Finite__Set_Ofinite @ SV99 @ SY3563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2303,plain,
! [SV635: $i,SV100: $i] :
( ( ! [SY3564: $i,SY3565: $i] :
( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SY3564 @ ( tc_fun @ SY3565 @ tc_bool ) ) @ SY3565 )
| ~ ( c_in @ SV100 @ SY3564 @ SY3565 )
| ~ ( c_in @ SV100 @ SV635 @ SY3565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2304,plain,
! [SV636: $i,SV101: $i] :
( ( ! [SY3566: $i,SY3567: $i] :
( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SY3566 @ ( tc_fun @ SY3567 @ tc_bool ) ) @ SY3567 )
| ~ ( c_in @ SV101 @ SY3566 @ SY3567 )
| ~ ( c_in @ SV101 @ SV636 @ SY3567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2305,plain,
! [SV637: $i,SV102: $i] :
( ( ! [SY3568: $i,SY3569: $i] :
( ( c_in @ SV102 @ ( c_Set_Oinsert @ SV637 @ SY3568 @ SY3569 ) @ SY3569 )
| ~ ( c_in @ SV102 @ SY3568 @ SY3569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2306,plain,
! [SV638: $i,SV103: $i] :
( ( ! [SY3570: $i,SY3571: $i] :
( ( c_in @ SV103 @ ( c_Set_Oinsert @ SV638 @ SY3570 @ SY3571 ) @ SY3571 )
| ~ ( c_in @ SV103 @ SY3570 @ SY3571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2307,plain,
! [SV639: $i,SV104: $i] :
( ( ! [SY3572: $i,SY3573: $i] :
( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SY3572 @ ( tc_fun @ SY3573 @ tc_bool ) ) @ SY3573 )
| ~ ( c_in @ SV104 @ SV639 @ SY3573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2308,plain,
! [SV640: $i,SV105: $i] :
( ( ! [SY3574: $i,SY3575: $i] :
( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV640 @ SY3574 @ ( tc_fun @ SY3575 @ tc_bool ) ) @ SY3575 )
| ~ ( c_in @ SV105 @ SY3574 @ SY3575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2309,plain,
! [SV641: $i,SV106: $i] :
( ( ! [SY3576: $i,SY3577: $i] :
( ( c_in @ SV106 @ SV641 @ SY3576 )
| ( SV106 = SY3577 )
| ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SY3577 @ SV641 @ SY3576 ) @ SY3576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2310,plain,
! [SV642: $i,SV107: $i] :
( ( ! [SY3578: $i,SY3579: $i] :
( ( c_in @ SV107 @ SV642 @ SY3578 )
| ( c_in @ SV107 @ SY3579 @ SY3578 )
| ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3579 @ SV642 @ ( tc_fun @ SY3578 @ tc_bool ) ) @ SY3578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2311,plain,
! [SV643: $i,SV108: $i] :
( ( ! [SY3580: $i] : ( c_in @ SV108 @ ( c_Set_Oinsert @ SV108 @ SV643 @ SY3580 ) @ SY3580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2312,plain,
! [SV644: $i,SV109: $i] :
( ( ! [SY3581: $i] : ( c_in @ SV109 @ ( c_Set_Oinsert @ SV109 @ SV644 @ SY3581 ) @ SY3581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2313,plain,
! [SV645: $i,SV110: $i] :
( ( ! [SY3582: $i] : ( c_in @ SV110 @ ( c_Set_Oinsert @ SV110 @ SV645 @ SY3582 ) @ SY3582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2314,plain,
! [SV646: $i,SV111: $i] :
( ( ! [SY3583: $i,SY3584: $i] :
( ( c_in @ SV111 @ SV646 @ SY3583 )
| ~ ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3584 @ SV646 @ ( tc_fun @ SY3583 @ tc_bool ) ) @ SY3583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2315,plain,
! [SV647: $i,SV112: $i] :
( ( ! [SY3585: $i,SY3586: $i] :
( ( c_in @ SV112 @ SV647 @ SY3585 )
| ~ ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SY3586 @ ( tc_fun @ SY3585 @ tc_bool ) ) @ SY3585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2316,plain,
! [SV648: $i,SV113: $i] :
( ( ! [SY3587: $i] :
( ( ( c_Set_Oinsert @ SV113 @ SV648 @ SY3587 )
= SV648 )
| ~ ( c_in @ SV113 @ SV648 @ SY3587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2317,plain,
! [SV649: $i,SV114: $i] :
( ( ! [SY3588: $i,SY3589: $i,SY3590: $i] :
( ~ ( c_in @ SV114 @ SV649 @ SY3588 )
| ( c_in @ ( hAPP @ SY3589 @ SV114 ) @ ( c_Set_Oimage @ SY3589 @ SV649 @ SY3588 @ SY3590 ) @ SY3590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2318,plain,
! [SV650: $i,SV115: $i] :
( ( ! [SY3591: $i,SY3592: $i,SY3593: $i] :
( ~ ( c_in @ SV115 @ SV650 @ SY3591 )
| ( c_in @ ( hAPP @ SY3592 @ SV115 ) @ ( c_Set_Oimage @ SY3592 @ SV650 @ SY3591 @ SY3593 ) @ SY3593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2319,plain,
! [SV651: $i,SV116: $i] :
( ( ! [SY3594: $i,SY3595: $i,SY3596: $i] :
( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SY3594 @ SY3595 @ SY3596 ) @ SY3596 )
| ~ ( c_in @ SV651 @ SY3594 @ SY3595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2320,plain,
! [SV652: $i,SV117: $i] :
( ( ! [SY3597: $i,SY3598: $i,SY3599: $i] :
( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SY3597 @ SY3598 @ SY3599 ) @ SY3599 )
| ~ ( c_in @ SV652 @ SY3597 @ SY3598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2321,plain,
! [SV653: $i,SV118: $i] :
( ( ! [SY3600: $i,SY3601: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SV653 @ SY3600 @ SY3601 ) @ SY3600 @ SY3601 @ SY3601 ) @ SV118 @ ( tc_prod @ SY3601 @ SY3601 ) )
| ~ ( c_in @ ( c_Pair @ SV653 @ SY3600 @ SY3601 @ SY3601 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SY3601 ) @ ( tc_prod @ SY3601 @ SY3601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2322,plain,
! [SV654: $i,SV119: $i] :
( ( ! [SY3602: $i,SY3603: $i,SY3604: $i,SY3605: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SY3602 @ SY3603 ) @ ( c_Product__Type_OSigma @ SY3604 @ SY3605 @ SY3602 @ SY3603 ) @ ( tc_fun @ ( tc_prod @ SY3602 @ SY3603 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY3605 @ SY3602 @ SY3603 ) ) @ ( hAPP @ SY3605 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY3605 @ SY3602 @ SY3603 ) ) @ ( tc_fun @ SY3603 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SY3604 @ ( tc_fun @ SY3602 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2323,plain,
! [SV655: $i,SV120: $i] :
( ( ! [SY3606: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SY3606 @ SY3606 ) @ tc_bool ) ) @ SY3606 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SY3606 @ SY3606 @ SY3606 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SY3606 @ SY3606 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV655 @ SY3606 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SY3606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2324,plain,
! [SV656: $i,SV121: $i] :
( ( ! [SY3607: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SY3607 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SY3607 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SY3607 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV121 @ SY3607 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2325,plain,
! [SV657: $i,SV122: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV122 @ SV657 ) @ ( c_Relation_OId @ SV657 ) @ ( tc_fun @ ( tc_prod @ SV657 @ SV657 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV122 @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2326,plain,
! [SV658: $i,SV123: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV123 @ ( c_Relation_OId @ SV658 ) @ ( tc_fun @ ( tc_prod @ SV658 @ SV658 ) @ tc_bool ) ) @ SV658 )
= ( c_Transitive__Closure_Ortrancl @ SV123 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2327,plain,
! [SV659: $i,SV124: $i] :
( ( ! [SY3608: $i,SY3609: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 @ SV659 @ ( tc_fun @ ( tc_prod @ SY3608 @ SY3609 ) @ tc_bool ) ) @ SY3608 @ SY3609 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV124 @ SY3608 @ SY3609 ) @ ( c_Relation_ODomain @ SV659 @ SY3608 @ SY3609 ) @ ( tc_fun @ SY3608 @ tc_bool ) ) @ ( tc_fun @ SY3608 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2328,plain,
! [SV660: $i,SV125: $i] :
( ( ! [SY3610: $i] : ( c_lessequals @ SV125 @ ( c_Set_Oinsert @ SV660 @ SV125 @ SY3610 ) @ ( tc_fun @ SY3610 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2329,plain,
! [SV661: $i,SV126: $i] :
( ( ! [SY3611: $i] :
( ( c_Finite__Set_Ofinite @ SV126 @ SV661 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY3611 @ SV126 @ SV661 ) @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2330,plain,
! [SV662: $i,SV127: $i] :
( ( ! [SY3612: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV127 @ SV662 @ SY3612 ) @ SY3612 )
| ~ ( c_Finite__Set_Ofinite @ SV662 @ SY3612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2331,plain,
! [SV663: $i,SV128: $i] :
( ( ! [SY3613: $i,SY3614: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SV663 @ SY3613 @ SY3614 ) @ SY3614 )
| ~ ( c_Relation_Otrans @ SV128 @ SY3613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2332,plain,
! [SV664: $i,SV129: $i] :
( ( ! [SY3615: $i,SY3616: $i,SY3617: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV129 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV664 @ SY3615 @ ( tc_fun @ SY3616 @ tc_bool ) ) @ SY3616 @ SY3617 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV129 @ SV664 @ SY3616 @ SY3617 ) @ ( c_Set_Oimage @ SV129 @ SY3615 @ SY3616 @ SY3617 ) @ ( tc_fun @ SY3617 @ tc_bool ) ) @ ( tc_fun @ SY3617 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2333,plain,
! [SV665: $i,SV130: $i] :
( ( ! [SY3618: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SY3618 @ tc_bool ) ) @ SY3618 )
| ~ ( c_Finite__Set_Ofinite @ SV665 @ SY3618 )
| ~ ( c_Finite__Set_Ofinite @ SV130 @ SY3618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2334,plain,
! [SV666: $i,SV131: $i] :
( ( ! [SY3619: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SY3619 @ tc_bool ) ) @ SY3619 )
| ~ ( c_Finite__Set_Ofinite @ SV666 @ SY3619 )
| ~ ( c_Finite__Set_Ofinite @ SV131 @ SY3619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2335,plain,
! [SV667: $i,SV132: $i] :
( ( ! [SY3620: $i,SY3621: $i,SY3622: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV132 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV667 @ SY3620 @ ( tc_fun @ SY3621 @ tc_bool ) ) @ SY3621 @ SY3622 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV132 @ SV667 @ SY3621 @ SY3622 ) @ ( c_Relation_OImage @ SV132 @ SY3620 @ SY3621 @ SY3622 ) @ ( tc_fun @ SY3622 @ tc_bool ) ) @ ( tc_fun @ SY3622 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2336,plain,
! [SV668: $i,SV133: $i] :
( ( ! [SY3623: $i,SY3624: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SV668 @ ( tc_fun @ SY3623 @ tc_bool ) ) @ SY3624 @ ( tc_fun @ SY3623 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV668 @ SY3624 @ ( tc_fun @ SY3623 @ tc_bool ) ) @ ( tc_fun @ SY3623 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY3624 @ SV133 @ ( tc_fun @ SY3623 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2337,plain,
! [SV669: $i,SV134: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ ( c_Relation_OId @ SV669 ) @ ( tc_fun @ ( tc_prod @ SV669 @ SV669 ) @ tc_bool ) ) @ SV669 )
| ~ ( c_Relation_Otrans @ SV134 @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2338,plain,
! [SV670: $i,SV135: $i] :
( ( ! [SY3625: $i,SY3626: $i] :
( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
| ( hBOOL @ ( hAPP @ SY3625 @ SV670 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3625 @ SV135 @ ( tc_fun @ SY3626 @ tc_bool ) ) @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2339,plain,
! [SV671: $i,SV136: $i] :
( ( ! [SY3627: $i,SY3628: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SV671 @ ( tc_fun @ SY3627 @ tc_bool ) ) @ SY3628 ) )
| ~ ( hBOOL @ ( hAPP @ SV671 @ SY3628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2340,plain,
! [SV672: $i,SV137: $i] :
( ( ! [SY3629: $i,SY3630: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV672 @ ( tc_fun @ SY3629 @ tc_bool ) ) @ SY3630 ) )
| ~ ( hBOOL @ ( hAPP @ SV137 @ SY3630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2341,plain,
! [SV673: $i,SV138: $i] :
( ( ! [SY3631: $i,SY3632: $i,SY3633: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 @ SV673 @ ( tc_fun @ SY3631 @ tc_bool ) ) @ ( c_COMBK @ SY3632 @ ( tc_fun @ SY3633 @ tc_bool ) @ SY3631 ) @ SY3631 @ SY3633 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV138 @ ( c_COMBK @ SY3632 @ ( tc_fun @ SY3633 @ tc_bool ) @ SY3631 ) @ SY3631 @ SY3633 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SY3632 @ ( tc_fun @ SY3633 @ tc_bool ) @ SY3631 ) @ SY3631 @ SY3633 ) @ ( tc_fun @ ( tc_prod @ SY3631 @ SY3633 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2342,plain,
! [SV674: $i,SV139: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV139 @ SV139 @ SV674 @ SV674 @ SV674 ) @ SV139 @ ( tc_fun @ ( tc_prod @ SV674 @ SV674 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV139 @ SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2343,plain,
! [SV675: $i,SV140: $i] :
( ( ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SY3634 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3635 @ SY3636 @ ( tc_fun @ ( tc_prod @ SY3634 @ SY3634 ) @ tc_bool ) ) @ SY3634 )
| ~ ( c_Relation_Orefl__on @ SV675 @ SY3636 @ SY3634 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SY3635 @ SY3634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2344,plain,
! [SV676: $i,SV141: $i] :
( ( ! [SY3637: $i,SY3638: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ SY3637 @ SV141 ) @ SY3638 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3637 @ SY3638 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2345,plain,
! [SV677: $i,SV142: $i] :
( ( ! [SY3639: $i,SY3640: $i] :
( ~ ( class_Lattices_Olattice @ SV142 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3639 @ SY3640 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3639 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ SY3640 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2346,plain,
! [SV678: $i,SV143: $i] :
( ( ! [SY3641: $i,SY3642: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3641 @ SY3642 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3641 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ SY3642 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2347,plain,
! [SV679: $i,SV144: $i] :
( ( ! [SY3643: $i,SY3644: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ SY3643 @ SV144 ) @ SY3644 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3643 @ SY3644 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2348,plain,
! [SV680: $i,SV145: $i] :
( ( ! [SY3645: $i,SY3646: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ SV680 @ ( tc_fun @ SY3645 @ tc_bool ) ) @ SY3646 @ ( tc_fun @ SY3645 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV680 @ SY3646 @ ( tc_fun @ SY3645 @ tc_bool ) ) @ ( tc_fun @ SY3645 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2349,plain,
! [SV681: $i,SV146: $i] :
( ( ! [SY3647: $i,SY3648: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ SY3647 @ ( tc_fun @ SY3648 @ tc_bool ) ) @ ( tc_fun @ SY3648 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SY3647 @ ( tc_fun @ SY3648 @ tc_bool ) ) @ ( tc_fun @ SY3648 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2350,plain,
! [SV682: $i,SV147: $i] :
( ( ! [SY3649: $i] :
( ( c_Finite__Set_Ofinite @ SV147 @ SV682 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV147 @ SY3649 @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2351,plain,
! [SV683: $i,SV148: $i] :
( ( ! [SY3650: $i] :
( ( c_Finite__Set_Ofinite @ SV148 @ SV683 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3650 @ SV148 @ ( tc_fun @ SV683 @ tc_bool ) ) @ SV683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2352,plain,
! [SV684: $i,SV150: $i] :
( ( ! [SY3651: $i,SY3652: $i,SY3653: $i,SY3654: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SY3651 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY3652 @ SY3653 @ SY3654 ) @ ( tc_fun @ SY3654 @ tc_bool ) @ SY3651 ) @ SY3651 @ SY3654 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SY3652 @ SY3651 @ SY3654 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV684 @ ( c_COMBK @ ( c_Set_Oinsert @ SY3652 @ SY3653 @ SY3654 ) @ ( tc_fun @ SY3654 @ tc_bool ) @ SY3651 ) @ SY3651 @ SY3654 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SY3651 ) @ ( c_COMBK @ SY3653 @ ( tc_fun @ SY3654 @ tc_bool ) @ SY3651 ) @ SY3651 @ SY3654 ) @ ( tc_fun @ ( tc_prod @ SY3651 @ SY3654 ) @ tc_bool ) ) @ ( tc_prod @ SY3651 @ SY3654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2353,plain,
! [SV685: $i,SV151: $i] :
( ( ! [SY3655: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SY3655 @ SY3655 ) @ tc_bool ) ) @ SY3655 )
| ~ ( c_Relation_Otrans @ SV685 @ SY3655 )
| ~ ( c_Relation_Otrans @ SV151 @ SY3655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2354,plain,
! [SV686: $i,SV152: $i] :
( ( ! [SY3656: $i,SY3657: $i] :
( ~ ( class_Lattices_Olattice @ SV152 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3656 @ SY3657 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY3656 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY3657 @ SV152 ) @ SV152 ) @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2355,plain,
! [SV687: $i,SV153: $i] :
( ( ! [SY3658: $i] :
( ~ ( class_Lattices_Olattice @ SV153 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SY3658 @ SV153 ) @ SV153 )
= SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2356,plain,
! [SV688: $i,SV154: $i] :
( ( ! [SY3659: $i] :
( ~ ( class_Lattices_Olattice @ SV154 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV688 @ SY3659 @ SV154 ) @ SV154 )
= SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2357,plain,
! [SV689: $i,SV155: $i] :
( ( ! [SY3660: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV155 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY3660 @ SV155 )
= SV689 )
| ~ ( c_lessequals @ SY3660 @ SV689 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2358,plain,
! [SV690: $i,SV156: $i] :
( ( ! [SY3661: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV156 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SY3661 @ SV156 )
= SY3661 )
| ~ ( c_lessequals @ SV690 @ SY3661 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2359,plain,
! [SV691: $i,SV157: $i] :
( ( ! [SY3662: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ SV691 @ ( tc_fun @ SY3662 @ tc_bool ) )
= SV691 )
| ~ ( c_lessequals @ SV157 @ SV691 @ ( tc_fun @ SY3662 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2360,plain,
! [SV692: $i,SV158: $i] :
( ( ! [SY3663: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV692 @ ( tc_fun @ SY3663 @ tc_bool ) )
= SV158 )
| ~ ( c_lessequals @ SV692 @ SV158 @ ( tc_fun @ SY3663 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2361,plain,
! [SV693: $i,SV159: $i] :
( ( ! [SY3664: $i,SY3665: $i,SY3666: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SY3664 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3665 @ SY3666 @ ( tc_fun @ ( tc_prod @ SY3664 @ SY3664 ) @ tc_bool ) ) @ SY3664 )
| ~ ( c_Relation_Orefl__on @ SV693 @ SY3666 @ SY3664 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SY3665 @ SY3664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2362,plain,
! [SV694: $i,SV160: $i] :
( ( ! [SY3667: $i,SY3668: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SV694 @ SY3667 @ SY3668 ) @ SY3668 )
| ~ ( c_Finite__Set_Ofinite @ SV694 @ SY3667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2363,plain,
! [SV695: $i,SV161: $i] :
( ( ! [SY3669: $i,SY3670: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SV695 @ SY3669 ) @ SY3670 @ ( tc_fun @ SY3669 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV695 @ SY3670 @ ( tc_fun @ SY3669 @ tc_bool ) ) @ SY3669 ) )
| ~ ( c_in @ SV161 @ SY3670 @ SY3669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2364,plain,
! [SV696: $i,SV162: $i] :
( ( ! [SY3671: $i,SY3672: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SV696 @ SY3671 @ SY3672 ) @ ( tc_fun @ SY3672 @ tc_bool ) )
= ( c_Set_Oinsert @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SY3671 @ ( tc_fun @ SY3672 @ tc_bool ) ) @ SY3672 ) )
| ~ ( c_in @ SV696 @ SV162 @ SY3672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2365,plain,
! [SV697: $i,SV163: $i] :
( ( ! [SY3673: $i,SY3674: $i,SY3675: $i] :
( ( c_Set_Oimage @ SV163 @ ( c_Set_Oinsert @ SV697 @ SY3673 @ SY3674 ) @ SY3674 @ SY3675 )
= ( c_Set_Oinsert @ ( hAPP @ SV163 @ SV697 ) @ ( c_Set_Oimage @ SV163 @ SY3673 @ SY3674 @ SY3675 ) @ SY3675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2366,plain,
! [SV698: $i,SV164: $i] :
( ( ! [SY3676: $i,SY3677: $i,SY3678: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SY3676 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3677 @ SY3678 @ ( tc_fun @ SY3676 @ tc_bool ) ) @ ( tc_fun @ SY3676 @ tc_bool ) )
| ~ ( c_lessequals @ SV698 @ SY3678 @ ( tc_fun @ SY3676 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SY3677 @ ( tc_fun @ SY3676 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2367,plain,
! [SV699: $i,SV165: $i] :
( ( ! [SY3679: $i,SY3680: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV165 @ SV699 @ ( tc_fun @ ( tc_prod @ SY3679 @ SY3680 ) @ tc_bool ) ) @ SY3679 @ SY3680 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV165 @ SY3679 @ SY3680 ) @ ( c_Relation_Oconverse @ SV699 @ SY3679 @ SY3680 ) @ ( tc_fun @ ( tc_prod @ SY3680 @ SY3679 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2368,plain,
! [SV700: $i,SV166: $i] :
( ( ! [SY3681: $i] :
( ~ ( class_Lattices_Olattice @ SV166 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV700 @ SY3681 @ SV166 ) @ SV700 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2369,plain,
! [SV701: $i,SV167: $i] :
( ( ! [SY3682: $i] :
( ~ ( class_Lattices_Olattice @ SV167 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV701 @ SY3682 @ SV167 ) @ SY3682 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2370,plain,
! [SV702: $i,SV168: $i] :
( ( ! [SY3683: $i,SY3684: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV168 )
| ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3683 @ SY3684 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SV702 @ SY3684 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SY3683 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2371,plain,
! [SV703: $i,SV169: $i] :
( ( ! [SY3685: $i,SY3686: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV169 )
| ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3685 @ SY3686 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV703 @ SY3686 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SY3685 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2372,plain,
! [SV704: $i,SV170: $i] :
( ( ! [SY3687: $i,SY3688: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV170 )
| ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3687 @ SY3688 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV704 @ SY3688 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SY3687 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2373,plain,
! [SV705: $i,SV171: $i] :
( ( ! [SY3689: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV171 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV705 @ SY3689 @ SV171 ) @ SY3689 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2374,plain,
! [SV706: $i,SV172: $i] :
( ( ! [SY3690: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV172 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV706 @ SY3690 @ SV172 ) @ SV706 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2375,plain,
! [SV707: $i,SV173: $i] :
( ( ! [SY3691: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV173 @ SV707 @ ( tc_fun @ SY3691 @ tc_bool ) ) @ SV173 @ ( tc_fun @ SY3691 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2376,plain,
! [SV708: $i,SV174: $i] :
( ( ! [SY3692: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV174 @ SV708 @ ( tc_fun @ SY3692 @ tc_bool ) ) @ SV708 @ ( tc_fun @ SY3692 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2377,plain,
! [SV709: $i,SV175: $i] :
( ( ! [SY3693: $i,SY3694: $i] :
( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SY3693 @ ( tc_fun @ SY3694 @ tc_bool ) ) @ ( tc_fun @ SY3694 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SY3693 @ ( tc_fun @ SY3694 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SY3694 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2378,plain,
! [SV710: $i,SV176: $i] :
( ( ! [SY3695: $i,SY3696: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SY3695 @ ( tc_fun @ SY3696 @ tc_bool ) ) @ ( tc_fun @ SY3696 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SY3695 @ ( tc_fun @ SY3696 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SY3696 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2379,plain,
! [SV711: $i,SV177: $i] :
( ( ! [SY3697: $i,SY3698: $i,SY3699: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV177 @ SV711 @ ( tc_fun @ SY3697 @ tc_bool ) ) @ ( c_COMBK @ SY3698 @ ( tc_fun @ SY3699 @ tc_bool ) @ SY3697 ) @ SY3697 @ SY3699 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV177 @ ( c_COMBK @ SY3698 @ ( tc_fun @ SY3699 @ tc_bool ) @ SY3697 ) @ SY3697 @ SY3699 ) @ ( c_Product__Type_OSigma @ SV711 @ ( c_COMBK @ SY3698 @ ( tc_fun @ SY3699 @ tc_bool ) @ SY3697 ) @ SY3697 @ SY3699 ) @ ( tc_fun @ ( tc_prod @ SY3697 @ SY3699 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2380,plain,
! [SV712: $i,SV178: $i] :
( ( ! [SY3700: $i,SY3701: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV178 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV712 @ SY3700 @ SV178 ) @ SY3701 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV712 @ SY3701 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3700 @ SY3701 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2381,plain,
! [SV713: $i,SV179: $i] :
( ( ! [SY3702: $i,SY3703: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV179 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3702 @ SY3703 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SY3702 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SY3703 @ SV179 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2382,plain,
! [SV714: $i,SV180: $i] :
( ( ! [SY3704: $i,SY3705: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV714 @ SY3704 @ ( tc_fun @ SY3705 @ tc_bool ) ) @ ( tc_fun @ SY3705 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SV714 @ ( tc_fun @ SY3705 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SY3704 @ ( tc_fun @ SY3705 @ tc_bool ) ) @ ( tc_fun @ SY3705 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2383,plain,
! [SV715: $i,SV181: $i] :
( ( ! [SY3706: $i,SY3707: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV181 @ SV715 @ ( tc_fun @ SY3706 @ tc_bool ) ) @ SY3707 @ ( tc_fun @ SY3706 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV181 @ SY3707 @ ( tc_fun @ SY3706 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV715 @ SY3707 @ ( tc_fun @ SY3706 @ tc_bool ) ) @ ( tc_fun @ SY3706 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2384,plain,
! [SV716: $i,SV182: $i] :
( ( ! [SY3708: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV182 @ SV716 @ SY3708 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2385,plain,
! [SV717: $i,SV183: $i] :
( ( ! [SY3709: $i,SY3710: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SY3709 ) @ SY3710 @ ( tc_fun @ SY3709 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SY3710 @ ( tc_fun @ SY3709 @ tc_bool ) )
| ~ ( c_in @ SV183 @ SY3710 @ SY3709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2386,plain,
! [SV718: $i,SV184: $i] :
( ( ! [SY3711: $i] :
( ~ ( class_Lattices_Olattice @ SV184 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SY3711 @ SV184 ) @ SV184 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SY3711 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2387,plain,
! [SV719: $i,SV185: $i] :
( ( ! [SY3712: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV185 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SY3712 @ SV185 ) @ SV185 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SY3712 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2388,plain,
! [SV720: $i,SV186: $i] :
( ( ! [SY3713: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SV720 @ ( tc_fun @ SY3713 @ tc_bool ) ) @ ( tc_fun @ SY3713 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SV720 @ ( tc_fun @ SY3713 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2389,plain,
! [SV721: $i,SV187: $i] :
( ( ! [SY3714: $i] :
( ( c_lessequals @ ( c_Relation_OField @ SV187 @ SV721 ) @ ( c_Relation_OField @ SY3714 @ SV721 ) @ ( tc_fun @ SV721 @ tc_bool ) )
| ~ ( c_lessequals @ SV187 @ SY3714 @ ( tc_fun @ ( tc_prod @ SV721 @ SV721 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2390,plain,
! [SV722: $i,SV188: $i] :
( ( ! [SY3715: $i,SY3716: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV188 @ SV722 @ ( tc_fun @ ( tc_prod @ SY3715 @ SY3716 ) @ tc_bool ) ) @ SY3715 @ SY3716 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV188 @ SY3715 @ SY3716 ) @ ( c_Relation_ORange @ SV722 @ SY3715 @ SY3716 ) @ ( tc_fun @ SY3716 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2391,plain,
! [SV723: $i,SV189: $i] :
( ( ! [SY3717: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV723 @ ( tc_fun @ ( tc_prod @ SY3717 @ SY3717 ) @ tc_bool ) ) @ SY3717 )
| ~ ( c_Wellfounded_Owf @ SV189 @ SY3717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2392,plain,
! [SV724: $i,SV190: $i] :
( ( ! [SY3718: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV190 @ SV724 @ ( tc_fun @ ( tc_prod @ SY3718 @ SY3718 ) @ tc_bool ) ) @ SY3718 )
| ~ ( c_Wellfounded_Owf @ SV724 @ SY3718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2393,plain,
! [SV725: $i,SV191: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV191 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV725 @ SV191 )
= SV725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2394,plain,
! [SV726: $i,SV192: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV192 @ ( tc_fun @ SV726 @ tc_bool ) )
= SV192 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2395,plain,
! [SV727: $i,SV193: $i] :
( ( ( c_Relation_OField @ SV193 @ SV727 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV193 @ SV727 @ SV727 ) @ ( c_Relation_ORange @ SV193 @ SV727 @ SV727 ) @ ( tc_fun @ SV727 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2396,plain,
! [SV728: $i,SV194: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV194 )
| ( c_lessequals @ SV728 @ SY3719 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3720 @ SV728 @ SV194 ) @ SY3719 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2397,plain,
! [SV729: $i,SV195: $i] :
( ( ! [SY3721: $i,SY3722: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV195 )
| ( c_lessequals @ SV729 @ SY3721 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SY3722 @ SV195 ) @ SY3721 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2398,plain,
! [SV730: $i,SV196: $i] :
( ( ! [SY3723: $i,SY3724: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV196 )
| ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3723 @ SY3724 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SV730 @ SY3724 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2399,plain,
! [SV731: $i,SV197: $i] :
( ( ! [SY3725: $i,SY3726: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV197 )
| ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3725 @ SY3726 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV731 @ SY3725 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2400,plain,
! [SV732: $i,SV198: $i] :
( ( ! [SY3727: $i,SY3728: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV198 )
| ( c_lessequals @ SV732 @ SY3727 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3728 @ SV732 @ SV198 ) @ SY3727 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2401,plain,
! [SV733: $i,SV199: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV199 )
| ( c_lessequals @ SV733 @ SY3729 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY3730 @ SV199 ) @ SY3729 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2402,plain,
! [SV734: $i,SV200: $i] :
( ( ! [SY3731: $i,SY3732: $i] :
( ( c_lessequals @ SV200 @ SV734 @ ( tc_fun @ SY3731 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY3732 @ ( tc_fun @ SY3731 @ tc_bool ) ) @ SV734 @ ( tc_fun @ SY3731 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2403,plain,
! [SV735: $i,SV201: $i] :
( ( ! [SY3733: $i,SY3734: $i] :
( ( c_lessequals @ SV201 @ SV735 @ ( tc_fun @ SY3733 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3734 @ SV201 @ ( tc_fun @ SY3733 @ tc_bool ) ) @ SV735 @ ( tc_fun @ SY3733 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2404,plain,
! [SV736: $i,SV202: $i] :
( ( ! [SY3735: $i] :
( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
| ~ ( c_Finite__Set_Ofinite @ SY3735 @ SV736 )
| ~ ( c_lessequals @ SV202 @ SY3735 @ ( tc_fun @ SV736 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2405,plain,
! [SV737: $i,SV203: $i] :
( ( ! [SY3736: $i] :
( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
| ~ ( c_lessequals @ SV203 @ SY3736 @ ( tc_fun @ SV737 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3736 @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2406,plain,
! [SV738: $i,SV204: $i] :
( ( ! [SY3737: $i,SY3738: $i,SY3739: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SY3737 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3738 @ SY3739 @ ( tc_fun @ SY3737 @ tc_bool ) ) @ ( tc_fun @ SY3737 @ tc_bool ) )
| ~ ( c_lessequals @ SV738 @ SY3739 @ ( tc_fun @ SY3737 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SY3738 @ ( tc_fun @ SY3737 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2407,plain,
! [SV739: $i,SV205: $i] :
( ( ! [SY3740: $i,SY3741: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SY3740 @ tc_bool ) ) @ SY3741 ) )
| ~ ( hBOOL @ ( hAPP @ SV739 @ SY3741 ) )
| ~ ( hBOOL @ ( hAPP @ SV205 @ SY3741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2408,plain,
! [SV740: $i,SV206: $i] :
( ( ! [SY3742: $i,SY3743: $i,SY3744: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SY3742 @ SY3743 ) @ ( c_Set_Oimage @ SV206 @ SY3744 @ SY3742 @ SY3743 ) @ ( tc_fun @ SY3743 @ tc_bool ) )
| ~ ( c_lessequals @ SV740 @ SY3744 @ ( tc_fun @ SY3742 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2409,plain,
! [SV741: $i,SV207: $i] :
( ( ! [SY3745: $i,SY3746: $i,SY3747: $i] :
( ~ ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SY3745 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY3746 @ SV207 @ SY3745 @ SY3747 ) @ ( c_Set_Oimage @ SY3746 @ SV741 @ SY3745 @ SY3747 ) @ ( tc_fun @ SY3747 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2410,plain,
! [SV742: $i,SV208: $i] :
( ( ! [SY3748: $i,SY3749: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SV742 @ SY3748 ) @ ( c_Set_Oinsert @ SV208 @ SY3749 @ SY3748 ) @ ( tc_fun @ SY3748 @ tc_bool ) )
| ~ ( c_lessequals @ SV742 @ SY3749 @ ( tc_fun @ SY3748 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2411,plain,
! [SV743: $i,SV209: $i] :
( ( ! [SY3750: $i] :
( ( c_Relation_Otrans @ SV209 @ SV743 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3750 @ SV209 @ SV743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2412,plain,
! [SV744: $i,SV210: $i] :
( ( ! [SY3751: $i,SY3752: $i,SY3753: $i] :
( ( c_Set_Oimage @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV744 @ SY3751 @ ( tc_fun @ SY3752 @ tc_bool ) ) @ SY3752 @ SY3753 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV210 @ SV744 @ SY3752 @ SY3753 ) @ ( c_Set_Oimage @ SV210 @ SY3751 @ SY3752 @ SY3753 ) @ ( tc_fun @ SY3753 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2413,plain,
! [SV745: $i,SV211: $i] :
( ( ! [SY3754: $i,SY3755: $i,SY3756: $i] :
( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SY3754 @ SY3754 ) @ SY3755 @ ( tc_prod @ SY3754 @ SY3754 ) )
| ~ ( c_in @ ( c_Pair @ SY3756 @ SV745 @ SY3754 @ SY3754 ) @ SY3755 @ ( tc_prod @ SY3754 @ SY3754 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SY3756 @ SY3754 @ SY3754 ) @ SY3755 @ ( tc_prod @ SY3754 @ SY3754 ) )
| ~ ( c_Relation_Otrans @ SY3755 @ SY3754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2414,plain,
! [SV746: $i,SV212: $i] :
( ( ! [SY3757: $i,SY3758: $i,SY3759: $i] :
( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SY3757 @ SY3757 ) @ SY3758 @ ( tc_prod @ SY3757 @ SY3757 ) )
| ~ ( c_in @ ( c_Pair @ SY3759 @ SV746 @ SY3757 @ SY3757 ) @ SY3758 @ ( tc_prod @ SY3757 @ SY3757 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SY3759 @ SY3757 @ SY3757 ) @ SY3758 @ ( tc_prod @ SY3757 @ SY3757 ) )
| ~ ( c_Relation_Otrans @ SY3758 @ SY3757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2415,plain,
! [SV747: $i,SV213: $i] :
( ( ! [SY3760: $i,SY3761: $i] :
( ( c_Wellfounded_Owf @ SV213 @ SV747 )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY3760 @ SY3761 @ SV747 @ SV747 ) @ SV213 @ ( tc_prod @ SV747 @ SV747 ) ) @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2416,plain,
! [SV748: $i,SV214: $i] :
( ( ! [SY3762: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV214 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( c_Relation_Orel__comp @ SY3762 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SY3762 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV214 @ SY3762 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2417,plain,
! [SV749: $i,SV215: $i] :
( ( ! [SY3763: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV749 @ ( tc_fun @ ( tc_prod @ SY3763 @ SY3763 ) @ tc_bool ) ) @ SY3763 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV215 @ SV215 @ SY3763 @ SY3763 @ SY3763 ) @ ( c_Relation_Orel__comp @ SV749 @ SV215 @ SY3763 @ SY3763 @ SY3763 ) @ ( tc_fun @ ( tc_prod @ SY3763 @ SY3763 ) @ tc_bool ) ) @ SV749 @ ( tc_fun @ ( tc_prod @ SY3763 @ SY3763 ) @ tc_bool ) ) @ SY3763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2418,plain,
! [SV750: $i,SV216: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV216 @ SV750 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV216 @ SV750 ) @ SV216 @ SV750 @ SV750 @ SV750 ) @ ( tc_fun @ ( tc_prod @ SV750 @ SV750 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2419,plain,
! [SV751: $i,SV217: $i] :
( ( ! [SY3764: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
| ~ ( c_Finite__Set_Ofinite @ SY3764 @ SV751 )
| ~ ( c_in @ SY3764 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2420,plain,
! [SV752: $i,SV218: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV218 @ ( c_Relation_Oconverse @ SV218 @ SV752 @ SV752 ) @ ( tc_fun @ ( tc_prod @ SV752 @ SV752 ) @ tc_bool ) ) @ SV752 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2421,plain,
! [SV753: $i,SV219: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV219 @ ( c_Relation_Oconverse @ SV219 @ SV753 @ SV753 ) @ ( tc_fun @ ( tc_prod @ SV753 @ SV753 ) @ tc_bool ) ) @ SV753 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2422,plain,
! [SV754: $i,SV220: $i] :
( ( ! [SY3765: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV220 @ SV754 ) @ SY3765 @ SV754 @ SV754 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV220 @ SY3765 @ ( tc_fun @ SV754 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2423,plain,
! [SV755: $i,SV221: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV221 @ SV755 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV221 @ SV755 ) @ ( c_Relation_OId @ SV755 ) @ ( tc_fun @ ( tc_prod @ SV755 @ SV755 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2424,plain,
! [SV756: $i,SV222: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV222 @ SV756 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SV756 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV222 @ SV756 ) @ SV222 @ SV756 @ SV756 @ SV756 ) @ ( tc_fun @ ( tc_prod @ SV756 @ SV756 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2425,plain,
! [SV757: $i,SV223: $i] :
( ( ! [SY3766: $i,SY3767: $i] :
( ~ ( c_in @ ( c_Pair @ SV223 @ SV757 @ SY3766 @ SY3766 ) @ ( c_Transitive__Closure_Ortrancl @ SY3767 @ SY3766 ) @ ( tc_prod @ SY3766 @ SY3766 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SY3766 @ SY3766 ) @ SY3767 @ ( tc_prod @ SY3766 @ SY3766 ) ) @ SY3766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2426,plain,
! [SV758: $i,SV224: $i] :
( ( ! [SY3768: $i,SY3769: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SY3768 @ SY3768 ) @ SY3769 @ ( tc_prod @ SY3768 @ SY3768 ) ) @ SY3768 )
| ( c_in @ ( c_Pair @ SV758 @ SV224 @ SY3768 @ SY3768 ) @ ( c_Transitive__Closure_Ortrancl @ SY3769 @ SY3768 ) @ ( tc_prod @ SY3768 @ SY3768 ) )
| ~ ( c_Wellfounded_Owf @ SY3769 @ SY3768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2427,plain,
! [SV759: $i,SV225: $i] :
( ( ! [SY3770: $i,SY3771: $i] :
( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV759 @ SV225 @ SY3770 @ SY3771 ) @ SY3771 @ SY3771 ) @ ( c_Transitive__Closure_Ortrancl @ SV759 @ SY3771 ) @ ( tc_prod @ SY3771 @ SY3771 ) )
| ~ ( c_in @ ( c_Pair @ SV225 @ SY3770 @ SY3771 @ SY3771 ) @ ( c_Transitive__Closure_Otrancl @ SV759 @ SY3771 ) @ ( tc_prod @ SY3771 @ SY3771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2428,plain,
! [SV760: $i,SV226: $i] :
( ( ! [SY3772: $i,SY3773: $i,SY3774: $i,SY3775: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SY3772 @ SY3773 ) @ ( c_Product__Type_OSigma @ SY3774 @ SY3775 @ SY3772 @ SY3773 ) @ ( tc_fun @ ( tc_prod @ SY3772 @ SY3773 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SY3775 @ SY3772 @ SY3773 ) @ SV226 @ SY3772 )
| ~ ( c_lessequals @ SV226 @ SY3774 @ ( tc_fun @ SY3772 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2429,plain,
! [SV761: $i,SV227: $i] :
( ( ! [SY3776: $i,SY3777: $i,SY3778: $i] :
( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SY3776 @ ( tc_fun @ SY3777 @ tc_bool ) @ SY3778 ) @ SY3778 @ SY3777 ) @ ( tc_fun @ SY3778 @ SY3777 ) )
| ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SY3776 @ SV227 @ SY3778 @ SY3777 ) ) @ SY3776 @ SY3777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2430,plain,
! [SV762: $i,SV228: $i] :
( ( ! [SY3779: $i,SY3780: $i,SY3781: $i] :
( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SV762 @ ( c_COMBK @ SY3779 @ ( tc_fun @ SY3780 @ tc_bool ) @ SY3781 ) @ SY3781 @ SY3780 ) @ ( tc_fun @ SY3781 @ SY3780 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV762 @ SY3779 @ SV228 @ SY3781 @ SY3780 ) @ SV762 @ SY3781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2431,plain,
! [SV763: $i,SV229: $i] :
( ( ! [SY3782: $i,SY3783: $i,SY3784: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SY3782 @ SY3783 ) @ SY3784 @ ( tc_fun @ SY3783 @ tc_bool ) )
| ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SY3784 @ ( tc_fun @ SY3783 @ tc_bool ) @ SY3782 ) @ SY3782 @ SY3783 ) @ ( tc_fun @ SY3782 @ SY3783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2432,plain,
! [SV764: $i,SV230: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV230 @ SV764 ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ SV230 @ SV764 ) @ ( c_COMBK @ ( c_Relation_OField @ SV230 @ SV764 ) @ ( tc_fun @ SV764 @ tc_bool ) @ SV764 ) @ SV764 @ SV764 ) @ ( tc_fun @ ( tc_prod @ SV764 @ SV764 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2433,plain,
! [SV765: $i,SV231: $i] :
( ( ! [SY3785: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SY3785 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SY3785 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SY3785 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SY3785 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2434,plain,
! [SV766: $i,SV232: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SV766 @ SV766 ) @ SV232 @ SV766 @ SV766 @ SV766 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SV766 @ SV766 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV232 @ SV766 )
| ~ ( c_Relation_Osym @ SV232 @ SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2435,plain,
! [SV767: $i,SV233: $i] :
( ( ! [SY3786: $i,SY3787: $i] :
( ( c_Wellfounded_Owf @ SV233 @ SV767 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SY3786 @ SY3787 @ SV233 @ SV767 ) @ SY3787 @ SV767 )
| ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SY3786 @ ( c_COMBK @ SY3787 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2436,plain,
! [SV768: $i,SV234: $i] :
( ( ! [SY3788: $i,SY3789: $i] :
( ( c_Wellfounded_Owf @ SV234 @ SV768 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SY3788 @ SY3789 @ SV234 @ SV768 ) @ SY3788 @ SV768 )
| ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SY3788 @ ( c_COMBK @ SY3789 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2437,plain,
! [SV769: $i,SV235: $i] :
( ( ! [SY3790: $i] :
( ( c_Relation_Orefl__on @ SV235 @ SV769 @ SY3790 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SV769 @ SY3790 ) @ SV235 @ SY3790 )
| ~ ( c_lessequals @ SV769 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SY3790 @ tc_bool ) @ SY3790 ) @ SY3790 @ SY3790 ) @ ( tc_fun @ ( tc_prod @ SY3790 @ SY3790 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2438,plain,
! [SV770: $i,SV236: $i] :
( ( ! [SY3791: $i] :
( ( c_Relation_Orefl__on @ SV236 @ SV770 @ SY3791 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SV770 @ SY3791 ) @ SV236 @ SY3791 )
| ~ ( c_lessequals @ SV770 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SY3791 @ tc_bool ) @ SY3791 ) @ SY3791 @ SY3791 ) @ ( tc_fun @ ( tc_prod @ SY3791 @ SY3791 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2439,plain,
! [SV771: $i,SV237: $i] :
( ( ! [SY3792: $i,SY3793: $i] :
( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
| ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SY3792 @ SY3793 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
| ~ ( c_lessequals @ SY3793 @ ( c_Product__Type_OSigma @ SY3792 @ ( c_COMBK @ SY3792 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3792 @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2440,plain,
! [SV772: $i,SV238: $i] :
( ( ! [SY3794: $i] :
( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SY3794 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SY3794 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SY3794 ) @ SY3794 @ SY3794 ) @ SV772 @ ( tc_prod @ SY3794 @ SY3794 ) )
| ~ ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SY3794 @ tc_bool ) @ SY3794 ) @ SY3794 @ SY3794 ) @ ( tc_fun @ ( tc_prod @ SY3794 @ SY3794 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2441,plain,
! [SV773: $i,SV239: $i] :
( ( ! [SY3795: $i] :
( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SY3795 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SY3795 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SY3795 ) @ SY3795 @ SY3795 ) @ SV773 @ ( tc_prod @ SY3795 @ SY3795 ) )
| ~ ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SY3795 @ tc_bool ) @ SY3795 ) @ SY3795 @ SY3795 ) @ ( tc_fun @ ( tc_prod @ SY3795 @ SY3795 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2442,plain,
! [SV774: $i,SV240: $i] :
( ( ! [SY3796: $i,SY3797: $i] :
( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SY3796 @ SY3796 ) @ ( c_Transitive__Closure_Otrancl @ SY3797 @ SY3796 ) @ ( tc_prod @ SY3796 @ SY3796 ) )
| ( SV240 = SV774 )
| ~ ( c_in @ ( c_Pair @ SV240 @ SV774 @ SY3796 @ SY3796 ) @ ( c_Transitive__Closure_Ortrancl @ SY3797 @ SY3796 ) @ ( tc_prod @ SY3796 @ SY3796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2443,plain,
! [SV775: $i,SV241: $i] :
( ( ! [SY3798: $i,SY3799: $i] :
( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SY3798 @ SY3798 ) @ ( c_Transitive__Closure_Otrancl @ SY3799 @ SY3798 ) @ ( tc_prod @ SY3798 @ SY3798 ) )
| ( SV241 = SV775 )
| ~ ( c_in @ ( c_Pair @ SV241 @ SV775 @ SY3798 @ SY3798 ) @ ( c_Transitive__Closure_Ortrancl @ SY3799 @ SY3798 ) @ ( tc_prod @ SY3798 @ SY3798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2444,plain,
! [SV776: $i,SV242: $i] :
( ( ! [SY3800: $i,SY3801: $i] :
( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SY3800 @ SY3800 ) @ ( c_Transitive__Closure_Ortrancl @ SY3801 @ SY3800 ) @ ( tc_prod @ SY3800 @ SY3800 ) )
| ~ ( c_in @ ( c_Pair @ SV242 @ SV776 @ SY3800 @ SY3800 ) @ ( c_Transitive__Closure_Otrancl @ SY3801 @ SY3800 ) @ ( tc_prod @ SY3800 @ SY3800 ) )
| ( SV242 = SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2445,plain,
! [SV777: $i,SV243: $i] :
( ( ! [SY3802: $i,SY3803: $i] :
( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SY3802 @ SY3803 ) @ SY3803 @ SY3803 ) @ SV777 @ ( tc_prod @ SY3803 @ SY3803 ) )
| ( c_in @ ( c_Pair @ SV243 @ SY3802 @ SY3803 @ SY3803 ) @ SV777 @ ( tc_prod @ SY3803 @ SY3803 ) )
| ~ ( c_in @ ( c_Pair @ SV243 @ SY3802 @ SY3803 @ SY3803 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SY3803 ) @ ( tc_prod @ SY3803 @ SY3803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2446,plain,
! [SV778: $i,SV244: $i] :
( ( ! [SY3804: $i,SY3805: $i,SY3806: $i] :
( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SY3804 @ SY3804 ) @ ( c_Transitive__Closure_Otrancl @ SY3805 @ SY3804 ) @ ( tc_prod @ SY3804 @ SY3804 ) )
| ~ ( c_in @ ( c_Pair @ SY3806 @ SV778 @ SY3804 @ SY3804 ) @ SY3805 @ ( tc_prod @ SY3804 @ SY3804 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SY3806 @ SY3804 @ SY3804 ) @ ( c_Transitive__Closure_Ortrancl @ SY3805 @ SY3804 ) @ ( tc_prod @ SY3804 @ SY3804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2447,plain,
! [SV779: $i,SV245: $i] :
( ( ! [SY3807: $i,SY3808: $i,SY3809: $i] :
( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SY3807 @ SY3807 ) @ ( c_Transitive__Closure_Otrancl @ SY3808 @ SY3807 ) @ ( tc_prod @ SY3807 @ SY3807 ) )
| ~ ( c_in @ ( c_Pair @ SY3809 @ SV779 @ SY3807 @ SY3807 ) @ ( c_Transitive__Closure_Ortrancl @ SY3808 @ SY3807 ) @ ( tc_prod @ SY3807 @ SY3807 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SY3809 @ SY3807 @ SY3807 ) @ SY3808 @ ( tc_prod @ SY3807 @ SY3807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2448,plain,
! [SV780: $i,SV246: $i] :
( ( ! [SY3810: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) @ SY3810 @ ( tc_fun @ SV780 @ tc_bool ) )
| ~ ( c_in @ SY3810 @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2449,plain,
! [SV781: $i,SV247: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV247 @ SV781 )
= ( c_Relation_Orel__comp @ SV247 @ ( c_Transitive__Closure_Ortrancl @ SV247 @ SV781 ) @ SV781 @ SV781 @ SV781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2450,plain,
! [SV782: $i,SV248: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV248 @ SV782 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV248 @ SV782 ) @ SV248 @ SV782 @ SV782 @ SV782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2451,plain,
! [SV783: $i,SV249: $i] :
( ( ! [SY3811: $i] :
( ( c_in @ SV249 @ ( c_Complete__Lattice_OInf__class_OInf @ SV783 @ ( tc_fun @ SY3811 @ tc_bool ) ) @ SY3811 )
| ~ ( c_in @ SV249 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV249 @ SV783 @ SY3811 ) @ SY3811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2452,plain,
! [SV784: $i,SV250: $i] :
( ( ! [SY3812: $i,SY3813: $i] :
( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SY3812 @ SY3813 ) @ ( c_Wellfounded_Oacc @ SY3812 @ SY3813 ) @ SY3813 )
| ~ ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SY3812 @ SY3813 ) @ SY3813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2453,plain,
! [SV785: $i,SV251: $i] :
( ( ! [SY3814: $i] :
( ( c_in @ SV251 @ ( c_Wellfounded_Oacc @ SV785 @ SY3814 ) @ SY3814 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV785 @ SV251 @ SY3814 ) @ ( c_Wellfounded_Oacc @ SV785 @ SY3814 ) @ SY3814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2454,plain,
! [SV786: $i,SV252: $i] :
( ( ! [SY3815: $i] :
( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
| ~ ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SY3815 ) ) )
| ~ ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SY3815 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2455,plain,
! [SV787: $i,SV253: $i] :
( ( ! [SY3816: $i,SY3817: $i] :
( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
| ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SY3816 @ SY3817 ) ) )
| ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SY3816 @ SY3817 ) @ SY3817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2456,plain,
! [SV788: $i,SV254: $i] :
( ( ! [SY3818: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV254 @ SV788 @ SY3818 ) @ ( c_Wellfounded_Oacc @ SV254 @ SY3818 ) @ SY3818 )
| ( c_in @ SV788 @ ( c_Wellfounded_Oacc @ SV254 @ SY3818 ) @ SY3818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2457,plain,
! [SV789: $i,SV255: $i] :
( ( ! [SY3819: $i,SY3820: $i] :
( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SY3819 @ SY3820 ) @ ( c_Wellfounded_Oacc @ SY3819 @ SY3820 ) @ SY3820 )
| ~ ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SY3819 @ SY3820 ) @ SY3820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2458,plain,
! [SV790: $i,SV256: $i] :
( ( ! [SY3821: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SY3821 ) ) )
| ~ ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SY3821 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2459,plain,
! [SV791: $i,SV257: $i] :
( ( ! [SY3822: $i,SY3823: $i] :
( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SY3822 @ SY3823 ) ) )
| ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SY3822 @ SY3823 ) @ SY3823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2460,plain,
! [SV792: $i,SV258: $i] :
( ( ! [SY3824: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SY3824 @ SV258 )
| ~ ( c_in @ SY3824 @ SV792 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2461,plain,
! [SV793: $i,SV259: $i] :
( ( ! [SY3825: $i] :
( ( c_lessequals @ SV259 @ ( c_Complete__Lattice_OSup__class_OSup @ SV793 @ ( tc_fun @ SY3825 @ tc_bool ) ) @ ( tc_fun @ SY3825 @ tc_bool ) )
| ~ ( c_in @ SV259 @ SV793 @ ( tc_fun @ SY3825 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2462,plain,
! [SV794: $i,SV260: $i] :
( ( ! [SY3826: $i,SY3827: $i] :
( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SY3826 ) @ ( tc_prod @ SY3826 @ SY3826 ) )
| ~ ( c_lessequals @ SY3827 @ SV794 @ ( tc_fun @ ( tc_prod @ SY3826 @ SY3826 ) @ tc_bool ) )
| ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SY3827 @ SY3826 ) @ ( tc_prod @ SY3826 @ SY3826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2463,plain,
! [SV795: $i,SV261: $i] :
( ( ! [SY3828: $i,SY3829: $i,SY3830: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SY3828 @ SY3829 @ SY3830 ) @ SV261 @ SY3829 )
| ~ ( c_in @ SV795 @ ( c_Relation_OImage @ SY3828 @ SV261 @ SY3829 @ SY3830 ) @ SY3830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2464,plain,
! [SV796: $i,SV262: $i] :
( ( ! [SY3831: $i,SY3832: $i,SY3833: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SY3831 @ SY3832 @ SY3833 ) @ SV262 @ SY3832 )
| ~ ( c_in @ SV796 @ ( c_Relation_OImage @ SY3831 @ SV262 @ SY3832 @ SY3833 ) @ SY3833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2465,plain,
! [SV797: $i,SV263: $i] :
( ( ! [SY3834: $i,SY3835: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SY3834 ) @ SV263 @ SY3834 )
| ~ ( c_in @ SY3835 @ SV263 @ SY3834 )
| ~ ( c_Wellfounded_Owf @ SV797 @ SY3834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2466,plain,
! [SV798: $i,SV264: $i] :
( ( ! [SY3836: $i,SY3837: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SY3836 ) @ SV264 @ SY3836 )
| ~ ( c_in @ SY3837 @ SV264 @ SY3836 )
| ~ ( c_Wellfounded_Owf @ SV798 @ SY3836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2467,plain,
! [SV799: $i,SV265: $i] :
( ( ! [SY3838: $i] :
( ( c_in @ SV265 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV265 @ SV799 @ SY3838 ) @ SY3838 )
| ~ ( c_in @ SV265 @ ( c_Complete__Lattice_OSup__class_OSup @ SV799 @ ( tc_fun @ SY3838 @ tc_bool ) ) @ SY3838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2468,plain,
! [SV800: $i,SV266: $i] :
( ( ! [SY3839: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
| ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SY3839 @ SV266 ) @ SV266 )
| ~ ( c_in @ SV800 @ SY3839 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2469,plain,
! [SV801: $i,SV267: $i] :
( ( ! [SY3840: $i,SY3841: $i,SY3842: $i] :
( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SY3840 @ SY3840 ) @ ( c_Transitive__Closure_Ortrancl @ SY3841 @ SY3840 ) @ ( tc_prod @ SY3840 @ SY3840 ) )
| ~ ( c_in @ ( c_Pair @ SY3842 @ SV801 @ SY3840 @ SY3840 ) @ SY3841 @ ( tc_prod @ SY3840 @ SY3840 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SY3842 @ SY3840 @ SY3840 ) @ ( c_Transitive__Closure_Ortrancl @ SY3841 @ SY3840 ) @ ( tc_prod @ SY3840 @ SY3840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2470,plain,
! [SV802: $i,SV268: $i] :
( ( ! [SY3843: $i,SY3844: $i,SY3845: $i] :
( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SY3843 @ SY3843 ) @ ( c_Transitive__Closure_Ortrancl @ SY3844 @ SY3843 ) @ ( tc_prod @ SY3843 @ SY3843 ) )
| ~ ( c_in @ ( c_Pair @ SY3845 @ SV802 @ SY3843 @ SY3843 ) @ ( c_Transitive__Closure_Ortrancl @ SY3844 @ SY3843 ) @ ( tc_prod @ SY3843 @ SY3843 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SY3845 @ SY3843 @ SY3843 ) @ SY3844 @ ( tc_prod @ SY3843 @ SY3843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2471,plain,
! [SV803: $i,SV269: $i] :
( ( ! [SY3846: $i,SY3847: $i,SY3848: $i] :
( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SY3846 @ SY3846 ) @ ( c_Transitive__Closure_Ortrancl @ SY3847 @ SY3846 ) @ ( tc_prod @ SY3846 @ SY3846 ) )
| ~ ( c_in @ ( c_Pair @ SY3848 @ SV803 @ SY3846 @ SY3846 ) @ ( c_Transitive__Closure_Ortrancl @ SY3847 @ SY3846 ) @ ( tc_prod @ SY3846 @ SY3846 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SY3848 @ SY3846 @ SY3846 ) @ ( c_Transitive__Closure_Ortrancl @ SY3847 @ SY3846 ) @ ( tc_prod @ SY3846 @ SY3846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2472,plain,
! [SV804: $i,SV270: $i] :
( ( ! [SY3849: $i] : ( c_in @ ( c_Pair @ SV270 @ SV270 @ SV804 @ SV804 ) @ ( c_Transitive__Closure_Ortrancl @ SY3849 @ SV804 ) @ ( tc_prod @ SV804 @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2473,plain,
! [SV805: $i,SV271: $i] :
( ( ! [SY3850: $i] : ( c_in @ ( c_Pair @ SV271 @ SV271 @ SV805 @ SV805 ) @ ( c_Transitive__Closure_Ortrancl @ SY3850 @ SV805 ) @ ( tc_prod @ SV805 @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2474,plain,
! [SV806: $i,SV272: $i] :
( ( ! [SY3851: $i,SY3852: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SV806 @ SY3851 @ SY3852 ) @ SY3851 @ SY3852 @ SY3852 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SY3852 ) @ ( tc_prod @ SY3852 @ SY3852 ) )
| ~ ( c_in @ ( c_Pair @ SV806 @ SY3851 @ SY3852 @ SY3852 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SY3852 ) @ ( tc_prod @ SY3852 @ SY3852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2475,plain,
! [SV807: $i,SV273: $i] :
( ( ! [SY3853: $i] :
( ~ ( class_Orderings_Olinorder @ SV273 )
| ( c_lessequals @ SV807 @ SY3853 @ SV273 )
| ( c_lessequals @ SY3853 @ SV807 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2476,plain,
! [SV808: $i,SV274: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV274 @ SV808 ) @ SV808 )
= ( c_Transitive__Closure_Ortrancl @ SV274 @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2477,plain,
! [SV809: $i,SV275: $i] :
( ( ! [SY3854: $i] :
( ( c_lessequals @ SV275 @ ( c_Product__Type_OSigma @ SV809 @ ( c_COMBK @ SV809 @ ( tc_fun @ SY3854 @ tc_bool ) @ SY3854 ) @ SY3854 @ SY3854 ) @ ( tc_fun @ ( tc_prod @ SY3854 @ SY3854 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV809 @ SV275 @ SY3854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2478,plain,
! [SV810: $i,SV276: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV276 @ SV810 ) @ SV810 )
= ( c_Transitive__Closure_Ortrancl @ SV276 @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2479,plain,
! [SV811: $i,SV277: $i] :
( ( ! [SY3855: $i,SY3856: $i,SY3857: $i,SY3858: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SY3855 @ SY3856 ) @ ( c_Relation_OImage @ SY3857 @ SY3858 @ SY3855 @ SY3856 ) @ ( tc_fun @ SY3856 @ tc_bool ) )
| ~ ( c_lessequals @ SV811 @ SY3858 @ ( tc_fun @ SY3855 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SY3857 @ ( tc_fun @ ( tc_prod @ SY3855 @ SY3856 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2480,plain,
! [SV812: $i,SV278: $i] :
( ( ! [SY3859: $i,SY3860: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SV812 @ SY3859 ) @ ( c_Relation_ODomain @ SY3860 @ SV812 @ SY3859 ) @ ( tc_fun @ SV812 @ tc_bool ) )
| ~ ( c_lessequals @ SV278 @ SY3860 @ ( tc_fun @ ( tc_prod @ SV812 @ SY3859 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2481,plain,
! [SV813: $i,SV279: $i] :
( ( ! [SY3861: $i,SY3862: $i] :
( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
| ~ ( c_lessequals @ SY3861 @ SV279 @ ( tc_fun @ SY3862 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY3861 @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2482,plain,
! [SV814: $i,SV280: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV280 )
| ( c_lessequals @ SV814 @ SV814 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2483,plain,
! [SV815: $i,SV281: $i] :
( ( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_lessequals @ SV815 @ SV815 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2484,plain,
! [SV816: $i,SV282: $i] :
( ( ! [SY3863: $i] :
( ( c_Wellfounded_Owf @ SV282 @ SV816 )
| ~ ( c_lessequals @ SV282 @ SY3863 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY3863 @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2485,plain,
! [SV817: $i,SV283: $i] :
( ( ! [SY3864: $i,SY3865: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
| ~ ( hBOOL @ ( hAPP @ SY3864 @ SV817 ) )
| ~ ( c_lessequals @ SY3864 @ SV283 @ ( tc_fun @ SY3865 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2486,plain,
! [SV818: $i,SV284: $i] :
( ( ! [SY3866: $i,SY3867: $i] :
( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SY3866 @ tc_bool ) )
| ~ ( c_lessequals @ SY3867 @ SV818 @ ( tc_fun @ SY3866 @ tc_bool ) )
| ~ ( c_lessequals @ SV284 @ SY3867 @ ( tc_fun @ SY3866 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2487,plain,
! [SV819: $i,SV285: $i] :
( ( c_lessequals @ SV285 @ SV285 @ ( tc_fun @ SV819 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2488,plain,
! [SV820: $i,SV286: $i] :
( ( c_lessequals @ SV286 @ SV286 @ ( tc_fun @ SV820 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2489,plain,
! [SV821: $i,SV287: $i] :
( ( ! [SY3868: $i,SY3869: $i] :
( ~ ( class_Orderings_Opreorder @ SV287 )
| ( c_lessequals @ SV821 @ SY3868 @ SV287 )
| ~ ( c_lessequals @ SY3869 @ SY3868 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SY3869 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2490,plain,
! [SV822: $i,SV288: $i] :
( ( ! [SY3870: $i,SY3871: $i] :
( ~ ( class_Orderings_Oorder @ SV288 )
| ( c_lessequals @ SV822 @ SY3870 @ SV288 )
| ~ ( c_lessequals @ SV822 @ SY3871 @ SV288 )
| ~ ( c_lessequals @ SY3871 @ SY3870 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2491,plain,
! [SV823: $i,SV289: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV289 @ SV823 @ SV823 ) @ SV823 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ SV289 @ SV823 ) @ SV823 @ SV823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2492,plain,
! [SV824: $i,SV290: $i] :
( ( ! [SY3872: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV290 @ SV824 ) @ ( c_Transitive__Closure_Ortrancl @ SY3872 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ ( c_Transitive__Closure_Ortrancl @ SY3872 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2493,plain,
! [SV825: $i,SV291: $i] :
( ( ! [SY3873: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV291 @ SV825 ) @ ( c_Product__Type_OSigma @ SY3873 @ ( c_COMBK @ SY3873 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV291 @ ( c_Product__Type_OSigma @ SY3873 @ ( c_COMBK @ SY3873 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2494,plain,
! [SV826: $i,SV292: $i] :
( ( ! [SY3874: $i] :
( ~ ( class_Orderings_Oorder @ SV292 )
| ( SV826 = SY3874 )
| ~ ( c_lessequals @ SV826 @ SY3874 @ SV292 )
| ~ ( c_lessequals @ SY3874 @ SV826 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2495,plain,
! [SV827: $i,SV293: $i] :
( ( ! [SY3875: $i] :
( ~ ( class_Orderings_Oorder @ SV293 )
| ( SV827 = SY3875 )
| ~ ( c_lessequals @ SY3875 @ SV827 @ SV293 )
| ~ ( c_lessequals @ SV827 @ SY3875 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2496,plain,
! [SV828: $i,SV294: $i] :
( ( ! [SY3876: $i] :
( ~ ( class_Orderings_Oorder @ SV294 )
| ( SV828 = SY3876 )
| ~ ( c_lessequals @ SY3876 @ SV828 @ SV294 )
| ~ ( c_lessequals @ SV828 @ SY3876 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2497,plain,
! [SV829: $i,SV295: $i] :
( ( ! [SY3877: $i] :
( ( SV295 = SV829 )
| ~ ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SY3877 @ tc_bool ) )
| ~ ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SY3877 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2498,plain,
! [SV830: $i,SV296: $i] :
( ( ! [SY3878: $i] :
( ( SV296 = SV830 )
| ~ ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SY3878 @ tc_bool ) )
| ~ ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SY3878 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2499,plain,
! [SV831: $i,SV297: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV297 @ SV831 ) @ ( c_Transitive__Closure_Ortrancl @ SV297 @ SV831 ) @ SV831 @ SV831 @ SV831 )
= ( c_Transitive__Closure_Ortrancl @ SV297 @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2500,plain,
! [SV832: $i,SV298: $i] :
( ( ! [SY3879: $i,SY3880: $i,SY3881: $i,SY3882: $i,SY3883: $i,SY3884: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SY3879 @ SY3880 @ SY3881 ) @ ( c_Product__Type_OSigma @ SY3882 @ ( c_COMBK @ SY3883 @ ( tc_fun @ SY3881 @ tc_bool ) @ SY3879 ) @ SY3879 @ SY3881 ) @ ( tc_fun @ ( tc_prod @ SY3879 @ SY3881 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY3884 @ ( c_COMBK @ SY3883 @ ( tc_fun @ SY3881 @ tc_bool ) @ SY3880 ) @ SY3880 @ SY3881 ) @ ( tc_fun @ ( tc_prod @ SY3880 @ SY3881 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SY3882 @ ( c_COMBK @ SY3884 @ ( tc_fun @ SY3880 @ tc_bool ) @ SY3879 ) @ SY3879 @ SY3880 ) @ ( tc_fun @ ( tc_prod @ SY3879 @ SY3880 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2501,plain,
! [SV833: $i,SV299: $i] :
( ( ! [SY3885: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV299 @ SV833 ) @ ( c_Transitive__Closure_Ortrancl @ SY3885 @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ SY3885 @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2502,plain,
! [SV834: $i,SV300: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV300 @ SV834 ) @ SV834 )
= ( c_Transitive__Closure_Ortrancl @ SV300 @ SV834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2503,plain,
! [SV835: $i,SV301: $i] :
( ( ( c_Relation_Orel__comp @ SV301 @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV835 ) @ SV835 @ SV835 @ SV835 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV301 @ SV835 ) @ SV301 @ SV835 @ SV835 @ SV835 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2504,plain,
! [SV836: $i,SV302: $i] :
( ( ! [SY3886: $i,SY3887: $i,SY3888: $i,SY3889: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SY3886 @ tc_bool ) @ SY3887 ) @ SY3887 @ SY3886 ) @ ( c_Product__Type_OSigma @ SY3888 @ ( c_COMBK @ SV836 @ ( tc_fun @ SY3886 @ tc_bool ) @ SY3887 ) @ SY3887 @ SY3886 ) @ ( tc_fun @ ( tc_prod @ SY3887 @ SY3886 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SY3888 @ ( tc_fun @ SY3887 @ tc_bool ) )
| ~ ( c_in @ SY3889 @ SV836 @ SY3886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2505,plain,
! [SV837: $i,SV303: $i] :
( ( ! [SY3890: $i,SY3891: $i,SY3892: $i,SY3893: $i] :
( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SY3890 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SY3891 @ ( tc_fun @ SY3892 @ tc_bool ) @ SY3890 ) @ SY3890 @ SY3892 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SY3891 @ ( tc_fun @ SY3892 @ tc_bool ) @ SY3890 ) @ SY3890 @ SY3892 ) @ ( tc_fun @ ( tc_prod @ SY3890 @ SY3892 ) @ tc_bool ) )
| ~ ( c_in @ SY3893 @ SY3891 @ SY3892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2506,plain,
! [SV838: $i,SV304: $i] :
( ( c_lessequals @ ( c_Relation_OId__on @ SV304 @ SV838 ) @ ( c_Product__Type_OSigma @ SV304 @ ( c_COMBK @ SV304 @ ( tc_fun @ SV838 @ tc_bool ) @ SV838 ) @ SV838 @ SV838 ) @ ( tc_fun @ ( tc_prod @ SV838 @ SV838 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2507,plain,
! [SV839: $i,SV305: $i] :
( ( ! [SY3894: $i] :
( ( c_lessequals @ SV305 @ ( c_Product__Type_OSigma @ SV839 @ ( c_COMBK @ SV839 @ ( tc_fun @ SY3894 @ tc_bool ) @ SY3894 ) @ SY3894 @ SY3894 ) @ ( tc_fun @ ( tc_prod @ SY3894 @ SY3894 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV839 @ SV305 @ SY3894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2508,plain,
! [SV840: $i,SV306: $i] :
( ( ! [SY3895: $i,SY3896: $i,SY3897: $i,SY3898: $i,SY3899: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SY3895 @ SY3896 @ SY3897 ) @ ( c_Relation_Orel__comp @ SY3898 @ SY3899 @ SY3895 @ SY3896 @ SY3897 ) @ ( tc_fun @ ( tc_prod @ SY3895 @ SY3897 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SY3899 @ ( tc_fun @ ( tc_prod @ SY3896 @ SY3897 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SY3898 @ ( tc_fun @ ( tc_prod @ SY3895 @ SY3896 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2509,plain,
! [SV841: $i,SV307: $i] :
( ( ! [SY3900: $i,SY3901: $i] :
( ( hAPP @ ( c_COMBK @ SV307 @ SV841 @ SY3900 ) @ SY3901 )
= SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2510,plain,
! [SV842: $i,SV308: $i] :
( ( ! [SY3902: $i,SY3903: $i,SY3904: $i,SY3905: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SY3902 @ SY3903 ) @ SY3904 @ ( tc_fun @ SY3903 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SY3905 @ ( c_COMBK @ SY3904 @ ( tc_fun @ SY3903 @ tc_bool ) @ SY3902 ) @ SY3902 @ SY3903 ) @ ( tc_fun @ ( tc_prod @ SY3902 @ SY3903 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2511,plain,
! [SV843: $i,SV309: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV309 @ SV843 ) @ SV843 )
| ~ ( c_Relation_Osym @ SV309 @ SV843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2512,plain,
! [SV844: $i,SV310: $i] :
( ( ! [SY3906: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SY3906 @ SV844 ) )
| ~ ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SY3906 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY3906 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2513,plain,
! [SV845: $i,SV311: $i] :
( ( ! [SY3907: $i,SY3908: $i,SY3909: $i] :
( ( c_in @ SV311 @ SV845 @ SY3907 )
| ( SV311 = SY3908 )
| ~ ( c_lessequals @ SY3909 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SY3907 @ tc_bool ) @ SY3907 ) @ SY3907 @ SY3907 ) @ ( tc_fun @ ( tc_prod @ SY3907 @ SY3907 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SY3908 @ SY3907 @ SY3907 ) @ ( c_Transitive__Closure_Ortrancl @ SY3909 @ SY3907 ) @ ( tc_prod @ SY3907 @ SY3907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2514,plain,
! [SV846: $i,SV312: $i] :
( ( ! [SY3910: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV312 @ SV846 ) @ ( c_Wellfounded_Oacc @ SY3910 @ SV846 ) @ ( tc_fun @ SV846 @ tc_bool ) )
| ~ ( c_lessequals @ SY3910 @ SV312 @ ( tc_fun @ ( tc_prod @ SV846 @ SV846 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2515,plain,
! [SV847: $i,SV313: $i] :
( ( ! [SY3911: $i,SY3912: $i,SY3913: $i] :
( ~ ( class_HOL_Oord @ SV313 )
| ( c_lessequals @ ( hAPP @ SV847 @ SY3911 ) @ ( hAPP @ SY3912 @ SY3911 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SY3912 @ ( tc_fun @ SY3913 @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2516,plain,
! [SV848: $i,SV314: $i] :
( ( ! [SY3914: $i,SY3915: $i] :
( ( c_in @ SV314 @ SV848 @ SY3914 )
| ~ ( c_in @ SV314 @ SY3915 @ SY3914 )
| ~ ( c_lessequals @ SY3915 @ SV848 @ ( tc_fun @ SY3914 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2517,plain,
! [SV849: $i,SV315: $i] :
( ( ! [SY3916: $i,SY3917: $i] :
( ( c_in @ SV315 @ SV849 @ SY3916 )
| ~ ( c_lessequals @ SY3917 @ SV849 @ ( tc_fun @ SY3916 @ tc_bool ) )
| ~ ( c_in @ SV315 @ SY3917 @ SY3916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2518,plain,
! [SV850: $i,SV316: $i] :
( ( ! [SY3918: $i,SY3919: $i] :
( ( c_in @ SV316 @ SV850 @ SY3918 )
| ~ ( c_in @ SV316 @ SY3919 @ SY3918 )
| ~ ( c_lessequals @ SY3919 @ SV850 @ ( tc_fun @ SY3918 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2519,plain,
! [SV851: $i,SV317: $i] :
( ( ! [SY3920: $i,SY3921: $i] :
( ( c_in @ SV317 @ SV851 @ SY3920 )
| ~ ( c_in @ SV317 @ SY3921 @ SY3920 )
| ~ ( c_lessequals @ SY3921 @ SV851 @ ( tc_fun @ SY3920 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2520,plain,
! [SV852: $i,SV318: $i] :
( ( ! [SY3922: $i] :
( ( c_in @ SV318 @ ( c_Transitive__Closure_Ortrancl @ SV852 @ SY3922 ) @ ( tc_prod @ SY3922 @ SY3922 ) )
| ~ ( c_in @ SV318 @ SV852 @ ( tc_prod @ SY3922 @ SY3922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2521,plain,
! [SV853: $i,SV319: $i] :
( ( ! [SY3923: $i,SY3924: $i] :
( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SY3923 @ SY3923 ) @ ( c_Transitive__Closure_Ortrancl @ SY3924 @ SY3923 ) @ ( tc_prod @ SY3923 @ SY3923 ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV853 @ SY3923 @ SY3923 ) @ ( c_Transitive__Closure_Otrancl @ SY3924 @ SY3923 ) @ ( tc_prod @ SY3923 @ SY3923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2522,plain,
! [SV854: $i,SV320: $i] :
( ( ! [SY3925: $i,SY3926: $i,SY3927: $i] :
( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SY3925 @ SY3925 ) @ ( c_Transitive__Closure_Otrancl @ SY3926 @ SY3925 ) @ ( tc_prod @ SY3925 @ SY3925 ) )
| ~ ( c_in @ ( c_Pair @ SY3927 @ SV854 @ SY3925 @ SY3925 ) @ ( c_Transitive__Closure_Ortrancl @ SY3926 @ SY3925 ) @ ( tc_prod @ SY3925 @ SY3925 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SY3927 @ SY3925 @ SY3925 ) @ ( c_Transitive__Closure_Otrancl @ SY3926 @ SY3925 ) @ ( tc_prod @ SY3925 @ SY3925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2523,plain,
! [SV855: $i,SV321: $i] :
( ( ! [SY3928: $i,SY3929: $i,SY3930: $i] :
( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SY3928 @ SY3928 ) @ ( c_Transitive__Closure_Otrancl @ SY3929 @ SY3928 ) @ ( tc_prod @ SY3928 @ SY3928 ) )
| ~ ( c_in @ ( c_Pair @ SY3930 @ SV855 @ SY3928 @ SY3928 ) @ ( c_Transitive__Closure_Otrancl @ SY3929 @ SY3928 ) @ ( tc_prod @ SY3928 @ SY3928 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SY3930 @ SY3928 @ SY3928 ) @ ( c_Transitive__Closure_Ortrancl @ SY3929 @ SY3928 ) @ ( tc_prod @ SY3928 @ SY3928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2524,plain,
! [SV856: $i,SV322: $i] :
( ( ! [SY3931: $i,SY3932: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV856 @ SV322 @ SY3931 @ SY3932 ) @ SY3932 @ SY3932 ) @ SV856 @ ( tc_prod @ SY3932 @ SY3932 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SY3931 @ SY3932 @ SY3932 ) @ ( c_Transitive__Closure_Otrancl @ SV856 @ SY3932 ) @ ( tc_prod @ SY3932 @ SY3932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2525,plain,
! [SV857: $i,SV323: $i] :
( ( ! [SY3933: $i,SY3934: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SY3933 @ SY3934 ) @ SY3933 @ SY3934 @ SY3934 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY3934 ) @ ( tc_prod @ SY3934 @ SY3934 ) )
| ( c_in @ ( c_Pair @ SV857 @ SY3933 @ SY3934 @ SY3934 ) @ SV323 @ ( tc_prod @ SY3934 @ SY3934 ) )
| ~ ( c_in @ ( c_Pair @ SV857 @ SY3933 @ SY3934 @ SY3934 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY3934 ) @ ( tc_prod @ SY3934 @ SY3934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2526,plain,
! [SV858: $i,SV324: $i] :
( ( ! [SY3935: $i] :
( ~ ( c_in @ ( c_Pair @ SV324 @ SV324 @ SV858 @ SV858 ) @ SY3935 @ ( tc_prod @ SV858 @ SV858 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY3935 @ SV858 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY3935 @ SV858 ) @ SV858 @ SV858 ) @ ( c_Transitive__Closure_Otrancl @ SY3935 @ SV858 ) @ ( tc_prod @ SV858 @ SV858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2527,plain,
! [SV859: $i,SV325: $i] :
( ( ! [SY3936: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV325 @ SV859 @ SY3936 ) @ SV859 @ ( tc_fun @ SY3936 @ tc_bool ) )
| ~ ( c_in @ SV325 @ ( c_Complete__Lattice_OSup__class_OSup @ SV859 @ ( tc_fun @ SY3936 @ tc_bool ) ) @ SY3936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2528,plain,
! [SV860: $i,SV326: $i] :
( ( ! [SY3937: $i,SY3938: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SV860 @ SY3937 @ SY3937 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY3938 @ SY3937 @ SY3937 ) @ SY3937 ) @ ( tc_prod @ SY3937 @ SY3937 ) )
| ~ ( c_in @ ( c_Pair @ SV860 @ SV326 @ SY3937 @ SY3937 ) @ ( c_Transitive__Closure_Ortrancl @ SY3938 @ SY3937 ) @ ( tc_prod @ SY3937 @ SY3937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2529,plain,
! [SV861: $i,SV327: $i] :
( ( ! [SY3939: $i,SY3940: $i] :
( ( c_in @ ( c_Pair @ SV327 @ SV861 @ SY3939 @ SY3939 ) @ ( c_Transitive__Closure_Ortrancl @ SY3940 @ SY3939 ) @ ( tc_prod @ SY3939 @ SY3939 ) )
| ~ ( c_in @ ( c_Pair @ SV861 @ SV327 @ SY3939 @ SY3939 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY3940 @ SY3939 @ SY3939 ) @ SY3939 ) @ ( tc_prod @ SY3939 @ SY3939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2530,plain,
! [SV862: $i,SV328: $i] :
( ( ! [SY3941: $i,SY3942: $i,SY3943: $i,SY3944: $i,SY3945: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SY3941 @ SY3942 @ SY3943 @ SY3944 @ SY3945 ) @ SY3943 @ SY3945 ) @ SY3941 @ ( tc_prod @ SY3943 @ SY3945 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SY3943 @ SY3944 ) @ ( c_Relation_Orel__comp @ SY3941 @ SY3942 @ SY3943 @ SY3945 @ SY3944 ) @ ( tc_prod @ SY3943 @ SY3944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2531,plain,
! [SV863: $i,SV329: $i] :
( ( ! [SY3946: $i,SY3947: $i,SY3948: $i,SY3949: $i,SY3950: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SY3946 @ SY3947 @ SY3948 @ SY3949 @ SY3950 ) @ SV863 @ SY3950 @ SY3949 ) @ SY3947 @ ( tc_prod @ SY3950 @ SY3949 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SY3948 @ SY3949 ) @ ( c_Relation_Orel__comp @ SY3946 @ SY3947 @ SY3948 @ SY3950 @ SY3949 ) @ ( tc_prod @ SY3948 @ SY3949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2532,plain,
! [SV864: $i,SV330: $i] :
( ( ! [SY3951: $i,SY3952: $i,SY3953: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SY3951 @ SY3952 @ SY3953 ) @ ( tc_fun @ SY3952 @ SY3953 ) )
| ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SY3951 @ SV330 @ SY3952 @ SY3953 ) ) @ ( hAPP @ SY3951 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SY3951 @ SV330 @ SY3952 @ SY3953 ) ) @ SY3953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2533,plain,
! [SV865: $i,SV331: $i] :
( ( ! [SY3954: $i,SY3955: $i,SY3956: $i,SY3957: $i] :
( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SY3954 @ SY3955 )
| ~ ( c_in @ SV865 @ SY3956 @ SY3957 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SY3956 @ ( c_COMBK @ SY3954 @ ( tc_fun @ SY3955 @ tc_bool ) @ SY3957 ) @ SY3957 @ SY3955 ) @ ( tc_fun @ SY3957 @ SY3955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2534,plain,
! [SV866: $i,SV332: $i] :
( ( ! [SY3958: $i,SY3959: $i,SY3960: $i] :
( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SY3958 @ SY3959 @ SY3960 ) @ ( tc_fun @ SY3959 @ SY3960 ) )
| ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SY3958 @ SV332 @ SY3959 @ SY3960 ) ) @ ( hAPP @ SY3958 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SY3958 @ SV332 @ SY3959 @ SY3960 ) ) @ SY3960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2535,plain,
! [SV867: $i,SV333: $i] :
( ( ! [SY3961: $i,SY3962: $i,SY3963: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV867 @ SY3961 @ SY3962 @ SY3963 ) @ ( tc_fun @ SY3962 @ SY3963 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV867 @ SY3961 @ SV333 @ SY3962 @ SY3963 ) @ SV867 @ SY3962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2536,plain,
! [SV868: $i,SV334: $i] :
( ( ! [SY3964: $i,SY3965: $i,SY3966: $i] :
( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SV868 @ SY3964 @ SY3965 @ SY3966 ) @ ( tc_fun @ SY3965 @ SY3966 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV868 @ SY3964 @ SV334 @ SY3965 @ SY3966 ) @ SV868 @ SY3965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2537,plain,
! [SV869: $i,SV335: $i] :
( ( ! [SY3967: $i,SY3968: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SV869 @ SY3967 @ SY3968 ) @ SV335 @ SY3968 )
| ~ ( c_in @ SV869 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SY3967 @ SY3968 ) @ ( tc_fun @ SY3968 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2538,plain,
! [SV870: $i,SV336: $i] :
( ( ( SV336
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ SV870 @ SV870 ) )
| ~ ( c_in @ SV336 @ ( c_Relation_OId @ SV870 ) @ ( tc_prod @ SV870 @ SV870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2539,plain,
! [SV871: $i,SV337: $i] :
( ( ! [SY3969: $i] :
( ( c_in @ SV337 @ ( c_Complete__Lattice_OInf__class_OInf @ SV871 @ ( tc_fun @ SY3969 @ tc_bool ) ) @ SY3969 )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV337 @ SV871 @ SY3969 ) @ SV871 @ ( tc_fun @ SY3969 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2540,plain,
! [SV872: $i,SV338: $i] :
( ( ( c_Wellfounded_Owf @ SV338 @ SV872 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV338 @ SV872 ) @ ( c_Wellfounded_Oacc @ SV338 @ SV872 ) @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2541,plain,
! [SV873: $i,SV339: $i] :
( ( ( c_Wellfounded_Owf @ SV339 @ SV873 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV339 @ SV873 ) @ ( c_Wellfounded_Oacc @ SV339 @ SV873 ) @ SV873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2542,plain,
! [SV874: $i,SV340: $i] :
( ( ! [SY3970: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV340 @ SV874 @ SY3970 ) @ SV340 @ SY3970 )
| ~ ( c_in @ SV874 @ ( c_Relation_OId__on @ SV340 @ SY3970 ) @ ( tc_prod @ SY3970 @ SY3970 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2543,plain,
! [SV875: $i,SV341: $i] :
( ( ! [SY3971: $i] :
( ( SV341
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SY3971 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SY3971 ) @ SY3971 @ SY3971 ) )
| ~ ( c_in @ SV341 @ ( c_Relation_OId__on @ SV875 @ SY3971 ) @ ( tc_prod @ SY3971 @ SY3971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2544,plain,
! [SV876: $i,SV342: $i] :
( ( ! [SY3972: $i,SY3973: $i,SY3974: $i,SY3975: $i] :
( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SY3972 @ SY3973 @ SY3974 )
= ( c_Recdef_Ocut @ SY3975 @ SV876 @ SY3972 @ SY3973 @ SY3974 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SY3975 @ SV876 @ SY3972 @ SY3973 @ SY3974 ) @ SY3972 @ SY3973 @ SY3973 ) @ SV876 @ ( tc_prod @ SY3973 @ SY3973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2545,plain,
! [SV877: $i,SV343: $i] :
( ( ! [SY3976: $i] :
( ( c_lessequals @ SV343 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV343 @ SV877 @ SV877 ) @ SV343 @ SV877 @ SV877 @ SV877 ) @ ( tc_fun @ ( tc_prod @ SV877 @ SV877 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SY3976 @ SV343 @ SV877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2546,plain,
! [SV878: $i,SV344: $i] :
( ( ( c_Nitpick_Orefl_H @ SV344 @ SV878 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ SV878 @ SV878 ) @ SV344 @ ( tc_prod @ SV878 @ SV878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2547,plain,
! [SV879: $i,SV345: $i] :
( ( ! [SY3977: $i,SY3978: $i,SY3979: $i] :
( ~ ( c_in @ SV345 @ SV879 @ SY3977 )
| ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SY3978 @ SY3977 ) @ SY3977 @ SY3977 ) @ SY3978 @ ( tc_prod @ SY3977 @ SY3977 ) )
| ~ ( c_in @ SY3979 @ SV879 @ SY3977 )
| ~ ( c_Wellfounded_Owf @ SY3978 @ SY3977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2548,plain,
! [SV880: $i,SV346: $i] :
( ( ! [SY3980: $i,SY3981: $i,SY3982: $i] :
( ~ ( c_in @ SV346 @ SV880 @ SY3980 )
| ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SY3981 @ SY3980 ) @ SY3980 @ SY3980 ) @ SY3981 @ ( tc_prod @ SY3980 @ SY3980 ) )
| ~ ( c_in @ SY3982 @ SV880 @ SY3980 )
| ~ ( c_Wellfounded_Owf @ SY3981 @ SY3980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2549,plain,
! [SV881: $i,SV347: $i] :
( ( ! [SY3983: $i,SY3984: $i,SY3985: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SY3983 @ SY3984 @ SY3985 ) @ SV881 @ SY3984 @ SY3985 ) @ SY3983 @ ( tc_prod @ SY3984 @ SY3985 ) )
| ~ ( c_in @ SV881 @ ( c_Relation_OImage @ SY3983 @ SV347 @ SY3984 @ SY3985 ) @ SY3985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2550,plain,
! [SV882: $i,SV348: $i] :
( ( ! [SY3986: $i,SY3987: $i,SY3988: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SY3986 @ SY3987 @ SY3988 ) @ SV882 @ SY3987 @ SY3988 ) @ SY3986 @ ( tc_prod @ SY3987 @ SY3988 ) )
| ~ ( c_in @ SV882 @ ( c_Relation_OImage @ SY3986 @ SV348 @ SY3987 @ SY3988 ) @ SY3988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2551,plain,
! [SV883: $i,SV349: $i] :
( ( ! [SY3989: $i,SY3990: $i] :
( ( SV349 = SV883 )
| ~ ( c_in @ ( c_Pair @ SV349 @ SV883 @ SY3989 @ SY3989 ) @ ( c_Transitive__Closure_Ortrancl @ SY3990 @ SY3989 ) @ ( tc_prod @ SY3989 @ SY3989 ) )
| ( c_in @ SV349 @ ( c_Relation_ODomain @ SY3990 @ SY3989 @ SY3989 ) @ SY3989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2552,plain,
! [SV884: $i,SV350: $i] :
( ( ! [SY3991: $i,SY3992: $i] :
( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SV884 @ SY3991 @ SY3992 ) @ SY3991 @ SY3992 ) @ SV884 @ ( tc_prod @ SY3991 @ SY3992 ) )
| ~ ( c_in @ SV350 @ ( c_Relation_ODomain @ SV884 @ SY3991 @ SY3992 ) @ SY3991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2553,plain,
! [SV885: $i,SV351: $i] :
( ( ! [SY3993: $i,SY3994: $i] :
( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SV885 @ SY3993 @ SY3994 ) @ SY3993 @ SY3994 ) @ SV885 @ ( tc_prod @ SY3993 @ SY3994 ) )
| ~ ( c_in @ SV351 @ ( c_Relation_ODomain @ SV885 @ SY3993 @ SY3994 ) @ SY3993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2554,plain,
! [SV886: $i,SV352: $i] :
( ( ! [SY3995: $i] :
( ( c_in @ SV352 @ ( c_Relation_ODomain @ SV886 @ SY3995 @ SY3995 ) @ SY3995 )
| ( c_in @ ( c_Pair @ SV352 @ SV352 @ SY3995 @ SY3995 ) @ ( c_Transitive__Closure_Ortrancl @ SV886 @ SY3995 ) @ ( tc_prod @ SY3995 @ SY3995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2555,plain,
! [SV887: $i,SV353: $i] :
( ( ! [SY3996: $i,SY3997: $i,SY3998: $i] :
( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
| ( hBOOL @ ( hAPP @ SV353 @ SY3996 ) )
| ~ ( c_in @ ( c_Pair @ SY3996 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SY3997 @ SY3998 ) @ SY3998 @ SY3998 ) @ SY3997 @ ( tc_prod @ SY3998 @ SY3998 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SY3997 @ SY3998 ) @ SY3998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2556,plain,
! [SV888: $i,SV354: $i] :
( ( ! [SY3999: $i,SY4000: $i] :
( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
| ( c_in @ SY3999 @ ( c_Wellfounded_Oacc @ SY4000 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY3999 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SY4000 ) @ t_a @ t_a ) @ SY4000 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SY4000 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2557,plain,
! [SV889: $i,SV355: $i] :
( ( ! [SY4001: $i,SY4002: $i] :
( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
| ( hBOOL @ ( hAPP @ SV355 @ SY4001 ) )
| ~ ( c_in @ ( c_Pair @ SY4001 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SY4002 ) @ t_a @ t_a ) @ SY4002 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SY4002 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2558,plain,
! [SV890: $i,SV356: $i] :
( ( ! [SY4003: $i,SY4004: $i] :
( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
| ( c_in @ SY4003 @ ( c_Wellfounded_Oacc @ SY4004 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4003 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SY4004 ) @ t_a @ t_a ) @ SY4004 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SY4004 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2559,plain,
! [SV891: $i,SV357: $i] :
( ( ! [SY4005: $i,SY4006: $i] :
( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SY4005 ) @ SY4005 )
| ~ ( c_in @ ( c_Pair @ SV357 @ SY4006 @ SY4005 @ SY4005 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SY4005 ) @ ( tc_prod @ SY4005 @ SY4005 ) )
| ~ ( c_in @ SY4006 @ ( c_Wellfounded_Oacc @ SV891 @ SY4005 ) @ SY4005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2560,plain,
! [SV892: $i,SV358: $i] :
( ( ! [SY4007: $i,SY4008: $i] :
( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SY4007 ) @ SY4007 )
| ~ ( c_in @ SY4008 @ ( c_Wellfounded_Oacc @ SV892 @ SY4007 ) @ SY4007 )
| ~ ( c_in @ ( c_Pair @ SV358 @ SY4008 @ SY4007 @ SY4007 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SY4007 ) @ ( tc_prod @ SY4007 @ SY4007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2561,plain,
! [SV893: $i,SV359: $i] :
( ( ! [SY4009: $i] :
( ( c_in @ SV359 @ ( c_Wellfounded_Oacc @ SV893 @ SY4009 ) @ SY4009 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV893 @ SV359 @ SY4009 ) @ SV359 @ SY4009 @ SY4009 ) @ SV893 @ ( tc_prod @ SY4009 @ SY4009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2562,plain,
! [SV894: $i,SV360: $i] :
( ( ! [SY4010: $i,SY4011: $i] :
( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
| ( hBOOL @ ( hAPP @ SV360 @ SY4010 ) )
| ~ ( c_in @ ( c_Pair @ SY4010 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SY4011 ) @ t_a @ t_a ) @ SY4011 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SY4011 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2563,plain,
! [SV895: $i,SV361: $i] :
( ( ! [SY4012: $i,SY4013: $i,SY4014: $i] :
( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
| ( hBOOL @ ( hAPP @ SV361 @ SY4012 ) )
| ~ ( c_in @ ( c_Pair @ SY4012 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SY4013 @ SY4014 ) @ SY4014 @ SY4014 ) @ SY4013 @ ( tc_prod @ SY4014 @ SY4014 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SY4013 @ SY4014 ) @ SY4014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2564,plain,
! [SV896: $i,SV362: $i] :
( ( ! [SY4015: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV362 @ SV896 @ SY4015 ) @ SV896 @ SY4015 @ SY4015 ) @ SV362 @ ( tc_prod @ SY4015 @ SY4015 ) )
| ( c_in @ SV896 @ ( c_Wellfounded_Oacc @ SV362 @ SY4015 ) @ SY4015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2565,plain,
! [SV897: $i,SV363: $i] :
( ( ! [SY4016: $i,SY4017: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SV897 @ SY4016 @ SY4017 ) @ SV363 @ SY4017 @ SY4016 ) @ SV897 @ ( tc_prod @ SY4017 @ SY4016 ) )
| ~ ( c_in @ SV363 @ ( c_Relation_ORange @ SV897 @ SY4017 @ SY4016 ) @ SY4016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2566,plain,
! [SV898: $i,SV364: $i] :
( ( ! [SY4018: $i,SY4019: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SV898 @ SY4018 @ SY4019 ) @ SV364 @ SY4019 @ SY4018 ) @ SV898 @ ( tc_prod @ SY4019 @ SY4018 ) )
| ~ ( c_in @ SV364 @ ( c_Relation_ORange @ SV898 @ SY4019 @ SY4018 ) @ SY4018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2567,plain,
! [SV899: $i,SV365: $i] :
( ( ! [SY4020: $i,SY4021: $i] :
( ~ ( c_in @ ( c_Pair @ SV365 @ SV899 @ SY4020 @ SY4020 ) @ SY4021 @ ( tc_prod @ SY4020 @ SY4020 ) )
| ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SY4020 @ SY4020 ) @ SY4021 @ ( tc_prod @ SY4020 @ SY4020 ) )
| ~ ( c_Wellfounded_Owf @ SY4021 @ SY4020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2568,plain,
! [SV900: $i,SV366: $i] :
( ( ! [SY4022: $i,SY4023: $i] :
( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SY4022 @ SY4022 ) @ ( c_Transitive__Closure_Otrancl @ SY4023 @ SY4022 ) @ ( tc_prod @ SY4022 @ SY4022 ) )
| ~ ( c_in @ ( c_Pair @ SV366 @ SV900 @ SY4022 @ SY4022 ) @ SY4023 @ ( tc_prod @ SY4022 @ SY4022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2569,plain,
! [SV901: $i,SV367: $i] :
( ( ! [SY4024: $i,SY4025: $i,SY4026: $i] :
( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SY4024 @ SY4024 ) @ ( c_Transitive__Closure_Otrancl @ SY4025 @ SY4024 ) @ ( tc_prod @ SY4024 @ SY4024 ) )
| ~ ( c_in @ ( c_Pair @ SY4026 @ SV901 @ SY4024 @ SY4024 ) @ ( c_Transitive__Closure_Otrancl @ SY4025 @ SY4024 ) @ ( tc_prod @ SY4024 @ SY4024 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SY4026 @ SY4024 @ SY4024 ) @ SY4025 @ ( tc_prod @ SY4024 @ SY4024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2570,plain,
! [SV902: $i,SV368: $i] :
( ( ! [SY4027: $i,SY4028: $i,SY4029: $i] :
( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SY4027 @ SY4027 ) @ ( c_Transitive__Closure_Otrancl @ SY4028 @ SY4027 ) @ ( tc_prod @ SY4027 @ SY4027 ) )
| ~ ( c_in @ ( c_Pair @ SY4029 @ SV902 @ SY4027 @ SY4027 ) @ SY4028 @ ( tc_prod @ SY4027 @ SY4027 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SY4029 @ SY4027 @ SY4027 ) @ ( c_Transitive__Closure_Otrancl @ SY4028 @ SY4027 ) @ ( tc_prod @ SY4027 @ SY4027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2571,plain,
! [SV903: $i,SV369: $i] :
( ( ! [SY4030: $i,SY4031: $i,SY4032: $i] :
( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SY4030 @ SY4031 ) @ SY4032 @ ( tc_prod @ SY4030 @ SY4031 ) )
| ~ ( c_in @ ( c_Pair @ SV903 @ SV369 @ SY4031 @ SY4030 ) @ ( c_Relation_Oconverse @ SY4032 @ SY4030 @ SY4031 ) @ ( tc_prod @ SY4031 @ SY4030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2572,plain,
! [SV904: $i,SV370: $i] :
( ( ! [SY4033: $i,SY4034: $i,SY4035: $i] :
( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SY4033 @ SY4034 ) @ ( c_Relation_Oconverse @ SY4035 @ SY4034 @ SY4033 ) @ ( tc_prod @ SY4033 @ SY4034 ) )
| ~ ( c_in @ ( c_Pair @ SV904 @ SV370 @ SY4034 @ SY4033 ) @ SY4035 @ ( tc_prod @ SY4034 @ SY4033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2573,plain,
! [SV905: $i,SV371: $i] :
( ( ! [SY4036: $i,SY4037: $i,SY4038: $i] :
( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SY4036 @ SY4037 ) @ ( c_Relation_Oconverse @ SY4038 @ SY4037 @ SY4036 ) @ ( tc_prod @ SY4036 @ SY4037 ) )
| ~ ( c_in @ ( c_Pair @ SV905 @ SV371 @ SY4037 @ SY4036 ) @ SY4038 @ ( tc_prod @ SY4037 @ SY4036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2574,plain,
! [SV906: $i,SV372: $i] :
( ( ! [SY4039: $i,SY4040: $i,SY4041: $i,SY4042: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SY4039 @ SY4040 @ SY4041 ) @ SY4042 )
= ( hAPP @ SV372 @ SY4042 ) )
| ~ ( c_in @ ( c_Pair @ SY4042 @ SY4039 @ SY4040 @ SY4040 ) @ SV906 @ ( tc_prod @ SY4040 @ SY4040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2575,plain,
! [SV907: $i,SV373: $i] :
( ( ! [SY4043: $i,SY4044: $i,SY4045: $i,SY4046: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SY4043 @ SY4044 @ SY4045 ) @ SY4046 )
= ( hAPP @ SV373 @ SY4046 ) )
| ~ ( c_in @ ( c_Pair @ SY4046 @ SY4043 @ SY4044 @ SY4044 ) @ SV907 @ ( tc_prod @ SY4044 @ SY4044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2576,plain,
! [SV908: $i,SV374: $i] :
( ( ! [SY4047: $i] :
( ( c_in @ SV374 @ ( c_Transitive__Closure_Otrancl @ SV908 @ SY4047 ) @ ( tc_prod @ SY4047 @ SY4047 ) )
| ~ ( c_in @ SV374 @ SV908 @ ( tc_prod @ SY4047 @ SY4047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2577,plain,
! [SV909: $i,SV375: $i] :
( ( ! [SY4048: $i,SY4049: $i] :
( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SY4048 @ SY4048 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4049 @ SY4048 ) @ SY4048 @ SY4048 ) @ ( tc_prod @ SY4048 @ SY4048 ) )
| ~ ( c_in @ ( c_Pair @ SV375 @ SV909 @ SY4048 @ SY4048 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4049 @ SY4048 @ SY4048 ) @ SY4048 ) @ ( tc_prod @ SY4048 @ SY4048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2578,plain,
! [SV910: $i,SV376: $i] :
( ( ! [SY4050: $i,SY4051: $i] :
( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SY4050 @ SY4050 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4051 @ SY4050 @ SY4050 ) @ SY4050 ) @ ( tc_prod @ SY4050 @ SY4050 ) )
| ~ ( c_in @ ( c_Pair @ SV376 @ SV910 @ SY4050 @ SY4050 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4051 @ SY4050 ) @ SY4050 @ SY4050 ) @ ( tc_prod @ SY4050 @ SY4050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2579,plain,
! [SV911: $i,SV377: $i] :
( ( ! [SY4052: $i] :
( ( c_in @ SV377 @ ( c_Wellfounded_Oacc @ SV911 @ SY4052 ) @ SY4052 )
| ~ ( c_Wellfounded_Owf @ SV911 @ SY4052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2580,plain,
! [SV912: $i,SV378: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV378 @ SV912 ) @ SV912 )
| ~ ( c_Relation_Osym @ SV378 @ SV912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2581,plain,
! [SV913: $i,SV379: $i] :
( ( ( c_Relation_Osym @ SV379 @ SV913 )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV379 @ SV913 @ SV913 ) @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2582,plain,
! [SV914: $i,SV380: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV380 @ SV914 @ SV914 ) @ SV914 )
| ~ ( c_Relation_Osym @ SV380 @ SV914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2583,plain,
! [SV915: $i,SV381: $i] :
( ( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV381 @ SV915 ) @ SV915 @ SV915 )
= ( c_Relation_ODomain @ SV381 @ SV915 @ SV915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2584,plain,
! [SV916: $i,SV383: $i] :
( ( ! [SY4053: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV383 ) @ SV916 @ SV383 @ SV383 @ SY4053 )
= SV916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2585,plain,
! [SV917: $i,SV384: $i] :
( ( ! [SY4054: $i] :
( ( c_Relation_Orel__comp @ SV384 @ ( c_Relation_OId @ SV917 ) @ SY4054 @ SV917 @ SV917 )
= SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2586,plain,
! [SV918: $i,SV385: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV385 @ SV918 ) @ SV918 @ SV918 ) @ SV918 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV385 @ SV918 @ SV918 ) @ SV918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2587,plain,
! [SV919: $i,SV386: $i] :
( ( ! [SY4055: $i] :
( ( c_Relation_Orefl__on @ SV386 @ SV919 @ SY4055 )
| ~ ( c_Relation_Orefl__on @ SV386 @ ( c_Relation_Oconverse @ SV919 @ SY4055 @ SY4055 ) @ SY4055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2588,plain,
! [SV920: $i,SV387: $i] :
( ( ! [SY4056: $i] :
( ( c_Relation_Orefl__on @ SV387 @ ( c_Relation_Oconverse @ SV920 @ SY4056 @ SY4056 ) @ SY4056 )
| ~ ( c_Relation_Orefl__on @ SV387 @ SV920 @ SY4056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2589,plain,
! [SV921: $i,SV388: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV388 @ SV388 @ SV921 @ SV921 @ SV921 ) @ SV921 )
| ~ ( c_Wellfounded_Owf @ SV388 @ SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2590,plain,
! [SV922: $i,SV389: $i] :
( ( ( c_Wellfounded_Owf @ SV389 @ SV922 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV389 @ SV389 @ SV922 @ SV922 @ SV922 ) @ SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2591,plain,
! [SV923: $i,SV390: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId @ SV390 ) @ SV923 @ SV390 @ SV390 )
= SV923 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2592,plain,
! [SV924: $i,SV391: $i] :
( ( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV391 @ SV924 ) @ SV924 @ SV924 )
= SV391 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2593,plain,
! [SV925: $i,SV392: $i] :
( ( ( ( c_Relation_Oconverse @ SV392 @ SV925 @ SV925 )
= SV392 )
| ~ ( c_Relation_Osym @ SV392 @ SV925 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2594,plain,
! [SV926: $i,SV393: $i] :
( ( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV393 @ SV926 ) @ SV926 @ SV926 )
= ( c_Relation_ORange @ SV393 @ SV926 @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2595,plain,
! [SV927: $i,SV394: $i] :
( ( ! [SY4057: $i,SY4058: $i,SY4059: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV394 @ SV927 @ SY4057 @ SY4058 @ SY4059 ) @ SY4057 @ SY4059 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV927 @ SY4058 @ SY4059 ) @ ( c_Relation_Oconverse @ SV394 @ SY4057 @ SY4058 ) @ SY4059 @ SY4058 @ SY4057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2596,plain,
! [SV928: $i,SV395: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId__on @ SV395 @ SV928 ) @ SV928 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2597,plain,
! [SV929: $i,SV396: $i] :
( ( c_Relation_Orefl__on @ SV396 @ ( c_Relation_OId__on @ SV396 @ SV929 ) @ SV929 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2598,plain,
! [SV930: $i,SV397: $i] :
( ( ! [SY4060: $i,SY4061: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SV930 @ SY4060 @ SY4061 ) @ SY4061 )
| ~ ( c_Wellfounded_Owf @ SV397 @ SY4060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2599,plain,
! [SV931: $i,SV398: $i] :
( ( ! [SY4062: $i,SY4063: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SV931 @ SY4062 @ SY4063 ) @ SY4063 )
| ~ ( c_Relation_Osym @ SV398 @ SY4062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2600,plain,
! [SV932: $i,SV400: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV400 @ SV932 ) @ SV932 )
| ~ ( c_Wellfounded_Owf @ SV400 @ SV932 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2601,plain,
! [SV933: $i,SV401: $i] :
( ( ! [SY4064: $i,SY4065: $i,SY4066: $i,SY4067: $i,SY4068: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SY4064 @ SY4065 @ SY4066 ) @ SY4067 @ SY4064 @ SY4066 @ SY4068 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SY4067 @ SY4065 @ SY4066 @ SY4068 ) @ SY4064 @ SY4065 @ SY4068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2602,plain,
! [SV934: $i,SV402: $i] :
( ( ! [SY4069: $i,SY4070: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV402 @ SV934 @ SY4069 @ SY4070 ) @ SY4070 @ SY4070 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV402 @ SY4069 @ SY4069 ) @ SV934 @ SY4069 @ SY4070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2603,plain,
! [SV935: $i,SV403: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV403 @ SV935 @ SV935 ) @ SV935 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV403 @ SV935 ) @ SV935 @ SV935 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2604,plain,
! [SV936: $i,SV404: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ SV404 @ SV936 ) @ SV936 @ SV936 )
= ( c_Relation_OId__on @ SV404 @ SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2605,plain,
! [SV937: $i,SV405: $i] :
( ( ! [SY4071: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV405 @ SV937 @ SY4071 ) @ SY4071 @ SV937 )
= ( c_Relation_ODomain @ SV405 @ SV937 @ SY4071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2606,plain,
! [SV938: $i,SV406: $i] :
( ( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV406 @ SV938 ) @ SV938 @ SV938 )
= SV406 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2607,plain,
! [SV939: $i,SV407: $i] :
( ( ! [SY4072: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV407 @ SV939 @ SY4072 ) @ SY4072 @ SV939 )
= SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2608,plain,
! [SV940: $i,SV408: $i] :
( ( ! [SY4073: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV408 @ SV940 @ SV940 ) @ SV408 @ SV940 @ SV940 @ SV940 )
= SV408 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4073 @ SV408 @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2609,plain,
! [SV941: $i,SV409: $i] :
( ( ! [SY4074: $i] :
( ( c_Relation_Orefl__on @ SV409 @ SV941 @ SY4074 )
| ~ ( c_Equiv__Relations_Oequiv @ SV409 @ SV941 @ SY4074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2610,plain,
! [SV942: $i,SV410: $i] :
( ( ! [SY4075: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ SV410 @ SV942 @ SY4075 ) @ ( tc_fun @ SY4075 @ tc_bool ) )
= SV410 )
| ~ ( c_Equiv__Relations_Oequiv @ SV410 @ SV942 @ SY4075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2611,plain,
! [SV943: $i,SV411: $i] :
( ( ! [SY4076: $i] :
( ( c_Relation_Osym @ SV411 @ SV943 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4076 @ SV411 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2612,plain,
! [SV944: $i,SV412: $i] :
( ( ! [SY4077: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV412 @ SV944 @ SY4077 ) @ SY4077 @ SV944 )
= ( c_Relation_ORange @ SV412 @ SV944 @ SY4077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2613,plain,
! [SV945: $i,SV413: $i] :
( ( ! [SY4078: $i] :
( ( c_Relation_ORange @ SV413 @ SV945 @ SY4078 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV413 @ SV945 @ SY4078 ) @ SY4078 @ SV945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2614,plain,
! [SV946: $i,SV414: $i] :
( ( ! [SY4079: $i] :
( ( c_Relation_Ototal__on @ SV414 @ SV946 @ SY4079 )
| ~ ( c_Relation_Ototal__on @ SV414 @ ( c_Relation_Oconverse @ SV946 @ SY4079 @ SY4079 ) @ SY4079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2615,plain,
! [SV947: $i,SV415: $i] :
( ( ! [SY4080: $i] :
( ( c_Relation_Ototal__on @ SV415 @ ( c_Relation_Oconverse @ SV947 @ SY4080 @ SY4080 ) @ SY4080 )
| ~ ( c_Relation_Ototal__on @ SV415 @ SV947 @ SY4080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2616,plain,
! [SV948: $i,SV416: $i] :
( ( ! [SY4081: $i,SY4082: $i] :
( ( SV416 = SV948 )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV948 @ SY4081 @ SY4081 ) @ ( c_Relation_OId__on @ SY4082 @ SY4081 ) @ ( tc_prod @ SY4081 @ SY4081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2617,plain,
! [SV949: $i,SV417: $i] :
( ( ! [SY4083: $i] :
( ( SV417 = SV949 )
| ~ ( c_in @ ( c_Pair @ SV417 @ SV949 @ SY4083 @ SY4083 ) @ ( c_Relation_OId @ SY4083 ) @ ( tc_prod @ SY4083 @ SY4083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2618,plain,
! [SV950: $i,SV418: $i] :
( ( ! [SY4084: $i] :
( ( c_in @ ( c_Pair @ SV418 @ SV418 @ SV950 @ SV950 ) @ SY4084 @ ( tc_prod @ SV950 @ SV950 ) )
| ~ ( c_Nitpick_Orefl_H @ SY4084 @ SV950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2619,plain,
! [SV951: $i,SV419: $i] :
( ( ! [SY4085: $i] :
( ~ ( c_in @ ( c_Pair @ SV419 @ SV419 @ SV951 @ SV951 ) @ SY4085 @ ( tc_prod @ SV951 @ SV951 ) )
| ~ ( c_Wellfounded_Owf @ SY4085 @ SV951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2620,plain,
! [SV952: $i,SV420: $i] :
( ( ! [SY4086: $i,SY4087: $i,SY4088: $i,SY4089: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SY4086 @ SY4086 ) @ ( c_Relation_Oinv__image @ SY4087 @ SY4088 @ SY4089 @ SY4086 ) @ ( tc_prod @ SY4086 @ SY4086 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY4088 @ SV420 ) @ ( hAPP @ SY4088 @ SV952 ) @ SY4089 @ SY4089 ) @ SY4087 @ ( tc_prod @ SY4089 @ SY4089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2621,plain,
! [SV953: $i,SV421: $i] :
( ( ! [SY4090: $i,SY4091: $i,SY4092: $i,SY4093: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SY4090 ) @ SY4091 @ SY4091 ) @ SY4092 @ ( tc_prod @ SY4091 @ SY4091 ) )
| ~ ( c_in @ ( c_Pair @ SV953 @ SY4090 @ SY4093 @ SY4093 ) @ ( c_Relation_Oinv__image @ SY4092 @ SV421 @ SY4091 @ SY4093 ) @ ( tc_prod @ SY4093 @ SY4093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2622,plain,
! [SV954: $i,SV422: $i] :
( ( ! [SY4094: $i,SY4095: $i] :
( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SY4094 @ SY4094 ) @ SY4095 @ ( tc_prod @ SY4094 @ SY4094 ) )
| ~ ( c_in @ ( c_Pair @ SV954 @ SV422 @ SY4094 @ SY4094 ) @ SY4095 @ ( tc_prod @ SY4094 @ SY4094 ) )
| ~ ( c_Relation_Osym @ SY4095 @ SY4094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2623,plain,
! [SV955: $i,SV423: $i] :
( ( ! [SY4096: $i,SY4097: $i] :
( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SY4096 @ SY4096 ) @ SY4097 @ ( tc_prod @ SY4096 @ SY4096 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV423 @ SY4096 @ SY4096 ) @ SY4097 @ ( tc_prod @ SY4096 @ SY4096 ) )
| ~ ( c_Relation_Osym @ SY4097 @ SY4096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2624,plain,
! [SV956: $i,SV424: $i] :
( ( ! [SY4098: $i,SY4099: $i,SY4100: $i,SY4101: $i,SY4102: $i,SY4103: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SY4098 @ SY4099 ) @ ( c_Relation_Orel__comp @ SY4100 @ SY4101 @ SY4098 @ SY4102 @ SY4099 ) @ ( tc_prod @ SY4098 @ SY4099 ) )
| ~ ( c_in @ ( c_Pair @ SY4103 @ SV956 @ SY4102 @ SY4099 ) @ SY4101 @ ( tc_prod @ SY4102 @ SY4099 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4103 @ SY4098 @ SY4102 ) @ SY4100 @ ( tc_prod @ SY4098 @ SY4102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2625,plain,
! [SV957: $i,SV425: $i] :
( ( ! [SY4104: $i,SY4105: $i,SY4106: $i] :
( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SY4104 @ SY4104 ) @ ( c_Transitive__Closure_Otrancl @ SY4105 @ SY4104 ) @ ( tc_prod @ SY4104 @ SY4104 ) )
| ~ ( c_in @ ( c_Pair @ SY4106 @ SV957 @ SY4104 @ SY4104 ) @ SY4105 @ ( tc_prod @ SY4104 @ SY4104 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SY4106 @ SY4104 @ SY4104 ) @ SY4105 @ ( tc_prod @ SY4104 @ SY4104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2626,plain,
! [SV958: $i,SV426: $i] :
( ( ! [SY4107: $i,SY4108: $i,SY4109: $i] :
( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SY4107 @ SY4107 ) @ ( c_Transitive__Closure_Otrancl @ SY4108 @ SY4107 ) @ ( tc_prod @ SY4107 @ SY4107 ) )
| ~ ( c_in @ ( c_Pair @ SY4109 @ SV958 @ SY4107 @ SY4107 ) @ ( c_Transitive__Closure_Otrancl @ SY4108 @ SY4107 ) @ ( tc_prod @ SY4107 @ SY4107 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4109 @ SY4107 @ SY4107 ) @ ( c_Transitive__Closure_Otrancl @ SY4108 @ SY4107 ) @ ( tc_prod @ SY4107 @ SY4107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2627,plain,
! [SV959: $i,SV427: $i] :
( ( c_in @ ( c_Pair @ SV427 @ SV427 @ SV959 @ SV959 ) @ ( c_Relation_OId @ SV959 ) @ ( tc_prod @ SV959 @ SV959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2628,plain,
! [SV960: $i,SV428: $i] :
( ( c_in @ ( c_Pair @ SV428 @ SV428 @ SV960 @ SV960 ) @ ( c_Relation_OId @ SV960 ) @ ( tc_prod @ SV960 @ SV960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2629,plain,
! [SV961: $i,SV429: $i] :
( ( ! [SY4110: $i,SY4111: $i,SY4112: $i,SY4113: $i] :
( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SY4110 @ SV961 ) @ SY4111 )
| ~ ( c_in @ SV961 @ SY4112 @ SY4113 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SY4112 @ SY4110 @ SY4113 @ SY4111 ) @ ( tc_fun @ SY4113 @ SY4111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2630,plain,
! [SV962: $i,SV430: $i] :
( ( ! [SY4114: $i,SY4115: $i,SY4116: $i,SY4117: $i] :
( ~ ( c_in @ SV430 @ SV962 @ SY4114 )
| ( c_in @ ( hAPP @ SY4115 @ SV430 ) @ ( hAPP @ SY4116 @ SV430 ) @ SY4117 )
| ~ ( c_in @ SY4115 @ ( c_FuncSet_OPi @ SV962 @ SY4116 @ SY4114 @ SY4117 ) @ ( tc_fun @ SY4114 @ SY4117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2631,plain,
! [SV963: $i,SV431: $i] :
( ( ! [SY4118: $i,SY4119: $i,SY4120: $i,SY4121: $i,SY4122: $i] :
( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SY4118 @ SY4119 @ SY4120 @ SY4120 ) @ SY4121 @ ( tc_prod @ SY4120 @ SY4120 ) )
| ~ ( c_in @ SY4119 @ SV963 @ SY4120 )
| ~ ( c_in @ SY4118 @ SV431 @ SY4120 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SY4122 @ SY4121 @ SY4120 ) @ ( tc_fun @ SY4120 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY4122 @ SY4121 @ SY4120 ) @ ( tc_fun @ SY4120 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4122 @ SY4121 @ SY4120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2632,plain,
! [SV964: $i,SV432: $i] :
( ( ! [SY4123: $i,SY4124: $i,SY4125: $i,SY4126: $i] :
( ~ ( c_in @ SV432 @ SV964 @ SY4123 )
| ~ ( c_in @ SY4124 @ SV964 @ SY4123 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4125 @ SY4126 @ SY4123 ) @ ( tc_fun @ SY4123 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4125 @ SY4126 @ SY4123 ) @ ( tc_fun @ SY4123 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4125 @ SY4126 @ SY4123 )
| ( c_in @ ( c_Pair @ SY4124 @ SV432 @ SY4123 @ SY4123 ) @ SY4126 @ ( tc_prod @ SY4123 @ SY4123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2633,plain,
! [SV965: $i,SV433: $i] :
( ( ! [SY4127: $i,SY4128: $i] :
( ( c_in @ SV433 @ SV965 @ SY4127 )
| ~ ( c_in @ SV965 @ SY4128 @ ( tc_fun @ SY4127 @ tc_bool ) )
| ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SY4128 @ ( tc_fun @ SY4127 @ tc_bool ) ) @ SY4127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2634,plain,
! [SV966: $i,SV434: $i] :
( ( ! [SY4129: $i,SY4130: $i] :
( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SY4129 @ tc_bool ) ) @ SY4129 )
| ~ ( c_in @ SV434 @ SY4130 @ SY4129 )
| ~ ( c_in @ SY4130 @ SV966 @ ( tc_fun @ SY4129 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2635,plain,
! [SV967: $i,SV435: $i] :
( ( ! [SY4131: $i,SY4132: $i] :
( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4131 @ SY4132 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4131 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV435 = SV967 )
| ( SV435 = SY4132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2636,plain,
! [SV968: $i,SV436: $i] :
( ( ! [SY4133: $i,SY4134: $i] :
( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4133 @ SY4134 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4133 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV968 = SY4134 )
| ( SV436 = SY4134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2637,plain,
! [SV969: $i,SV437: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV437 @ SV437 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV969 @ SV437 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2638,plain,
! [SV970: $i,SV438: $i] :
( ( ! [SY4135: $i] :
~ ( c_in @ ( c_Pair @ SV438 @ SV970 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4135 @ SV438 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2639,plain,
! [SV971: $i,SV439: $i] :
( ( ! [SY4136: $i,SY4137: $i] :
( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4136 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV971 = SY4137 )
| ~ ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4136 @ SY4137 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2640,plain,
! [SV972: $i,SV440: $i] :
( ( ! [SY4138: $i] :
( ( SV440 = SV972 )
| ( SV972 = SV440 )
| ( c_in @ ( c_Pair @ SV440 @ SV972 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4138 @ SV440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2641,plain,
! [SV973: $i,SV441: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV441 @ SV441 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV973 @ SV441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2642,plain,
! [SV974: $i,SV442: $i] :
( ( ! [SY4139: $i] :
~ ( c_in @ ( c_Pair @ SV442 @ SV974 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4139 @ SV974 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2643,plain,
! [SV975: $i,SV443: $i] :
( ( ! [SY4140: $i,SY4141: $i] :
( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4140 @ SY4141 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4140 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV443 = SV975 )
| ( SV975 = SY4141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2644,plain,
! [SV976: $i,SV444: $i] :
( ( ! [SY4142: $i,SY4143: $i] :
( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4142 @ SY4143 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4142 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV444 = SY4143 )
| ( SV976 = SY4143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2645,plain,
! [SV977: $i,SV445: $i] :
( ( ! [SY4144: $i] :
( ( SV445 = SV977 )
| ( SV445 = SV977 )
| ( c_in @ ( c_Pair @ SV445 @ SV977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SY4144 @ SV977 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2646,plain,
! [SV978: $i,SV446: $i] :
( ( ! [SY4145: $i,SY4146: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4145 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV446 = SY4146 )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SY4145 @ SY4146 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2647,plain,
! [SV979: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV447 @ SV979 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV447 = SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2648,plain,
! [SV980: $i,SV448: $i] :
( ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV448 @ SV980 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV448 = SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2649,plain,
! [SV981: $i,SV449: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ SV449 @ SV981 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV449 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2650,plain,
! [SV982: $i,SV450: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV450 @ SV982 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV450 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2651,plain,
! [SV983: $i,SV451: $i] :
( ( ! [SY4147: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SV983 @ SY4147 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV983 = SY4147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2652,plain,
! [SV452: $i] :
( ( ( c_in @ SV452 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ ( c_Relation_Oconverse @ SV452 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2653,plain,
! [SV453: $i] :
( ( ( c_in @ ( c_Relation_Oconverse @ SV453 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV453 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2654,plain,
! [SV984: $i,SV454: $i] :
( ( ! [SY4148: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SV984 @ SY4148 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV984 = SY4148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2655,plain,
! [SV985: $i,SV455: $i] :
( ( ! [SY4149: $i,SY4150: $i,SY4151: $i,SY4152: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SY4149 @ SY4150 ) @ ( c_Product__Type_OSigma @ SY4151 @ SY4152 @ SY4149 @ SY4150 ) @ ( tc_prod @ SY4149 @ SY4150 ) )
| ~ ( c_in @ SV985 @ ( hAPP @ SY4152 @ SV455 ) @ SY4150 )
| ~ ( c_in @ SV455 @ SY4151 @ SY4149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2656,plain,
! [SV986: $i,SV456: $i] :
( ( ! [SY4153: $i,SY4154: $i,SY4155: $i,SY4156: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SY4153 @ SY4154 ) @ ( c_Product__Type_OSigma @ SY4155 @ SY4156 @ SY4153 @ SY4154 ) @ ( tc_prod @ SY4153 @ SY4154 ) )
| ~ ( c_in @ SV986 @ ( hAPP @ SY4156 @ SV456 ) @ SY4154 )
| ~ ( c_in @ SV456 @ SY4155 @ SY4153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2657,plain,
! [SV987: $i,SV457: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SY4157 ) @ SY4157 )
| ~ ( c_in @ ( c_Pair @ SV457 @ SY4158 @ SY4157 @ SY4157 ) @ SV987 @ ( tc_prod @ SY4157 @ SY4157 ) )
| ~ ( c_in @ SY4158 @ ( c_Wellfounded_Oacc @ SV987 @ SY4157 ) @ SY4157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2658,plain,
! [SV988: $i,SV458: $i] :
( ( ! [SY4159: $i,SY4160: $i] :
( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SY4159 ) @ SY4159 )
| ~ ( c_in @ ( c_Pair @ SV458 @ SY4160 @ SY4159 @ SY4159 ) @ SV988 @ ( tc_prod @ SY4159 @ SY4159 ) )
| ~ ( c_in @ SY4160 @ ( c_Wellfounded_Oacc @ SV988 @ SY4159 ) @ SY4159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2659,plain,
! [SV989: $i,SV459: $i] :
( ( ! [SY4161: $i,SY4162: $i,SY4163: $i,SY4164: $i] :
( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SY4161 @ SY4162 @ SY4163 ) @ SY4163 )
| ~ ( c_in @ ( c_Pair @ SY4164 @ SV459 @ SY4162 @ SY4163 ) @ SV989 @ ( tc_prod @ SY4162 @ SY4163 ) )
| ~ ( c_in @ SY4164 @ SY4161 @ SY4162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2660,plain,
! [SV990: $i,SV460: $i] :
( ( ! [SY4165: $i,SY4166: $i,SY4167: $i,SY4168: $i] :
( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SY4165 @ SY4166 @ SY4167 ) @ SY4167 )
| ~ ( c_in @ ( c_Pair @ SY4168 @ SV460 @ SY4166 @ SY4167 ) @ SV990 @ ( tc_prod @ SY4166 @ SY4167 ) )
| ~ ( c_in @ SY4168 @ SY4165 @ SY4166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2661,plain,
! [SV991: $i,SV461: $i] :
( ( ! [SY4169: $i,SY4170: $i] :
( ( c_in @ SV461 @ SV991 @ SY4169 )
| ~ ( c_in @ ( c_Pair @ SV461 @ SY4170 @ SY4169 @ SY4169 ) @ ( c_Relation_OId__on @ SV991 @ SY4169 ) @ ( tc_prod @ SY4169 @ SY4169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2662,plain,
! [SV992: $i,SV462: $i] :
( ( ! [SY4171: $i] :
( ( c_in @ ( c_Pair @ SV462 @ SV462 @ SV992 @ SV992 ) @ ( c_Relation_OId__on @ SY4171 @ SV992 ) @ ( tc_prod @ SV992 @ SV992 ) )
| ~ ( c_in @ SV462 @ SY4171 @ SV992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2663,plain,
! [SV993: $i,SV463: $i] :
( ( ! [SY4172: $i,SY4173: $i,SY4174: $i] :
( ( c_in @ SV463 @ SV993 @ SY4172 )
| ~ ( c_in @ ( c_Pair @ SY4173 @ SV463 @ SY4172 @ SY4172 ) @ SY4174 @ ( tc_prod @ SY4172 @ SY4172 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SY4174 @ SY4172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2664,plain,
! [SV994: $i,SV464: $i] :
( ( ! [SY4175: $i,SY4176: $i,SY4177: $i] :
( ( c_in @ SV464 @ SV994 @ SY4175 )
| ~ ( c_in @ ( c_Pair @ SV464 @ SY4176 @ SY4175 @ SY4175 ) @ SY4177 @ ( tc_prod @ SY4175 @ SY4175 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SY4177 @ SY4175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2665,plain,
! [SV995: $i,SV465: $i] :
( ( ! [SY4178: $i,SY4179: $i,SY4180: $i] :
( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SY4178 @ SY4179 ) @ SY4179 )
| ~ ( c_in @ ( c_Pair @ SY4180 @ SV465 @ SY4178 @ SY4179 ) @ SV995 @ ( tc_prod @ SY4178 @ SY4179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2666,plain,
! [SV996: $i,SV466: $i] :
( ( ! [SY4181: $i,SY4182: $i,SY4183: $i] :
( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SY4181 @ SY4182 ) @ SY4182 )
| ~ ( c_in @ ( c_Pair @ SY4183 @ SV466 @ SY4181 @ SY4182 ) @ SV996 @ ( tc_prod @ SY4181 @ SY4182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2667,plain,
! [SV997: $i,SV467: $i] :
( ( ! [SY4184: $i,SY4185: $i,SY4186: $i] :
( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SY4184 @ SY4185 ) @ SY4184 )
| ~ ( c_in @ ( c_Pair @ SV467 @ SY4186 @ SY4184 @ SY4185 ) @ SV997 @ ( tc_prod @ SY4184 @ SY4185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2668,plain,
! [SV998: $i,SV468: $i] :
( ( ! [SY4187: $i,SY4188: $i,SY4189: $i] :
( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SY4187 @ SY4188 ) @ SY4187 )
| ~ ( c_in @ ( c_Pair @ SV468 @ SY4189 @ SY4187 @ SY4188 ) @ SV998 @ ( tc_prod @ SY4187 @ SY4188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2669,plain,
! [SV999: $i,SV469: $i] :
( ( ! [SY4190: $i,SY4191: $i,SY4192: $i,SY4193: $i] :
( ( c_in @ SV469 @ ( hAPP @ SV999 @ SY4190 ) @ SY4191 )
| ~ ( c_in @ ( c_Pair @ SY4190 @ SV469 @ SY4192 @ SY4191 ) @ ( c_Product__Type_OSigma @ SY4193 @ SV999 @ SY4192 @ SY4191 ) @ ( tc_prod @ SY4192 @ SY4191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2670,plain,
! [SV1000: $i,SV470: $i] :
( ( ! [SY4194: $i,SY4195: $i,SY4196: $i,SY4197: $i] :
( ( c_in @ SV470 @ SV1000 @ SY4194 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SY4195 @ SY4194 @ SY4196 ) @ ( c_Product__Type_OSigma @ SV1000 @ SY4197 @ SY4194 @ SY4196 ) @ ( tc_prod @ SY4194 @ SY4196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2671,plain,
! [SV1001: $i,SV471: $i] :
( ( ! [SY4198: $i,SY4199: $i,SY4200: $i] :
( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SY4198 @ SY4198 ) @ SY4199 @ ( tc_prod @ SY4198 @ SY4198 ) )
| ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SY4198 @ SY4198 ) @ SY4199 @ ( tc_prod @ SY4198 @ SY4198 ) )
| ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SY4200 @ SY4198 )
| ~ ( c_in @ SV1001 @ SY4200 @ SY4198 )
| ~ ( c_Relation_Ototal__on @ SY4200 @ SY4199 @ SY4198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2672,plain,
! [SV1002: $i,SV472: $i] :
( ( ! [SY4201: $i,SY4202: $i] :
( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SY4201 @ ( tc_prod @ SV1002 @ SV1002 ) )
| ~ ( c_in @ SV472 @ SY4202 @ SV1002 )
| ~ ( c_Relation_Orefl__on @ SY4202 @ SY4201 @ SV1002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2673,plain,
! [SV1003: $i,SV473: $i] :
( ( ! [SY4203: $i,SY4204: $i,SY4205: $i] :
( ( c_in @ SV473 @ SV1003 @ SY4203 )
| ~ ( c_in @ ( c_Pair @ SY4204 @ SV473 @ SY4203 @ SY4203 ) @ SY4205 @ ( tc_prod @ SY4203 @ SY4203 ) )
| ~ ( c_Relation_Orefl__on @ SV1003 @ SY4205 @ SY4203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2674,plain,
! [SV1004: $i,SV474: $i] :
( ( ! [SY4206: $i,SY4207: $i,SY4208: $i] :
( ( c_in @ SV474 @ SV1004 @ SY4206 )
| ~ ( c_in @ ( c_Pair @ SV474 @ SY4207 @ SY4206 @ SY4206 ) @ SY4208 @ ( tc_prod @ SY4206 @ SY4206 ) )
| ~ ( c_Relation_Orefl__on @ SV1004 @ SY4208 @ SY4206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2675,plain,
! [SV1005: $i,SV475: $i] :
( ( ! [SY4209: $i,SY4210: $i] :
( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SY4209 @ ( tc_prod @ SV1005 @ SV1005 ) )
| ~ ( c_in @ SV475 @ SY4210 @ SV1005 )
| ~ ( c_Relation_Orefl__on @ SY4210 @ SY4209 @ SV1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2676,plain,
! [SV1006: $i,SV476: $i] :
( ( ! [SY4211: $i,SY4212: $i] :
( ~ ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SY4211 @ SY4212 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4211 = SY4212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2677,plain,
! [SV1007: $i,SV477: $i] :
( ( ! [SY4213: $i,SY4214: $i] :
( ~ ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4213 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV477 = SY4214 )
| ( SV477 = SY4214 )
| ~ ( c_in @ SY4213 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SY4214 )
| ( c_in @ ( c_Pair @ SV477 @ SY4214 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4213 @ SV1007 @ SY4214 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2678,plain,
! [SV1008: $i,SV478: $i] :
( ( ! [SY4215: $i,SY4216: $i] :
( ( SV478 = SV1008 )
| ( SV478 = SY4215 )
| ~ ( c_in @ SY4216 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SY4215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4216 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SY4215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4216 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2679,plain,
! [SV1009: $i,SV479: $i] :
( ( ! [SY4217: $i,SY4218: $i,SY4219: $i] :
( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4217 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1009 = SY4218 )
| ( SV479 = SY4218 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4217 @ SY4219 @ SY4218 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4217 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4219 = SY4218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2680,plain,
! [SV1010: $i,SV480: $i] :
( ( ! [SY4220: $i,SY4221: $i] :
( ( SV480 = SV1010 )
| ~ ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4220 @ SY4221 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4220 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4221 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SY4221 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4220 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SY4221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2681,plain,
! [SV1011: $i,SV481: $i] :
( ( ! [SY4222: $i,SY4223: $i] :
( ~ ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4222 @ SY4223 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4222 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4223 = SV481 )
| ( c_in @ ( c_Pair @ SY4223 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4222 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2682,plain,
! [SV1012: $i,SV482: $i] :
( ( ! [SY4224: $i,SY4225: $i] :
( ~ ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4224 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4225 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4224 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY4225 = SV1012 )
| ~ ( c_in @ SY4224 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4225 = SV482 )
| ( c_in @ ( c_Pair @ SY4225 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4224 @ SY4225 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2683,plain,
! [SV1013: $i,SV483: $i] :
( ( ! [SY4226: $i,SY4227: $i] :
( ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4226 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV483 = SV1013 )
| ~ ( c_in @ SY4226 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4227 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4226 @ SY4227 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4226 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2684,plain,
! [SV1014: $i,SV484: $i] :
( ( ! [SY4228: $i,SY4229: $i,SY4230: $i] :
( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4228 @ SY4229 @ SY4230 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4228 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SY4229 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SY4230 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4228 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SY4228 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4229 = SY4230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2685,plain,
! [SV1015: $i,SV485: $i] :
( ( ! [SY4231: $i,SY4232: $i,SY4233: $i] :
( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4231 @ SY4232 @ SY4233 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4231 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4233 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4231 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SY4232 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SY4231 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4232 = SY4233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2686,plain,
! [SV1016: $i,SV486: $i] :
( ( ! [SY4234: $i] :
( ( SV486 = SV1016 )
| ( SV1016 = SV486 )
| ~ ( c_in @ SY4234 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4234 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2687,plain,
! [SV1017: $i,SV487: $i] :
( ( ! [SY4235: $i,SY4236: $i,SY4237: $i] :
( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4235 @ SY4236 @ SY4237 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4235 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SY4236 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4235 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4236 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4235 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SY4235 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4236 = SY4237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2688,plain,
! [SV1018: $i,SV488: $i] :
( ( ! [SY4238: $i] :
( ~ ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4238 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV488 = SV1018 )
| ~ ( c_in @ SY4238 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4238 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2689,plain,
! [SV1019: $i,SV489: $i] :
( ( ! [SY4239: $i,SY4240: $i] :
( ~ ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4239 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY4240 = SV1019 )
| ~ ( c_in @ SY4239 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SY4240 )
| ( c_in @ ( c_Pair @ SY4240 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4239 @ SV489 @ SY4240 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2690,plain,
! [SV1020: $i,SV490: $i] :
( ( ! [SY4241: $i,SY4242: $i,SY4243: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4241 @ SY4242 @ SY4243 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4241 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1020 = SY4243 )
| ( SV490 = SY4243 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SY4241 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4242 = SY4243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2691,plain,
! [SV1021: $i,SV491: $i] :
( ( ! [SY4244: $i,SY4245: $i] :
( ~ ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SY4244 @ SY4245 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4244 = SY4245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2692,plain,
! [SV1022: $i,SV492: $i] :
( ( ! [SY4246: $i,SY4247: $i] :
( ~ ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4246 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1022 = SY4247 )
| ( SY4247 = SV1022 )
| ~ ( c_in @ SY4246 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4247 = SV492 )
| ( c_in @ ( c_Pair @ SY4247 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4246 @ SY4247 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2693,plain,
! [SV1023: $i,SV493: $i] :
( ( ! [SY4248: $i,SY4249: $i] :
( ( SV493 = SV1023 )
| ( SY4248 = SV493 )
| ~ ( c_in @ SY4249 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SY4248 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4249 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4248 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4249 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2694,plain,
! [SV1024: $i,SV494: $i] :
( ( ! [SY4250: $i,SY4251: $i,SY4252: $i] :
( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4250 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV494 = SY4251 )
| ( SV1024 = SY4251 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4250 @ SY4251 @ SY4252 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4250 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4251 = SY4252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2695,plain,
! [SV1025: $i,SV495: $i] :
( ( ! [SY4253: $i,SY4254: $i] :
( ( SV495 = SV1025 )
| ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4253 @ SV1025 @ SY4254 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4253 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SY4254 )
| ( c_in @ ( c_Pair @ SY4254 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4253 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SY4254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2696,plain,
! [SV1026: $i,SV496: $i] :
( ( ! [SY4255: $i,SY4256: $i] :
( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4255 @ SV1026 @ SY4256 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4255 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1026 = SY4256 )
| ( c_in @ ( c_Pair @ SV496 @ SY4256 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4255 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2697,plain,
! [SV1027: $i,SV497: $i] :
( ( ! [SY4257: $i,SY4258: $i] :
( ~ ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4257 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SY4258 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4257 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SY4258 )
| ~ ( c_in @ SY4257 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SY4258 )
| ( c_in @ ( c_Pair @ SV497 @ SY4258 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4257 @ SV1027 @ SY4258 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2698,plain,
! [SV1028: $i,SV498: $i] :
( ( ! [SY4259: $i,SY4260: $i] :
( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4259 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV498 = SV1028 )
| ~ ( c_in @ SY4259 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SY4260 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4259 @ SV498 @ SY4260 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4259 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2699,plain,
! [SV1029: $i,SV499: $i] :
( ( ! [SY4261: $i,SY4262: $i,SY4263: $i] :
( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4261 @ SY4262 @ SY4263 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4261 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1029 = SY4263 )
| ~ ( c_in @ ( c_Pair @ SY4262 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4261 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SY4261 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4262 = SY4263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2700,plain,
! [SV1030: $i,SV500: $i] :
( ( ! [SY4264: $i,SY4265: $i,SY4266: $i] :
( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4264 @ SY4265 @ SY4266 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4264 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SY4265 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4264 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SY4266 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SY4264 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4265 = SY4266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2701,plain,
! [SV1031: $i,SV501: $i] :
( ( ! [SY4267: $i] :
( ( SV501 = SV1031 )
| ( SV501 = SV1031 )
| ~ ( c_in @ SY4267 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4267 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2702,plain,
! [SV1032: $i,SV502: $i] :
( ( ! [SY4268: $i,SY4269: $i,SY4270: $i] :
( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4268 @ SY4269 @ SY4270 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4268 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4270 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4268 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SY4270 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4268 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SY4268 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4269 = SY4270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2703,plain,
! [SV1033: $i,SV503: $i] :
( ( ! [SY4271: $i] :
( ~ ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4271 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV503 = SV1033 )
| ~ ( c_in @ SY4271 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4271 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2704,plain,
! [SV1034: $i,SV504: $i] :
( ( ! [SY4272: $i,SY4273: $i] :
( ~ ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4272 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV504 = SY4273 )
| ~ ( c_in @ SY4272 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4273 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SY4273 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4272 @ SY4273 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2705,plain,
! [SV1035: $i,SV505: $i] :
( ( ! [SY4274: $i,SY4275: $i,SY4276: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4274 @ SY4275 @ SY4276 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4274 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SY4275 )
| ( SV1035 = SY4275 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SY4274 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4275 = SY4276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2706,plain,
! [SV1036: $i,SV506: $i] :
( ( ! [SY4277: $i] :
( ~ ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4277 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4277 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV506 = SV1036 )
| ~ ( c_in @ SY4277 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2707,plain,
! [SV1037: $i,SV507: $i] :
( ( ! [SY4278: $i] :
( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4278 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4278 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1037 = SV507 )
| ~ ( c_in @ SY4278 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2708,plain,
! [SV1038: $i,SV508: $i] :
( ( ! [SY4279: $i] :
( ( c_in @ SV508 @ SV1038 @ SY4279 )
| ~ ( hBOOL @ ( hAPP @ SV1038 @ SV508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2709,plain,
! [SV1039: $i,SV509: $i] :
( ( ! [SY4280: $i] :
( ( hBOOL @ ( hAPP @ SV509 @ SV1039 ) )
| ~ ( c_in @ SV1039 @ SV509 @ SY4280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2710,plain,
! [SV510: $i] :
( ( v_thesis____ = $true )
| ( ( ~ ( c_in @ SV510 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV510 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2711,plain,
! [SV1040: $i,SV511: $i] :
( ( ! [SY4281: $i] :
( ~ ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4281 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4281 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SY4281 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2712,plain,
! [SV1041: $i,SV512: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SV1041 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1041 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2713,plain,
! [SV1042: $i,SV513: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV513 @ SV1042 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1042 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2714,plain,
! [SV1043: $i,SV514: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV514 @ SV1043 ) )
| ~ ( class_Lattices_Olattice @ SV1043 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2715,plain,
! [SV1044: $i,SV515: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV515 @ SV1044 ) )
| ~ ( class_Lattices_Olattice @ SV1044 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2716,plain,
! [SV1045: $i,SV516: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV516 @ SV1045 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV1045 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2717,plain,
! [SV1046: $i,SV517: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SV1046 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1046 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2718,plain,
! [SV1047: $i,SV518: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV518 @ SV1047 ) )
| ~ ( class_Orderings_Opreorder @ SV1047 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2719,plain,
! [SV1048: $i,SV519: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV519 @ SV1048 ) )
| ~ ( class_Lattices_Olattice @ SV1048 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2720,plain,
! [SV1049: $i,SV520: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV520 @ SV1049 ) )
| ~ ( class_Orderings_Oorder @ SV1049 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2721,plain,
! [SV1050: $i,SV521: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV521 @ SV1050 ) )
| ~ ( class_HOL_Oord @ SV1050 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2722,plain,
! [SV1051: $i,SV522: $i] :
( ( c_fequal @ SV522 @ SV522 @ SV1051 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2723,plain,
! [SV1052: $i,SV523: $i] :
( ( ! [SY4282: $i] :
( ( SV523 = SV1052 )
| ~ ( c_fequal @ SV523 @ SV1052 @ SY4282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2724,plain,
! [SV1053: $i,SV524: $i] :
( ( ! [SY4283: $i,SY4284: $i,SY4285: $i,SY4286: $i,SY4287: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SY4283 @ SY4284 @ SY4285 )
!= ( c_Recdef_Ocut @ SY4286 @ SV1053 @ SY4283 @ SY4284 @ SY4285 ) )
| ( ( hAPP @ SV524 @ SY4287 )
= ( hAPP @ SY4286 @ SY4287 ) )
| ~ ( c_in @ ( c_Pair @ SY4287 @ SY4283 @ SY4284 @ SY4284 ) @ SV1053 @ ( tc_prod @ SY4284 @ SY4284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2725,plain,
! [SV1054: $i,SV525: $i] :
( ( ! [SY4288: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV525 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SY4288 @ SV525 )
!= SY4288 )
| ( c_lessequals @ SV1054 @ SY4288 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2726,plain,
! [SV1055: $i,SV526: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 @ SV1055 @ SV1055 )
!= SV526 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2727,plain,
! [SV1056: $i,SV527: $i] :
( ( ! [SY4289: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV527 @ SV1056 @ ( tc_fun @ SY4289 @ tc_bool ) )
!= SV1056 )
| ( c_lessequals @ SV527 @ SV1056 @ ( tc_fun @ SY4289 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2728,plain,
! [SV1057: $i,SV528: $i] :
( ( ! [SY4290: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV528 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SY4290 @ SV528 )
!= SV1057 )
| ( c_lessequals @ SV1057 @ SY4290 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2729,plain,
! [SV1058: $i,SV529: $i] :
( ( ! [SY4291: $i,SY4292: $i,SY4293: $i,SY4294: $i] :
( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SY4291 @ tc_bool ) @ SY4292 ) @ SY4292 @ SY4291 )
!= ( c_Product__Type_OSigma @ SY4293 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SY4291 @ tc_bool ) @ SY4292 ) @ SY4292 @ SY4291 ) )
| ~ ( c_in @ SY4294 @ SV1058 @ SY4291 )
| ( SV529 = SY4293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2730,plain,
! [SV1059: $i,SV530: $i] :
( ( ! [SY4295: $i,SY4296: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SV1059 @ ( tc_fun @ SY4295 @ tc_bool ) ) @ SY4296 @ ( tc_fun @ SY4295 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1059 @ SY4296 @ ( tc_fun @ SY4295 @ tc_bool ) ) @ ( tc_fun @ SY4295 @ tc_bool ) ) )
| ( c_lessequals @ SY4296 @ SV530 @ ( tc_fun @ SY4295 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2731,plain,
! [SV1060: $i,SV531: $i] :
( ( ! [SY4297: $i,SY4298: $i,SY4299: $i,SY4300: $i] :
( ( ( c_Pair @ SV531 @ SV1060 @ SY4297 @ SY4298 )
!= ( c_Pair @ SY4299 @ SY4300 @ SY4297 @ SY4298 ) )
| ( SV1060 = SY4300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2732,plain,
! [SV1061: $i,SV532: $i] :
( ( ( ( c_Relation_Oconverse @ SV532 @ SV1061 @ SV1061 )
!= SV532 )
| ( c_Relation_Osym @ SV532 @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2733,plain,
! [SV1062: $i,SV533: $i] :
( ( ! [SY4301: $i,SY4302: $i] :
( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SY4301 )
!= ( c_Set_Oinsert @ SV533 @ SY4302 @ SY4301 ) )
| ( c_in @ SV533 @ SY4302 @ SY4301 )
| ( c_in @ SV533 @ SV1062 @ SY4301 )
| ( SV1062 = SY4302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2734,plain,
! [SV1063: $i,SV534: $i] :
( ( ! [SY4303: $i,SY4304: $i,SY4305: $i,SY4306: $i] :
( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SY4303 @ SY4304 @ SY4305 @ SY4306 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SY4303 @ SY4304 @ SY4305 @ SY4306 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SY4303 @ SY4304 @ SY4305 @ SY4306 )
= ( c_Recdef_Ocut @ SV1063 @ SY4303 @ SY4304 @ SY4305 @ SY4306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2735,plain,
! [SV1064: $i,SV535: $i] :
( ( ! [SY4307: $i,SY4308: $i,SY4309: $i,SY4310: $i] :
( ( ( c_Pair @ SV535 @ SV1064 @ SY4307 @ SY4308 )
!= ( c_Pair @ SY4309 @ SY4310 @ SY4307 @ SY4308 ) )
| ( SV535 = SY4309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2736,plain,
! [SV537: $i,SV2: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV2 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV537 @ SV537 @ SV2 )
= SV537 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2737,plain,
! [SV1065: $i,SV539: $i,SV4: $i] :
( ( ! [SY4311: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV4 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV539 @ SV1065 @ SV4 ) @ SY4311 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV539 @ SY4311 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1065 @ SY4311 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2738,plain,
! [SV1066: $i,SV540: $i,SV5: $i] :
( ( ! [SY4312: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV5 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SY4312 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1066 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SY4312 @ SV5 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2739,plain,
! [SV1067: $i,SV541: $i,SV6: $i] :
( ( ! [SY4313: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV541 @ SV1067 @ ( tc_fun @ SY4313 @ tc_bool ) ) @ ( tc_fun @ SY4313 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SV541 @ ( tc_fun @ SY4313 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SV1067 @ ( tc_fun @ SY4313 @ tc_bool ) ) @ ( tc_fun @ SY4313 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2740,plain,
! [SV1068: $i,SV542: $i,SV7: $i] :
( ( ! [SY4314: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV542 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ SY4314 @ ( tc_fun @ SV1068 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV7 @ SY4314 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV542 @ SY4314 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ ( tc_fun @ SV1068 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2741,plain,
! [SV1069: $i,SV543: $i,SV8: $i] :
( ( ! [SY4315: $i,SY4316: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV8 @ SV543 @ ( tc_fun @ SV1069 @ tc_bool ) ) @ SY4315 @ SV1069 @ SY4316 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV8 @ SY4315 @ SV1069 @ SY4316 ) @ ( c_Product__Type_OSigma @ SV543 @ SY4315 @ SV1069 @ SY4316 ) @ ( tc_fun @ ( tc_prod @ SV1069 @ SY4316 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2742,plain,
! [SV1070: $i,SV544: $i,SV9: $i] :
( ( ! [SY4317: $i,SY4318: $i,SY4319: $i] :
( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SY4317 )
| ~ ( c_in @ SV544 @ SY4318 @ SY4319 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SY4318 @ SY4319 @ SY4317 ) @ SV1070 @ ( tc_fun @ SY4317 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2743,plain,
! [SV1071: $i,SV545: $i,SV10: $i] :
( ( ! [SY4320: $i,SY4321: $i] :
( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
| ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SY4320 @ SY4321 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4320 @ SY4321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2744,plain,
! [SV1072: $i,SV546: $i,SV11: $i] :
( ( ! [SY4322: $i] :
( ( c_lessequals @ SV11 @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY4322 @ SV11 @ SV1072 ) @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2745,plain,
! [SV1073: $i,SV547: $i,SV12: $i] :
( ( ! [SY4323: $i] :
( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SV547 @ SV1073 @ SY4323 ) @ ( tc_fun @ SY4323 @ tc_bool ) )
| ~ ( c_lessequals @ SV12 @ SV1073 @ ( tc_fun @ SY4323 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2746,plain,
! [SV1074: $i,SV549: $i,SV14: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV14 @ SV549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1074 @ SV549 ) @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV14 @ SV1074 @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) ) @ SV549 ) @ ( tc_fun @ ( tc_prod @ SV549 @ SV549 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2747,plain,
! [SV1075: $i,SV550: $i,SV15: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV15 )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SV550 @ SV1075 @ SV15 ) @ SV15 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV550 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1075 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2748,plain,
! [SV1076: $i,SV551: $i,SV16: $i] :
( ( ! [SY4324: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV16 @ SV551 @ SV1076 ) @ SY4324 @ ( tc_fun @ SV1076 @ tc_bool ) )
= ( c_Set_Oinsert @ SV16 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV551 @ SY4324 @ ( tc_fun @ SV1076 @ tc_bool ) ) @ SV1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2749,plain,
! [SV1077: $i,SV552: $i,SV17: $i] :
( ( ! [SY4325: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ ( c_Set_Oinsert @ SV552 @ SV1077 @ SY4325 ) @ ( tc_fun @ SY4325 @ tc_bool ) )
= ( c_Set_Oinsert @ SV552 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ SV1077 @ ( tc_fun @ SY4325 @ tc_bool ) ) @ SY4325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2750,plain,
! [SV554: $i,SV19: $i] :
( ( ( c_Relation_Otrans @ SV19 @ SV554 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV19 @ SV554 @ SV554 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2751,plain,
! [SV555: $i,SV20: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV20 @ SV555 @ SV555 ) @ SV555 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV20 @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2752,plain,
! [SV1078: $i,SV556: $i,SV21: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV21 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV556 @ SV1078 @ SV21 ) @ SV21 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV556 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1078 @ SV21 ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2753,plain,
! [SV1079: $i,SV557: $i,SV22: $i] :
( ( ! [SY4326: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV22 @ SV557 @ SV1079 ) @ ( c_Set_Oinsert @ SV22 @ SY4326 @ SV1079 ) @ ( tc_fun @ SV1079 @ tc_bool ) )
= ( c_Set_Oinsert @ SV22 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV557 @ SY4326 @ ( tc_fun @ SV1079 @ tc_bool ) ) @ SV1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2754,plain,
! [SV1080: $i,SV558: $i,SV23: $i] :
( ( ( c_Set_Oinsert @ SV23 @ ( c_Set_Oinsert @ SV23 @ SV558 @ SV1080 ) @ SV1080 )
= ( c_Set_Oinsert @ SV23 @ SV558 @ SV1080 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2755,plain,
! [SV1081: $i,SV559: $i,SV24: $i] :
( ( ! [SY4327: $i] :
( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
| ( SV1081 = SV559 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1081 @ SV24 @ SY4327 ) @ SV559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2756,plain,
! [SV1082: $i,SV560: $i,SV25: $i] :
( ( ! [SY4328: $i,SY4329: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV25 @ SV560 @ SV1082 @ SY4328 ) @ SY4329 @ ( tc_prod @ SV1082 @ SY4328 ) ) @ SV1082 @ SY4328 )
= ( c_Set_Oinsert @ SV25 @ ( c_Relation_ODomain @ SY4329 @ SV1082 @ SY4328 ) @ SV1082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2757,plain,
! [SV1083: $i,SV561: $i,SV26: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SV1083 @ SV1083 ) @ tc_bool ) ) @ SV1083 )
| ~ ( c_Relation_Osym @ SV561 @ SV1083 )
| ~ ( c_Relation_Osym @ SV26 @ SV1083 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2758,plain,
! [SV1084: $i,SV562: $i,SV27: $i] :
( ( ! [SY4330: $i,SY4331: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 @ SV562 @ ( tc_fun @ ( tc_prod @ SV1084 @ SY4330 ) @ tc_bool ) ) @ SY4331 @ SV1084 @ SY4330 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV27 @ SY4331 @ SV1084 @ SY4330 ) @ ( c_Relation_OImage @ SV562 @ SY4331 @ SV1084 @ SY4330 ) @ ( tc_fun @ SY4330 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2759,plain,
! [SV1085: $i,SV563: $i,SV28: $i] :
( ( ! [SY4332: $i,SY4333: $i] :
( ( c_Relation_OImage @ SV28 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV563 @ SV1085 @ ( tc_fun @ SY4332 @ tc_bool ) ) @ SY4332 @ SY4333 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV28 @ SV563 @ SY4332 @ SY4333 ) @ ( c_Relation_OImage @ SV28 @ SV1085 @ SY4332 @ SY4333 ) @ ( tc_fun @ SY4333 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2760,plain,
! [SV1086: $i,SV564: $i,SV29: $i] :
( ( ! [SY4334: $i] :
( ( c_Set_Oinsert @ SV29 @ ( c_Set_Oinsert @ SV564 @ SV1086 @ SY4334 ) @ SY4334 )
= ( c_Set_Oinsert @ SV564 @ ( c_Set_Oinsert @ SV29 @ SV1086 @ SY4334 ) @ SY4334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2761,plain,
! [SV1087: $i,SV565: $i,SV30: $i] :
( ( ! [SY4335: $i] :
( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV565 @ SV1087 @ ( tc_fun @ ( tc_prod @ SY4335 @ SY4335 ) @ tc_bool ) ) @ SY4335 ) @ ( tc_prod @ SY4335 @ SY4335 ) )
| ~ ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SV1087 @ SY4335 ) @ ( tc_prod @ SY4335 @ SY4335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2762,plain,
! [SV1088: $i,SV566: $i,SV31: $i] :
( ( ! [SY4336: $i] :
( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 @ SV1088 @ ( tc_fun @ ( tc_prod @ SY4336 @ SY4336 ) @ tc_bool ) ) @ SY4336 ) @ ( tc_prod @ SY4336 @ SY4336 ) )
| ~ ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SV566 @ SY4336 ) @ ( tc_prod @ SY4336 @ SY4336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2763,plain,
! [SV1089: $i,SV567: $i,SV32: $i] :
( ( ! [SY4337: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ SV1089 @ ( tc_fun @ SY4337 @ tc_bool ) ) @ ( tc_fun @ SY4337 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV1089 @ ( tc_fun @ SY4337 @ tc_bool ) ) @ ( tc_fun @ SY4337 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2764,plain,
! [SV1090: $i,SV568: $i,SV33: $i] :
( ( ! [SY4338: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ SV568 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SY4338 @ ( tc_fun @ SV1090 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV568 @ SY4338 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ ( tc_fun @ SV1090 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2765,plain,
! [SV1091: $i,SV569: $i,SV34: $i] :
( ( ! [SY4339: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV34 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ SV1091 @ SV34 ) @ SY4339 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1091 @ SY4339 @ SV34 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2766,plain,
! [SV1092: $i,SV570: $i,SV35: $i] :
( ( ! [SY4340: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ SY4340 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ SY4340 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2767,plain,
! [SV1093: $i,SV571: $i,SV36: $i] :
( ( ! [SY4341: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ SY4341 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ SY4341 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2768,plain,
! [SV1094: $i,SV572: $i,SV37: $i] :
( ( ! [SY4342: $i] :
( ~ ( class_Lattices_Olattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ SV1094 @ SV37 ) @ SY4342 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1094 @ SY4342 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2769,plain,
! [SV1095: $i,SV574: $i,SV39: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) )
= SV39 )
| ~ ( c_lessequals @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2770,plain,
! [SV1096: $i,SV575: $i,SV40: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV40 @ SV575 @ ( tc_fun @ SV1096 @ tc_bool ) )
= SV575 )
| ~ ( c_lessequals @ SV575 @ SV40 @ ( tc_fun @ SV1096 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2771,plain,
! [SV1097: $i,SV576: $i,SV41: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SV1097 @ SV41 )
= SV576 )
| ~ ( c_lessequals @ SV576 @ SV1097 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2772,plain,
! [SV1098: $i,SV577: $i,SV42: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV42 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SV1098 @ SV42 )
= SV1098 )
| ~ ( c_lessequals @ SV1098 @ SV577 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2773,plain,
! [SV1099: $i,SV578: $i,SV43: $i] :
( ( ! [SY4343: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SY4343 @ ( tc_fun @ SV1099 @ tc_bool ) )
| ~ ( c_lessequals @ SV578 @ SY4343 @ ( tc_fun @ SV1099 @ tc_bool ) )
| ~ ( c_lessequals @ SV43 @ SY4343 @ ( tc_fun @ SV1099 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2774,plain,
! [SV1100: $i,SV579: $i,SV44: $i] :
( ( c_lessequals @ SV44 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV579 @ SV44 @ ( tc_fun @ SV1100 @ tc_bool ) ) @ ( tc_fun @ SV1100 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2775,plain,
! [SV1101: $i,SV580: $i,SV45: $i] :
( ( c_lessequals @ SV45 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV45 @ SV580 @ ( tc_fun @ SV1101 @ tc_bool ) ) @ ( tc_fun @ SV1101 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2776,plain,
! [SV1102: $i,SV581: $i,SV46: $i] :
( ( ! [SY4344: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SY4344 @ ( tc_fun @ SV1102 @ tc_bool ) )
| ~ ( c_lessequals @ SV581 @ SY4344 @ ( tc_fun @ SV1102 @ tc_bool ) )
| ~ ( c_lessequals @ SV46 @ SY4344 @ ( tc_fun @ SV1102 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2777,plain,
! [SV1103: $i,SV582: $i,SV47: $i] :
( ( ! [SY4345: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV47 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SY4345 @ SV47 )
| ~ ( c_lessequals @ SV1103 @ SY4345 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SY4345 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2778,plain,
! [SV1104: $i,SV583: $i,SV48: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV48 )
| ( c_lessequals @ SV583 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV583 @ SV1104 @ SV48 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2779,plain,
! [SV1105: $i,SV584: $i,SV49: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV49 )
| ( c_lessequals @ SV584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1105 @ SV584 @ SV49 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2780,plain,
! [SV1106: $i,SV585: $i,SV50: $i] :
( ( ! [SY4346: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV50 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SY4346 @ SV50 )
| ~ ( c_lessequals @ SV1106 @ SY4346 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SY4346 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2781,plain,
! [SV1107: $i,SV586: $i,SV51: $i] :
( ( ! [SY4347: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV51 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SY4347 @ SV51 )
| ~ ( c_lessequals @ SV1107 @ SY4347 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SY4347 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2782,plain,
! [SV1108: $i,SV587: $i,SV52: $i] :
( ( ~ ( class_Lattices_Olattice @ SV52 )
| ( c_lessequals @ SV587 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1108 @ SV587 @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2783,plain,
! [SV1109: $i,SV588: $i,SV53: $i] :
( ( ~ ( class_Lattices_Olattice @ SV53 )
| ( c_lessequals @ SV588 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV588 @ SV1109 @ SV53 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2784,plain,
! [SV1110: $i,SV589: $i,SV54: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV54 @ SV589 @ ( tc_fun @ SV1110 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV589 @ SV54 @ ( tc_fun @ SV1110 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2785,plain,
! [SV1111: $i,SV590: $i,SV55: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV590 @ SV1111 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1111 @ SV590 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2786,plain,
! [SV1112: $i,SV591: $i,SV56: $i] :
( ( ~ ( class_Lattices_Olattice @ SV56 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV591 @ SV1112 @ SV56 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1112 @ SV591 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2787,plain,
! [SV1113: $i,SV592: $i,SV57: $i] :
( ( ! [SY4348: $i] :
( ~ ( class_Lattices_Olattice @ SV57 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1113 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SY4348 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1113 @ SY4348 @ SV57 ) @ SV57 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2788,plain,
! [SV1114: $i,SV593: $i,SV58: $i] :
( ( ! [SY4349: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV593 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV593 @ SY4349 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4349 @ SV58 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV58 @ SV593 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SY4349 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4349 @ SV58 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2789,plain,
! [SV1115: $i,SV595: $i,SV60: $i] :
( ( ! [SY4350: $i] :
( ( c_in @ SV60 @ SV595 @ SV1115 )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SY4350 @ SV1115 ) @ SV595 @ ( tc_fun @ SV1115 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2790,plain,
! [SV1116: $i,SV596: $i,SV61: $i] :
( ( ! [SY4351: $i,SY4352: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV596 @ ( tc_fun @ SV1116 @ tc_bool ) ) @ SY4351 @ SV1116 @ SY4352 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV61 @ SY4351 @ SV1116 @ SY4352 ) @ ( c_Product__Type_OSigma @ SV596 @ SY4351 @ SV1116 @ SY4352 ) @ ( tc_fun @ ( tc_prod @ SV1116 @ SY4352 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2791,plain,
! [SV1117: $i,SV597: $i,SV62: $i] :
( ( ! [SY4353: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SV597 @ SV1117 ) @ SY4353 ) )
| ~ ( hBOOL @ ( hAPP @ SV597 @ SY4353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2792,plain,
! [SV1118: $i,SV598: $i,SV63: $i] :
( ( ! [SY4354: $i,SY4355: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SV1118 @ SY4354 @ SY4355 ) @ SY4355 )
= ( c_Set_Oimage @ SV63 @ SV1118 @ SY4354 @ SY4355 ) )
| ~ ( c_in @ SV598 @ SV1118 @ SY4354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2793,plain,
! [SV1119: $i,SV599: $i,SV64: $i] :
( ( ! [SY4356: $i] :
( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SV1119 @ SY4356 ) @ ( tc_fun @ SY4356 @ tc_bool ) )
| ~ ( c_lessequals @ SV64 @ SV1119 @ ( tc_fun @ SY4356 @ tc_bool ) )
| ( c_in @ SV599 @ SV64 @ SY4356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2794,plain,
! [SV1120: $i,SV600: $i,SV65: $i] :
( ( ! [SY4357: $i] :
( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SV1120 @ tc_bool ) )
| ( c_in @ SY4357 @ SV65 @ SV1120 )
| ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SY4357 @ SV600 @ SV1120 ) @ ( tc_fun @ SV1120 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2795,plain,
! [SV1121: $i,SV601: $i,SV66: $i] :
( ( ! [SY4358: $i] :
( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SV1121 @ SY4358 ) @ ( tc_fun @ SY4358 @ tc_bool ) )
| ~ ( c_lessequals @ SV66 @ SV1121 @ ( tc_fun @ SY4358 @ tc_bool ) )
| ( c_in @ SV601 @ SV66 @ SY4358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2796,plain,
! [SV1122: $i,SV602: $i,SV67: $i] :
( ( ! [SY4359: $i] :
( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SV1122 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SY4359 @ SV602 @ SV1122 ) @ ( tc_fun @ SV1122 @ tc_bool ) )
| ( c_in @ SY4359 @ SV67 @ SV1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2797,plain,
! [SV1123: $i,SV603: $i,SV68: $i] :
( ( ! [SY4360: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SV603 @ ( tc_fun @ ( tc_prod @ SV1123 @ SY4360 ) @ tc_bool ) ) @ SV1123 @ SY4360 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV68 @ SV1123 @ SY4360 ) @ ( c_Relation_Oconverse @ SV603 @ SV1123 @ SY4360 ) @ ( tc_fun @ ( tc_prod @ SY4360 @ SV1123 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2798,plain,
! [SV1124: $i,SV604: $i,SV69: $i] :
( ( ! [SY4361: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Set_Oinsert @ SV604 @ SV1124 @ SY4361 ) @ ( tc_fun @ SY4361 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV1124 @ ( tc_fun @ SY4361 @ tc_bool ) ) )
| ( c_in @ SV604 @ SV69 @ SY4361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2799,plain,
! [SV1125: $i,SV605: $i,SV70: $i] :
( ( ! [SY4362: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV70 @ SV605 @ SV1125 ) @ SY4362 @ ( tc_fun @ SV1125 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV605 @ SY4362 @ ( tc_fun @ SV1125 @ tc_bool ) ) )
| ( c_in @ SV70 @ SY4362 @ SV1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2800,plain,
! [SV1126: $i,SV606: $i,SV71: $i] :
( ( ! [SY4363: $i,SY4364: $i,SY4365: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV606 @ ( tc_fun @ ( tc_prod @ SV1126 @ SY4363 ) @ tc_bool ) ) @ SY4364 @ SV1126 @ SY4363 @ SY4365 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SY4364 @ SV1126 @ SY4363 @ SY4365 ) @ ( c_Relation_Orel__comp @ SV606 @ SY4364 @ SV1126 @ SY4363 @ SY4365 ) @ ( tc_fun @ ( tc_prod @ SV1126 @ SY4365 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2801,plain,
! [SV1127: $i,SV607: $i,SV72: $i] :
( ( ! [SY4366: $i,SY4367: $i,SY4368: $i] :
( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1127 @ ( tc_fun @ ( tc_prod @ SY4366 @ SY4367 ) @ tc_bool ) ) @ SY4368 @ SY4366 @ SY4367 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SV607 @ SY4368 @ SY4366 @ SY4367 ) @ ( c_Relation_Orel__comp @ SV72 @ SV1127 @ SY4368 @ SY4366 @ SY4367 ) @ ( tc_fun @ ( tc_prod @ SY4368 @ SY4367 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2802,plain,
! [SV1128: $i,SV609: $i,SV74: $i] :
( ( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV74 @ SV609 @ ( tc_fun @ ( tc_prod @ SV1128 @ SV1128 ) @ tc_bool ) ) @ SV1128 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ SV74 @ SV1128 ) @ ( c_Relation_OField @ SV609 @ SV1128 ) @ ( tc_fun @ SV1128 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2803,plain,
! [SV1129: $i,SV610: $i,SV75: $i] :
( ( ! [SY4369: $i] :
( ( c_lessequals @ SV75 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4369 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) ) @ ( tc_fun @ SV1129 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2804,plain,
! [SV1130: $i,SV611: $i,SV76: $i] :
( ( ! [SY4370: $i] :
( ( c_lessequals @ SV76 @ SV611 @ ( tc_fun @ SV1130 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV611 @ SY4370 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2805,plain,
! [SV1131: $i,SV612: $i,SV77: $i] :
( ( ! [SY4371: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ( c_lessequals @ SV612 @ SV1131 @ SV77 )
| ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SY4371 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2806,plain,
! [SV1132: $i,SV613: $i,SV78: $i] :
( ( ! [SY4372: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ( c_lessequals @ SV613 @ SV1132 @ SV78 )
| ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4372 @ SV1132 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2807,plain,
! [SV1133: $i,SV614: $i,SV79: $i] :
( ( ! [SY4373: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV79 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SY4373 @ SV79 )
| ~ ( c_lessequals @ SV614 @ SY4373 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2808,plain,
! [SV1134: $i,SV615: $i,SV80: $i] :
( ( ! [SY4374: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV80 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SY4374 @ SV80 )
| ~ ( c_lessequals @ SV1134 @ SY4374 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2809,plain,
! [SV1135: $i,SV616: $i,SV81: $i] :
( ( ! [SY4375: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV81 )
| ( c_lessequals @ SV616 @ SV1135 @ SV81 )
| ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SY4375 @ SV81 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2810,plain,
! [SV1136: $i,SV617: $i,SV82: $i] :
( ( ! [SY4376: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( c_lessequals @ SV617 @ SV1136 @ SV82 )
| ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4376 @ SV1136 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2811,plain,
! [SV1137: $i,SV618: $i,SV83: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV83 @ SV618 @ ( tc_fun @ SV1137 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV618 @ SV83 @ ( tc_fun @ SV1137 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2812,plain,
! [SV1138: $i,SV619: $i,SV84: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV84 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV619 @ SV1138 @ SV84 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1138 @ SV619 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2813,plain,
! [SV1139: $i,SV620: $i,SV85: $i] :
( ( ~ ( class_Lattices_Olattice @ SV85 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SV1139 @ SV85 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1139 @ SV620 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2814,plain,
! [SV1140: $i,SV621: $i,SV86: $i] :
( ( ! [SY4377: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV86 @ SV621 @ ( tc_fun @ ( tc_prod @ SV1140 @ SY4377 ) @ tc_bool ) ) @ SV1140 @ SY4377 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV86 @ SV1140 @ SY4377 ) @ ( c_Relation_ODomain @ SV621 @ SV1140 @ SY4377 ) @ ( tc_fun @ SV1140 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2815,plain,
! [SV1141: $i,SV622: $i,SV87: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SV622 @ ( tc_fun @ SV1141 @ tc_bool ) ) @ ( tc_fun @ SV1141 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV87 @ SV622 @ ( tc_fun @ SV1141 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2816,plain,
! [SV1142: $i,SV623: $i,SV88: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) @ SV88 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2817,plain,
! [SV1143: $i,SV624: $i,SV89: $i] :
( ( ~ ( class_Lattices_Olattice @ SV89 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) @ SV89 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2818,plain,
! [SV625: $i,SV90: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV90 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV625 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2819,plain,
! [SV1144: $i,SV626: $i,SV91: $i] :
( ( ! [SY4378: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV91 @ SV626 @ ( tc_fun @ ( tc_prod @ SV1144 @ SY4378 ) @ tc_bool ) ) @ SV1144 @ SY4378 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV91 @ SV1144 @ SY4378 ) @ ( c_Relation_ORange @ SV626 @ SV1144 @ SY4378 ) @ ( tc_fun @ SY4378 @ tc_bool ) ) @ ( tc_fun @ SY4378 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2820,plain,
! [SV1145: $i,SV627: $i,SV92: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV92 @ SV627 ) @ ( c_Transitive__Closure_Ortrancl @ SV1145 @ SV627 ) @ ( tc_fun @ ( tc_prod @ SV627 @ SV627 ) @ tc_bool ) ) @ SV627 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV92 @ SV1145 @ ( tc_fun @ ( tc_prod @ SV627 @ SV627 ) @ tc_bool ) ) @ SV627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2821,plain,
! [SV1146: $i,SV628: $i,SV93: $i] :
( ( ! [SY4379: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1146 @ SV93 @ ( tc_fun @ SY4379 @ tc_bool ) ) @ SV628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2822,plain,
! [SV1147: $i,SV629: $i,SV94: $i] :
( ( ! [SY4380: $i] :
( ( hBOOL @ ( hAPP @ SV94 @ SV629 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SV1147 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ SV629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2823,plain,
! [SV1148: $i,SV630: $i,SV95: $i] :
( ( ! [SY4381: $i,SY4382: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV95 @ SV630 @ SV1148 @ SY4381 ) @ SY4382 @ ( tc_prod @ SV1148 @ SY4381 ) ) @ SV1148 @ SY4381 )
= ( c_Set_Oinsert @ SV630 @ ( c_Relation_ORange @ SY4382 @ SV1148 @ SY4381 ) @ SY4381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2824,plain,
! [SV1149: $i,SV631: $i,SV96: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1149 ) @ tc_bool ) ) @ SV1149 )
| ~ ( c_Relation_Osym @ SV631 @ SV1149 )
| ~ ( c_Relation_Osym @ SV96 @ SV1149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2825,plain,
! [SV632: $i,SV97: $i] :
( ( ( ( c_Transitive__Closure_Otrancl @ SV97 @ SV632 )
= SV97 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV97 @ SV632 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2826,plain,
! [SV1150: $i,SV633: $i,SV98: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV633 @ ( tc_fun @ SV1150 @ tc_bool ) ) @ SV1150 )
| ~ ( c_Finite__Set_Ofinite @ SV633 @ SV1150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2827,plain,
! [SV1151: $i,SV634: $i,SV99: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV634 @ ( tc_fun @ SV1151 @ tc_bool ) ) @ SV1151 )
| ~ ( c_Finite__Set_Ofinite @ SV99 @ SV1151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2828,plain,
! [SV1152: $i,SV635: $i,SV100: $i] :
( ( ! [SY4383: $i] :
( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SY4383 @ tc_bool ) ) @ SY4383 )
| ~ ( c_in @ SV100 @ SV1152 @ SY4383 )
| ~ ( c_in @ SV100 @ SV635 @ SY4383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2829,plain,
! [SV1153: $i,SV636: $i,SV101: $i] :
( ( ! [SY4384: $i] :
( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SY4384 @ tc_bool ) ) @ SY4384 )
| ~ ( c_in @ SV101 @ SV1153 @ SY4384 )
| ~ ( c_in @ SV101 @ SV636 @ SY4384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2830,plain,
! [SV1154: $i,SV637: $i,SV102: $i] :
( ( ! [SY4385: $i] :
( ( c_in @ SV102 @ ( c_Set_Oinsert @ SV637 @ SV1154 @ SY4385 ) @ SY4385 )
| ~ ( c_in @ SV102 @ SV1154 @ SY4385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2831,plain,
! [SV1155: $i,SV638: $i,SV103: $i] :
( ( ! [SY4386: $i] :
( ( c_in @ SV103 @ ( c_Set_Oinsert @ SV638 @ SV1155 @ SY4386 ) @ SY4386 )
| ~ ( c_in @ SV103 @ SV1155 @ SY4386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2832,plain,
! [SV1156: $i,SV639: $i,SV104: $i] :
( ( ! [SY4387: $i] :
( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1156 @ ( tc_fun @ SY4387 @ tc_bool ) ) @ SY4387 )
| ~ ( c_in @ SV104 @ SV639 @ SY4387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2833,plain,
! [SV1157: $i,SV640: $i,SV105: $i] :
( ( ! [SY4388: $i] :
( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV640 @ SV1157 @ ( tc_fun @ SY4388 @ tc_bool ) ) @ SY4388 )
| ~ ( c_in @ SV105 @ SV1157 @ SY4388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2834,plain,
! [SV1158: $i,SV641: $i,SV106: $i] :
( ( ! [SY4389: $i] :
( ( c_in @ SV106 @ SV641 @ SV1158 )
| ( SV106 = SY4389 )
| ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SY4389 @ SV641 @ SV1158 ) @ SV1158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2835,plain,
! [SV1159: $i,SV642: $i,SV107: $i] :
( ( ! [SY4390: $i] :
( ( c_in @ SV107 @ SV642 @ SV1159 )
| ( c_in @ SV107 @ SY4390 @ SV1159 )
| ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4390 @ SV642 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ SV1159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2836,plain,
! [SV1160: $i,SV643: $i,SV108: $i] :
( ( c_in @ SV108 @ ( c_Set_Oinsert @ SV108 @ SV643 @ SV1160 ) @ SV1160 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2837,plain,
! [SV1161: $i,SV644: $i,SV109: $i] :
( ( c_in @ SV109 @ ( c_Set_Oinsert @ SV109 @ SV644 @ SV1161 ) @ SV1161 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2838,plain,
! [SV1162: $i,SV645: $i,SV110: $i] :
( ( c_in @ SV110 @ ( c_Set_Oinsert @ SV110 @ SV645 @ SV1162 ) @ SV1162 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2839,plain,
! [SV1163: $i,SV646: $i,SV111: $i] :
( ( ! [SY4391: $i] :
( ( c_in @ SV111 @ SV646 @ SV1163 )
| ~ ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4391 @ SV646 @ ( tc_fun @ SV1163 @ tc_bool ) ) @ SV1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2840,plain,
! [SV1164: $i,SV647: $i,SV112: $i] :
( ( ! [SY4392: $i] :
( ( c_in @ SV112 @ SV647 @ SV1164 )
| ~ ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SY4392 @ ( tc_fun @ SV1164 @ tc_bool ) ) @ SV1164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2841,plain,
! [SV1165: $i,SV648: $i,SV113: $i] :
( ( ( ( c_Set_Oinsert @ SV113 @ SV648 @ SV1165 )
= SV648 )
| ~ ( c_in @ SV113 @ SV648 @ SV1165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2842,plain,
! [SV1166: $i,SV649: $i,SV114: $i] :
( ( ! [SY4393: $i,SY4394: $i] :
( ~ ( c_in @ SV114 @ SV649 @ SV1166 )
| ( c_in @ ( hAPP @ SY4393 @ SV114 ) @ ( c_Set_Oimage @ SY4393 @ SV649 @ SV1166 @ SY4394 ) @ SY4394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2843,plain,
! [SV1167: $i,SV650: $i,SV115: $i] :
( ( ! [SY4395: $i,SY4396: $i] :
( ~ ( c_in @ SV115 @ SV650 @ SV1167 )
| ( c_in @ ( hAPP @ SY4395 @ SV115 ) @ ( c_Set_Oimage @ SY4395 @ SV650 @ SV1167 @ SY4396 ) @ SY4396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2844,plain,
! [SV1168: $i,SV651: $i,SV116: $i] :
( ( ! [SY4397: $i,SY4398: $i] :
( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SV1168 @ SY4397 @ SY4398 ) @ SY4398 )
| ~ ( c_in @ SV651 @ SV1168 @ SY4397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2845,plain,
! [SV1169: $i,SV652: $i,SV117: $i] :
( ( ! [SY4399: $i,SY4400: $i] :
( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SV1169 @ SY4399 @ SY4400 ) @ SY4400 )
| ~ ( c_in @ SV652 @ SV1169 @ SY4399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2846,plain,
! [SV1170: $i,SV653: $i,SV118: $i] :
( ( ! [SY4401: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SV653 @ SV1170 @ SY4401 ) @ SV1170 @ SY4401 @ SY4401 ) @ SV118 @ ( tc_prod @ SY4401 @ SY4401 ) )
| ~ ( c_in @ ( c_Pair @ SV653 @ SV1170 @ SY4401 @ SY4401 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SY4401 ) @ ( tc_prod @ SY4401 @ SY4401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2847,plain,
! [SV1171: $i,SV654: $i,SV119: $i] :
( ( ! [SY4402: $i,SY4403: $i,SY4404: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SY4402 ) @ ( c_Product__Type_OSigma @ SY4403 @ SY4404 @ SV1171 @ SY4402 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SY4402 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4404 @ SV1171 @ SY4402 ) ) @ ( hAPP @ SY4404 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4404 @ SV1171 @ SY4402 ) ) @ ( tc_fun @ SY4402 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SY4403 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2848,plain,
! [SV1172: $i,SV655: $i,SV120: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV655 @ SV1172 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2849,plain,
! [SV1173: $i,SV656: $i,SV121: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV121 @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2850,plain,
! [SV1174: $i,SV659: $i,SV124: $i] :
( ( ! [SY4405: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 @ SV659 @ ( tc_fun @ ( tc_prod @ SV1174 @ SY4405 ) @ tc_bool ) ) @ SV1174 @ SY4405 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV124 @ SV1174 @ SY4405 ) @ ( c_Relation_ODomain @ SV659 @ SV1174 @ SY4405 ) @ ( tc_fun @ SV1174 @ tc_bool ) ) @ ( tc_fun @ SV1174 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2851,plain,
! [SV1175: $i,SV660: $i,SV125: $i] :
( ( c_lessequals @ SV125 @ ( c_Set_Oinsert @ SV660 @ SV125 @ SV1175 ) @ ( tc_fun @ SV1175 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2852,plain,
! [SV1176: $i,SV661: $i,SV126: $i] :
( ( ( c_Finite__Set_Ofinite @ SV126 @ SV661 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1176 @ SV126 @ SV661 ) @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2853,plain,
! [SV1177: $i,SV662: $i,SV127: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV127 @ SV662 @ SV1177 ) @ SV1177 )
| ~ ( c_Finite__Set_Ofinite @ SV662 @ SV1177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2854,plain,
! [SV1178: $i,SV663: $i,SV128: $i] :
( ( ! [SY4406: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SV663 @ SV1178 @ SY4406 ) @ SY4406 )
| ~ ( c_Relation_Otrans @ SV128 @ SV1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2855,plain,
! [SV1179: $i,SV664: $i,SV129: $i] :
( ( ! [SY4407: $i,SY4408: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV129 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV664 @ SV1179 @ ( tc_fun @ SY4407 @ tc_bool ) ) @ SY4407 @ SY4408 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV129 @ SV664 @ SY4407 @ SY4408 ) @ ( c_Set_Oimage @ SV129 @ SV1179 @ SY4407 @ SY4408 ) @ ( tc_fun @ SY4408 @ tc_bool ) ) @ ( tc_fun @ SY4408 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2856,plain,
! [SV1180: $i,SV665: $i,SV130: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 )
| ~ ( c_Finite__Set_Ofinite @ SV665 @ SV1180 )
| ~ ( c_Finite__Set_Ofinite @ SV130 @ SV1180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2857,plain,
! [SV1181: $i,SV666: $i,SV131: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ SV1181 )
| ~ ( c_Finite__Set_Ofinite @ SV666 @ SV1181 )
| ~ ( c_Finite__Set_Ofinite @ SV131 @ SV1181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2858,plain,
! [SV1182: $i,SV667: $i,SV132: $i] :
( ( ! [SY4409: $i,SY4410: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV132 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV667 @ SV1182 @ ( tc_fun @ SY4409 @ tc_bool ) ) @ SY4409 @ SY4410 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV132 @ SV667 @ SY4409 @ SY4410 ) @ ( c_Relation_OImage @ SV132 @ SV1182 @ SY4409 @ SY4410 ) @ ( tc_fun @ SY4410 @ tc_bool ) ) @ ( tc_fun @ SY4410 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2859,plain,
! [SV1183: $i,SV668: $i,SV133: $i] :
( ( ! [SY4411: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SV668 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SY4411 @ ( tc_fun @ SV1183 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV668 @ SY4411 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ ( tc_fun @ SV1183 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4411 @ SV133 @ ( tc_fun @ SV1183 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2860,plain,
! [SV669: $i,SV134: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ ( c_Relation_OId @ SV669 ) @ ( tc_fun @ ( tc_prod @ SV669 @ SV669 ) @ tc_bool ) ) @ SV669 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV134 @ SV669 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2861,plain,
! [SV1184: $i,SV670: $i,SV135: $i] :
( ( ! [SY4412: $i] :
( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
| ( hBOOL @ ( hAPP @ SV1184 @ SV670 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1184 @ SV135 @ ( tc_fun @ SY4412 @ tc_bool ) ) @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2862,plain,
! [SV1185: $i,SV671: $i,SV136: $i] :
( ( ! [SY4413: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SV671 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SY4413 ) )
| ~ ( hBOOL @ ( hAPP @ SV671 @ SY4413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2863,plain,
! [SV1186: $i,SV672: $i,SV137: $i] :
( ( ! [SY4414: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV672 @ ( tc_fun @ SV1186 @ tc_bool ) ) @ SY4414 ) )
| ~ ( hBOOL @ ( hAPP @ SV137 @ SY4414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2864,plain,
! [SV1187: $i,SV673: $i,SV138: $i] :
( ( ! [SY4415: $i,SY4416: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 @ SV673 @ ( tc_fun @ SV1187 @ tc_bool ) ) @ ( c_COMBK @ SY4415 @ ( tc_fun @ SY4416 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4416 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV138 @ ( c_COMBK @ SY4415 @ ( tc_fun @ SY4416 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4416 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SY4415 @ ( tc_fun @ SY4416 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4416 ) @ ( tc_fun @ ( tc_prod @ SV1187 @ SY4416 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2865,plain,
! [SV674: $i,SV139: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV139 @ SV139 @ SV674 @ SV674 @ SV674 ) @ SV139 @ ( tc_fun @ ( tc_prod @ SV674 @ SV674 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV139 @ SV674 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2866,plain,
! [SV1188: $i,SV675: $i,SV140: $i] :
( ( ! [SY4417: $i,SY4418: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4417 @ SY4418 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV675 @ SY4418 @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SY4417 @ SV1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2867,plain,
! [SV1189: $i,SV676: $i,SV141: $i] :
( ( ! [SY4419: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ SV1189 @ SV141 ) @ SY4419 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1189 @ SY4419 @ SV141 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2868,plain,
! [SV1190: $i,SV677: $i,SV142: $i] :
( ( ! [SY4420: $i] :
( ~ ( class_Lattices_Olattice @ SV142 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ SY4420 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ SY4420 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2869,plain,
! [SV1191: $i,SV678: $i,SV143: $i] :
( ( ! [SY4421: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ SY4421 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ SY4421 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2870,plain,
! [SV1192: $i,SV679: $i,SV144: $i] :
( ( ! [SY4422: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ SV1192 @ SV144 ) @ SY4422 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1192 @ SY4422 @ SV144 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2871,plain,
! [SV1193: $i,SV680: $i,SV145: $i] :
( ( ! [SY4423: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ SV680 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SY4423 @ ( tc_fun @ SV1193 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV680 @ SY4423 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ ( tc_fun @ SV1193 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2872,plain,
! [SV1194: $i,SV681: $i,SV146: $i] :
( ( ! [SY4424: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ SV1194 @ ( tc_fun @ SY4424 @ tc_bool ) ) @ ( tc_fun @ SY4424 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SV1194 @ ( tc_fun @ SY4424 @ tc_bool ) ) @ ( tc_fun @ SY4424 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2873,plain,
! [SV1195: $i,SV682: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofinite @ SV147 @ SV682 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV147 @ SV1195 @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2874,plain,
! [SV1196: $i,SV683: $i,SV148: $i] :
( ( ( c_Finite__Set_Ofinite @ SV148 @ SV683 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1196 @ SV148 @ ( tc_fun @ SV683 @ tc_bool ) ) @ SV683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2875,plain,
! [SV1197: $i,SV684: $i,SV150: $i] :
( ( ! [SY4425: $i,SY4426: $i,SY4427: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY4425 @ SY4426 @ SY4427 ) @ ( tc_fun @ SY4427 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4427 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SY4425 @ SV1197 @ SY4427 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV684 @ ( c_COMBK @ ( c_Set_Oinsert @ SY4425 @ SY4426 @ SY4427 ) @ ( tc_fun @ SY4427 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4427 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ SY4426 @ ( tc_fun @ SY4427 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4427 ) @ ( tc_fun @ ( tc_prod @ SV1197 @ SY4427 ) @ tc_bool ) ) @ ( tc_prod @ SV1197 @ SY4427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2876,plain,
! [SV1198: $i,SV685: $i,SV151: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SV1198 @ SV1198 ) @ tc_bool ) ) @ SV1198 )
| ~ ( c_Relation_Otrans @ SV685 @ SV1198 )
| ~ ( c_Relation_Otrans @ SV151 @ SV1198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2877,plain,
! [SV1199: $i,SV686: $i,SV152: $i] :
( ( ! [SY4428: $i] :
( ~ ( class_Lattices_Olattice @ SV152 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1199 @ SY4428 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1199 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY4428 @ SV152 ) @ SV152 ) @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2878,plain,
! [SV1200: $i,SV687: $i,SV153: $i] :
( ( ~ ( class_Lattices_Olattice @ SV153 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SV1200 @ SV153 ) @ SV153 )
= SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2879,plain,
! [SV1201: $i,SV688: $i,SV154: $i] :
( ( ~ ( class_Lattices_Olattice @ SV154 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV688 @ SV1201 @ SV154 ) @ SV154 )
= SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2880,plain,
! [SV1202: $i,SV689: $i,SV155: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV155 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1202 @ SV155 )
= SV689 )
| ~ ( c_lessequals @ SV1202 @ SV689 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2881,plain,
! [SV1203: $i,SV690: $i,SV156: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV156 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SV1203 @ SV156 )
= SV1203 )
| ~ ( c_lessequals @ SV690 @ SV1203 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2882,plain,
! [SV1204: $i,SV691: $i,SV157: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) )
= SV691 )
| ~ ( c_lessequals @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2883,plain,
! [SV1205: $i,SV692: $i,SV158: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV692 @ ( tc_fun @ SV1205 @ tc_bool ) )
= SV158 )
| ~ ( c_lessequals @ SV692 @ SV158 @ ( tc_fun @ SV1205 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2884,plain,
! [SV1206: $i,SV693: $i,SV159: $i] :
( ( ! [SY4429: $i,SY4430: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4429 @ SY4430 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV693 @ SY4430 @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SY4429 @ SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2885,plain,
! [SV1207: $i,SV694: $i,SV160: $i] :
( ( ! [SY4431: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SV694 @ SV1207 @ SY4431 ) @ SY4431 )
| ~ ( c_Finite__Set_Ofinite @ SV694 @ SV1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2886,plain,
! [SV1208: $i,SV695: $i,SV161: $i] :
( ( ! [SY4432: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SV695 @ SV1208 ) @ SY4432 @ ( tc_fun @ SV1208 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV695 @ SY4432 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) )
| ~ ( c_in @ SV161 @ SY4432 @ SV1208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2887,plain,
! [SV1209: $i,SV696: $i,SV162: $i] :
( ( ! [SY4433: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SV696 @ SV1209 @ SY4433 ) @ ( tc_fun @ SY4433 @ tc_bool ) )
= ( c_Set_Oinsert @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SV1209 @ ( tc_fun @ SY4433 @ tc_bool ) ) @ SY4433 ) )
| ~ ( c_in @ SV696 @ SV162 @ SY4433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2888,plain,
! [SV1210: $i,SV697: $i,SV163: $i] :
( ( ! [SY4434: $i,SY4435: $i] :
( ( c_Set_Oimage @ SV163 @ ( c_Set_Oinsert @ SV697 @ SV1210 @ SY4434 ) @ SY4434 @ SY4435 )
= ( c_Set_Oinsert @ ( hAPP @ SV163 @ SV697 ) @ ( c_Set_Oimage @ SV163 @ SV1210 @ SY4434 @ SY4435 ) @ SY4435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2889,plain,
! [SV1211: $i,SV698: $i,SV164: $i] :
( ( ! [SY4436: $i,SY4437: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4436 @ SY4437 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV698 @ SY4437 @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SY4436 @ ( tc_fun @ SV1211 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2890,plain,
! [SV1212: $i,SV699: $i,SV165: $i] :
( ( ! [SY4438: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV165 @ SV699 @ ( tc_fun @ ( tc_prod @ SV1212 @ SY4438 ) @ tc_bool ) ) @ SV1212 @ SY4438 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV165 @ SV1212 @ SY4438 ) @ ( c_Relation_Oconverse @ SV699 @ SV1212 @ SY4438 ) @ ( tc_fun @ ( tc_prod @ SY4438 @ SV1212 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2891,plain,
! [SV1213: $i,SV700: $i,SV166: $i] :
( ( ~ ( class_Lattices_Olattice @ SV166 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV700 @ SV1213 @ SV166 ) @ SV700 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2892,plain,
! [SV1214: $i,SV701: $i,SV167: $i] :
( ( ~ ( class_Lattices_Olattice @ SV167 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV701 @ SV1214 @ SV167 ) @ SV1214 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2893,plain,
! [SV1215: $i,SV702: $i,SV168: $i] :
( ( ! [SY4439: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV168 )
| ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SY4439 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SV702 @ SY4439 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2894,plain,
! [SV1216: $i,SV703: $i,SV169: $i] :
( ( ! [SY4440: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV169 )
| ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SY4440 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV703 @ SY4440 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2895,plain,
! [SV1217: $i,SV704: $i,SV170: $i] :
( ( ! [SY4441: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV170 )
| ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SY4441 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV704 @ SY4441 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2896,plain,
! [SV1218: $i,SV705: $i,SV171: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV171 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV705 @ SV1218 @ SV171 ) @ SV1218 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2897,plain,
! [SV1219: $i,SV706: $i,SV172: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV172 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV706 @ SV1219 @ SV172 ) @ SV706 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2898,plain,
! [SV1220: $i,SV707: $i,SV173: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV173 @ SV707 @ ( tc_fun @ SV1220 @ tc_bool ) ) @ SV173 @ ( tc_fun @ SV1220 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2899,plain,
! [SV1221: $i,SV708: $i,SV174: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV174 @ SV708 @ ( tc_fun @ SV1221 @ tc_bool ) ) @ SV708 @ ( tc_fun @ SV1221 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2900,plain,
! [SV1222: $i,SV709: $i,SV175: $i] :
( ( ! [SY4442: $i] :
( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SY4442 @ tc_bool ) ) @ ( tc_fun @ SY4442 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SY4442 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SY4442 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2901,plain,
! [SV1223: $i,SV710: $i,SV176: $i] :
( ( ! [SY4443: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SY4443 @ tc_bool ) ) @ ( tc_fun @ SY4443 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SY4443 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SY4443 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2902,plain,
! [SV1224: $i,SV711: $i,SV177: $i] :
( ( ! [SY4444: $i,SY4445: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV177 @ SV711 @ ( tc_fun @ SV1224 @ tc_bool ) ) @ ( c_COMBK @ SY4444 @ ( tc_fun @ SY4445 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4445 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV177 @ ( c_COMBK @ SY4444 @ ( tc_fun @ SY4445 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4445 ) @ ( c_Product__Type_OSigma @ SV711 @ ( c_COMBK @ SY4444 @ ( tc_fun @ SY4445 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4445 ) @ ( tc_fun @ ( tc_prod @ SV1224 @ SY4445 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2903,plain,
! [SV1225: $i,SV712: $i,SV178: $i] :
( ( ! [SY4446: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV178 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV712 @ SV1225 @ SV178 ) @ SY4446 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV712 @ SY4446 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1225 @ SY4446 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(2904,plain,
! [SV1226: $i,SV713: $i,SV179: $i] :
( ( ! [SY4447: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV179 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1226 @ SY4447 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1226 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SY4447 @ SV179 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2905,plain,
! [SV1227: $i,SV714: $i,SV180: $i] :
( ( ! [SY4448: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV714 @ SV1227 @ ( tc_fun @ SY4448 @ tc_bool ) ) @ ( tc_fun @ SY4448 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SV714 @ ( tc_fun @ SY4448 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SV1227 @ ( tc_fun @ SY4448 @ tc_bool ) ) @ ( tc_fun @ SY4448 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2906,plain,
! [SV1228: $i,SV715: $i,SV181: $i] :
( ( ! [SY4449: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV181 @ SV715 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SY4449 @ ( tc_fun @ SV1228 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV181 @ SY4449 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV715 @ SY4449 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ ( tc_fun @ SV1228 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2907,plain,
! [SV1229: $i,SV716: $i,SV182: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV182 @ SV716 @ SV1229 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2908,plain,
! [SV1230: $i,SV717: $i,SV183: $i] :
( ( ! [SY4450: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SY4450 @ ( tc_fun @ SV1230 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SY4450 @ ( tc_fun @ SV1230 @ tc_bool ) )
| ~ ( c_in @ SV183 @ SY4450 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2909,plain,
! [SV1231: $i,SV718: $i,SV184: $i] :
( ( ~ ( class_Lattices_Olattice @ SV184 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) @ SV184 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2910,plain,
! [SV1232: $i,SV719: $i,SV185: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV185 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) @ SV185 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2911,plain,
! [SV1233: $i,SV720: $i,SV186: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SV720 @ ( tc_fun @ SV1233 @ tc_bool ) ) @ ( tc_fun @ SV1233 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV186 @ SV720 @ ( tc_fun @ SV1233 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2912,plain,
! [SV1234: $i,SV721: $i,SV187: $i] :
( ( ( c_lessequals @ ( c_Relation_OField @ SV187 @ SV721 ) @ ( c_Relation_OField @ SV1234 @ SV721 ) @ ( tc_fun @ SV721 @ tc_bool ) )
| ~ ( c_lessequals @ SV187 @ SV1234 @ ( tc_fun @ ( tc_prod @ SV721 @ SV721 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2913,plain,
! [SV1235: $i,SV722: $i,SV188: $i] :
( ( ! [SY4451: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV188 @ SV722 @ ( tc_fun @ ( tc_prod @ SV1235 @ SY4451 ) @ tc_bool ) ) @ SV1235 @ SY4451 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV188 @ SV1235 @ SY4451 ) @ ( c_Relation_ORange @ SV722 @ SV1235 @ SY4451 ) @ ( tc_fun @ SY4451 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2914,plain,
! [SV1236: $i,SV723: $i,SV189: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1236 @ SV1236 ) @ tc_bool ) ) @ SV1236 )
| ~ ( c_Wellfounded_Owf @ SV189 @ SV1236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2915,plain,
! [SV1237: $i,SV724: $i,SV190: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV190 @ SV724 @ ( tc_fun @ ( tc_prod @ SV1237 @ SV1237 ) @ tc_bool ) ) @ SV1237 )
| ~ ( c_Wellfounded_Owf @ SV724 @ SV1237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2916,plain,
! [SV725: $i,SV191: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV191 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV725 @ SV191 )
= SV725 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2917,plain,
! [SV1238: $i,SV728: $i,SV194: $i] :
( ( ! [SY4452: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV194 )
| ( c_lessequals @ SV728 @ SV1238 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4452 @ SV728 @ SV194 ) @ SV1238 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2918,plain,
! [SV1239: $i,SV729: $i,SV195: $i] :
( ( ! [SY4453: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV195 )
| ( c_lessequals @ SV729 @ SV1239 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SY4453 @ SV195 ) @ SV1239 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2919,plain,
! [SV1240: $i,SV730: $i,SV196: $i] :
( ( ! [SY4454: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV196 )
| ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SY4454 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SV730 @ SY4454 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2920,plain,
! [SV1241: $i,SV731: $i,SV197: $i] :
( ( ! [SY4455: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV197 )
| ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SY4455 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV731 @ SV1241 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2921,plain,
! [SV1242: $i,SV732: $i,SV198: $i] :
( ( ! [SY4456: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV198 )
| ( c_lessequals @ SV732 @ SV1242 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4456 @ SV732 @ SV198 ) @ SV1242 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2922,plain,
! [SV1243: $i,SV733: $i,SV199: $i] :
( ( ! [SY4457: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV199 )
| ( c_lessequals @ SV733 @ SV1243 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4457 @ SV199 ) @ SV1243 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2923,plain,
! [SV1244: $i,SV734: $i,SV200: $i] :
( ( ! [SY4458: $i] :
( ( c_lessequals @ SV200 @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY4458 @ ( tc_fun @ SV1244 @ tc_bool ) ) @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2924,plain,
! [SV1245: $i,SV735: $i,SV201: $i] :
( ( ! [SY4459: $i] :
( ( c_lessequals @ SV201 @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4459 @ SV201 @ ( tc_fun @ SV1245 @ tc_bool ) ) @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2925,plain,
! [SV1246: $i,SV736: $i,SV202: $i] :
( ( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
| ~ ( c_Finite__Set_Ofinite @ SV1246 @ SV736 )
| ~ ( c_lessequals @ SV202 @ SV1246 @ ( tc_fun @ SV736 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2926,plain,
! [SV1247: $i,SV737: $i,SV203: $i] :
( ( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
| ~ ( c_lessequals @ SV203 @ SV1247 @ ( tc_fun @ SV737 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1247 @ SV737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2927,plain,
! [SV1248: $i,SV738: $i,SV204: $i] :
( ( ! [SY4460: $i,SY4461: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4460 @ SY4461 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV738 @ SY4461 @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SY4460 @ ( tc_fun @ SV1248 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2928,plain,
! [SV1249: $i,SV739: $i,SV205: $i] :
( ( ! [SY4462: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SY4462 ) )
| ~ ( hBOOL @ ( hAPP @ SV739 @ SY4462 ) )
| ~ ( hBOOL @ ( hAPP @ SV205 @ SY4462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2929,plain,
! [SV1250: $i,SV740: $i,SV206: $i] :
( ( ! [SY4463: $i,SY4464: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SV1250 @ SY4463 ) @ ( c_Set_Oimage @ SV206 @ SY4464 @ SV1250 @ SY4463 ) @ ( tc_fun @ SY4463 @ tc_bool ) )
| ~ ( c_lessequals @ SV740 @ SY4464 @ ( tc_fun @ SV1250 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2930,plain,
! [SV1251: $i,SV741: $i,SV207: $i] :
( ( ! [SY4465: $i,SY4466: $i] :
( ~ ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY4465 @ SV207 @ SV1251 @ SY4466 ) @ ( c_Set_Oimage @ SY4465 @ SV741 @ SV1251 @ SY4466 ) @ ( tc_fun @ SY4466 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2931,plain,
! [SV1252: $i,SV742: $i,SV208: $i] :
( ( ! [SY4467: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SV742 @ SV1252 ) @ ( c_Set_Oinsert @ SV208 @ SY4467 @ SV1252 ) @ ( tc_fun @ SV1252 @ tc_bool ) )
| ~ ( c_lessequals @ SV742 @ SY4467 @ ( tc_fun @ SV1252 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2932,plain,
! [SV1253: $i,SV743: $i,SV209: $i] :
( ( ( c_Relation_Otrans @ SV209 @ SV743 )
| ~ ( c_Equiv__Relations_Oequiv @ SV1253 @ SV209 @ SV743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2933,plain,
! [SV1254: $i,SV744: $i,SV210: $i] :
( ( ! [SY4468: $i,SY4469: $i] :
( ( c_Set_Oimage @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV744 @ SV1254 @ ( tc_fun @ SY4468 @ tc_bool ) ) @ SY4468 @ SY4469 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV210 @ SV744 @ SY4468 @ SY4469 ) @ ( c_Set_Oimage @ SV210 @ SV1254 @ SY4468 @ SY4469 ) @ ( tc_fun @ SY4469 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2934,plain,
! [SV1255: $i,SV745: $i,SV211: $i] :
( ( ! [SY4470: $i,SY4471: $i] :
( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SY4470 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SY4471 @ SV745 @ SV1255 @ SV1255 ) @ SY4470 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SY4471 @ SV1255 @ SV1255 ) @ SY4470 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SY4470 @ SV1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2935,plain,
! [SV1256: $i,SV746: $i,SV212: $i] :
( ( ! [SY4472: $i,SY4473: $i] :
( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SY4472 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SY4473 @ SV746 @ SV1256 @ SV1256 ) @ SY4472 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SY4473 @ SV1256 @ SV1256 ) @ SY4472 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SY4472 @ SV1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2936,plain,
! [SV1257: $i,SV747: $i,SV213: $i] :
( ( ! [SY4474: $i] :
( ( c_Wellfounded_Owf @ SV213 @ SV747 )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1257 @ SY4474 @ SV747 @ SV747 ) @ SV213 @ ( tc_prod @ SV747 @ SV747 ) ) @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2937,plain,
! [SV1258: $i,SV748: $i,SV214: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV214 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( c_Relation_Orel__comp @ SV1258 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV214 @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2938,plain,
! [SV1259: $i,SV749: $i,SV215: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV215 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( c_Relation_Orel__comp @ SV749 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2939,plain,
! [SV1260: $i,SV751: $i,SV217: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
| ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV751 )
| ~ ( c_in @ SV1260 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2940,plain,
! [SV1261: $i,SV754: $i,SV220: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV220 @ SV754 ) @ SV1261 @ SV754 @ SV754 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV220 @ SV1261 @ ( tc_fun @ SV754 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2941,plain,
! [SV1262: $i,SV757: $i,SV223: $i] :
( ( ! [SY4475: $i] :
( ~ ( c_in @ ( c_Pair @ SV223 @ SV757 @ SV1262 @ SV1262 ) @ ( c_Transitive__Closure_Ortrancl @ SY4475 @ SV1262 ) @ ( tc_prod @ SV1262 @ SV1262 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SV1262 @ SV1262 ) @ SY4475 @ ( tc_prod @ SV1262 @ SV1262 ) ) @ SV1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2942,plain,
! [SV1263: $i,SV758: $i,SV224: $i] :
( ( ! [SY4476: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SV1263 @ SV1263 ) @ SY4476 @ ( tc_prod @ SV1263 @ SV1263 ) ) @ SV1263 )
| ( c_in @ ( c_Pair @ SV758 @ SV224 @ SV1263 @ SV1263 ) @ ( c_Transitive__Closure_Ortrancl @ SY4476 @ SV1263 ) @ ( tc_prod @ SV1263 @ SV1263 ) )
| ~ ( c_Wellfounded_Owf @ SY4476 @ SV1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2943,plain,
! [SV1264: $i,SV759: $i,SV225: $i] :
( ( ! [SY4477: $i] :
( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV759 @ SV225 @ SV1264 @ SY4477 ) @ SY4477 @ SY4477 ) @ ( c_Transitive__Closure_Ortrancl @ SV759 @ SY4477 ) @ ( tc_prod @ SY4477 @ SY4477 ) )
| ~ ( c_in @ ( c_Pair @ SV225 @ SV1264 @ SY4477 @ SY4477 ) @ ( c_Transitive__Closure_Otrancl @ SV759 @ SY4477 ) @ ( tc_prod @ SY4477 @ SY4477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2944,plain,
! [SV1265: $i,SV760: $i,SV226: $i] :
( ( ! [SY4478: $i,SY4479: $i,SY4480: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SY4478 ) @ ( c_Product__Type_OSigma @ SY4479 @ SY4480 @ SV1265 @ SY4478 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SY4478 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SY4480 @ SV1265 @ SY4478 ) @ SV226 @ SV1265 )
| ~ ( c_lessequals @ SV226 @ SY4479 @ ( tc_fun @ SV1265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2945,plain,
! [SV1266: $i,SV761: $i,SV227: $i] :
( ( ! [SY4481: $i,SY4482: $i] :
( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SV1266 @ ( tc_fun @ SY4481 @ tc_bool ) @ SY4482 ) @ SY4482 @ SY4481 ) @ ( tc_fun @ SY4482 @ SY4481 ) )
| ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SV1266 @ SV227 @ SY4482 @ SY4481 ) ) @ SV1266 @ SY4481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2946,plain,
! [SV1267: $i,SV762: $i,SV228: $i] :
( ( ! [SY4483: $i,SY4484: $i] :
( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SV762 @ ( c_COMBK @ SV1267 @ ( tc_fun @ SY4483 @ tc_bool ) @ SY4484 ) @ SY4484 @ SY4483 ) @ ( tc_fun @ SY4484 @ SY4483 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV762 @ SV1267 @ SV228 @ SY4484 @ SY4483 ) @ SV762 @ SY4484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2947,plain,
! [SV1268: $i,SV763: $i,SV229: $i] :
( ( ! [SY4485: $i,SY4486: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SV1268 @ SY4485 ) @ SY4486 @ ( tc_fun @ SY4485 @ tc_bool ) )
| ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SY4486 @ ( tc_fun @ SY4485 @ tc_bool ) @ SV1268 ) @ SV1268 @ SY4485 ) @ ( tc_fun @ SV1268 @ SY4485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2948,plain,
! [SV1269: $i,SV765: $i,SV231: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2949,plain,
! [SV766: $i,SV232: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SV766 @ SV766 ) @ SV232 @ SV766 @ SV766 @ SV766 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SV766 @ SV766 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV232 @ SV766 )
| ~ ( c_Relation_Osym @ SV232 @ SV766 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2950,plain,
! [SV1270: $i,SV767: $i,SV233: $i] :
( ( ! [SY4487: $i] :
( ( c_Wellfounded_Owf @ SV233 @ SV767 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1270 @ SY4487 @ SV233 @ SV767 ) @ SY4487 @ SV767 )
| ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SV1270 @ ( c_COMBK @ SY4487 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2951,plain,
! [SV1271: $i,SV768: $i,SV234: $i] :
( ( ! [SY4488: $i] :
( ( c_Wellfounded_Owf @ SV234 @ SV768 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1271 @ SY4488 @ SV234 @ SV768 ) @ SV1271 @ SV768 )
| ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SV1271 @ ( c_COMBK @ SY4488 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2952,plain,
! [SV1272: $i,SV769: $i,SV235: $i] :
( ( ( c_Relation_Orefl__on @ SV235 @ SV769 @ SV1272 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SV769 @ SV1272 ) @ SV235 @ SV1272 )
| ~ ( c_lessequals @ SV769 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SV1272 @ tc_bool ) @ SV1272 ) @ SV1272 @ SV1272 ) @ ( tc_fun @ ( tc_prod @ SV1272 @ SV1272 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2953,plain,
! [SV1273: $i,SV770: $i,SV236: $i] :
( ( ( c_Relation_Orefl__on @ SV236 @ SV770 @ SV1273 )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SV770 @ SV1273 ) @ SV236 @ SV1273 )
| ~ ( c_lessequals @ SV770 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SV1273 @ tc_bool ) @ SV1273 ) @ SV1273 @ SV1273 ) @ ( tc_fun @ ( tc_prod @ SV1273 @ SV1273 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(2954,plain,
! [SV1274: $i,SV771: $i,SV237: $i] :
( ( ! [SY4489: $i] :
( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
| ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SY4489 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
| ~ ( c_lessequals @ SY4489 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(2955,plain,
! [SV1275: $i,SV772: $i,SV238: $i] :
( ( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SV1275 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ SV1275 @ SV1275 ) @ SV772 @ ( tc_prod @ SV1275 @ SV1275 ) )
| ~ ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SV1275 @ tc_bool ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ ( tc_prod @ SV1275 @ SV1275 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2956,plain,
! [SV1276: $i,SV773: $i,SV239: $i] :
( ( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SV1276 )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ SV1276 @ SV1276 ) @ SV773 @ ( tc_prod @ SV1276 @ SV1276 ) )
| ~ ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SV1276 @ tc_bool ) @ SV1276 ) @ SV1276 @ SV1276 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1276 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(2957,plain,
! [SV1277: $i,SV774: $i,SV240: $i] :
( ( ! [SY4490: $i] :
( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Otrancl @ SY4490 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
| ( SV240 = SV774 )
| ~ ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Ortrancl @ SY4490 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2958,plain,
! [SV1278: $i,SV775: $i,SV241: $i] :
( ( ! [SY4491: $i] :
( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Otrancl @ SY4491 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
| ( SV241 = SV775 )
| ~ ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Ortrancl @ SY4491 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2959,plain,
! [SV1279: $i,SV776: $i,SV242: $i] :
( ( ! [SY4492: $i] :
( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Ortrancl @ SY4492 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
| ~ ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Otrancl @ SY4492 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
| ( SV242 = SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2960,plain,
! [SV1280: $i,SV777: $i,SV243: $i] :
( ( ! [SY4493: $i] :
( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SV1280 @ SY4493 ) @ SY4493 @ SY4493 ) @ SV777 @ ( tc_prod @ SY4493 @ SY4493 ) )
| ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SY4493 @ SY4493 ) @ SV777 @ ( tc_prod @ SY4493 @ SY4493 ) )
| ~ ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SY4493 @ SY4493 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SY4493 ) @ ( tc_prod @ SY4493 @ SY4493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2961,plain,
! [SV1281: $i,SV778: $i,SV244: $i] :
( ( ! [SY4494: $i,SY4495: $i] :
( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SY4494 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SY4495 @ SV778 @ SV1281 @ SV1281 ) @ SY4494 @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SY4495 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SY4494 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2962,plain,
! [SV1282: $i,SV779: $i,SV245: $i] :
( ( ! [SY4496: $i,SY4497: $i] :
( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SY4496 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SY4497 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SY4496 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SY4497 @ SV1282 @ SV1282 ) @ SY4496 @ ( tc_prod @ SV1282 @ SV1282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(2963,plain,
! [SV1283: $i,SV780: $i,SV246: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) @ SV1283 @ ( tc_fun @ SV780 @ tc_bool ) )
| ~ ( c_in @ SV1283 @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2964,plain,
! [SV1284: $i,SV783: $i,SV249: $i] :
( ( ( c_in @ SV249 @ ( c_Complete__Lattice_OInf__class_OInf @ SV783 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
| ~ ( c_in @ SV249 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV249 @ SV783 @ SV1284 ) @ SV1284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2965,plain,
! [SV1285: $i,SV784: $i,SV250: $i] :
( ( ! [SY4498: $i] :
( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SV1285 @ SY4498 ) @ ( c_Wellfounded_Oacc @ SV1285 @ SY4498 ) @ SY4498 )
| ~ ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SV1285 @ SY4498 ) @ SY4498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2966,plain,
! [SV1286: $i,SV785: $i,SV251: $i] :
( ( ( c_in @ SV251 @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV785 @ SV251 @ SV1286 ) @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2967,plain,
! [SV1287: $i,SV786: $i,SV252: $i] :
( ( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
| ~ ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SV1287 ) ) )
| ~ ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SV1287 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2968,plain,
! [SV1288: $i,SV787: $i,SV253: $i] :
( ( ! [SY4499: $i] :
( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
| ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SY4499 ) ) )
| ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SY4499 ) @ SY4499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2969,plain,
! [SV1289: $i,SV788: $i,SV254: $i] :
( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV254 @ SV788 @ SV1289 ) @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 )
| ( c_in @ SV788 @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2970,plain,
! [SV1290: $i,SV789: $i,SV255: $i] :
( ( ! [SY4500: $i] :
( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SV1290 @ SY4500 ) @ ( c_Wellfounded_Oacc @ SV1290 @ SY4500 ) @ SY4500 )
| ~ ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SV1290 @ SY4500 ) @ SY4500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2971,plain,
! [SV1291: $i,SV790: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SV1291 ) ) )
| ~ ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SV1291 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2972,plain,
! [SV1292: $i,SV791: $i,SV257: $i] :
( ( ! [SY4501: $i] :
( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SY4501 ) ) )
| ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SY4501 ) @ SY4501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2973,plain,
! [SV1293: $i,SV792: $i,SV258: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SV1293 @ SV258 )
| ~ ( c_in @ SV1293 @ SV792 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2974,plain,
! [SV1294: $i,SV793: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ ( c_Complete__Lattice_OSup__class_OSup @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) ) @ ( tc_fun @ SV1294 @ tc_bool ) )
| ~ ( c_in @ SV259 @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2975,plain,
! [SV1295: $i,SV794: $i,SV260: $i] :
( ( ! [SY4502: $i] :
( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
| ~ ( c_lessequals @ SY4502 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) )
| ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SY4502 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2976,plain,
! [SV1296: $i,SV795: $i,SV261: $i] :
( ( ! [SY4503: $i,SY4504: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SV1296 @ SY4503 @ SY4504 ) @ SV261 @ SY4503 )
| ~ ( c_in @ SV795 @ ( c_Relation_OImage @ SV1296 @ SV261 @ SY4503 @ SY4504 ) @ SY4504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2977,plain,
! [SV1297: $i,SV796: $i,SV262: $i] :
( ( ! [SY4505: $i,SY4506: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SV1297 @ SY4505 @ SY4506 ) @ SV262 @ SY4505 )
| ~ ( c_in @ SV796 @ ( c_Relation_OImage @ SV1297 @ SV262 @ SY4505 @ SY4506 ) @ SY4506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2978,plain,
! [SV1298: $i,SV797: $i,SV263: $i] :
( ( ! [SY4507: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
| ~ ( c_in @ SY4507 @ SV263 @ SV1298 )
| ~ ( c_Wellfounded_Owf @ SV797 @ SV1298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2979,plain,
! [SV1299: $i,SV798: $i,SV264: $i] :
( ( ! [SY4508: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
| ~ ( c_in @ SY4508 @ SV264 @ SV1299 )
| ~ ( c_Wellfounded_Owf @ SV798 @ SV1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2980,plain,
! [SV1300: $i,SV799: $i,SV265: $i] :
( ( ( c_in @ SV265 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV265 @ SV799 @ SV1300 ) @ SV1300 )
| ~ ( c_in @ SV265 @ ( c_Complete__Lattice_OSup__class_OSup @ SV799 @ ( tc_fun @ SV1300 @ tc_bool ) ) @ SV1300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2981,plain,
! [SV1301: $i,SV800: $i,SV266: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
| ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1301 @ SV266 ) @ SV266 )
| ~ ( c_in @ SV800 @ SV1301 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2982,plain,
! [SV1302: $i,SV801: $i,SV267: $i] :
( ( ! [SY4509: $i,SY4510: $i] :
( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SY4509 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SY4510 @ SV801 @ SV1302 @ SV1302 ) @ SY4509 @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SY4510 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SY4509 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2983,plain,
! [SV1303: $i,SV802: $i,SV268: $i] :
( ( ! [SY4511: $i,SY4512: $i] :
( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SY4511 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SY4512 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SY4511 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SY4512 @ SV1303 @ SV1303 ) @ SY4511 @ ( tc_prod @ SV1303 @ SV1303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2984,plain,
! [SV1304: $i,SV803: $i,SV269: $i] :
( ( ! [SY4513: $i,SY4514: $i] :
( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SY4513 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SY4514 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SY4513 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SY4514 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SY4513 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2985,plain,
! [SV1305: $i,SV804: $i,SV270: $i] :
( ( c_in @ ( c_Pair @ SV270 @ SV270 @ SV804 @ SV804 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV804 ) @ ( tc_prod @ SV804 @ SV804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2986,plain,
! [SV1306: $i,SV805: $i,SV271: $i] :
( ( c_in @ ( c_Pair @ SV271 @ SV271 @ SV805 @ SV805 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV805 ) @ ( tc_prod @ SV805 @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(2987,plain,
! [SV1307: $i,SV806: $i,SV272: $i] :
( ( ! [SY4515: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SV806 @ SV1307 @ SY4515 ) @ SV1307 @ SY4515 @ SY4515 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SY4515 ) @ ( tc_prod @ SY4515 @ SY4515 ) )
| ~ ( c_in @ ( c_Pair @ SV806 @ SV1307 @ SY4515 @ SY4515 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SY4515 ) @ ( tc_prod @ SY4515 @ SY4515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2988,plain,
! [SV1308: $i,SV807: $i,SV273: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV273 )
| ( c_lessequals @ SV807 @ SV1308 @ SV273 )
| ( c_lessequals @ SV1308 @ SV807 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2989,plain,
! [SV1309: $i,SV809: $i,SV275: $i] :
( ( ( c_lessequals @ SV275 @ ( c_Product__Type_OSigma @ SV809 @ ( c_COMBK @ SV809 @ ( tc_fun @ SV1309 @ tc_bool ) @ SV1309 ) @ SV1309 @ SV1309 ) @ ( tc_fun @ ( tc_prod @ SV1309 @ SV1309 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV809 @ SV275 @ SV1309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2990,plain,
! [SV1310: $i,SV811: $i,SV277: $i] :
( ( ! [SY4516: $i,SY4517: $i,SY4518: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SY4516 ) @ ( c_Relation_OImage @ SY4517 @ SY4518 @ SV1310 @ SY4516 ) @ ( tc_fun @ SY4516 @ tc_bool ) )
| ~ ( c_lessequals @ SV811 @ SY4518 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SY4517 @ ( tc_fun @ ( tc_prod @ SV1310 @ SY4516 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2991,plain,
! [SV1311: $i,SV812: $i,SV278: $i] :
( ( ! [SY4519: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SV812 @ SV1311 ) @ ( c_Relation_ODomain @ SY4519 @ SV812 @ SV1311 ) @ ( tc_fun @ SV812 @ tc_bool ) )
| ~ ( c_lessequals @ SV278 @ SY4519 @ ( tc_fun @ ( tc_prod @ SV812 @ SV1311 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2992,plain,
! [SV1312: $i,SV813: $i,SV279: $i] :
( ( ! [SY4520: $i] :
( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
| ~ ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SY4520 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2993,plain,
! [SV814: $i,SV280: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV280 ) )
= $true )
| ( ( c_lessequals @ SV814 @ SV814 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2994,plain,
! [SV815: $i,SV281: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV281 ) )
= $true )
| ( ( c_lessequals @ SV815 @ SV815 @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2995,plain,
! [SV1313: $i,SV816: $i,SV282: $i] :
( ( ( c_Wellfounded_Owf @ SV282 @ SV816 )
| ~ ( c_lessequals @ SV282 @ SV1313 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1313 @ SV816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2996,plain,
! [SV1314: $i,SV817: $i,SV283: $i] :
( ( ! [SY4521: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
| ~ ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) )
| ~ ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SY4521 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2997,plain,
! [SV1315: $i,SV818: $i,SV284: $i] :
( ( ! [SY4522: $i] :
( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
| ~ ( c_lessequals @ SY4522 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
| ~ ( c_lessequals @ SV284 @ SY4522 @ ( tc_fun @ SV1315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2998,plain,
! [SV1316: $i,SV821: $i,SV287: $i] :
( ( ! [SY4523: $i] :
( ~ ( class_Orderings_Opreorder @ SV287 )
| ( c_lessequals @ SV821 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SY4523 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SY4523 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2999,plain,
! [SV1317: $i,SV822: $i,SV288: $i] :
( ( ! [SY4524: $i] :
( ~ ( class_Orderings_Oorder @ SV288 )
| ( c_lessequals @ SV822 @ SV1317 @ SV288 )
| ~ ( c_lessequals @ SV822 @ SY4524 @ SV288 )
| ~ ( c_lessequals @ SY4524 @ SV1317 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3000,plain,
! [SV1318: $i,SV824: $i,SV290: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV290 @ SV824 ) @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3001,plain,
! [SV1319: $i,SV825: $i,SV291: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV291 @ SV825 ) @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV291 @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3002,plain,
! [SV1320: $i,SV826: $i,SV292: $i] :
( ( ~ ( class_Orderings_Oorder @ SV292 )
| ( SV826 = SV1320 )
| ~ ( c_lessequals @ SV826 @ SV1320 @ SV292 )
| ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3003,plain,
! [SV1321: $i,SV827: $i,SV293: $i] :
( ( ~ ( class_Orderings_Oorder @ SV293 )
| ( SV827 = SV1321 )
| ~ ( c_lessequals @ SV1321 @ SV827 @ SV293 )
| ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3004,plain,
! [SV1322: $i,SV828: $i,SV294: $i] :
( ( ~ ( class_Orderings_Oorder @ SV294 )
| ( SV828 = SV1322 )
| ~ ( c_lessequals @ SV1322 @ SV828 @ SV294 )
| ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3005,plain,
! [SV1323: $i,SV829: $i,SV295: $i] :
( ( ( SV295 = SV829 )
| ~ ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SV1323 @ tc_bool ) )
| ~ ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3006,plain,
! [SV1324: $i,SV830: $i,SV296: $i] :
( ( ( SV296 = SV830 )
| ~ ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SV1324 @ tc_bool ) )
| ~ ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3007,plain,
! [SV1325: $i,SV832: $i,SV298: $i] :
( ( ! [SY4525: $i,SY4526: $i,SY4527: $i,SY4528: $i,SY4529: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SY4525 @ SY4526 ) @ ( c_Product__Type_OSigma @ SY4527 @ ( c_COMBK @ SY4528 @ ( tc_fun @ SY4526 @ tc_bool ) @ SV1325 ) @ SV1325 @ SY4526 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SY4526 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY4529 @ ( c_COMBK @ SY4528 @ ( tc_fun @ SY4526 @ tc_bool ) @ SY4525 ) @ SY4525 @ SY4526 ) @ ( tc_fun @ ( tc_prod @ SY4525 @ SY4526 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SY4527 @ ( c_COMBK @ SY4529 @ ( tc_fun @ SY4525 @ tc_bool ) @ SV1325 ) @ SV1325 @ SY4525 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SY4525 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3008,plain,
! [SV1326: $i,SV833: $i,SV299: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV299 @ SV833 ) @ ( c_Transitive__Closure_Ortrancl @ SV1326 @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ SV1326 @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3009,plain,
! [SV1327: $i,SV836: $i,SV302: $i] :
( ( ! [SY4530: $i,SY4531: $i,SY4532: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SY4530 ) @ SY4530 @ SV1327 ) @ ( c_Product__Type_OSigma @ SY4531 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SY4530 ) @ SY4530 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SY4530 @ SV1327 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SY4531 @ ( tc_fun @ SY4530 @ tc_bool ) )
| ~ ( c_in @ SY4532 @ SV836 @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3010,plain,
! [SV1328: $i,SV837: $i,SV303: $i] :
( ( ! [SY4533: $i,SY4534: $i,SY4535: $i] :
( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SY4533 @ ( tc_fun @ SY4534 @ tc_bool ) @ SV1328 ) @ SV1328 @ SY4534 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SY4533 @ ( tc_fun @ SY4534 @ tc_bool ) @ SV1328 ) @ SV1328 @ SY4534 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SY4534 ) @ tc_bool ) )
| ~ ( c_in @ SY4535 @ SY4533 @ SY4534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3011,plain,
! [SV1329: $i,SV839: $i,SV305: $i] :
( ( ( c_lessequals @ SV305 @ ( c_Product__Type_OSigma @ SV839 @ ( c_COMBK @ SV839 @ ( tc_fun @ SV1329 @ tc_bool ) @ SV1329 ) @ SV1329 @ SV1329 ) @ ( tc_fun @ ( tc_prod @ SV1329 @ SV1329 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV839 @ SV305 @ SV1329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3012,plain,
! [SV1330: $i,SV840: $i,SV306: $i] :
( ( ! [SY4536: $i,SY4537: $i,SY4538: $i,SY4539: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SY4536 @ SY4537 ) @ ( c_Relation_Orel__comp @ SY4538 @ SY4539 @ SV1330 @ SY4536 @ SY4537 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SY4537 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SY4539 @ ( tc_fun @ ( tc_prod @ SY4536 @ SY4537 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SY4538 @ ( tc_fun @ ( tc_prod @ SV1330 @ SY4536 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3013,plain,
! [SV1331: $i,SV841: $i,SV307: $i] :
( ( ! [SY4540: $i] :
( ( hAPP @ ( c_COMBK @ SV307 @ SV841 @ SV1331 ) @ SY4540 )
= SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3014,plain,
! [SV1332: $i,SV842: $i,SV308: $i] :
( ( ! [SY4541: $i,SY4542: $i,SY4543: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SY4541 ) @ SY4542 @ ( tc_fun @ SY4541 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SY4543 @ ( c_COMBK @ SY4542 @ ( tc_fun @ SY4541 @ tc_bool ) @ SV1332 ) @ SV1332 @ SY4541 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SY4541 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3015,plain,
! [SV843: $i,SV309: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV309 @ SV843 ) @ SV843 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV309 @ SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(3016,plain,
! [SV1333: $i,SV844: $i,SV310: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) )
| ~ ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1333 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3017,plain,
! [SV1334: $i,SV845: $i,SV311: $i] :
( ( ! [SY4544: $i,SY4545: $i] :
( ( c_in @ SV311 @ SV845 @ SV1334 )
| ( SV311 = SY4544 )
| ~ ( c_lessequals @ SY4545 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SY4544 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SY4545 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(3018,plain,
! [SV1335: $i,SV846: $i,SV312: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV312 @ SV846 ) @ ( c_Wellfounded_Oacc @ SV1335 @ SV846 ) @ ( tc_fun @ SV846 @ tc_bool ) )
| ~ ( c_lessequals @ SV1335 @ SV312 @ ( tc_fun @ ( tc_prod @ SV846 @ SV846 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3019,plain,
! [SV1336: $i,SV847: $i,SV313: $i] :
( ( ! [SY4546: $i,SY4547: $i] :
( ~ ( class_HOL_Oord @ SV313 )
| ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SY4546 @ SV1336 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SY4546 @ ( tc_fun @ SY4547 @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3020,plain,
! [SV1337: $i,SV848: $i,SV314: $i] :
( ( ! [SY4548: $i] :
( ( c_in @ SV314 @ SV848 @ SV1337 )
| ~ ( c_in @ SV314 @ SY4548 @ SV1337 )
| ~ ( c_lessequals @ SY4548 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3021,plain,
! [SV1338: $i,SV849: $i,SV315: $i] :
( ( ! [SY4549: $i] :
( ( c_in @ SV315 @ SV849 @ SV1338 )
| ~ ( c_lessequals @ SY4549 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) )
| ~ ( c_in @ SV315 @ SY4549 @ SV1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3022,plain,
! [SV1339: $i,SV850: $i,SV316: $i] :
( ( ! [SY4550: $i] :
( ( c_in @ SV316 @ SV850 @ SV1339 )
| ~ ( c_in @ SV316 @ SY4550 @ SV1339 )
| ~ ( c_lessequals @ SY4550 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3023,plain,
! [SV1340: $i,SV851: $i,SV317: $i] :
( ( ! [SY4551: $i] :
( ( c_in @ SV317 @ SV851 @ SV1340 )
| ~ ( c_in @ SV317 @ SY4551 @ SV1340 )
| ~ ( c_lessequals @ SY4551 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3024,plain,
! [SV1341: $i,SV852: $i,SV318: $i] :
( ( ( c_in @ SV318 @ ( c_Transitive__Closure_Ortrancl @ SV852 @ SV1341 ) @ ( tc_prod @ SV1341 @ SV1341 ) )
| ~ ( c_in @ SV318 @ SV852 @ ( tc_prod @ SV1341 @ SV1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3025,plain,
! [SV1342: $i,SV853: $i,SV319: $i] :
( ( ! [SY4552: $i] :
( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Ortrancl @ SY4552 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Otrancl @ SY4552 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3026,plain,
! [SV1343: $i,SV854: $i,SV320: $i] :
( ( ! [SY4553: $i,SY4554: $i] :
( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SY4553 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SY4554 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SY4553 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SY4554 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SY4553 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3027,plain,
! [SV1344: $i,SV855: $i,SV321: $i] :
( ( ! [SY4555: $i,SY4556: $i] :
( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SY4555 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SY4556 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SY4555 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SY4556 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SY4555 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3028,plain,
! [SV1345: $i,SV856: $i,SV322: $i] :
( ( ! [SY4557: $i] :
( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV856 @ SV322 @ SV1345 @ SY4557 ) @ SY4557 @ SY4557 ) @ SV856 @ ( tc_prod @ SY4557 @ SY4557 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV1345 @ SY4557 @ SY4557 ) @ ( c_Transitive__Closure_Otrancl @ SV856 @ SY4557 ) @ ( tc_prod @ SY4557 @ SY4557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3029,plain,
! [SV1346: $i,SV857: $i,SV323: $i] :
( ( ! [SY4558: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SV1346 @ SY4558 ) @ SV1346 @ SY4558 @ SY4558 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY4558 ) @ ( tc_prod @ SY4558 @ SY4558 ) )
| ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SY4558 @ SY4558 ) @ SV323 @ ( tc_prod @ SY4558 @ SY4558 ) )
| ~ ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SY4558 @ SY4558 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SY4558 ) @ ( tc_prod @ SY4558 @ SY4558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3030,plain,
! [SV1347: $i,SV858: $i,SV324: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV324 @ SV324 @ SV858 @ SV858 ) @ SV1347 @ ( tc_prod @ SV858 @ SV858 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ SV858 @ SV858 ) @ ( c_Transitive__Closure_Otrancl @ SV1347 @ SV858 ) @ ( tc_prod @ SV858 @ SV858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3031,plain,
! [SV1348: $i,SV859: $i,SV325: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV325 @ SV859 @ SV1348 ) @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) )
| ~ ( c_in @ SV325 @ ( c_Complete__Lattice_OSup__class_OSup @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SV1348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3032,plain,
! [SV1349: $i,SV860: $i,SV326: $i] :
( ( ! [SY4559: $i] :
( ( c_in @ ( c_Pair @ SV326 @ SV860 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY4559 @ SV1349 @ SV1349 ) @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) )
| ~ ( c_in @ ( c_Pair @ SV860 @ SV326 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ SY4559 @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3033,plain,
! [SV1350: $i,SV861: $i,SV327: $i] :
( ( ! [SY4560: $i] :
( ( c_in @ ( c_Pair @ SV327 @ SV861 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ SY4560 @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) )
| ~ ( c_in @ ( c_Pair @ SV861 @ SV327 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY4560 @ SV1350 @ SV1350 ) @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3034,plain,
! [SV1351: $i,SV862: $i,SV328: $i] :
( ( ! [SY4561: $i,SY4562: $i,SY4563: $i,SY4564: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SY4561 @ SY4562 @ SY4563 @ SY4564 ) @ SY4562 @ SY4564 ) @ SV1351 @ ( tc_prod @ SY4562 @ SY4564 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SY4562 @ SY4563 ) @ ( c_Relation_Orel__comp @ SV1351 @ SY4561 @ SY4562 @ SY4564 @ SY4563 ) @ ( tc_prod @ SY4562 @ SY4563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3035,plain,
! [SV1352: $i,SV863: $i,SV329: $i] :
( ( ! [SY4565: $i,SY4566: $i,SY4567: $i,SY4568: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SY4565 @ SY4566 @ SY4567 @ SY4568 ) @ SV863 @ SY4568 @ SY4567 ) @ SY4565 @ ( tc_prod @ SY4568 @ SY4567 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SY4566 @ SY4567 ) @ ( c_Relation_Orel__comp @ SV1352 @ SY4565 @ SY4566 @ SY4568 @ SY4567 ) @ ( tc_prod @ SY4566 @ SY4567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3036,plain,
! [SV1353: $i,SV864: $i,SV330: $i] :
( ( ! [SY4569: $i,SY4570: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SV1353 @ SY4569 @ SY4570 ) @ ( tc_fun @ SY4569 @ SY4570 ) )
| ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SY4569 @ SY4570 ) ) @ ( hAPP @ SV1353 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SY4569 @ SY4570 ) ) @ SY4570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3037,plain,
! [SV1354: $i,SV865: $i,SV331: $i] :
( ( ! [SY4571: $i,SY4572: $i,SY4573: $i] :
( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SY4571 )
| ~ ( c_in @ SV865 @ SY4572 @ SY4573 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SY4572 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SY4571 @ tc_bool ) @ SY4573 ) @ SY4573 @ SY4571 ) @ ( tc_fun @ SY4573 @ SY4571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3038,plain,
! [SV1355: $i,SV866: $i,SV332: $i] :
( ( ! [SY4574: $i,SY4575: $i] :
( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SV1355 @ SY4574 @ SY4575 ) @ ( tc_fun @ SY4574 @ SY4575 ) )
| ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SY4574 @ SY4575 ) ) @ ( hAPP @ SV1355 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SY4574 @ SY4575 ) ) @ SY4575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3039,plain,
! [SV1356: $i,SV867: $i,SV333: $i] :
( ( ! [SY4576: $i,SY4577: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV867 @ SV1356 @ SY4576 @ SY4577 ) @ ( tc_fun @ SY4576 @ SY4577 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV867 @ SV1356 @ SV333 @ SY4576 @ SY4577 ) @ SV867 @ SY4576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3040,plain,
! [SV1357: $i,SV868: $i,SV334: $i] :
( ( ! [SY4578: $i,SY4579: $i] :
( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SV868 @ SV1357 @ SY4578 @ SY4579 ) @ ( tc_fun @ SY4578 @ SY4579 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV868 @ SV1357 @ SV334 @ SY4578 @ SY4579 ) @ SV868 @ SY4578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3041,plain,
! [SV1358: $i,SV869: $i,SV335: $i] :
( ( ! [SY4580: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SV869 @ SV1358 @ SY4580 ) @ SV335 @ SY4580 )
| ~ ( c_in @ SV869 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SV1358 @ SY4580 ) @ ( tc_fun @ SY4580 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3042,plain,
! [SV870: $i,SV336: $i] :
( ( ( SV336
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ SV870 @ SV870 ) )
= $true )
| ( ( ~ ( c_in @ SV336 @ ( c_Relation_OId @ SV870 ) @ ( tc_prod @ SV870 @ SV870 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(3043,plain,
! [SV1359: $i,SV871: $i,SV337: $i] :
( ( ( c_in @ SV337 @ ( c_Complete__Lattice_OInf__class_OInf @ SV871 @ ( tc_fun @ SV1359 @ tc_bool ) ) @ SV1359 )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV337 @ SV871 @ SV1359 ) @ SV871 @ ( tc_fun @ SV1359 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3044,plain,
! [SV872: $i,SV338: $i] :
( ( ( c_Wellfounded_Owf @ SV338 @ SV872 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV338 @ SV872 ) @ ( c_Wellfounded_Oacc @ SV338 @ SV872 ) @ SV872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(3045,plain,
! [SV873: $i,SV339: $i] :
( ( ( c_Wellfounded_Owf @ SV339 @ SV873 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV339 @ SV873 ) @ ( c_Wellfounded_Oacc @ SV339 @ SV873 ) @ SV873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(3046,plain,
! [SV1360: $i,SV874: $i,SV340: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV340 @ SV874 @ SV1360 ) @ SV340 @ SV1360 )
| ~ ( c_in @ SV874 @ ( c_Relation_OId__on @ SV340 @ SV1360 ) @ ( tc_prod @ SV1360 @ SV1360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3047,plain,
! [SV1361: $i,SV875: $i,SV341: $i] :
( ( ( SV341
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ SV1361 @ SV1361 ) )
| ~ ( c_in @ SV341 @ ( c_Relation_OId__on @ SV875 @ SV1361 ) @ ( tc_prod @ SV1361 @ SV1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3048,plain,
! [SV1362: $i,SV876: $i,SV342: $i] :
( ( ! [SY4581: $i,SY4582: $i,SY4583: $i] :
( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SV1362 @ SY4581 @ SY4582 )
= ( c_Recdef_Ocut @ SY4583 @ SV876 @ SV1362 @ SY4581 @ SY4582 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SY4583 @ SV876 @ SV1362 @ SY4581 @ SY4582 ) @ SV1362 @ SY4581 @ SY4581 ) @ SV876 @ ( tc_prod @ SY4581 @ SY4581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3049,plain,
! [SV1363: $i,SV877: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV343 @ SV877 @ SV877 ) @ SV343 @ SV877 @ SV877 @ SV877 ) @ ( tc_fun @ ( tc_prod @ SV877 @ SV877 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV1363 @ SV343 @ SV877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3050,plain,
! [SV878: $i,SV344: $i] :
( ( ( c_Nitpick_Orefl_H @ SV344 @ SV878 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ SV878 @ SV878 ) @ SV344 @ ( tc_prod @ SV878 @ SV878 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(3051,plain,
! [SV1364: $i,SV879: $i,SV345: $i] :
( ( ! [SY4584: $i,SY4585: $i] :
( ~ ( c_in @ SV345 @ SV879 @ SV1364 )
| ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SY4584 @ SV1364 ) @ SV1364 @ SV1364 ) @ SY4584 @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_in @ SY4585 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SY4584 @ SV1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3052,plain,
! [SV1365: $i,SV880: $i,SV346: $i] :
( ( ! [SY4586: $i,SY4587: $i] :
( ~ ( c_in @ SV346 @ SV880 @ SV1365 )
| ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SY4586 @ SV1365 ) @ SV1365 @ SV1365 ) @ SY4586 @ ( tc_prod @ SV1365 @ SV1365 ) )
| ~ ( c_in @ SY4587 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SY4586 @ SV1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3053,plain,
! [SV1366: $i,SV881: $i,SV347: $i] :
( ( ! [SY4588: $i,SY4589: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SV1366 @ SY4588 @ SY4589 ) @ SV881 @ SY4588 @ SY4589 ) @ SV1366 @ ( tc_prod @ SY4588 @ SY4589 ) )
| ~ ( c_in @ SV881 @ ( c_Relation_OImage @ SV1366 @ SV347 @ SY4588 @ SY4589 ) @ SY4589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3054,plain,
! [SV1367: $i,SV882: $i,SV348: $i] :
( ( ! [SY4590: $i,SY4591: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SV1367 @ SY4590 @ SY4591 ) @ SV882 @ SY4590 @ SY4591 ) @ SV1367 @ ( tc_prod @ SY4590 @ SY4591 ) )
| ~ ( c_in @ SV882 @ ( c_Relation_OImage @ SV1367 @ SV348 @ SY4590 @ SY4591 ) @ SY4591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3055,plain,
! [SV1368: $i,SV883: $i,SV349: $i] :
( ( ! [SY4592: $i] :
( ( SV349 = SV883 )
| ~ ( c_in @ ( c_Pair @ SV349 @ SV883 @ SV1368 @ SV1368 ) @ ( c_Transitive__Closure_Ortrancl @ SY4592 @ SV1368 ) @ ( tc_prod @ SV1368 @ SV1368 ) )
| ( c_in @ SV349 @ ( c_Relation_ODomain @ SY4592 @ SV1368 @ SV1368 ) @ SV1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3056,plain,
! [SV1369: $i,SV884: $i,SV350: $i] :
( ( ! [SY4593: $i] :
( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SV884 @ SV1369 @ SY4593 ) @ SV1369 @ SY4593 ) @ SV884 @ ( tc_prod @ SV1369 @ SY4593 ) )
| ~ ( c_in @ SV350 @ ( c_Relation_ODomain @ SV884 @ SV1369 @ SY4593 ) @ SV1369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3057,plain,
! [SV1370: $i,SV885: $i,SV351: $i] :
( ( ! [SY4594: $i] :
( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SV885 @ SV1370 @ SY4594 ) @ SV1370 @ SY4594 ) @ SV885 @ ( tc_prod @ SV1370 @ SY4594 ) )
| ~ ( c_in @ SV351 @ ( c_Relation_ODomain @ SV885 @ SV1370 @ SY4594 ) @ SV1370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3058,plain,
! [SV1371: $i,SV886: $i,SV352: $i] :
( ( ( c_in @ SV352 @ ( c_Relation_ODomain @ SV886 @ SV1371 @ SV1371 ) @ SV1371 )
| ( c_in @ ( c_Pair @ SV352 @ SV352 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Ortrancl @ SV886 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3059,plain,
! [SV1372: $i,SV887: $i,SV353: $i] :
( ( ! [SY4595: $i,SY4596: $i] :
( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
| ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
| ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SY4595 @ SY4596 ) @ SY4596 @ SY4596 ) @ SY4595 @ ( tc_prod @ SY4596 @ SY4596 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SY4595 @ SY4596 ) @ SY4596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3060,plain,
! [SV1373: $i,SV888: $i,SV354: $i] :
( ( ! [SY4597: $i] :
( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
| ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SY4597 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SY4597 ) @ t_a @ t_a ) @ SY4597 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SY4597 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3061,plain,
! [SV1374: $i,SV889: $i,SV355: $i] :
( ( ! [SY4598: $i] :
( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
| ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
| ~ ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SY4598 ) @ t_a @ t_a ) @ SY4598 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SY4598 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3062,plain,
! [SV1375: $i,SV890: $i,SV356: $i] :
( ( ! [SY4599: $i] :
( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
| ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SY4599 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SY4599 ) @ t_a @ t_a ) @ SY4599 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SY4599 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3063,plain,
! [SV1376: $i,SV891: $i,SV357: $i] :
( ( ! [SY4600: $i] :
( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
| ~ ( c_in @ ( c_Pair @ SV357 @ SY4600 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
| ~ ( c_in @ SY4600 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3064,plain,
! [SV1377: $i,SV892: $i,SV358: $i] :
( ( ! [SY4601: $i] :
( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
| ~ ( c_in @ SY4601 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
| ~ ( c_in @ ( c_Pair @ SV358 @ SY4601 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3065,plain,
! [SV1378: $i,SV893: $i,SV359: $i] :
( ( ( c_in @ SV359 @ ( c_Wellfounded_Oacc @ SV893 @ SV1378 ) @ SV1378 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV893 @ SV359 @ SV1378 ) @ SV359 @ SV1378 @ SV1378 ) @ SV893 @ ( tc_prod @ SV1378 @ SV1378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3066,plain,
! [SV1379: $i,SV894: $i,SV360: $i] :
( ( ! [SY4602: $i] :
( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
| ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
| ~ ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SY4602 ) @ t_a @ t_a ) @ SY4602 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SY4602 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3067,plain,
! [SV1380: $i,SV895: $i,SV361: $i] :
( ( ! [SY4603: $i,SY4604: $i] :
( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
| ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
| ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SY4603 @ SY4604 ) @ SY4604 @ SY4604 ) @ SY4603 @ ( tc_prod @ SY4604 @ SY4604 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SY4603 @ SY4604 ) @ SY4604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3068,plain,
! [SV1381: $i,SV896: $i,SV362: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV362 @ SV896 @ SV1381 ) @ SV896 @ SV1381 @ SV1381 ) @ SV362 @ ( tc_prod @ SV1381 @ SV1381 ) )
| ( c_in @ SV896 @ ( c_Wellfounded_Oacc @ SV362 @ SV1381 ) @ SV1381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3069,plain,
! [SV1382: $i,SV897: $i,SV363: $i] :
( ( ! [SY4605: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SV897 @ SV1382 @ SY4605 ) @ SV363 @ SY4605 @ SV1382 ) @ SV897 @ ( tc_prod @ SY4605 @ SV1382 ) )
| ~ ( c_in @ SV363 @ ( c_Relation_ORange @ SV897 @ SY4605 @ SV1382 ) @ SV1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3070,plain,
! [SV1383: $i,SV898: $i,SV364: $i] :
( ( ! [SY4606: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SV898 @ SV1383 @ SY4606 ) @ SV364 @ SY4606 @ SV1383 ) @ SV898 @ ( tc_prod @ SY4606 @ SV1383 ) )
| ~ ( c_in @ SV364 @ ( c_Relation_ORange @ SV898 @ SY4606 @ SV1383 ) @ SV1383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3071,plain,
! [SV1384: $i,SV899: $i,SV365: $i] :
( ( ! [SY4607: $i] :
( ~ ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SY4607 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SY4607 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_Wellfounded_Owf @ SY4607 @ SV1384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3072,plain,
! [SV1385: $i,SV900: $i,SV366: $i] :
( ( ! [SY4608: $i] :
( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SY4608 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ SY4608 @ ( tc_prod @ SV1385 @ SV1385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3073,plain,
! [SV1386: $i,SV901: $i,SV367: $i] :
( ( ! [SY4609: $i,SY4610: $i] :
( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SY4609 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SY4610 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SY4609 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SY4610 @ SV1386 @ SV1386 ) @ SY4609 @ ( tc_prod @ SV1386 @ SV1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3074,plain,
! [SV1387: $i,SV902: $i,SV368: $i] :
( ( ! [SY4611: $i,SY4612: $i] :
( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SY4611 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SY4612 @ SV902 @ SV1387 @ SV1387 ) @ SY4611 @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SY4612 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SY4611 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3075,plain,
! [SV1388: $i,SV903: $i,SV369: $i] :
( ( ! [SY4613: $i,SY4614: $i] :
( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SV1388 @ SY4613 ) @ SY4614 @ ( tc_prod @ SV1388 @ SY4613 ) )
| ~ ( c_in @ ( c_Pair @ SV903 @ SV369 @ SY4613 @ SV1388 ) @ ( c_Relation_Oconverse @ SY4614 @ SV1388 @ SY4613 ) @ ( tc_prod @ SY4613 @ SV1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3076,plain,
! [SV1389: $i,SV904: $i,SV370: $i] :
( ( ! [SY4615: $i,SY4616: $i] :
( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SV1389 @ SY4615 ) @ ( c_Relation_Oconverse @ SY4616 @ SY4615 @ SV1389 ) @ ( tc_prod @ SV1389 @ SY4615 ) )
| ~ ( c_in @ ( c_Pair @ SV904 @ SV370 @ SY4615 @ SV1389 ) @ SY4616 @ ( tc_prod @ SY4615 @ SV1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3077,plain,
! [SV1390: $i,SV905: $i,SV371: $i] :
( ( ! [SY4617: $i,SY4618: $i] :
( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SV1390 @ SY4617 ) @ ( c_Relation_Oconverse @ SY4618 @ SY4617 @ SV1390 ) @ ( tc_prod @ SV1390 @ SY4617 ) )
| ~ ( c_in @ ( c_Pair @ SV905 @ SV371 @ SY4617 @ SV1390 ) @ SY4618 @ ( tc_prod @ SY4617 @ SV1390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3078,plain,
! [SV1391: $i,SV906: $i,SV372: $i] :
( ( ! [SY4619: $i,SY4620: $i,SY4621: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SY4619 @ SY4620 ) @ SY4621 )
= ( hAPP @ SV372 @ SY4621 ) )
| ~ ( c_in @ ( c_Pair @ SY4621 @ SV1391 @ SY4619 @ SY4619 ) @ SV906 @ ( tc_prod @ SY4619 @ SY4619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3079,plain,
! [SV1392: $i,SV907: $i,SV373: $i] :
( ( ! [SY4622: $i,SY4623: $i,SY4624: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SY4622 @ SY4623 ) @ SY4624 )
= ( hAPP @ SV373 @ SY4624 ) )
| ~ ( c_in @ ( c_Pair @ SY4624 @ SV1392 @ SY4622 @ SY4622 ) @ SV907 @ ( tc_prod @ SY4622 @ SY4622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3080,plain,
! [SV1393: $i,SV908: $i,SV374: $i] :
( ( ( c_in @ SV374 @ ( c_Transitive__Closure_Otrancl @ SV908 @ SV1393 ) @ ( tc_prod @ SV1393 @ SV1393 ) )
| ~ ( c_in @ SV374 @ SV908 @ ( tc_prod @ SV1393 @ SV1393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3081,plain,
! [SV1394: $i,SV909: $i,SV375: $i] :
( ( ! [SY4625: $i] :
( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4625 @ SV1394 ) @ SV1394 @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) )
| ~ ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4625 @ SV1394 @ SV1394 ) @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3082,plain,
! [SV1395: $i,SV910: $i,SV376: $i] :
( ( ! [SY4626: $i] :
( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4626 @ SV1395 @ SV1395 ) @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) )
| ~ ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4626 @ SV1395 ) @ SV1395 @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3083,plain,
! [SV1396: $i,SV911: $i,SV377: $i] :
( ( ( c_in @ SV377 @ ( c_Wellfounded_Oacc @ SV911 @ SV1396 ) @ SV1396 )
| ~ ( c_Wellfounded_Owf @ SV911 @ SV1396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3084,plain,
! [SV912: $i,SV378: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV378 @ SV912 ) @ SV912 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV378 @ SV912 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(3085,plain,
! [SV913: $i,SV379: $i] :
( ( ( c_Relation_Osym @ SV379 @ SV913 )
= $true )
| ( ( ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV379 @ SV913 @ SV913 ) @ SV913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(3086,plain,
! [SV914: $i,SV380: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV380 @ SV914 @ SV914 ) @ SV914 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV380 @ SV914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(3087,plain,
! [SV1397: $i,SV916: $i,SV383: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV383 ) @ SV916 @ SV383 @ SV383 @ SV1397 )
= SV916 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3088,plain,
! [SV1398: $i,SV917: $i,SV384: $i] :
( ( ( c_Relation_Orel__comp @ SV384 @ ( c_Relation_OId @ SV917 ) @ SV1398 @ SV917 @ SV917 )
= SV384 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3089,plain,
! [SV918: $i,SV385: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV385 @ SV918 ) @ SV918 @ SV918 ) @ SV918 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV385 @ SV918 @ SV918 ) @ SV918 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(3090,plain,
! [SV1399: $i,SV919: $i,SV386: $i] :
( ( ( c_Relation_Orefl__on @ SV386 @ SV919 @ SV1399 )
| ~ ( c_Relation_Orefl__on @ SV386 @ ( c_Relation_Oconverse @ SV919 @ SV1399 @ SV1399 ) @ SV1399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3091,plain,
! [SV1400: $i,SV920: $i,SV387: $i] :
( ( ( c_Relation_Orefl__on @ SV387 @ ( c_Relation_Oconverse @ SV920 @ SV1400 @ SV1400 ) @ SV1400 )
| ~ ( c_Relation_Orefl__on @ SV387 @ SV920 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3092,plain,
! [SV921: $i,SV388: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV388 @ SV388 @ SV921 @ SV921 @ SV921 ) @ SV921 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV388 @ SV921 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(3093,plain,
! [SV922: $i,SV389: $i] :
( ( ( c_Wellfounded_Owf @ SV389 @ SV922 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV389 @ SV389 @ SV922 @ SV922 @ SV922 ) @ SV922 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(3094,plain,
! [SV925: $i,SV392: $i] :
( ( ( ( c_Relation_Oconverse @ SV392 @ SV925 @ SV925 )
= SV392 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV392 @ SV925 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(3095,plain,
! [SV1401: $i,SV927: $i,SV394: $i] :
( ( ! [SY4627: $i,SY4628: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV394 @ SV927 @ SV1401 @ SY4627 @ SY4628 ) @ SV1401 @ SY4628 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV927 @ SY4627 @ SY4628 ) @ ( c_Relation_Oconverse @ SV394 @ SV1401 @ SY4627 ) @ SY4628 @ SY4627 @ SV1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3096,plain,
! [SV1402: $i,SV930: $i,SV397: $i] :
( ( ! [SY4629: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SV930 @ SV1402 @ SY4629 ) @ SY4629 )
| ~ ( c_Wellfounded_Owf @ SV397 @ SV1402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3097,plain,
! [SV1403: $i,SV931: $i,SV398: $i] :
( ( ! [SY4630: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SV931 @ SV1403 @ SY4630 ) @ SY4630 )
| ~ ( c_Relation_Osym @ SV398 @ SV1403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3098,plain,
! [SV932: $i,SV400: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV400 @ SV932 ) @ SV932 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV400 @ SV932 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(3099,plain,
! [SV1404: $i,SV933: $i,SV401: $i] :
( ( ! [SY4631: $i,SY4632: $i,SY4633: $i,SY4634: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SV1404 @ SY4631 @ SY4632 ) @ SY4633 @ SV1404 @ SY4632 @ SY4634 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SY4633 @ SY4631 @ SY4632 @ SY4634 ) @ SV1404 @ SY4631 @ SY4634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3100,plain,
! [SV1405: $i,SV934: $i,SV402: $i] :
( ( ! [SY4635: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV402 @ SV934 @ SV1405 @ SY4635 ) @ SY4635 @ SY4635 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV402 @ SV1405 @ SV1405 ) @ SV934 @ SV1405 @ SY4635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3101,plain,
! [SV1406: $i,SV937: $i,SV405: $i] :
( ( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV405 @ SV937 @ SV1406 ) @ SV1406 @ SV937 )
= ( c_Relation_ODomain @ SV405 @ SV937 @ SV1406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3102,plain,
! [SV1407: $i,SV939: $i,SV407: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV407 @ SV939 @ SV1407 ) @ SV1407 @ SV939 )
= SV407 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3103,plain,
! [SV1408: $i,SV940: $i,SV408: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV408 @ SV940 @ SV940 ) @ SV408 @ SV940 @ SV940 @ SV940 )
= SV408 )
| ~ ( c_Equiv__Relations_Oequiv @ SV1408 @ SV408 @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3104,plain,
! [SV1409: $i,SV941: $i,SV409: $i] :
( ( ( c_Relation_Orefl__on @ SV409 @ SV941 @ SV1409 )
| ~ ( c_Equiv__Relations_Oequiv @ SV409 @ SV941 @ SV1409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3105,plain,
! [SV1410: $i,SV942: $i,SV410: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ SV410 @ SV942 @ SV1410 ) @ ( tc_fun @ SV1410 @ tc_bool ) )
= SV410 )
| ~ ( c_Equiv__Relations_Oequiv @ SV410 @ SV942 @ SV1410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3106,plain,
! [SV1411: $i,SV943: $i,SV411: $i] :
( ( ( c_Relation_Osym @ SV411 @ SV943 )
| ~ ( c_Equiv__Relations_Oequiv @ SV1411 @ SV411 @ SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3107,plain,
! [SV1412: $i,SV944: $i,SV412: $i] :
( ( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV412 @ SV944 @ SV1412 ) @ SV1412 @ SV944 )
= ( c_Relation_ORange @ SV412 @ SV944 @ SV1412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3108,plain,
! [SV1413: $i,SV945: $i,SV413: $i] :
( ( ( c_Relation_ORange @ SV413 @ SV945 @ SV1413 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV413 @ SV945 @ SV1413 ) @ SV1413 @ SV945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3109,plain,
! [SV1414: $i,SV946: $i,SV414: $i] :
( ( ( c_Relation_Ototal__on @ SV414 @ SV946 @ SV1414 )
| ~ ( c_Relation_Ototal__on @ SV414 @ ( c_Relation_Oconverse @ SV946 @ SV1414 @ SV1414 ) @ SV1414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3110,plain,
! [SV1415: $i,SV947: $i,SV415: $i] :
( ( ( c_Relation_Ototal__on @ SV415 @ ( c_Relation_Oconverse @ SV947 @ SV1415 @ SV1415 ) @ SV1415 )
| ~ ( c_Relation_Ototal__on @ SV415 @ SV947 @ SV1415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3111,plain,
! [SV1416: $i,SV948: $i,SV416: $i] :
( ( ! [SY4636: $i] :
( ( SV416 = SV948 )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV948 @ SV1416 @ SV1416 ) @ ( c_Relation_OId__on @ SY4636 @ SV1416 ) @ ( tc_prod @ SV1416 @ SV1416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3112,plain,
! [SV1417: $i,SV949: $i,SV417: $i] :
( ( ( SV417 = SV949 )
| ~ ( c_in @ ( c_Pair @ SV417 @ SV949 @ SV1417 @ SV1417 ) @ ( c_Relation_OId @ SV1417 ) @ ( tc_prod @ SV1417 @ SV1417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3113,plain,
! [SV1418: $i,SV950: $i,SV418: $i] :
( ( ( c_in @ ( c_Pair @ SV418 @ SV418 @ SV950 @ SV950 ) @ SV1418 @ ( tc_prod @ SV950 @ SV950 ) )
| ~ ( c_Nitpick_Orefl_H @ SV1418 @ SV950 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3114,plain,
! [SV1419: $i,SV951: $i,SV419: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV419 @ SV419 @ SV951 @ SV951 ) @ SV1419 @ ( tc_prod @ SV951 @ SV951 ) )
| ~ ( c_Wellfounded_Owf @ SV1419 @ SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3115,plain,
! [SV1420: $i,SV952: $i,SV420: $i] :
( ( ! [SY4637: $i,SY4638: $i,SY4639: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SY4637 @ SY4638 @ SY4639 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY4638 @ SV420 ) @ ( hAPP @ SY4638 @ SV952 ) @ SY4639 @ SY4639 ) @ SY4637 @ ( tc_prod @ SY4639 @ SY4639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3116,plain,
! [SV1421: $i,SV953: $i,SV421: $i] :
( ( ! [SY4640: $i,SY4641: $i,SY4642: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SY4640 @ SY4640 ) @ SY4641 @ ( tc_prod @ SY4640 @ SY4640 ) )
| ~ ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SY4642 @ SY4642 ) @ ( c_Relation_Oinv__image @ SY4641 @ SV421 @ SY4640 @ SY4642 ) @ ( tc_prod @ SY4642 @ SY4642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3117,plain,
! [SV1422: $i,SV954: $i,SV422: $i] :
( ( ! [SY4643: $i] :
( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SY4643 @ ( tc_prod @ SV1422 @ SV1422 ) )
| ~ ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SY4643 @ ( tc_prod @ SV1422 @ SV1422 ) )
| ~ ( c_Relation_Osym @ SY4643 @ SV1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3118,plain,
! [SV1423: $i,SV955: $i,SV423: $i] :
( ( ! [SY4644: $i] :
( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SY4644 @ ( tc_prod @ SV1423 @ SV1423 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SY4644 @ ( tc_prod @ SV1423 @ SV1423 ) )
| ~ ( c_Relation_Osym @ SY4644 @ SV1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3119,plain,
! [SV1424: $i,SV956: $i,SV424: $i] :
( ( ! [SY4645: $i,SY4646: $i,SY4647: $i,SY4648: $i,SY4649: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SY4645 ) @ ( c_Relation_Orel__comp @ SY4646 @ SY4647 @ SV1424 @ SY4648 @ SY4645 ) @ ( tc_prod @ SV1424 @ SY4645 ) )
| ~ ( c_in @ ( c_Pair @ SY4649 @ SV956 @ SY4648 @ SY4645 ) @ SY4647 @ ( tc_prod @ SY4648 @ SY4645 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4649 @ SV1424 @ SY4648 ) @ SY4646 @ ( tc_prod @ SV1424 @ SY4648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3120,plain,
! [SV1425: $i,SV957: $i,SV425: $i] :
( ( ! [SY4650: $i,SY4651: $i] :
( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SY4650 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SY4651 @ SV957 @ SV1425 @ SV1425 ) @ SY4650 @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SY4651 @ SV1425 @ SV1425 ) @ SY4650 @ ( tc_prod @ SV1425 @ SV1425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3121,plain,
! [SV1426: $i,SV958: $i,SV426: $i] :
( ( ! [SY4652: $i,SY4653: $i] :
( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SY4652 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SY4653 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SY4652 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4653 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SY4652 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3122,plain,
! [SV1427: $i,SV961: $i,SV429: $i] :
( ( ! [SY4654: $i,SY4655: $i,SY4656: $i] :
( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SY4654 )
| ~ ( c_in @ SV961 @ SY4655 @ SY4656 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SY4655 @ SV1427 @ SY4656 @ SY4654 ) @ ( tc_fun @ SY4656 @ SY4654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3123,plain,
! [SV1428: $i,SV962: $i,SV430: $i] :
( ( ! [SY4657: $i,SY4658: $i,SY4659: $i] :
( ~ ( c_in @ SV430 @ SV962 @ SV1428 )
| ( c_in @ ( hAPP @ SY4657 @ SV430 ) @ ( hAPP @ SY4658 @ SV430 ) @ SY4659 )
| ~ ( c_in @ SY4657 @ ( c_FuncSet_OPi @ SV962 @ SY4658 @ SV1428 @ SY4659 ) @ ( tc_fun @ SV1428 @ SY4659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3124,plain,
! [SV1429: $i,SV963: $i,SV431: $i] :
( ( ! [SY4660: $i,SY4661: $i,SY4662: $i,SY4663: $i] :
( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SV1429 @ SY4660 @ SY4661 @ SY4661 ) @ SY4662 @ ( tc_prod @ SY4661 @ SY4661 ) )
| ~ ( c_in @ SY4660 @ SV963 @ SY4661 )
| ~ ( c_in @ SV1429 @ SV431 @ SY4661 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SY4663 @ SY4662 @ SY4661 ) @ ( tc_fun @ SY4661 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY4663 @ SY4662 @ SY4661 ) @ ( tc_fun @ SY4661 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4663 @ SY4662 @ SY4661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3125,plain,
! [SV1430: $i,SV964: $i,SV432: $i] :
( ( ! [SY4664: $i,SY4665: $i,SY4666: $i] :
( ~ ( c_in @ SV432 @ SV964 @ SV1430 )
| ~ ( c_in @ SY4664 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4665 @ SY4666 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4665 @ SY4666 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4665 @ SY4666 @ SV1430 )
| ( c_in @ ( c_Pair @ SY4664 @ SV432 @ SV1430 @ SV1430 ) @ SY4666 @ ( tc_prod @ SV1430 @ SV1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3126,plain,
! [SV1431: $i,SV965: $i,SV433: $i] :
( ( ! [SY4667: $i] :
( ( c_in @ SV433 @ SV965 @ SV1431 )
| ~ ( c_in @ SV965 @ SY4667 @ ( tc_fun @ SV1431 @ tc_bool ) )
| ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SY4667 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3127,plain,
! [SV1432: $i,SV966: $i,SV434: $i] :
( ( ! [SY4668: $i] :
( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
| ~ ( c_in @ SV434 @ SY4668 @ SV1432 )
| ~ ( c_in @ SY4668 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3128,plain,
! [SV1433: $i,SV967: $i,SV435: $i] :
( ( ! [SY4669: $i] :
( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SY4669 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV435 = SV967 )
| ( SV435 = SY4669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3129,plain,
! [SV1434: $i,SV968: $i,SV436: $i] :
( ( ! [SY4670: $i] :
( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SY4670 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV968 = SY4670 )
| ( SV436 = SY4670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3130,plain,
! [SV969: $i,SV437: $i] :
( ( c_in @ ( c_Pair @ SV437 @ SV437 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV969 @ SV437 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(3131,plain,
! [SV1435: $i,SV970: $i,SV438: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV438 @ SV970 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1435 @ SV438 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3132,plain,
! [SV1436: $i,SV971: $i,SV439: $i] :
( ( ! [SY4671: $i] :
( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1436 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV971 = SY4671 )
| ~ ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1436 @ SY4671 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3133,plain,
! [SV1437: $i,SV972: $i,SV440: $i] :
( ( ( SV440 = SV972 )
| ( SV972 = SV440 )
| ( c_in @ ( c_Pair @ SV440 @ SV972 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1437 @ SV440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3134,plain,
! [SV973: $i,SV441: $i] :
( ( c_in @ ( c_Pair @ SV441 @ SV441 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV973 @ SV441 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(3135,plain,
! [SV1438: $i,SV974: $i,SV442: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV442 @ SV974 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1438 @ SV974 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3136,plain,
! [SV1439: $i,SV975: $i,SV443: $i] :
( ( ! [SY4672: $i] :
( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SY4672 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV443 = SV975 )
| ( SV975 = SY4672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3137,plain,
! [SV1440: $i,SV976: $i,SV444: $i] :
( ( ! [SY4673: $i] :
( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SY4673 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV444 = SY4673 )
| ( SV976 = SY4673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3138,plain,
! [SV1441: $i,SV977: $i,SV445: $i] :
( ( ( SV445 = SV977 )
| ( SV445 = SV977 )
| ( c_in @ ( c_Pair @ SV445 @ SV977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1441 @ SV977 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3139,plain,
! [SV1442: $i,SV978: $i,SV446: $i] :
( ( ! [SY4674: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1442 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV446 = SY4674 )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1442 @ SY4674 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3140,plain,
! [SV979: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV979 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV447 @ SV979 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV447 = SV979 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(3141,plain,
! [SV980: $i,SV448: $i] :
( ( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV448 @ SV980 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( SV448 = SV980 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(3142,plain,
! [SV981: $i,SV449: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ SV449 @ SV981 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV449 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(3143,plain,
! [SV982: $i,SV450: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV450 @ SV982 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV450 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(3144,plain,
! [SV1443: $i,SV983: $i,SV451: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SV983 @ SV1443 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV983 = SV1443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3145,plain,
! [SV452: $i] :
( ( ( c_in @ ( c_Relation_Oconverse @ SV452 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ SV452 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(3146,plain,
! [SV453: $i] :
( ( ( c_in @ SV453 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Relation_Oconverse @ SV453 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(3147,plain,
! [SV1444: $i,SV984: $i,SV454: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SV984 @ SV1444 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV984 = SV1444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3148,plain,
! [SV1445: $i,SV985: $i,SV455: $i] :
( ( ! [SY4675: $i,SY4676: $i,SY4677: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SY4675 ) @ ( c_Product__Type_OSigma @ SY4676 @ SY4677 @ SV1445 @ SY4675 ) @ ( tc_prod @ SV1445 @ SY4675 ) )
| ~ ( c_in @ SV985 @ ( hAPP @ SY4677 @ SV455 ) @ SY4675 )
| ~ ( c_in @ SV455 @ SY4676 @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3149,plain,
! [SV1446: $i,SV986: $i,SV456: $i] :
( ( ! [SY4678: $i,SY4679: $i,SY4680: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SY4678 ) @ ( c_Product__Type_OSigma @ SY4679 @ SY4680 @ SV1446 @ SY4678 ) @ ( tc_prod @ SV1446 @ SY4678 ) )
| ~ ( c_in @ SV986 @ ( hAPP @ SY4680 @ SV456 ) @ SY4678 )
| ~ ( c_in @ SV456 @ SY4679 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3150,plain,
! [SV1447: $i,SV987: $i,SV457: $i] :
( ( ! [SY4681: $i] :
( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
| ~ ( c_in @ ( c_Pair @ SV457 @ SY4681 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) )
| ~ ( c_in @ SY4681 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3151,plain,
! [SV1448: $i,SV988: $i,SV458: $i] :
( ( ! [SY4682: $i] :
( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
| ~ ( c_in @ ( c_Pair @ SV458 @ SY4682 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SY4682 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3152,plain,
! [SV1449: $i,SV989: $i,SV459: $i] :
( ( ! [SY4683: $i,SY4684: $i,SY4685: $i] :
( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SY4683 @ SY4684 ) @ SY4684 )
| ~ ( c_in @ ( c_Pair @ SY4685 @ SV459 @ SY4683 @ SY4684 ) @ SV989 @ ( tc_prod @ SY4683 @ SY4684 ) )
| ~ ( c_in @ SY4685 @ SV1449 @ SY4683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3153,plain,
! [SV1450: $i,SV990: $i,SV460: $i] :
( ( ! [SY4686: $i,SY4687: $i,SY4688: $i] :
( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SY4686 @ SY4687 ) @ SY4687 )
| ~ ( c_in @ ( c_Pair @ SY4688 @ SV460 @ SY4686 @ SY4687 ) @ SV990 @ ( tc_prod @ SY4686 @ SY4687 ) )
| ~ ( c_in @ SY4688 @ SV1450 @ SY4686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3154,plain,
! [SV1451: $i,SV991: $i,SV461: $i] :
( ( ! [SY4689: $i] :
( ( c_in @ SV461 @ SV991 @ SV1451 )
| ~ ( c_in @ ( c_Pair @ SV461 @ SY4689 @ SV1451 @ SV1451 ) @ ( c_Relation_OId__on @ SV991 @ SV1451 ) @ ( tc_prod @ SV1451 @ SV1451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3155,plain,
! [SV1452: $i,SV992: $i,SV462: $i] :
( ( ( c_in @ ( c_Pair @ SV462 @ SV462 @ SV992 @ SV992 ) @ ( c_Relation_OId__on @ SV1452 @ SV992 ) @ ( tc_prod @ SV992 @ SV992 ) )
| ~ ( c_in @ SV462 @ SV1452 @ SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3156,plain,
! [SV1453: $i,SV993: $i,SV463: $i] :
( ( ! [SY4690: $i,SY4691: $i] :
( ( c_in @ SV463 @ SV993 @ SV1453 )
| ~ ( c_in @ ( c_Pair @ SY4690 @ SV463 @ SV1453 @ SV1453 ) @ SY4691 @ ( tc_prod @ SV1453 @ SV1453 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SY4691 @ SV1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3157,plain,
! [SV1454: $i,SV994: $i,SV464: $i] :
( ( ! [SY4692: $i,SY4693: $i] :
( ( c_in @ SV464 @ SV994 @ SV1454 )
| ~ ( c_in @ ( c_Pair @ SV464 @ SY4692 @ SV1454 @ SV1454 ) @ SY4693 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SY4693 @ SV1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3158,plain,
! [SV1455: $i,SV995: $i,SV465: $i] :
( ( ! [SY4694: $i,SY4695: $i] :
( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SV1455 @ SY4694 ) @ SY4694 )
| ~ ( c_in @ ( c_Pair @ SY4695 @ SV465 @ SV1455 @ SY4694 ) @ SV995 @ ( tc_prod @ SV1455 @ SY4694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3159,plain,
! [SV1456: $i,SV996: $i,SV466: $i] :
( ( ! [SY4696: $i,SY4697: $i] :
( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SV1456 @ SY4696 ) @ SY4696 )
| ~ ( c_in @ ( c_Pair @ SY4697 @ SV466 @ SV1456 @ SY4696 ) @ SV996 @ ( tc_prod @ SV1456 @ SY4696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3160,plain,
! [SV1457: $i,SV997: $i,SV467: $i] :
( ( ! [SY4698: $i,SY4699: $i] :
( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SV1457 @ SY4698 ) @ SV1457 )
| ~ ( c_in @ ( c_Pair @ SV467 @ SY4699 @ SV1457 @ SY4698 ) @ SV997 @ ( tc_prod @ SV1457 @ SY4698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3161,plain,
! [SV1458: $i,SV998: $i,SV468: $i] :
( ( ! [SY4700: $i,SY4701: $i] :
( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SV1458 @ SY4700 ) @ SV1458 )
| ~ ( c_in @ ( c_Pair @ SV468 @ SY4701 @ SV1458 @ SY4700 ) @ SV998 @ ( tc_prod @ SV1458 @ SY4700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3162,plain,
! [SV1459: $i,SV999: $i,SV469: $i] :
( ( ! [SY4702: $i,SY4703: $i,SY4704: $i] :
( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SY4702 )
| ~ ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SY4703 @ SY4702 ) @ ( c_Product__Type_OSigma @ SY4704 @ SV999 @ SY4703 @ SY4702 ) @ ( tc_prod @ SY4703 @ SY4702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3163,plain,
! [SV1460: $i,SV1000: $i,SV470: $i] :
( ( ! [SY4705: $i,SY4706: $i,SY4707: $i] :
( ( c_in @ SV470 @ SV1000 @ SV1460 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SY4705 @ SV1460 @ SY4706 ) @ ( c_Product__Type_OSigma @ SV1000 @ SY4707 @ SV1460 @ SY4706 ) @ ( tc_prod @ SV1460 @ SY4706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3164,plain,
! [SV1461: $i,SV1001: $i,SV471: $i] :
( ( ! [SY4708: $i,SY4709: $i] :
( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SY4708 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SY4708 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SY4709 @ SV1461 )
| ~ ( c_in @ SV1001 @ SY4709 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SY4709 @ SY4708 @ SV1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3165,plain,
! [SV1462: $i,SV1002: $i,SV472: $i] :
( ( ! [SY4710: $i] :
( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
| ~ ( c_in @ SV472 @ SY4710 @ SV1002 )
| ~ ( c_Relation_Orefl__on @ SY4710 @ SV1462 @ SV1002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3166,plain,
! [SV1463: $i,SV1003: $i,SV473: $i] :
( ( ! [SY4711: $i,SY4712: $i] :
( ( c_in @ SV473 @ SV1003 @ SV1463 )
| ~ ( c_in @ ( c_Pair @ SY4711 @ SV473 @ SV1463 @ SV1463 ) @ SY4712 @ ( tc_prod @ SV1463 @ SV1463 ) )
| ~ ( c_Relation_Orefl__on @ SV1003 @ SY4712 @ SV1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3167,plain,
! [SV1464: $i,SV1004: $i,SV474: $i] :
( ( ! [SY4713: $i,SY4714: $i] :
( ( c_in @ SV474 @ SV1004 @ SV1464 )
| ~ ( c_in @ ( c_Pair @ SV474 @ SY4713 @ SV1464 @ SV1464 ) @ SY4714 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1004 @ SY4714 @ SV1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3168,plain,
! [SV1465: $i,SV1005: $i,SV475: $i] :
( ( ! [SY4715: $i] :
( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
| ~ ( c_in @ SV475 @ SY4715 @ SV1005 )
| ~ ( c_Relation_Orefl__on @ SY4715 @ SV1465 @ SV1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3169,plain,
! [SV1466: $i,SV1006: $i,SV476: $i] :
( ( ! [SY4716: $i] :
( ~ ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SY4716 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1466 = SY4716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3170,plain,
! [SV1467: $i,SV1007: $i,SV477: $i] :
( ( ! [SY4717: $i] :
( ~ ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV477 = SY4717 )
| ( SV477 = SY4717 )
| ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SY4717 )
| ( c_in @ ( c_Pair @ SV477 @ SY4717 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SY4717 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3171,plain,
! [SV1468: $i,SV1008: $i,SV478: $i] :
( ( ! [SY4718: $i] :
( ( SV478 = SV1008 )
| ( SV478 = SV1468 )
| ~ ( c_in @ SY4718 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SY4718 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4718 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3172,plain,
! [SV1469: $i,SV1009: $i,SV479: $i] :
( ( ! [SY4719: $i,SY4720: $i] :
( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1009 = SY4719 )
| ( SV479 = SY4719 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SY4720 @ SY4719 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4720 = SY4719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3173,plain,
! [SV1470: $i,SV1010: $i,SV480: $i] :
( ( ! [SY4721: $i] :
( ( SV480 = SV1010 )
| ~ ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SY4721 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4721 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SY4721 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SY4721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3174,plain,
! [SV1471: $i,SV1011: $i,SV481: $i] :
( ( ! [SY4722: $i] :
( ~ ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SY4722 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4722 = SV481 )
| ( c_in @ ( c_Pair @ SY4722 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3175,plain,
! [SV1472: $i,SV1012: $i,SV482: $i] :
( ( ! [SY4723: $i] :
( ~ ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4723 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY4723 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4723 = SV482 )
| ( c_in @ ( c_Pair @ SY4723 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SY4723 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3176,plain,
! [SV1473: $i,SV1013: $i,SV483: $i] :
( ( ! [SY4724: $i] :
( ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV483 = SV1013 )
| ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4724 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SY4724 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3177,plain,
! [SV1474: $i,SV1014: $i,SV484: $i] :
( ( ! [SY4725: $i,SY4726: $i] :
( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SY4725 @ SY4726 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SY4725 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SY4726 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4725 = SY4726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3178,plain,
! [SV1475: $i,SV1015: $i,SV485: $i] :
( ( ! [SY4727: $i,SY4728: $i] :
( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SY4727 @ SY4728 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4728 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SY4727 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4727 = SY4728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3179,plain,
! [SV1476: $i,SV1016: $i,SV486: $i] :
( ( ( SV486 = SV1016 )
| ( SV1016 = SV486 )
| ~ ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3180,plain,
! [SV1477: $i,SV1017: $i,SV487: $i] :
( ( ! [SY4729: $i,SY4730: $i] :
( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SY4729 @ SY4730 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SY4729 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4729 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4729 = SY4730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3181,plain,
! [SV1478: $i,SV1018: $i,SV488: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV488 = SV1018 )
| ~ ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3182,plain,
! [SV1479: $i,SV1019: $i,SV489: $i] :
( ( ! [SY4731: $i] :
( ~ ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY4731 = SV1019 )
| ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SY4731 )
| ( c_in @ ( c_Pair @ SY4731 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SY4731 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3183,plain,
! [SV1480: $i,SV1020: $i,SV490: $i] :
( ( ! [SY4732: $i,SY4733: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SY4732 @ SY4733 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1020 = SY4733 )
| ( SV490 = SY4733 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4732 = SY4733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3184,plain,
! [SV1481: $i,SV1021: $i,SV491: $i] :
( ( ! [SY4734: $i] :
( ~ ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SY4734 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1481 = SY4734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3185,plain,
! [SV1482: $i,SV1022: $i,SV492: $i] :
( ( ! [SY4735: $i] :
( ~ ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1022 = SY4735 )
| ( SY4735 = SV1022 )
| ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4735 = SV492 )
| ( c_in @ ( c_Pair @ SY4735 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SY4735 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3186,plain,
! [SV1483: $i,SV1023: $i,SV493: $i] :
( ( ! [SY4736: $i] :
( ( SV493 = SV1023 )
| ( SV1483 = SV493 )
| ~ ( c_in @ SY4736 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SY4736 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY4736 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3187,plain,
! [SV1484: $i,SV1024: $i,SV494: $i] :
( ( ! [SY4737: $i,SY4738: $i] :
( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV494 = SY4737 )
| ( SV1024 = SY4737 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SY4737 @ SY4738 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4737 = SY4738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3188,plain,
! [SV1485: $i,SV1025: $i,SV495: $i] :
( ( ! [SY4739: $i] :
( ( SV495 = SV1025 )
| ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SY4739 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SY4739 )
| ( c_in @ ( c_Pair @ SY4739 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SY4739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3189,plain,
! [SV1486: $i,SV1026: $i,SV496: $i] :
( ( ! [SY4740: $i] :
( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SY4740 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1026 = SY4740 )
| ( c_in @ ( c_Pair @ SV496 @ SY4740 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3190,plain,
! [SV1487: $i,SV1027: $i,SV497: $i] :
( ( ! [SY4741: $i] :
( ~ ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SY4741 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SY4741 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SY4741 )
| ( c_in @ ( c_Pair @ SV497 @ SY4741 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SY4741 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3191,plain,
! [SV1488: $i,SV1028: $i,SV498: $i] :
( ( ! [SY4742: $i] :
( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV498 = SV1028 )
| ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SY4742 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SY4742 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3192,plain,
! [SV1489: $i,SV1029: $i,SV499: $i] :
( ( ! [SY4743: $i,SY4744: $i] :
( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SY4743 @ SY4744 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1029 = SY4744 )
| ~ ( c_in @ ( c_Pair @ SY4743 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4743 = SY4744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3193,plain,
! [SV1490: $i,SV1030: $i,SV500: $i] :
( ( ! [SY4745: $i,SY4746: $i] :
( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SY4745 @ SY4746 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SY4745 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SY4746 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4745 = SY4746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3194,plain,
! [SV1491: $i,SV1031: $i,SV501: $i] :
( ( ( SV501 = SV1031 )
| ( SV501 = SV1031 )
| ~ ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3195,plain,
! [SV1492: $i,SV1032: $i,SV502: $i] :
( ( ! [SY4747: $i,SY4748: $i] :
( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SY4747 @ SY4748 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4748 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SY4748 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4747 = SY4748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3196,plain,
! [SV1493: $i,SV1033: $i,SV503: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV503 = SV1033 )
| ~ ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3197,plain,
! [SV1494: $i,SV1034: $i,SV504: $i] :
( ( ! [SY4749: $i] :
( ~ ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV504 = SY4749 )
| ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4749 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SY4749 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SY4749 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3198,plain,
! [SV1495: $i,SV1035: $i,SV505: $i] :
( ( ! [SY4750: $i,SY4751: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SY4750 @ SY4751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SY4750 )
| ( SV1035 = SY4750 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4750 = SY4751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3199,plain,
! [SV1496: $i,SV1036: $i,SV506: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV506 = SV1036 )
| ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3200,plain,
! [SV1497: $i,SV1037: $i,SV507: $i] :
( ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1037 = SV507 )
| ~ ( c_in @ SV1497 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3201,plain,
! [SV1498: $i,SV1038: $i,SV508: $i] :
( ( ( c_in @ SV508 @ SV1038 @ SV1498 )
| ~ ( hBOOL @ ( hAPP @ SV1038 @ SV508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3202,plain,
! [SV1499: $i,SV1039: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ SV509 @ SV1039 ) )
| ~ ( c_in @ SV1039 @ SV509 @ SV1499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3203,plain,
! [SV510: $i] :
( ( ( ~ ( c_in @ SV510 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV510 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( v_thesis____ = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(3204,plain,
! [SV1500: $i,SV1040: $i,SV511: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3205,plain,
! [SV1041: $i,SV512: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SV1041 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1041 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(3206,plain,
! [SV1042: $i,SV513: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV513 @ SV1042 ) )
= $true )
| ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1042 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(3207,plain,
! [SV1043: $i,SV514: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV514 @ SV1043 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1043 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(3208,plain,
! [SV1044: $i,SV515: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV515 @ SV1044 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1044 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(3209,plain,
! [SV1045: $i,SV516: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV516 @ SV1045 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV1045 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(3210,plain,
! [SV1046: $i,SV517: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SV1046 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1046 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(3211,plain,
! [SV1047: $i,SV518: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV518 @ SV1047 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(3212,plain,
! [SV1048: $i,SV519: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV519 @ SV1048 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1048 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(3213,plain,
! [SV1049: $i,SV520: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV520 @ SV1049 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1049 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(3214,plain,
! [SV1050: $i,SV521: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV521 @ SV1050 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV1050 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(3215,plain,
! [SV1501: $i,SV1052: $i,SV523: $i] :
( ( ( SV523 = SV1052 )
| ~ ( c_fequal @ SV523 @ SV1052 @ SV1501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3216,plain,
! [SV1502: $i,SV1053: $i,SV524: $i] :
( ( ! [SY4752: $i,SY4753: $i,SY4754: $i,SY4755: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SY4752 @ SY4753 )
!= ( c_Recdef_Ocut @ SY4754 @ SV1053 @ SV1502 @ SY4752 @ SY4753 ) )
| ( ( hAPP @ SV524 @ SY4755 )
= ( hAPP @ SY4754 @ SY4755 ) )
| ~ ( c_in @ ( c_Pair @ SY4755 @ SV1502 @ SY4752 @ SY4752 ) @ SV1053 @ ( tc_prod @ SY4752 @ SY4752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3217,plain,
! [SV1503: $i,SV1054: $i,SV525: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV525 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SV1503 @ SV525 )
!= SV1503 )
| ( c_lessequals @ SV1054 @ SV1503 @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3218,plain,
! [SV1055: $i,SV526: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 @ SV1055 @ SV1055 )
!= SV526 )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(3219,plain,
! [SV1504: $i,SV1056: $i,SV527: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) )
!= SV1056 )
| ( c_lessequals @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3220,plain,
! [SV1505: $i,SV1057: $i,SV528: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV528 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SV1505 @ SV528 )
!= SV1057 )
| ( c_lessequals @ SV1057 @ SV1505 @ SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3221,plain,
! [SV1506: $i,SV1058: $i,SV529: $i] :
( ( ! [SY4756: $i,SY4757: $i,SY4758: $i] :
( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SY4756 ) @ SY4756 @ SV1506 )
!= ( c_Product__Type_OSigma @ SY4757 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SY4756 ) @ SY4756 @ SV1506 ) )
| ~ ( c_in @ SY4758 @ SV1058 @ SV1506 )
| ( SV529 = SY4757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3222,plain,
! [SV1507: $i,SV1059: $i,SV530: $i] :
( ( ! [SY4759: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SV1059 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ SY4759 @ ( tc_fun @ SV1507 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1059 @ SY4759 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ ( tc_fun @ SV1507 @ tc_bool ) ) )
| ( c_lessequals @ SY4759 @ SV530 @ ( tc_fun @ SV1507 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3223,plain,
! [SV1508: $i,SV1060: $i,SV531: $i] :
( ( ! [SY4760: $i,SY4761: $i,SY4762: $i] :
( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SY4760 )
!= ( c_Pair @ SY4761 @ SY4762 @ SV1508 @ SY4760 ) )
| ( SV1060 = SY4762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3224,plain,
! [SV1061: $i,SV532: $i] :
( ( ( ( c_Relation_Oconverse @ SV532 @ SV1061 @ SV1061 )
!= SV532 )
= $true )
| ( ( c_Relation_Osym @ SV532 @ SV1061 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(3225,plain,
! [SV1509: $i,SV1062: $i,SV533: $i] :
( ( ! [SY4763: $i] :
( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
!= ( c_Set_Oinsert @ SV533 @ SY4763 @ SV1509 ) )
| ( c_in @ SV533 @ SY4763 @ SV1509 )
| ( c_in @ SV533 @ SV1062 @ SV1509 )
| ( SV1062 = SY4763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3226,plain,
! [SV1510: $i,SV1063: $i,SV534: $i] :
( ( ! [SY4764: $i,SY4765: $i,SY4766: $i] :
( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SY4764 @ SY4765 @ SY4766 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SY4764 @ SY4765 @ SY4766 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SY4764 @ SY4765 @ SY4766 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SY4764 @ SY4765 @ SY4766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3227,plain,
! [SV1511: $i,SV1064: $i,SV535: $i] :
( ( ! [SY4767: $i,SY4768: $i,SY4769: $i] :
( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SY4767 )
!= ( c_Pair @ SY4768 @ SY4769 @ SV1511 @ SY4767 ) )
| ( SV535 = SY4768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3228,plain,
! [SV537: $i,SV2: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV2 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV537 @ SV537 @ SV2 )
= SV537 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(3229,plain,
! [SV1512: $i,SV1065: $i,SV539: $i,SV4: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV4 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV539 @ SV1065 @ SV4 ) @ SV1512 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV539 @ SV1512 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1065 @ SV1512 @ SV4 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3230,plain,
! [SV1513: $i,SV1066: $i,SV540: $i,SV5: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV5 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1513 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1066 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1513 @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3231,plain,
! [SV1514: $i,SV1067: $i,SV541: $i,SV6: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV541 @ SV1067 @ ( tc_fun @ SV1514 @ tc_bool ) ) @ ( tc_fun @ SV1514 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SV541 @ ( tc_fun @ SV1514 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV6 @ SV1067 @ ( tc_fun @ SV1514 @ tc_bool ) ) @ ( tc_fun @ SV1514 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3232,plain,
! [SV1515: $i,SV1068: $i,SV542: $i,SV7: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV542 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ SV1515 @ ( tc_fun @ SV1068 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV7 @ SV1515 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV542 @ SV1515 @ ( tc_fun @ SV1068 @ tc_bool ) ) @ ( tc_fun @ SV1068 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3233,plain,
! [SV1516: $i,SV1069: $i,SV543: $i,SV8: $i] :
( ( ! [SY4770: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV8 @ SV543 @ ( tc_fun @ SV1069 @ tc_bool ) ) @ SV1516 @ SV1069 @ SY4770 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV8 @ SV1516 @ SV1069 @ SY4770 ) @ ( c_Product__Type_OSigma @ SV543 @ SV1516 @ SV1069 @ SY4770 ) @ ( tc_fun @ ( tc_prod @ SV1069 @ SY4770 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3234,plain,
! [SV1517: $i,SV1070: $i,SV544: $i,SV9: $i] :
( ( ! [SY4771: $i,SY4772: $i] :
( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
| ~ ( c_in @ SV544 @ SY4771 @ SY4772 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SY4771 @ SY4772 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3235,plain,
! [SV1518: $i,SV1071: $i,SV545: $i,SV10: $i] :
( ( ! [SY4773: $i] :
( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
| ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SY4773 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1518 @ SY4773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3236,plain,
! [SV1519: $i,SV1072: $i,SV546: $i,SV11: $i] :
( ( ( c_lessequals @ SV11 @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1519 @ SV11 @ SV1072 ) @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3237,plain,
! [SV1520: $i,SV1073: $i,SV547: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SV547 @ SV1073 @ SV1520 ) @ ( tc_fun @ SV1520 @ tc_bool ) )
| ~ ( c_lessequals @ SV12 @ SV1073 @ ( tc_fun @ SV1520 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3238,plain,
! [SV1075: $i,SV550: $i,SV15: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV15 ) )
= $true )
| ( ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SV550 @ SV1075 @ SV15 ) @ SV15 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV550 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1075 @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(3239,plain,
! [SV1521: $i,SV1076: $i,SV551: $i,SV16: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV16 @ SV551 @ SV1076 ) @ SV1521 @ ( tc_fun @ SV1076 @ tc_bool ) )
= ( c_Set_Oinsert @ SV16 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV551 @ SV1521 @ ( tc_fun @ SV1076 @ tc_bool ) ) @ SV1076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3240,plain,
! [SV1522: $i,SV1077: $i,SV552: $i,SV17: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ ( c_Set_Oinsert @ SV552 @ SV1077 @ SV1522 ) @ ( tc_fun @ SV1522 @ tc_bool ) )
= ( c_Set_Oinsert @ SV552 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV17 @ SV1077 @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3241,plain,
! [SV554: $i,SV19: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV19 @ SV554 @ SV554 ) @ SV554 )
= $false )
| ( ( c_Relation_Otrans @ SV19 @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(3242,plain,
! [SV555: $i,SV20: $i] :
( ( ( c_Relation_Otrans @ SV20 @ SV555 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV20 @ SV555 @ SV555 ) @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(3243,plain,
! [SV1078: $i,SV556: $i,SV21: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV21 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV556 @ SV1078 @ SV21 ) @ SV21 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV556 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1078 @ SV21 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(3244,plain,
! [SV1523: $i,SV1079: $i,SV557: $i,SV22: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV22 @ SV557 @ SV1079 ) @ ( c_Set_Oinsert @ SV22 @ SV1523 @ SV1079 ) @ ( tc_fun @ SV1079 @ tc_bool ) )
= ( c_Set_Oinsert @ SV22 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV557 @ SV1523 @ ( tc_fun @ SV1079 @ tc_bool ) ) @ SV1079 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3245,plain,
! [SV1524: $i,SV1081: $i,SV559: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
| ( SV1081 = SV559 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1081 @ SV24 @ SV1524 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3246,plain,
! [SV1525: $i,SV1082: $i,SV560: $i,SV25: $i] :
( ( ! [SY4774: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV25 @ SV560 @ SV1082 @ SV1525 ) @ SY4774 @ ( tc_prod @ SV1082 @ SV1525 ) ) @ SV1082 @ SV1525 )
= ( c_Set_Oinsert @ SV25 @ ( c_Relation_ODomain @ SY4774 @ SV1082 @ SV1525 ) @ SV1082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3247,plain,
! [SV1083: $i,SV561: $i,SV26: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SV1083 @ SV1083 ) @ tc_bool ) ) @ SV1083 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV561 @ SV1083 )
| ~ ( c_Relation_Osym @ SV26 @ SV1083 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(3248,plain,
! [SV1526: $i,SV1084: $i,SV562: $i,SV27: $i] :
( ( ! [SY4775: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 @ SV562 @ ( tc_fun @ ( tc_prod @ SV1084 @ SV1526 ) @ tc_bool ) ) @ SY4775 @ SV1084 @ SV1526 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV27 @ SY4775 @ SV1084 @ SV1526 ) @ ( c_Relation_OImage @ SV562 @ SY4775 @ SV1084 @ SV1526 ) @ ( tc_fun @ SV1526 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3249,plain,
! [SV1527: $i,SV1085: $i,SV563: $i,SV28: $i] :
( ( ! [SY4776: $i] :
( ( c_Relation_OImage @ SV28 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV563 @ SV1085 @ ( tc_fun @ SV1527 @ tc_bool ) ) @ SV1527 @ SY4776 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV28 @ SV563 @ SV1527 @ SY4776 ) @ ( c_Relation_OImage @ SV28 @ SV1085 @ SV1527 @ SY4776 ) @ ( tc_fun @ SY4776 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3250,plain,
! [SV1528: $i,SV1086: $i,SV564: $i,SV29: $i] :
( ( ( c_Set_Oinsert @ SV29 @ ( c_Set_Oinsert @ SV564 @ SV1086 @ SV1528 ) @ SV1528 )
= ( c_Set_Oinsert @ SV564 @ ( c_Set_Oinsert @ SV29 @ SV1086 @ SV1528 ) @ SV1528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3251,plain,
! [SV1529: $i,SV1087: $i,SV565: $i,SV30: $i] :
( ( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV565 @ SV1087 @ ( tc_fun @ ( tc_prod @ SV1529 @ SV1529 ) @ tc_bool ) ) @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) )
| ~ ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SV1087 @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3252,plain,
! [SV1530: $i,SV1088: $i,SV566: $i,SV31: $i] :
( ( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 @ SV1088 @ ( tc_fun @ ( tc_prod @ SV1530 @ SV1530 ) @ tc_bool ) ) @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) )
| ~ ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SV566 @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3253,plain,
! [SV1531: $i,SV1089: $i,SV567: $i,SV32: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ SV1089 @ ( tc_fun @ SV1531 @ tc_bool ) ) @ ( tc_fun @ SV1531 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV567 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV1089 @ ( tc_fun @ SV1531 @ tc_bool ) ) @ ( tc_fun @ SV1531 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3254,plain,
! [SV1532: $i,SV1090: $i,SV568: $i,SV33: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ SV568 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SV1532 @ ( tc_fun @ SV1090 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV568 @ SV1532 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ ( tc_fun @ SV1090 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3255,plain,
! [SV1533: $i,SV1091: $i,SV569: $i,SV34: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV34 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ SV1091 @ SV34 ) @ SV1533 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1091 @ SV1533 @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3256,plain,
! [SV1534: $i,SV1092: $i,SV570: $i,SV35: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ SV1534 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ SV1534 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3257,plain,
! [SV1535: $i,SV1093: $i,SV571: $i,SV36: $i] :
( ( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ SV1535 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ SV1535 @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3258,plain,
! [SV1536: $i,SV1094: $i,SV572: $i,SV37: $i] :
( ( ~ ( class_Lattices_Olattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ SV1094 @ SV37 ) @ SV1536 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1094 @ SV1536 @ SV37 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3259,plain,
! [SV1095: $i,SV574: $i,SV39: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) )
= SV39 )
= $true )
| ( ( ~ ( c_lessequals @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(3260,plain,
! [SV1096: $i,SV575: $i,SV40: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV40 @ SV575 @ ( tc_fun @ SV1096 @ tc_bool ) )
= SV575 )
= $true )
| ( ( ~ ( c_lessequals @ SV575 @ SV40 @ ( tc_fun @ SV1096 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(3261,plain,
! [SV1097: $i,SV576: $i,SV41: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV41 ) )
= $true )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SV1097 @ SV41 )
= SV576 )
| ~ ( c_lessequals @ SV576 @ SV1097 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3262,plain,
! [SV1098: $i,SV577: $i,SV42: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV42 ) )
= $true )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SV1098 @ SV42 )
= SV1098 )
| ~ ( c_lessequals @ SV1098 @ SV577 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3263,plain,
! [SV1537: $i,SV1099: $i,SV578: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
| ~ ( c_lessequals @ SV578 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
| ~ ( c_lessequals @ SV43 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3264,plain,
! [SV1538: $i,SV1102: $i,SV581: $i,SV46: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
| ~ ( c_lessequals @ SV581 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
| ~ ( c_lessequals @ SV46 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3265,plain,
! [SV1539: $i,SV1103: $i,SV582: $i,SV47: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV47 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3266,plain,
! [SV1104: $i,SV583: $i,SV48: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV48 ) )
= $true )
| ( ( c_lessequals @ SV583 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV583 @ SV1104 @ SV48 ) @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(3267,plain,
! [SV1105: $i,SV584: $i,SV49: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV49 ) )
= $true )
| ( ( c_lessequals @ SV584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1105 @ SV584 @ SV49 ) @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(3268,plain,
! [SV1540: $i,SV1106: $i,SV585: $i,SV50: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV50 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3269,plain,
! [SV1541: $i,SV1107: $i,SV586: $i,SV51: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV51 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3270,plain,
! [SV1108: $i,SV587: $i,SV52: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV52 ) )
= $true )
| ( ( c_lessequals @ SV587 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1108 @ SV587 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3271,plain,
! [SV1109: $i,SV588: $i,SV53: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV53 ) )
= $true )
| ( ( c_lessequals @ SV588 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV588 @ SV1109 @ SV53 ) @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3272,plain,
! [SV1111: $i,SV590: $i,SV55: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV55 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV590 @ SV1111 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1111 @ SV590 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(3273,plain,
! [SV1112: $i,SV591: $i,SV56: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV56 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV591 @ SV1112 @ SV56 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1112 @ SV591 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(3274,plain,
! [SV1542: $i,SV1113: $i,SV592: $i,SV57: $i] :
( ( ~ ( class_Lattices_Olattice @ SV57 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1113 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1542 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1113 @ SV1542 @ SV57 ) @ SV57 ) @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3275,plain,
! [SV1543: $i,SV1114: $i,SV593: $i,SV58: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV58 @ SV593 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV593 @ SV1543 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1543 @ SV58 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV58 @ SV593 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SV1543 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1543 @ SV58 @ ( tc_fun @ SV1114 @ tc_bool ) ) @ ( tc_fun @ SV1114 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3276,plain,
! [SV1544: $i,SV1115: $i,SV595: $i,SV60: $i] :
( ( ( c_in @ SV60 @ SV595 @ SV1115 )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SV1544 @ SV1115 ) @ SV595 @ ( tc_fun @ SV1115 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3277,plain,
! [SV1545: $i,SV1116: $i,SV596: $i,SV61: $i] :
( ( ! [SY4777: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV596 @ ( tc_fun @ SV1116 @ tc_bool ) ) @ SV1545 @ SV1116 @ SY4777 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV61 @ SV1545 @ SV1116 @ SY4777 ) @ ( c_Product__Type_OSigma @ SV596 @ SV1545 @ SV1116 @ SY4777 ) @ ( tc_fun @ ( tc_prod @ SV1116 @ SY4777 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3278,plain,
! [SV1546: $i,SV1117: $i,SV597: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SV597 @ SV1117 ) @ SV1546 ) )
| ~ ( hBOOL @ ( hAPP @ SV597 @ SV1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3279,plain,
! [SV1547: $i,SV1118: $i,SV598: $i,SV63: $i] :
( ( ! [SY4778: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SY4778 ) @ SY4778 )
= ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SY4778 ) )
| ~ ( c_in @ SV598 @ SV1118 @ SV1547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3280,plain,
! [SV1548: $i,SV1119: $i,SV599: $i,SV64: $i] :
( ( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SV1119 @ SV1548 ) @ ( tc_fun @ SV1548 @ tc_bool ) )
| ~ ( c_lessequals @ SV64 @ SV1119 @ ( tc_fun @ SV1548 @ tc_bool ) )
| ( c_in @ SV599 @ SV64 @ SV1548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3281,plain,
! [SV1549: $i,SV1120: $i,SV600: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SV1120 @ tc_bool ) )
| ( c_in @ SV1549 @ SV65 @ SV1120 )
| ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV1549 @ SV600 @ SV1120 ) @ ( tc_fun @ SV1120 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3282,plain,
! [SV1550: $i,SV1121: $i,SV601: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SV1121 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
| ~ ( c_lessequals @ SV66 @ SV1121 @ ( tc_fun @ SV1550 @ tc_bool ) )
| ( c_in @ SV601 @ SV66 @ SV1550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3283,plain,
! [SV1551: $i,SV1122: $i,SV602: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SV1122 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SV1551 @ SV602 @ SV1122 ) @ ( tc_fun @ SV1122 @ tc_bool ) )
| ( c_in @ SV1551 @ SV67 @ SV1122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3284,plain,
! [SV1552: $i,SV1123: $i,SV603: $i,SV68: $i] :
( ( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SV603 @ ( tc_fun @ ( tc_prod @ SV1123 @ SV1552 ) @ tc_bool ) ) @ SV1123 @ SV1552 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV68 @ SV1123 @ SV1552 ) @ ( c_Relation_Oconverse @ SV603 @ SV1123 @ SV1552 ) @ ( tc_fun @ ( tc_prod @ SV1552 @ SV1123 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3285,plain,
! [SV1553: $i,SV1124: $i,SV604: $i,SV69: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Set_Oinsert @ SV604 @ SV1124 @ SV1553 ) @ ( tc_fun @ SV1553 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV1124 @ ( tc_fun @ SV1553 @ tc_bool ) ) )
| ( c_in @ SV604 @ SV69 @ SV1553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3286,plain,
! [SV1554: $i,SV1125: $i,SV605: $i,SV70: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV70 @ SV605 @ SV1125 ) @ SV1554 @ ( tc_fun @ SV1125 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV605 @ SV1554 @ ( tc_fun @ SV1125 @ tc_bool ) ) )
| ( c_in @ SV70 @ SV1554 @ SV1125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3287,plain,
! [SV1555: $i,SV1126: $i,SV606: $i,SV71: $i] :
( ( ! [SY4779: $i,SY4780: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV606 @ ( tc_fun @ ( tc_prod @ SV1126 @ SV1555 ) @ tc_bool ) ) @ SY4779 @ SV1126 @ SV1555 @ SY4780 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SY4779 @ SV1126 @ SV1555 @ SY4780 ) @ ( c_Relation_Orel__comp @ SV606 @ SY4779 @ SV1126 @ SV1555 @ SY4780 ) @ ( tc_fun @ ( tc_prod @ SV1126 @ SY4780 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3288,plain,
! [SV1556: $i,SV1127: $i,SV607: $i,SV72: $i] :
( ( ! [SY4781: $i,SY4782: $i] :
( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1127 @ ( tc_fun @ ( tc_prod @ SV1556 @ SY4781 ) @ tc_bool ) ) @ SY4782 @ SV1556 @ SY4781 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SV607 @ SY4782 @ SV1556 @ SY4781 ) @ ( c_Relation_Orel__comp @ SV72 @ SV1127 @ SY4782 @ SV1556 @ SY4781 ) @ ( tc_fun @ ( tc_prod @ SY4782 @ SY4781 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3289,plain,
! [SV1557: $i,SV1129: $i,SV610: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) ) @ ( tc_fun @ SV1129 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3290,plain,
! [SV1558: $i,SV1130: $i,SV611: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ SV611 @ ( tc_fun @ SV1130 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV611 @ SV1558 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3291,plain,
! [SV1559: $i,SV1131: $i,SV612: $i,SV77: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ( c_lessequals @ SV612 @ SV1131 @ SV77 )
| ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SV1559 @ SV77 ) @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3292,plain,
! [SV1560: $i,SV1132: $i,SV613: $i,SV78: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ( c_lessequals @ SV613 @ SV1132 @ SV78 )
| ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1560 @ SV1132 @ SV78 ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3293,plain,
! [SV1561: $i,SV1133: $i,SV614: $i,SV79: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV79 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SV1561 @ SV79 )
| ~ ( c_lessequals @ SV614 @ SV1561 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3294,plain,
! [SV1562: $i,SV1134: $i,SV615: $i,SV80: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV80 )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SV1562 @ SV80 )
| ~ ( c_lessequals @ SV1134 @ SV1562 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3295,plain,
! [SV1563: $i,SV1135: $i,SV616: $i,SV81: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV81 )
| ( c_lessequals @ SV616 @ SV1135 @ SV81 )
| ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SV1563 @ SV81 ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3296,plain,
! [SV1564: $i,SV1136: $i,SV617: $i,SV82: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( c_lessequals @ SV617 @ SV1136 @ SV82 )
| ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1564 @ SV1136 @ SV82 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3297,plain,
! [SV1138: $i,SV619: $i,SV84: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV84 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV619 @ SV1138 @ SV84 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1138 @ SV619 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(3298,plain,
! [SV1139: $i,SV620: $i,SV85: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV85 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SV1139 @ SV85 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1139 @ SV620 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(3299,plain,
! [SV1565: $i,SV1140: $i,SV621: $i,SV86: $i] :
( ( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV86 @ SV621 @ ( tc_fun @ ( tc_prod @ SV1140 @ SV1565 ) @ tc_bool ) ) @ SV1140 @ SV1565 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV86 @ SV1140 @ SV1565 ) @ ( c_Relation_ODomain @ SV621 @ SV1140 @ SV1565 ) @ ( tc_fun @ SV1140 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3300,plain,
! [SV1142: $i,SV623: $i,SV88: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) @ SV88 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(3301,plain,
! [SV1143: $i,SV624: $i,SV89: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV89 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) @ SV89 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(3302,plain,
! [SV625: $i,SV90: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV90 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV625 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(3303,plain,
! [SV1566: $i,SV1144: $i,SV626: $i,SV91: $i] :
( ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV91 @ SV626 @ ( tc_fun @ ( tc_prod @ SV1144 @ SV1566 ) @ tc_bool ) ) @ SV1144 @ SV1566 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV91 @ SV1144 @ SV1566 ) @ ( c_Relation_ORange @ SV626 @ SV1144 @ SV1566 ) @ ( tc_fun @ SV1566 @ tc_bool ) ) @ ( tc_fun @ SV1566 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3304,plain,
! [SV1567: $i,SV1146: $i,SV628: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1146 @ SV93 @ ( tc_fun @ SV1567 @ tc_bool ) ) @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3305,plain,
! [SV1568: $i,SV1147: $i,SV629: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ SV629 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SV1147 @ ( tc_fun @ SV1568 @ tc_bool ) ) @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3306,plain,
! [SV1569: $i,SV1148: $i,SV630: $i,SV95: $i] :
( ( ! [SY4783: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV95 @ SV630 @ SV1148 @ SV1569 ) @ SY4783 @ ( tc_prod @ SV1148 @ SV1569 ) ) @ SV1148 @ SV1569 )
= ( c_Set_Oinsert @ SV630 @ ( c_Relation_ORange @ SY4783 @ SV1148 @ SV1569 ) @ SV1569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3307,plain,
! [SV1149: $i,SV631: $i,SV96: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1149 ) @ tc_bool ) ) @ SV1149 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV631 @ SV1149 )
| ~ ( c_Relation_Osym @ SV96 @ SV1149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3308,plain,
! [SV632: $i,SV97: $i] :
( ( ( c_Relation_Otrans @ SV97 @ SV632 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV97 @ SV632 )
= SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3309,plain,
! [SV1150: $i,SV633: $i,SV98: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV633 @ ( tc_fun @ SV1150 @ tc_bool ) ) @ SV1150 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV633 @ SV1150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3310,plain,
! [SV1151: $i,SV634: $i,SV99: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV634 @ ( tc_fun @ SV1151 @ tc_bool ) ) @ SV1151 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV99 @ SV1151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(3311,plain,
! [SV1570: $i,SV1152: $i,SV635: $i,SV100: $i] :
( ( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
| ~ ( c_in @ SV100 @ SV1152 @ SV1570 )
| ~ ( c_in @ SV100 @ SV635 @ SV1570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3312,plain,
! [SV1571: $i,SV1153: $i,SV636: $i,SV101: $i] :
( ( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
| ~ ( c_in @ SV101 @ SV1153 @ SV1571 )
| ~ ( c_in @ SV101 @ SV636 @ SV1571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3313,plain,
! [SV1572: $i,SV1154: $i,SV637: $i,SV102: $i] :
( ( ( c_in @ SV102 @ ( c_Set_Oinsert @ SV637 @ SV1154 @ SV1572 ) @ SV1572 )
| ~ ( c_in @ SV102 @ SV1154 @ SV1572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3314,plain,
! [SV1573: $i,SV1155: $i,SV638: $i,SV103: $i] :
( ( ( c_in @ SV103 @ ( c_Set_Oinsert @ SV638 @ SV1155 @ SV1573 ) @ SV1573 )
| ~ ( c_in @ SV103 @ SV1155 @ SV1573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3315,plain,
! [SV1574: $i,SV1156: $i,SV639: $i,SV104: $i] :
( ( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1156 @ ( tc_fun @ SV1574 @ tc_bool ) ) @ SV1574 )
| ~ ( c_in @ SV104 @ SV639 @ SV1574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3316,plain,
! [SV1575: $i,SV1157: $i,SV640: $i,SV105: $i] :
( ( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV640 @ SV1157 @ ( tc_fun @ SV1575 @ tc_bool ) ) @ SV1575 )
| ~ ( c_in @ SV105 @ SV1157 @ SV1575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3317,plain,
! [SV1576: $i,SV1158: $i,SV641: $i,SV106: $i] :
( ( ( c_in @ SV106 @ SV641 @ SV1158 )
| ( SV106 = SV1576 )
| ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SV1576 @ SV641 @ SV1158 ) @ SV1158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3318,plain,
! [SV1577: $i,SV1159: $i,SV642: $i,SV107: $i] :
( ( ( c_in @ SV107 @ SV642 @ SV1159 )
| ( c_in @ SV107 @ SV1577 @ SV1159 )
| ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1577 @ SV642 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ SV1159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3319,plain,
! [SV1578: $i,SV1163: $i,SV646: $i,SV111: $i] :
( ( ( c_in @ SV111 @ SV646 @ SV1163 )
| ~ ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1578 @ SV646 @ ( tc_fun @ SV1163 @ tc_bool ) ) @ SV1163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3320,plain,
! [SV1579: $i,SV1164: $i,SV647: $i,SV112: $i] :
( ( ( c_in @ SV112 @ SV647 @ SV1164 )
| ~ ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SV1579 @ ( tc_fun @ SV1164 @ tc_bool ) ) @ SV1164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3321,plain,
! [SV1165: $i,SV648: $i,SV113: $i] :
( ( ( ( c_Set_Oinsert @ SV113 @ SV648 @ SV1165 )
= SV648 )
= $true )
| ( ( ~ ( c_in @ SV113 @ SV648 @ SV1165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(3322,plain,
! [SV1580: $i,SV1166: $i,SV649: $i,SV114: $i] :
( ( ! [SY4784: $i] :
( ~ ( c_in @ SV114 @ SV649 @ SV1166 )
| ( c_in @ ( hAPP @ SV1580 @ SV114 ) @ ( c_Set_Oimage @ SV1580 @ SV649 @ SV1166 @ SY4784 ) @ SY4784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3323,plain,
! [SV1581: $i,SV1167: $i,SV650: $i,SV115: $i] :
( ( ! [SY4785: $i] :
( ~ ( c_in @ SV115 @ SV650 @ SV1167 )
| ( c_in @ ( hAPP @ SV1581 @ SV115 ) @ ( c_Set_Oimage @ SV1581 @ SV650 @ SV1167 @ SY4785 ) @ SY4785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3324,plain,
! [SV1582: $i,SV1168: $i,SV651: $i,SV116: $i] :
( ( ! [SY4786: $i] :
( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SV1168 @ SV1582 @ SY4786 ) @ SY4786 )
| ~ ( c_in @ SV651 @ SV1168 @ SV1582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3325,plain,
! [SV1583: $i,SV1169: $i,SV652: $i,SV117: $i] :
( ( ! [SY4787: $i] :
( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SV1169 @ SV1583 @ SY4787 ) @ SY4787 )
| ~ ( c_in @ SV652 @ SV1169 @ SV1583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3326,plain,
! [SV1584: $i,SV1170: $i,SV653: $i,SV118: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SV653 @ SV1170 @ SV1584 ) @ SV1170 @ SV1584 @ SV1584 ) @ SV118 @ ( tc_prod @ SV1584 @ SV1584 ) )
| ~ ( c_in @ ( c_Pair @ SV653 @ SV1170 @ SV1584 @ SV1584 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SV1584 ) @ ( tc_prod @ SV1584 @ SV1584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3327,plain,
! [SV1585: $i,SV1171: $i,SV654: $i,SV119: $i] :
( ( ! [SY4788: $i,SY4789: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SY4788 @ SY4789 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4789 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SY4789 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4789 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SY4788 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3328,plain,
! [SV1172: $i,SV655: $i,SV120: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV655 @ SV1172 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(3329,plain,
! [SV1173: $i,SV656: $i,SV121: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV121 @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(3330,plain,
! [SV1586: $i,SV1174: $i,SV659: $i,SV124: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 @ SV659 @ ( tc_fun @ ( tc_prod @ SV1174 @ SV1586 ) @ tc_bool ) ) @ SV1174 @ SV1586 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV124 @ SV1174 @ SV1586 ) @ ( c_Relation_ODomain @ SV659 @ SV1174 @ SV1586 ) @ ( tc_fun @ SV1174 @ tc_bool ) ) @ ( tc_fun @ SV1174 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3331,plain,
! [SV1176: $i,SV661: $i,SV126: $i] :
( ( ( c_Finite__Set_Ofinite @ SV126 @ SV661 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1176 @ SV126 @ SV661 ) @ SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(3332,plain,
! [SV1177: $i,SV662: $i,SV127: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV127 @ SV662 @ SV1177 ) @ SV1177 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV662 @ SV1177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3333,plain,
! [SV1587: $i,SV1178: $i,SV663: $i,SV128: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SV663 @ SV1178 @ SV1587 ) @ SV1587 )
| ~ ( c_Relation_Otrans @ SV128 @ SV1178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3334,plain,
! [SV1588: $i,SV1179: $i,SV664: $i,SV129: $i] :
( ( ! [SY4790: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV129 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV664 @ SV1179 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ SV1588 @ SY4790 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV129 @ SV664 @ SV1588 @ SY4790 ) @ ( c_Set_Oimage @ SV129 @ SV1179 @ SV1588 @ SY4790 ) @ ( tc_fun @ SY4790 @ tc_bool ) ) @ ( tc_fun @ SY4790 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3335,plain,
! [SV1180: $i,SV665: $i,SV130: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV665 @ SV1180 )
| ~ ( c_Finite__Set_Ofinite @ SV130 @ SV1180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(3336,plain,
! [SV1181: $i,SV666: $i,SV131: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ SV1181 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV666 @ SV1181 )
| ~ ( c_Finite__Set_Ofinite @ SV131 @ SV1181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3337,plain,
! [SV1589: $i,SV1182: $i,SV667: $i,SV132: $i] :
( ( ! [SY4791: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV132 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV667 @ SV1182 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ SV1589 @ SY4791 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV132 @ SV667 @ SV1589 @ SY4791 ) @ ( c_Relation_OImage @ SV132 @ SV1182 @ SV1589 @ SY4791 ) @ ( tc_fun @ SY4791 @ tc_bool ) ) @ ( tc_fun @ SY4791 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3338,plain,
! [SV1590: $i,SV1183: $i,SV668: $i,SV133: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SV668 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV668 @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ ( tc_fun @ SV1183 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1590 @ SV133 @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3339,plain,
! [SV669: $i,SV134: $i] :
( ( ( c_Relation_Otrans @ SV134 @ SV669 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 @ ( c_Relation_OId @ SV669 ) @ ( tc_fun @ ( tc_prod @ SV669 @ SV669 ) @ tc_bool ) ) @ SV669 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3340,plain,
! [SV1591: $i,SV1184: $i,SV670: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
| ( hBOOL @ ( hAPP @ SV1184 @ SV670 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1184 @ SV135 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3341,plain,
! [SV1592: $i,SV1185: $i,SV671: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SV671 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SV1592 ) )
| ~ ( hBOOL @ ( hAPP @ SV671 @ SV1592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3342,plain,
! [SV1593: $i,SV1186: $i,SV672: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV672 @ ( tc_fun @ SV1186 @ tc_bool ) ) @ SV1593 ) )
| ~ ( hBOOL @ ( hAPP @ SV137 @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3343,plain,
! [SV1594: $i,SV1187: $i,SV673: $i,SV138: $i] :
( ( ! [SY4792: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 @ SV673 @ ( tc_fun @ SV1187 @ tc_bool ) ) @ ( c_COMBK @ SV1594 @ ( tc_fun @ SY4792 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4792 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV138 @ ( c_COMBK @ SV1594 @ ( tc_fun @ SY4792 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4792 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1594 @ ( tc_fun @ SY4792 @ tc_bool ) @ SV1187 ) @ SV1187 @ SY4792 ) @ ( tc_fun @ ( tc_prod @ SV1187 @ SY4792 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3344,plain,
! [SV674: $i,SV139: $i] :
( ( ( c_Relation_Otrans @ SV139 @ SV674 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV139 @ SV139 @ SV674 @ SV674 @ SV674 ) @ SV139 @ ( tc_fun @ ( tc_prod @ SV674 @ SV674 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(3345,plain,
! [SV1595: $i,SV1188: $i,SV675: $i,SV140: $i] :
( ( ! [SY4793: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SY4793 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV675 @ SY4793 @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3346,plain,
! [SV1596: $i,SV1189: $i,SV676: $i,SV141: $i] :
( ( ~ ( class_Lattices_Olattice @ SV141 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ SV1189 @ SV141 ) @ SV1596 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1189 @ SV1596 @ SV141 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3347,plain,
! [SV1597: $i,SV1190: $i,SV677: $i,SV142: $i] :
( ( ~ ( class_Lattices_Olattice @ SV142 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ SV1597 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ SV1597 @ SV142 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3348,plain,
! [SV1598: $i,SV1191: $i,SV678: $i,SV143: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV143 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ SV1598 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ SV1598 @ SV143 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3349,plain,
! [SV1599: $i,SV1192: $i,SV679: $i,SV144: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV144 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ SV1192 @ SV144 ) @ SV1599 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1192 @ SV1599 @ SV144 ) @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3350,plain,
! [SV1600: $i,SV1193: $i,SV680: $i,SV145: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ SV680 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1600 @ ( tc_fun @ SV1193 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV145 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV680 @ SV1600 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ ( tc_fun @ SV1193 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3351,plain,
! [SV1601: $i,SV1194: $i,SV681: $i,SV146: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ SV1194 @ ( tc_fun @ SV1601 @ tc_bool ) ) @ ( tc_fun @ SV1601 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV681 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SV1194 @ ( tc_fun @ SV1601 @ tc_bool ) ) @ ( tc_fun @ SV1601 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3352,plain,
! [SV1195: $i,SV682: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofinite @ SV147 @ SV682 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV147 @ SV1195 @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV682 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3353,plain,
! [SV1196: $i,SV683: $i,SV148: $i] :
( ( ( c_Finite__Set_Ofinite @ SV148 @ SV683 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1196 @ SV148 @ ( tc_fun @ SV683 @ tc_bool ) ) @ SV683 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3354,plain,
! [SV1602: $i,SV1197: $i,SV684: $i,SV150: $i] :
( ( ! [SY4794: $i,SY4795: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SY4794 @ SY4795 ) @ ( tc_fun @ SY4795 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4795 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SV1602 @ SV1197 @ SY4795 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV684 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SY4794 @ SY4795 ) @ ( tc_fun @ SY4795 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4795 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ SY4794 @ ( tc_fun @ SY4795 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4795 ) @ ( tc_fun @ ( tc_prod @ SV1197 @ SY4795 ) @ tc_bool ) ) @ ( tc_prod @ SV1197 @ SY4795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3355,plain,
! [SV1198: $i,SV685: $i,SV151: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SV1198 @ SV1198 ) @ tc_bool ) ) @ SV1198 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV685 @ SV1198 )
| ~ ( c_Relation_Otrans @ SV151 @ SV1198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3356,plain,
! [SV1603: $i,SV1199: $i,SV686: $i,SV152: $i] :
( ( ~ ( class_Lattices_Olattice @ SV152 )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1199 @ SV1603 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1199 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1603 @ SV152 ) @ SV152 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3357,plain,
! [SV1200: $i,SV687: $i,SV153: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV153 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SV1200 @ SV153 ) @ SV153 )
= SV687 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3358,plain,
! [SV1201: $i,SV688: $i,SV154: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV154 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV688 @ SV1201 @ SV154 ) @ SV154 )
= SV688 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(3359,plain,
! [SV1202: $i,SV689: $i,SV155: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV155 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1202 @ SV155 )
= SV689 )
| ~ ( c_lessequals @ SV1202 @ SV689 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3360,plain,
! [SV1203: $i,SV690: $i,SV156: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV156 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SV1203 @ SV156 )
= SV1203 )
| ~ ( c_lessequals @ SV690 @ SV1203 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3361,plain,
! [SV1204: $i,SV691: $i,SV157: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) )
= SV691 )
= $true )
| ( ( ~ ( c_lessequals @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3362,plain,
! [SV1205: $i,SV692: $i,SV158: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV692 @ ( tc_fun @ SV1205 @ tc_bool ) )
= SV158 )
= $true )
| ( ( ~ ( c_lessequals @ SV692 @ SV158 @ ( tc_fun @ SV1205 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3363,plain,
! [SV1604: $i,SV1206: $i,SV693: $i,SV159: $i] :
( ( ! [SY4796: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SY4796 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV693 @ SY4796 @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3364,plain,
! [SV1605: $i,SV1207: $i,SV694: $i,SV160: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SV694 @ SV1207 @ SV1605 ) @ SV1605 )
| ~ ( c_Finite__Set_Ofinite @ SV694 @ SV1207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3365,plain,
! [SV1606: $i,SV1208: $i,SV695: $i,SV161: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SV695 @ SV1208 ) @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV695 @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) )
| ~ ( c_in @ SV161 @ SV1606 @ SV1208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3366,plain,
! [SV1607: $i,SV1209: $i,SV696: $i,SV162: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SV696 @ SV1209 @ SV1607 ) @ ( tc_fun @ SV1607 @ tc_bool ) )
= ( c_Set_Oinsert @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SV1209 @ ( tc_fun @ SV1607 @ tc_bool ) ) @ SV1607 ) )
| ~ ( c_in @ SV696 @ SV162 @ SV1607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3367,plain,
! [SV1608: $i,SV1210: $i,SV697: $i,SV163: $i] :
( ( ! [SY4797: $i] :
( ( c_Set_Oimage @ SV163 @ ( c_Set_Oinsert @ SV697 @ SV1210 @ SV1608 ) @ SV1608 @ SY4797 )
= ( c_Set_Oinsert @ ( hAPP @ SV163 @ SV697 ) @ ( c_Set_Oimage @ SV163 @ SV1210 @ SV1608 @ SY4797 ) @ SY4797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3368,plain,
! [SV1609: $i,SV1211: $i,SV698: $i,SV164: $i] :
( ( ! [SY4798: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SY4798 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV698 @ SY4798 @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3369,plain,
! [SV1610: $i,SV1212: $i,SV699: $i,SV165: $i] :
( ( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV165 @ SV699 @ ( tc_fun @ ( tc_prod @ SV1212 @ SV1610 ) @ tc_bool ) ) @ SV1212 @ SV1610 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV165 @ SV1212 @ SV1610 ) @ ( c_Relation_Oconverse @ SV699 @ SV1212 @ SV1610 ) @ ( tc_fun @ ( tc_prod @ SV1610 @ SV1212 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3370,plain,
! [SV1213: $i,SV700: $i,SV166: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV166 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV700 @ SV1213 @ SV166 ) @ SV700 @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3371,plain,
! [SV1214: $i,SV701: $i,SV167: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV167 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV701 @ SV1214 @ SV167 ) @ SV1214 @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(3372,plain,
! [SV1611: $i,SV1215: $i,SV702: $i,SV168: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV168 )
| ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1611 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3373,plain,
! [SV1612: $i,SV1216: $i,SV703: $i,SV169: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV169 )
| ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1612 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3374,plain,
! [SV1613: $i,SV1217: $i,SV704: $i,SV170: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV170 )
| ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1613 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3375,plain,
! [SV1218: $i,SV705: $i,SV171: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV171 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV705 @ SV1218 @ SV171 ) @ SV1218 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3376,plain,
! [SV1219: $i,SV706: $i,SV172: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV172 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV706 @ SV1219 @ SV172 ) @ SV706 @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3377,plain,
! [SV1614: $i,SV1222: $i,SV709: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) @ ( tc_fun @ SV1614 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SV1614 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3378,plain,
! [SV1615: $i,SV1223: $i,SV710: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ ( tc_fun @ SV1615 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SV1615 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3379,plain,
! [SV1616: $i,SV1224: $i,SV711: $i,SV177: $i] :
( ( ! [SY4799: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV177 @ SV711 @ ( tc_fun @ SV1224 @ tc_bool ) ) @ ( c_COMBK @ SV1616 @ ( tc_fun @ SY4799 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4799 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV177 @ ( c_COMBK @ SV1616 @ ( tc_fun @ SY4799 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4799 ) @ ( c_Product__Type_OSigma @ SV711 @ ( c_COMBK @ SV1616 @ ( tc_fun @ SY4799 @ tc_bool ) @ SV1224 ) @ SV1224 @ SY4799 ) @ ( tc_fun @ ( tc_prod @ SV1224 @ SY4799 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3380,plain,
! [SV1617: $i,SV1225: $i,SV712: $i,SV178: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV178 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV712 @ SV1225 @ SV178 ) @ SV1617 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV712 @ SV1617 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1225 @ SV1617 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3381,plain,
! [SV1618: $i,SV1226: $i,SV713: $i,SV179: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV179 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1226 @ SV1618 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1226 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1618 @ SV179 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3382,plain,
! [SV1619: $i,SV1227: $i,SV714: $i,SV180: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV714 @ SV1227 @ ( tc_fun @ SV1619 @ tc_bool ) ) @ ( tc_fun @ SV1619 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SV714 @ ( tc_fun @ SV1619 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV180 @ SV1227 @ ( tc_fun @ SV1619 @ tc_bool ) ) @ ( tc_fun @ SV1619 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3383,plain,
! [SV1620: $i,SV1228: $i,SV715: $i,SV181: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV181 @ SV715 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ SV1620 @ ( tc_fun @ SV1228 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV181 @ SV1620 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV715 @ SV1620 @ ( tc_fun @ SV1228 @ tc_bool ) ) @ ( tc_fun @ SV1228 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3384,plain,
! [SV1621: $i,SV1230: $i,SV717: $i,SV183: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
| ~ ( c_in @ SV183 @ SV1621 @ SV1230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3385,plain,
! [SV1231: $i,SV718: $i,SV184: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV184 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) @ SV184 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3386,plain,
! [SV1232: $i,SV719: $i,SV185: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV185 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) @ SV185 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3387,plain,
! [SV1234: $i,SV721: $i,SV187: $i] :
( ( ( c_lessequals @ ( c_Relation_OField @ SV187 @ SV721 ) @ ( c_Relation_OField @ SV1234 @ SV721 ) @ ( tc_fun @ SV721 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV187 @ SV1234 @ ( tc_fun @ ( tc_prod @ SV721 @ SV721 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3388,plain,
! [SV1622: $i,SV1235: $i,SV722: $i,SV188: $i] :
( ( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV188 @ SV722 @ ( tc_fun @ ( tc_prod @ SV1235 @ SV1622 ) @ tc_bool ) ) @ SV1235 @ SV1622 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV188 @ SV1235 @ SV1622 ) @ ( c_Relation_ORange @ SV722 @ SV1235 @ SV1622 ) @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3389,plain,
! [SV1236: $i,SV723: $i,SV189: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1236 @ SV1236 ) @ tc_bool ) ) @ SV1236 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV189 @ SV1236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3390,plain,
! [SV1237: $i,SV724: $i,SV190: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV190 @ SV724 @ ( tc_fun @ ( tc_prod @ SV1237 @ SV1237 ) @ tc_bool ) ) @ SV1237 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV724 @ SV1237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3391,plain,
! [SV725: $i,SV191: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV191 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV725 @ SV191 )
= SV725 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3392,plain,
! [SV1623: $i,SV1238: $i,SV728: $i,SV194: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV194 )
| ( c_lessequals @ SV728 @ SV1238 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1623 @ SV728 @ SV194 ) @ SV1238 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3393,plain,
! [SV1624: $i,SV1239: $i,SV729: $i,SV195: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV195 )
| ( c_lessequals @ SV729 @ SV1239 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SV1624 @ SV195 ) @ SV1239 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3394,plain,
! [SV1625: $i,SV1240: $i,SV730: $i,SV196: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV196 )
| ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SV1625 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SV730 @ SV1625 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3395,plain,
! [SV1626: $i,SV1241: $i,SV731: $i,SV197: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV197 )
| ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SV1626 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV731 @ SV1241 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3396,plain,
! [SV1627: $i,SV1242: $i,SV732: $i,SV198: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV198 )
| ( c_lessequals @ SV732 @ SV1242 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1627 @ SV732 @ SV198 ) @ SV1242 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3397,plain,
! [SV1628: $i,SV1243: $i,SV733: $i,SV199: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV199 )
| ( c_lessequals @ SV733 @ SV1243 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV1628 @ SV199 ) @ SV1243 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3398,plain,
! [SV1629: $i,SV1244: $i,SV734: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV1629 @ ( tc_fun @ SV1244 @ tc_bool ) ) @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3399,plain,
! [SV1630: $i,SV1245: $i,SV735: $i,SV201: $i] :
( ( ( c_lessequals @ SV201 @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1630 @ SV201 @ ( tc_fun @ SV1245 @ tc_bool ) ) @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3400,plain,
! [SV1246: $i,SV736: $i,SV202: $i] :
( ( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1246 @ SV736 )
| ~ ( c_lessequals @ SV202 @ SV1246 @ ( tc_fun @ SV736 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3401,plain,
! [SV1247: $i,SV737: $i,SV203: $i] :
( ( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
= $true )
| ( ( ~ ( c_lessequals @ SV203 @ SV1247 @ ( tc_fun @ SV737 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1247 @ SV737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3402,plain,
! [SV1631: $i,SV1248: $i,SV738: $i,SV204: $i] :
( ( ! [SY4800: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SY4800 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV738 @ SY4800 @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3403,plain,
! [SV1632: $i,SV1249: $i,SV739: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV1632 ) )
| ~ ( hBOOL @ ( hAPP @ SV739 @ SV1632 ) )
| ~ ( hBOOL @ ( hAPP @ SV205 @ SV1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3404,plain,
! [SV1633: $i,SV1250: $i,SV740: $i,SV206: $i] :
( ( ! [SY4801: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SV1250 @ SV1633 ) @ ( c_Set_Oimage @ SV206 @ SY4801 @ SV1250 @ SV1633 ) @ ( tc_fun @ SV1633 @ tc_bool ) )
| ~ ( c_lessequals @ SV740 @ SY4801 @ ( tc_fun @ SV1250 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3405,plain,
! [SV1634: $i,SV1251: $i,SV741: $i,SV207: $i] :
( ( ! [SY4802: $i] :
( ~ ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SV1634 @ SV207 @ SV1251 @ SY4802 ) @ ( c_Set_Oimage @ SV1634 @ SV741 @ SV1251 @ SY4802 ) @ ( tc_fun @ SY4802 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3406,plain,
! [SV1635: $i,SV1252: $i,SV742: $i,SV208: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SV742 @ SV1252 ) @ ( c_Set_Oinsert @ SV208 @ SV1635 @ SV1252 ) @ ( tc_fun @ SV1252 @ tc_bool ) )
| ~ ( c_lessequals @ SV742 @ SV1635 @ ( tc_fun @ SV1252 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3407,plain,
! [SV1253: $i,SV743: $i,SV209: $i] :
( ( ( c_Relation_Otrans @ SV209 @ SV743 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1253 @ SV209 @ SV743 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3408,plain,
! [SV1636: $i,SV1254: $i,SV744: $i,SV210: $i] :
( ( ! [SY4803: $i] :
( ( c_Set_Oimage @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV744 @ SV1254 @ ( tc_fun @ SV1636 @ tc_bool ) ) @ SV1636 @ SY4803 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV210 @ SV744 @ SV1636 @ SY4803 ) @ ( c_Set_Oimage @ SV210 @ SV1254 @ SV1636 @ SY4803 ) @ ( tc_fun @ SY4803 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3409,plain,
! [SV1637: $i,SV1255: $i,SV745: $i,SV211: $i] :
( ( ! [SY4804: $i] :
( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SY4804 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SY4804 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3410,plain,
! [SV1638: $i,SV1256: $i,SV746: $i,SV212: $i] :
( ( ! [SY4805: $i] :
( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SY4805 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SY4805 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3411,plain,
! [SV1639: $i,SV1257: $i,SV747: $i,SV213: $i] :
( ( ( c_Wellfounded_Owf @ SV213 @ SV747 )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1257 @ SV1639 @ SV747 @ SV747 ) @ SV213 @ ( tc_prod @ SV747 @ SV747 ) ) @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3412,plain,
! [SV1258: $i,SV748: $i,SV214: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV214 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( c_Relation_Orel__comp @ SV1258 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV214 @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3413,plain,
! [SV1259: $i,SV749: $i,SV215: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV215 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( c_Relation_Orel__comp @ SV749 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3414,plain,
! [SV1260: $i,SV751: $i,SV217: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV751 )
| ~ ( c_in @ SV1260 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3415,plain,
! [SV1640: $i,SV1262: $i,SV757: $i,SV223: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV223 @ SV757 @ SV1262 @ SV1262 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1262 ) @ ( tc_prod @ SV1262 @ SV1262 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SV1262 @ SV1262 ) @ SV1640 @ ( tc_prod @ SV1262 @ SV1262 ) ) @ SV1262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3416,plain,
! [SV1641: $i,SV1263: $i,SV758: $i,SV224: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SV1263 @ SV1263 ) @ SV1641 @ ( tc_prod @ SV1263 @ SV1263 ) ) @ SV1263 )
| ( c_in @ ( c_Pair @ SV758 @ SV224 @ SV1263 @ SV1263 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1263 ) @ ( tc_prod @ SV1263 @ SV1263 ) )
| ~ ( c_Wellfounded_Owf @ SV1641 @ SV1263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3417,plain,
! [SV1642: $i,SV1264: $i,SV759: $i,SV225: $i] :
( ( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV759 @ SV225 @ SV1264 @ SV1642 ) @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
| ~ ( c_in @ ( c_Pair @ SV225 @ SV1264 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3418,plain,
! [SV1643: $i,SV1265: $i,SV760: $i,SV226: $i] :
( ( ! [SY4806: $i,SY4807: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SY4806 @ SY4807 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SY4807 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
| ~ ( c_lessequals @ SV226 @ SY4806 @ ( tc_fun @ SV1265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3419,plain,
! [SV1644: $i,SV1266: $i,SV761: $i,SV227: $i] :
( ( ! [SY4808: $i] :
( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SV1266 @ ( tc_fun @ SV1644 @ tc_bool ) @ SY4808 ) @ SY4808 @ SV1644 ) @ ( tc_fun @ SY4808 @ SV1644 ) )
| ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SV1266 @ SV227 @ SY4808 @ SV1644 ) ) @ SV1266 @ SV1644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3420,plain,
! [SV1645: $i,SV1267: $i,SV762: $i,SV228: $i] :
( ( ! [SY4809: $i] :
( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SV762 @ ( c_COMBK @ SV1267 @ ( tc_fun @ SV1645 @ tc_bool ) @ SY4809 ) @ SY4809 @ SV1645 ) @ ( tc_fun @ SY4809 @ SV1645 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV762 @ SV1267 @ SV228 @ SY4809 @ SV1645 ) @ SV762 @ SY4809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3421,plain,
! [SV1646: $i,SV1268: $i,SV763: $i,SV229: $i] :
( ( ! [SY4810: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SV1268 @ SV1646 ) @ SY4810 @ ( tc_fun @ SV1646 @ tc_bool ) )
| ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SY4810 @ ( tc_fun @ SV1646 @ tc_bool ) @ SV1268 ) @ SV1268 @ SV1646 ) @ ( tc_fun @ SV1268 @ SV1646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3422,plain,
! [SV1269: $i,SV765: $i,SV231: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3423,plain,
! [SV766: $i,SV232: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV232 @ SV766 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV232 @ SV766 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SV766 @ SV766 ) @ SV232 @ SV766 @ SV766 @ SV766 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SV766 @ SV766 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3424,plain,
! [SV1647: $i,SV1270: $i,SV767: $i,SV233: $i] :
( ( ( c_Wellfounded_Owf @ SV233 @ SV767 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1270 @ SV1647 @ SV233 @ SV767 ) @ SV1647 @ SV767 )
| ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SV1270 @ ( c_COMBK @ SV1647 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3425,plain,
! [SV1648: $i,SV1271: $i,SV768: $i,SV234: $i] :
( ( ( c_Wellfounded_Owf @ SV234 @ SV768 )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1271 @ SV1648 @ SV234 @ SV768 ) @ SV1271 @ SV768 )
| ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SV1271 @ ( c_COMBK @ SV1648 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3426,plain,
! [SV1272: $i,SV769: $i,SV235: $i] :
( ( ( c_Relation_Orefl__on @ SV235 @ SV769 @ SV1272 )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SV769 @ SV1272 ) @ SV235 @ SV1272 )
| ~ ( c_lessequals @ SV769 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SV1272 @ tc_bool ) @ SV1272 ) @ SV1272 @ SV1272 ) @ ( tc_fun @ ( tc_prod @ SV1272 @ SV1272 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3427,plain,
! [SV1273: $i,SV770: $i,SV236: $i] :
( ( ( c_Relation_Orefl__on @ SV236 @ SV770 @ SV1273 )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SV770 @ SV1273 ) @ SV236 @ SV1273 )
| ~ ( c_lessequals @ SV770 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SV1273 @ tc_bool ) @ SV1273 ) @ SV1273 @ SV1273 ) @ ( tc_fun @ ( tc_prod @ SV1273 @ SV1273 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3428,plain,
! [SV1649: $i,SV1274: $i,SV771: $i,SV237: $i] :
( ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
| ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
| ~ ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3429,plain,
! [SV1275: $i,SV772: $i,SV238: $i] :
( ( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SV1275 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ SV1275 @ SV1275 ) @ SV772 @ ( tc_prod @ SV1275 @ SV1275 ) )
| ~ ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SV1275 @ tc_bool ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ ( tc_prod @ SV1275 @ SV1275 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3430,plain,
! [SV1276: $i,SV773: $i,SV239: $i] :
( ( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SV1276 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ SV1276 @ SV1276 ) @ SV773 @ ( tc_prod @ SV1276 @ SV1276 ) )
| ~ ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SV1276 @ tc_bool ) @ SV1276 ) @ SV1276 @ SV1276 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1276 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3431,plain,
! [SV1650: $i,SV1277: $i,SV774: $i,SV240: $i] :
( ( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Otrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
| ( SV240 = SV774 )
| ~ ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Ortrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3432,plain,
! [SV1651: $i,SV1278: $i,SV775: $i,SV241: $i] :
( ( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Otrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
| ( SV241 = SV775 )
| ~ ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Ortrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3433,plain,
! [SV1652: $i,SV1279: $i,SV776: $i,SV242: $i] :
( ( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Ortrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
| ~ ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Otrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
| ( SV242 = SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3434,plain,
! [SV1653: $i,SV1280: $i,SV777: $i,SV243: $i] :
( ( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SV1280 @ SV1653 ) @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
| ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
| ~ ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SV1653 ) @ ( tc_prod @ SV1653 @ SV1653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3435,plain,
! [SV1654: $i,SV1281: $i,SV778: $i,SV244: $i] :
( ( ! [SY4811: $i] :
( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SY4811 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SY4811 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3436,plain,
! [SV1655: $i,SV1282: $i,SV779: $i,SV245: $i] :
( ( ! [SY4812: $i] :
( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SY4812 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SY4812 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3437,plain,
! [SV1283: $i,SV780: $i,SV246: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) @ SV1283 @ ( tc_fun @ SV780 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV1283 @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2963]) ).
thf(3438,plain,
! [SV1284: $i,SV783: $i,SV249: $i] :
( ( ( c_in @ SV249 @ ( c_Complete__Lattice_OInf__class_OInf @ SV783 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true )
| ( ( ~ ( c_in @ SV249 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV249 @ SV783 @ SV1284 ) @ SV1284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2964]) ).
thf(3439,plain,
! [SV1656: $i,SV1285: $i,SV784: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SV1285 @ SV1656 ) @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 )
| ~ ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3440,plain,
! [SV1286: $i,SV785: $i,SV251: $i] :
( ( ( c_in @ SV251 @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV785 @ SV251 @ SV1286 ) @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3441,plain,
! [SV1287: $i,SV786: $i,SV252: $i] :
( ( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SV1287 ) ) )
| ~ ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SV1287 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3442,plain,
! [SV1657: $i,SV1288: $i,SV787: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
| ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SV1657 ) ) )
| ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SV1657 ) @ SV1657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3443,plain,
! [SV1289: $i,SV788: $i,SV254: $i] :
( ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV254 @ SV788 @ SV1289 ) @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 ) )
= $true )
| ( ( c_in @ SV788 @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3444,plain,
! [SV1658: $i,SV1290: $i,SV789: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SV1290 @ SV1658 ) @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 )
| ~ ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3445,plain,
! [SV1291: $i,SV790: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SV1291 ) ) )
| ~ ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SV1291 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3446,plain,
! [SV1659: $i,SV1292: $i,SV791: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SV1659 ) ) )
| ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SV1659 ) @ SV1659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3447,plain,
! [SV1293: $i,SV792: $i,SV258: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SV1293 @ SV258 )
| ~ ( c_in @ SV1293 @ SV792 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3448,plain,
! [SV1294: $i,SV793: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ ( c_Complete__Lattice_OSup__class_OSup @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) ) @ ( tc_fun @ SV1294 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV259 @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3449,plain,
! [SV1660: $i,SV1295: $i,SV794: $i,SV260: $i] :
( ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
| ~ ( c_lessequals @ SV1660 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) )
| ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV1660 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3450,plain,
! [SV1661: $i,SV1296: $i,SV795: $i,SV261: $i] :
( ( ! [SY4813: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SV1296 @ SV1661 @ SY4813 ) @ SV261 @ SV1661 )
| ~ ( c_in @ SV795 @ ( c_Relation_OImage @ SV1296 @ SV261 @ SV1661 @ SY4813 ) @ SY4813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3451,plain,
! [SV1662: $i,SV1297: $i,SV796: $i,SV262: $i] :
( ( ! [SY4814: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SV1297 @ SV1662 @ SY4814 ) @ SV262 @ SV1662 )
| ~ ( c_in @ SV796 @ ( c_Relation_OImage @ SV1297 @ SV262 @ SV1662 @ SY4814 ) @ SY4814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3452,plain,
! [SV1663: $i,SV1298: $i,SV797: $i,SV263: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
| ~ ( c_in @ SV1663 @ SV263 @ SV1298 )
| ~ ( c_Wellfounded_Owf @ SV797 @ SV1298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3453,plain,
! [SV1664: $i,SV1299: $i,SV798: $i,SV264: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
| ~ ( c_in @ SV1664 @ SV264 @ SV1299 )
| ~ ( c_Wellfounded_Owf @ SV798 @ SV1299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3454,plain,
! [SV1300: $i,SV799: $i,SV265: $i] :
( ( ( c_in @ SV265 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV265 @ SV799 @ SV1300 ) @ SV1300 )
= $true )
| ( ( ~ ( c_in @ SV265 @ ( c_Complete__Lattice_OSup__class_OSup @ SV799 @ ( tc_fun @ SV1300 @ tc_bool ) ) @ SV1300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3455,plain,
! [SV1301: $i,SV800: $i,SV266: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV266 ) )
= $true )
| ( ( ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1301 @ SV266 ) @ SV266 )
| ~ ( c_in @ SV800 @ SV1301 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3456,plain,
! [SV1665: $i,SV1302: $i,SV801: $i,SV267: $i] :
( ( ! [SY4815: $i] :
( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SY4815 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SY4815 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3457,plain,
! [SV1666: $i,SV1303: $i,SV802: $i,SV268: $i] :
( ( ! [SY4816: $i] :
( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SY4816 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SY4816 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3458,plain,
! [SV1667: $i,SV1304: $i,SV803: $i,SV269: $i] :
( ( ! [SY4817: $i] :
( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SY4817 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SY4817 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3459,plain,
! [SV1668: $i,SV1307: $i,SV806: $i,SV272: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SV806 @ SV1307 @ SV1668 ) @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) )
| ~ ( c_in @ ( c_Pair @ SV806 @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3460,plain,
! [SV1308: $i,SV807: $i,SV273: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV273 ) )
= $true )
| ( ( ( c_lessequals @ SV807 @ SV1308 @ SV273 )
| ( c_lessequals @ SV1308 @ SV807 @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(3461,plain,
! [SV1309: $i,SV809: $i,SV275: $i] :
( ( ( c_lessequals @ SV275 @ ( c_Product__Type_OSigma @ SV809 @ ( c_COMBK @ SV809 @ ( tc_fun @ SV1309 @ tc_bool ) @ SV1309 ) @ SV1309 @ SV1309 ) @ ( tc_fun @ ( tc_prod @ SV1309 @ SV1309 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV809 @ SV275 @ SV1309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3462,plain,
! [SV1669: $i,SV1310: $i,SV811: $i,SV277: $i] :
( ( ! [SY4818: $i,SY4819: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SY4818 @ SY4819 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
| ~ ( c_lessequals @ SV811 @ SY4819 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SY4818 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3463,plain,
! [SV1670: $i,SV1311: $i,SV812: $i,SV278: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SV812 @ SV1311 ) @ ( c_Relation_ODomain @ SV1670 @ SV812 @ SV1311 ) @ ( tc_fun @ SV812 @ tc_bool ) )
| ~ ( c_lessequals @ SV278 @ SV1670 @ ( tc_fun @ ( tc_prod @ SV812 @ SV1311 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3464,plain,
! [SV1671: $i,SV1312: $i,SV813: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
| ~ ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SV1671 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3465,plain,
! [SV814: $i,SV280: $i] :
( ( ( class_Orderings_Opreorder @ SV280 )
= $false )
| ( ( c_lessequals @ SV814 @ SV814 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3466,plain,
! [SV815: $i,SV281: $i] :
( ( ( class_Orderings_Oorder @ SV281 )
= $false )
| ( ( c_lessequals @ SV815 @ SV815 @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3467,plain,
! [SV1313: $i,SV816: $i,SV282: $i] :
( ( ( c_Wellfounded_Owf @ SV282 @ SV816 )
= $true )
| ( ( ~ ( c_lessequals @ SV282 @ SV1313 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1313 @ SV816 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3468,plain,
! [SV1672: $i,SV1314: $i,SV817: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
| ~ ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) )
| ~ ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SV1672 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3469,plain,
! [SV1673: $i,SV1315: $i,SV818: $i,SV284: $i] :
( ( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
| ~ ( c_lessequals @ SV1673 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
| ~ ( c_lessequals @ SV284 @ SV1673 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3470,plain,
! [SV1674: $i,SV1316: $i,SV821: $i,SV287: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV287 )
| ( c_lessequals @ SV821 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3471,plain,
! [SV1675: $i,SV1317: $i,SV822: $i,SV288: $i] :
( ( ~ ( class_Orderings_Oorder @ SV288 )
| ( c_lessequals @ SV822 @ SV1317 @ SV288 )
| ~ ( c_lessequals @ SV822 @ SV1675 @ SV288 )
| ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3472,plain,
! [SV1318: $i,SV824: $i,SV290: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV290 @ SV824 ) @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV290 @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3473,plain,
! [SV1319: $i,SV825: $i,SV291: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV291 @ SV825 ) @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV291 @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3474,plain,
! [SV1320: $i,SV826: $i,SV292: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV292 ) )
= $true )
| ( ( ( SV826 = SV1320 )
| ~ ( c_lessequals @ SV826 @ SV1320 @ SV292 )
| ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3475,plain,
! [SV1321: $i,SV827: $i,SV293: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV293 ) )
= $true )
| ( ( ( SV827 = SV1321 )
| ~ ( c_lessequals @ SV1321 @ SV827 @ SV293 )
| ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3003]) ).
thf(3476,plain,
! [SV1322: $i,SV828: $i,SV294: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV294 ) )
= $true )
| ( ( ( SV828 = SV1322 )
| ~ ( c_lessequals @ SV1322 @ SV828 @ SV294 )
| ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3477,plain,
! [SV1323: $i,SV829: $i,SV295: $i] :
( ( ( SV295 = SV829 )
= $true )
| ( ( ~ ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SV1323 @ tc_bool ) )
| ~ ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3478,plain,
! [SV1324: $i,SV830: $i,SV296: $i] :
( ( ( SV296 = SV830 )
= $true )
| ( ( ~ ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SV1324 @ tc_bool ) )
| ~ ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3479,plain,
! [SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ! [SY4820: $i,SY4821: $i,SY4822: $i,SY4823: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SY4820 ) @ ( c_Product__Type_OSigma @ SY4821 @ ( c_COMBK @ SY4822 @ ( tc_fun @ SY4820 @ tc_bool ) @ SV1325 ) @ SV1325 @ SY4820 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SY4820 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY4823 @ ( c_COMBK @ SY4822 @ ( tc_fun @ SY4820 @ tc_bool ) @ SV1676 ) @ SV1676 @ SY4820 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SY4820 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SY4821 @ ( c_COMBK @ SY4823 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3480,plain,
! [SV1326: $i,SV833: $i,SV299: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV299 @ SV833 ) @ ( c_Transitive__Closure_Ortrancl @ SV1326 @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV299 @ SV1326 @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3481,plain,
! [SV1677: $i,SV1327: $i,SV836: $i,SV302: $i] :
( ( ! [SY4824: $i,SY4825: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SY4824 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SY4824 @ ( tc_fun @ SV1677 @ tc_bool ) )
| ~ ( c_in @ SY4825 @ SV836 @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3482,plain,
! [SV1678: $i,SV1328: $i,SV837: $i,SV303: $i] :
( ( ! [SY4826: $i,SY4827: $i] :
( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SY4826 @ tc_bool ) @ SV1328 ) @ SV1328 @ SY4826 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SY4826 @ tc_bool ) @ SV1328 ) @ SV1328 @ SY4826 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SY4826 ) @ tc_bool ) )
| ~ ( c_in @ SY4827 @ SV1678 @ SY4826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3483,plain,
! [SV1329: $i,SV839: $i,SV305: $i] :
( ( ( c_lessequals @ SV305 @ ( c_Product__Type_OSigma @ SV839 @ ( c_COMBK @ SV839 @ ( tc_fun @ SV1329 @ tc_bool ) @ SV1329 ) @ SV1329 @ SV1329 ) @ ( tc_fun @ ( tc_prod @ SV1329 @ SV1329 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV839 @ SV305 @ SV1329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3484,plain,
! [SV1679: $i,SV1330: $i,SV840: $i,SV306: $i] :
( ( ! [SY4828: $i,SY4829: $i,SY4830: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SY4828 ) @ ( c_Relation_Orel__comp @ SY4829 @ SY4830 @ SV1330 @ SV1679 @ SY4828 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SY4828 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SY4830 @ ( tc_fun @ ( tc_prod @ SV1679 @ SY4828 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SY4829 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3485,plain,
! [SV1680: $i,SV1331: $i,SV841: $i,SV307: $i] :
( ( ( hAPP @ ( c_COMBK @ SV307 @ SV841 @ SV1331 ) @ SV1680 )
= SV307 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3486,plain,
! [SV1681: $i,SV1332: $i,SV842: $i,SV308: $i] :
( ( ! [SY4831: $i,SY4832: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SV1681 ) @ SY4831 @ ( tc_fun @ SV1681 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SY4832 @ ( c_COMBK @ SY4831 @ ( tc_fun @ SV1681 @ tc_bool ) @ SV1332 ) @ SV1332 @ SV1681 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1681 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3487,plain,
! [SV843: $i,SV309: $i] :
( ( ( c_Relation_Osym @ SV309 @ SV843 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV309 @ SV843 ) @ SV843 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3488,plain,
! [SV1333: $i,SV844: $i,SV310: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1333 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3489,plain,
! [SV1682: $i,SV1334: $i,SV845: $i,SV311: $i] :
( ( ! [SY4833: $i] :
( ( c_in @ SV311 @ SV845 @ SV1334 )
| ( SV311 = SV1682 )
| ~ ( c_lessequals @ SY4833 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SY4833 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3490,plain,
! [SV1335: $i,SV846: $i,SV312: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV312 @ SV846 ) @ ( c_Wellfounded_Oacc @ SV1335 @ SV846 ) @ ( tc_fun @ SV846 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1335 @ SV312 @ ( tc_fun @ ( tc_prod @ SV846 @ SV846 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3491,plain,
! [SV1683: $i,SV1336: $i,SV847: $i,SV313: $i] :
( ( ! [SY4834: $i] :
( ~ ( class_HOL_Oord @ SV313 )
| ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SY4834 @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3492,plain,
! [SV1684: $i,SV1337: $i,SV848: $i,SV314: $i] :
( ( ( c_in @ SV314 @ SV848 @ SV1337 )
| ~ ( c_in @ SV314 @ SV1684 @ SV1337 )
| ~ ( c_lessequals @ SV1684 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3493,plain,
! [SV1685: $i,SV1338: $i,SV849: $i,SV315: $i] :
( ( ( c_in @ SV315 @ SV849 @ SV1338 )
| ~ ( c_lessequals @ SV1685 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) )
| ~ ( c_in @ SV315 @ SV1685 @ SV1338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3494,plain,
! [SV1686: $i,SV1339: $i,SV850: $i,SV316: $i] :
( ( ( c_in @ SV316 @ SV850 @ SV1339 )
| ~ ( c_in @ SV316 @ SV1686 @ SV1339 )
| ~ ( c_lessequals @ SV1686 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3495,plain,
! [SV1687: $i,SV1340: $i,SV851: $i,SV317: $i] :
( ( ( c_in @ SV317 @ SV851 @ SV1340 )
| ~ ( c_in @ SV317 @ SV1687 @ SV1340 )
| ~ ( c_lessequals @ SV1687 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3496,plain,
! [SV1341: $i,SV852: $i,SV318: $i] :
( ( ( c_in @ SV318 @ ( c_Transitive__Closure_Ortrancl @ SV852 @ SV1341 ) @ ( tc_prod @ SV1341 @ SV1341 ) )
= $true )
| ( ( ~ ( c_in @ SV318 @ SV852 @ ( tc_prod @ SV1341 @ SV1341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3497,plain,
! [SV1688: $i,SV1342: $i,SV853: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Ortrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) )
| ~ ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Otrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3498,plain,
! [SV1689: $i,SV1343: $i,SV854: $i,SV320: $i] :
( ( ! [SY4835: $i] :
( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SY4835 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SY4835 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3499,plain,
! [SV1690: $i,SV1344: $i,SV855: $i,SV321: $i] :
( ( ! [SY4836: $i] :
( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SY4836 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SY4836 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3500,plain,
! [SV1691: $i,SV1345: $i,SV856: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV856 @ SV322 @ SV1345 @ SV1691 ) @ SV1691 @ SV1691 ) @ SV856 @ ( tc_prod @ SV1691 @ SV1691 ) )
| ~ ( c_in @ ( c_Pair @ SV322 @ SV1345 @ SV1691 @ SV1691 ) @ ( c_Transitive__Closure_Otrancl @ SV856 @ SV1691 ) @ ( tc_prod @ SV1691 @ SV1691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3501,plain,
! [SV1692: $i,SV1346: $i,SV857: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SV1346 @ SV1692 ) @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) )
| ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ SV323 @ ( tc_prod @ SV1692 @ SV1692 ) )
| ~ ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3502,plain,
! [SV1347: $i,SV858: $i,SV324: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV324 @ SV324 @ SV858 @ SV858 ) @ SV1347 @ ( tc_prod @ SV858 @ SV858 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ SV858 @ SV858 ) @ ( c_Transitive__Closure_Otrancl @ SV1347 @ SV858 ) @ ( tc_prod @ SV858 @ SV858 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3503,plain,
! [SV1348: $i,SV859: $i,SV325: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV325 @ SV859 @ SV1348 ) @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV325 @ ( c_Complete__Lattice_OSup__class_OSup @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SV1348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3504,plain,
! [SV1693: $i,SV1349: $i,SV860: $i,SV326: $i] :
( ( ( c_in @ ( c_Pair @ SV326 @ SV860 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1693 @ SV1349 @ SV1349 ) @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) )
| ~ ( c_in @ ( c_Pair @ SV860 @ SV326 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3505,plain,
! [SV1694: $i,SV1350: $i,SV861: $i,SV327: $i] :
( ( ( c_in @ ( c_Pair @ SV327 @ SV861 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) )
| ~ ( c_in @ ( c_Pair @ SV861 @ SV327 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1694 @ SV1350 @ SV1350 ) @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3506,plain,
! [SV1695: $i,SV1351: $i,SV862: $i,SV328: $i] :
( ( ! [SY4837: $i,SY4838: $i,SY4839: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SY4837 @ SY4838 @ SY4839 ) @ SY4837 @ SY4839 ) @ SV1351 @ ( tc_prod @ SY4837 @ SY4839 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SY4837 @ SY4838 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SY4837 @ SY4839 @ SY4838 ) @ ( tc_prod @ SY4837 @ SY4838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3507,plain,
! [SV1696: $i,SV1352: $i,SV863: $i,SV329: $i] :
( ( ! [SY4840: $i,SY4841: $i,SY4842: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SY4840 @ SY4841 @ SY4842 ) @ SV863 @ SY4842 @ SY4841 ) @ SV1696 @ ( tc_prod @ SY4842 @ SY4841 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SY4840 @ SY4841 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SY4840 @ SY4842 @ SY4841 ) @ ( tc_prod @ SY4840 @ SY4841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3508,plain,
! [SV1697: $i,SV1353: $i,SV864: $i,SV330: $i] :
( ( ! [SY4843: $i] :
( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SV1353 @ SV1697 @ SY4843 ) @ ( tc_fun @ SV1697 @ SY4843 ) )
| ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SY4843 ) ) @ ( hAPP @ SV1353 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SY4843 ) ) @ SY4843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3509,plain,
! [SV1698: $i,SV1354: $i,SV865: $i,SV331: $i] :
( ( ! [SY4844: $i,SY4845: $i] :
( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
| ~ ( c_in @ SV865 @ SY4844 @ SY4845 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SY4844 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SY4845 ) @ SY4845 @ SV1698 ) @ ( tc_fun @ SY4845 @ SV1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3510,plain,
! [SV1699: $i,SV1355: $i,SV866: $i,SV332: $i] :
( ( ! [SY4846: $i] :
( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SV1355 @ SV1699 @ SY4846 ) @ ( tc_fun @ SV1699 @ SY4846 ) )
| ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SY4846 ) ) @ ( hAPP @ SV1355 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SY4846 ) ) @ SY4846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3511,plain,
! [SV1700: $i,SV1356: $i,SV867: $i,SV333: $i] :
( ( ! [SY4847: $i] :
( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV867 @ SV1356 @ SV1700 @ SY4847 ) @ ( tc_fun @ SV1700 @ SY4847 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV867 @ SV1356 @ SV333 @ SV1700 @ SY4847 ) @ SV867 @ SV1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3512,plain,
! [SV1701: $i,SV1357: $i,SV868: $i,SV334: $i] :
( ( ! [SY4848: $i] :
( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SV868 @ SV1357 @ SV1701 @ SY4848 ) @ ( tc_fun @ SV1701 @ SY4848 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV868 @ SV1357 @ SV334 @ SV1701 @ SY4848 ) @ SV868 @ SV1701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3513,plain,
! [SV1702: $i,SV1358: $i,SV869: $i,SV335: $i] :
( ( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SV869 @ SV1358 @ SV1702 ) @ SV335 @ SV1702 )
| ~ ( c_in @ SV869 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SV1358 @ SV1702 ) @ ( tc_fun @ SV1702 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3514,plain,
! [SV870: $i,SV336: $i] :
( ( ( c_in @ SV336 @ ( c_Relation_OId @ SV870 ) @ ( tc_prod @ SV870 @ SV870 ) )
= $false )
| ( ( SV336
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV336 @ SV870 ) @ SV870 @ SV870 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3042]) ).
thf(3515,plain,
! [SV1359: $i,SV871: $i,SV337: $i] :
( ( ( c_in @ SV337 @ ( c_Complete__Lattice_OInf__class_OInf @ SV871 @ ( tc_fun @ SV1359 @ tc_bool ) ) @ SV1359 )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV337 @ SV871 @ SV1359 ) @ SV871 @ ( tc_fun @ SV1359 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3516,plain,
! [SV872: $i,SV338: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV338 @ SV872 ) @ ( c_Wellfounded_Oacc @ SV338 @ SV872 ) @ SV872 )
= $false )
| ( ( c_Wellfounded_Owf @ SV338 @ SV872 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3517,plain,
! [SV873: $i,SV339: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV339 @ SV873 ) @ ( c_Wellfounded_Oacc @ SV339 @ SV873 ) @ SV873 )
= $false )
| ( ( c_Wellfounded_Owf @ SV339 @ SV873 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3518,plain,
! [SV1360: $i,SV874: $i,SV340: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV340 @ SV874 @ SV1360 ) @ SV340 @ SV1360 )
= $true )
| ( ( ~ ( c_in @ SV874 @ ( c_Relation_OId__on @ SV340 @ SV1360 ) @ ( tc_prod @ SV1360 @ SV1360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3046]) ).
thf(3519,plain,
! [SV1361: $i,SV875: $i,SV341: $i] :
( ( ( SV341
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ SV1361 @ SV1361 ) )
= $true )
| ( ( ~ ( c_in @ SV341 @ ( c_Relation_OId__on @ SV875 @ SV1361 ) @ ( tc_prod @ SV1361 @ SV1361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3520,plain,
! [SV1703: $i,SV1362: $i,SV876: $i,SV342: $i] :
( ( ! [SY4849: $i,SY4850: $i] :
( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SV1362 @ SV1703 @ SY4849 )
= ( c_Recdef_Ocut @ SY4850 @ SV876 @ SV1362 @ SV1703 @ SY4849 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SY4850 @ SV876 @ SV1362 @ SV1703 @ SY4849 ) @ SV1362 @ SV1703 @ SV1703 ) @ SV876 @ ( tc_prod @ SV1703 @ SV1703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3521,plain,
! [SV1363: $i,SV877: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV343 @ SV877 @ SV877 ) @ SV343 @ SV877 @ SV877 @ SV877 ) @ ( tc_fun @ ( tc_prod @ SV877 @ SV877 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1363 @ SV343 @ SV877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3522,plain,
! [SV878: $i,SV344: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV344 @ SV878 ) @ SV878 @ SV878 ) @ SV344 @ ( tc_prod @ SV878 @ SV878 ) )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV344 @ SV878 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3523,plain,
! [SV1704: $i,SV1364: $i,SV879: $i,SV345: $i] :
( ( ! [SY4851: $i] :
( ~ ( c_in @ SV345 @ SV879 @ SV1364 )
| ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_in @ SY4851 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3524,plain,
! [SV1705: $i,SV1365: $i,SV880: $i,SV346: $i] :
( ( ! [SY4852: $i] :
( ~ ( c_in @ SV346 @ SV880 @ SV1365 )
| ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
| ~ ( c_in @ SY4852 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3525,plain,
! [SV1706: $i,SV1366: $i,SV881: $i,SV347: $i] :
( ( ! [SY4853: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SV1366 @ SV1706 @ SY4853 ) @ SV881 @ SV1706 @ SY4853 ) @ SV1366 @ ( tc_prod @ SV1706 @ SY4853 ) )
| ~ ( c_in @ SV881 @ ( c_Relation_OImage @ SV1366 @ SV347 @ SV1706 @ SY4853 ) @ SY4853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3526,plain,
! [SV1707: $i,SV1367: $i,SV882: $i,SV348: $i] :
( ( ! [SY4854: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SV1367 @ SV1707 @ SY4854 ) @ SV882 @ SV1707 @ SY4854 ) @ SV1367 @ ( tc_prod @ SV1707 @ SY4854 ) )
| ~ ( c_in @ SV882 @ ( c_Relation_OImage @ SV1367 @ SV348 @ SV1707 @ SY4854 ) @ SY4854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3527,plain,
! [SV1708: $i,SV1368: $i,SV883: $i,SV349: $i] :
( ( ( SV349 = SV883 )
| ~ ( c_in @ ( c_Pair @ SV349 @ SV883 @ SV1368 @ SV1368 ) @ ( c_Transitive__Closure_Ortrancl @ SV1708 @ SV1368 ) @ ( tc_prod @ SV1368 @ SV1368 ) )
| ( c_in @ SV349 @ ( c_Relation_ODomain @ SV1708 @ SV1368 @ SV1368 ) @ SV1368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3528,plain,
! [SV1709: $i,SV1369: $i,SV884: $i,SV350: $i] :
( ( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SV884 @ SV1369 @ SV1709 ) @ SV1369 @ SV1709 ) @ SV884 @ ( tc_prod @ SV1369 @ SV1709 ) )
| ~ ( c_in @ SV350 @ ( c_Relation_ODomain @ SV884 @ SV1369 @ SV1709 ) @ SV1369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3529,plain,
! [SV1710: $i,SV1370: $i,SV885: $i,SV351: $i] :
( ( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SV885 @ SV1370 @ SV1710 ) @ SV1370 @ SV1710 ) @ SV885 @ ( tc_prod @ SV1370 @ SV1710 ) )
| ~ ( c_in @ SV351 @ ( c_Relation_ODomain @ SV885 @ SV1370 @ SV1710 ) @ SV1370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3530,plain,
! [SV1371: $i,SV886: $i,SV352: $i] :
( ( ( c_in @ SV352 @ ( c_Relation_ODomain @ SV886 @ SV1371 @ SV1371 ) @ SV1371 )
= $true )
| ( ( c_in @ ( c_Pair @ SV352 @ SV352 @ SV1371 @ SV1371 ) @ ( c_Transitive__Closure_Ortrancl @ SV886 @ SV1371 ) @ ( tc_prod @ SV1371 @ SV1371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3531,plain,
! [SV1711: $i,SV1372: $i,SV887: $i,SV353: $i] :
( ( ! [SY4855: $i] :
( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
| ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
| ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SY4855 ) @ SY4855 @ SY4855 ) @ SV1711 @ ( tc_prod @ SY4855 @ SY4855 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SY4855 ) @ SY4855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3532,plain,
! [SV1712: $i,SV1373: $i,SV888: $i,SV354: $i] :
( ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
| ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3533,plain,
! [SV1713: $i,SV1374: $i,SV889: $i,SV355: $i] :
( ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
| ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
| ~ ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3534,plain,
! [SV1714: $i,SV1375: $i,SV890: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
| ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3535,plain,
! [SV1715: $i,SV1376: $i,SV891: $i,SV357: $i] :
( ( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
| ~ ( c_in @ ( c_Pair @ SV357 @ SV1715 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
| ~ ( c_in @ SV1715 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3536,plain,
! [SV1716: $i,SV1377: $i,SV892: $i,SV358: $i] :
( ( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
| ~ ( c_in @ SV1716 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
| ~ ( c_in @ ( c_Pair @ SV358 @ SV1716 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3537,plain,
! [SV1378: $i,SV893: $i,SV359: $i] :
( ( ( c_in @ SV359 @ ( c_Wellfounded_Oacc @ SV893 @ SV1378 ) @ SV1378 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV893 @ SV359 @ SV1378 ) @ SV359 @ SV1378 @ SV1378 ) @ SV893 @ ( tc_prod @ SV1378 @ SV1378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3538,plain,
! [SV1717: $i,SV1379: $i,SV894: $i,SV360: $i] :
( ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
| ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
| ~ ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3539,plain,
! [SV1718: $i,SV1380: $i,SV895: $i,SV361: $i] :
( ( ! [SY4856: $i] :
( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
| ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
| ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SY4856 ) @ SY4856 @ SY4856 ) @ SV1718 @ ( tc_prod @ SY4856 @ SY4856 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SY4856 ) @ SY4856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3540,plain,
! [SV1381: $i,SV896: $i,SV362: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV362 @ SV896 @ SV1381 ) @ SV896 @ SV1381 @ SV1381 ) @ SV362 @ ( tc_prod @ SV1381 @ SV1381 ) )
= $true )
| ( ( c_in @ SV896 @ ( c_Wellfounded_Oacc @ SV362 @ SV1381 ) @ SV1381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3541,plain,
! [SV1719: $i,SV1382: $i,SV897: $i,SV363: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SV897 @ SV1382 @ SV1719 ) @ SV363 @ SV1719 @ SV1382 ) @ SV897 @ ( tc_prod @ SV1719 @ SV1382 ) )
| ~ ( c_in @ SV363 @ ( c_Relation_ORange @ SV897 @ SV1719 @ SV1382 ) @ SV1382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3542,plain,
! [SV1720: $i,SV1383: $i,SV898: $i,SV364: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SV898 @ SV1383 @ SV1720 ) @ SV364 @ SV1720 @ SV1383 ) @ SV898 @ ( tc_prod @ SV1720 @ SV1383 ) )
| ~ ( c_in @ SV364 @ ( c_Relation_ORange @ SV898 @ SV1720 @ SV1383 ) @ SV1383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3543,plain,
! [SV1721: $i,SV1384: $i,SV899: $i,SV365: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_Wellfounded_Owf @ SV1721 @ SV1384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3544,plain,
! [SV1722: $i,SV1385: $i,SV900: $i,SV366: $i] :
( ( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1722 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
| ~ ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ SV1722 @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3545,plain,
! [SV1723: $i,SV1386: $i,SV901: $i,SV367: $i] :
( ( ! [SY4857: $i] :
( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SY4857 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SY4857 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3546,plain,
! [SV1724: $i,SV1387: $i,SV902: $i,SV368: $i] :
( ( ! [SY4858: $i] :
( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SY4858 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SY4858 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3547,plain,
! [SV1725: $i,SV1388: $i,SV903: $i,SV369: $i] :
( ( ! [SY4859: $i] :
( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SV1388 @ SV1725 ) @ SY4859 @ ( tc_prod @ SV1388 @ SV1725 ) )
| ~ ( c_in @ ( c_Pair @ SV903 @ SV369 @ SV1725 @ SV1388 ) @ ( c_Relation_Oconverse @ SY4859 @ SV1388 @ SV1725 ) @ ( tc_prod @ SV1725 @ SV1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3548,plain,
! [SV1726: $i,SV1389: $i,SV904: $i,SV370: $i] :
( ( ! [SY4860: $i] :
( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SV1389 @ SV1726 ) @ ( c_Relation_Oconverse @ SY4860 @ SV1726 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1726 ) )
| ~ ( c_in @ ( c_Pair @ SV904 @ SV370 @ SV1726 @ SV1389 ) @ SY4860 @ ( tc_prod @ SV1726 @ SV1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3549,plain,
! [SV1727: $i,SV1390: $i,SV905: $i,SV371: $i] :
( ( ! [SY4861: $i] :
( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SV1390 @ SV1727 ) @ ( c_Relation_Oconverse @ SY4861 @ SV1727 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1727 ) )
| ~ ( c_in @ ( c_Pair @ SV905 @ SV371 @ SV1727 @ SV1390 ) @ SY4861 @ ( tc_prod @ SV1727 @ SV1390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3550,plain,
! [SV1728: $i,SV1391: $i,SV906: $i,SV372: $i] :
( ( ! [SY4862: $i,SY4863: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SV1728 @ SY4862 ) @ SY4863 )
= ( hAPP @ SV372 @ SY4863 ) )
| ~ ( c_in @ ( c_Pair @ SY4863 @ SV1391 @ SV1728 @ SV1728 ) @ SV906 @ ( tc_prod @ SV1728 @ SV1728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3551,plain,
! [SV1729: $i,SV1392: $i,SV907: $i,SV373: $i] :
( ( ! [SY4864: $i,SY4865: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SV1729 @ SY4864 ) @ SY4865 )
= ( hAPP @ SV373 @ SY4865 ) )
| ~ ( c_in @ ( c_Pair @ SY4865 @ SV1392 @ SV1729 @ SV1729 ) @ SV907 @ ( tc_prod @ SV1729 @ SV1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3552,plain,
! [SV1393: $i,SV908: $i,SV374: $i] :
( ( ( c_in @ SV374 @ ( c_Transitive__Closure_Otrancl @ SV908 @ SV1393 ) @ ( tc_prod @ SV1393 @ SV1393 ) )
= $true )
| ( ( ~ ( c_in @ SV374 @ SV908 @ ( tc_prod @ SV1393 @ SV1393 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3553,plain,
! [SV1730: $i,SV1394: $i,SV909: $i,SV375: $i] :
( ( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1730 @ SV1394 ) @ SV1394 @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) )
| ~ ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1730 @ SV1394 @ SV1394 ) @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3554,plain,
! [SV1731: $i,SV1395: $i,SV910: $i,SV376: $i] :
( ( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1731 @ SV1395 @ SV1395 ) @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) )
| ~ ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1731 @ SV1395 ) @ SV1395 @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3555,plain,
! [SV1396: $i,SV911: $i,SV377: $i] :
( ( ( c_in @ SV377 @ ( c_Wellfounded_Oacc @ SV911 @ SV1396 ) @ SV1396 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV911 @ SV1396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3556,plain,
! [SV912: $i,SV378: $i] :
( ( ( c_Relation_Osym @ SV378 @ SV912 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV378 @ SV912 ) @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3557,plain,
! [SV913: $i,SV379: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV379 @ SV913 @ SV913 ) @ SV913 )
= $false )
| ( ( c_Relation_Osym @ SV379 @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3558,plain,
! [SV914: $i,SV380: $i] :
( ( ( c_Relation_Osym @ SV380 @ SV914 )
= $false )
| ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV380 @ SV914 @ SV914 ) @ SV914 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3559,plain,
! [SV918: $i,SV385: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV385 @ SV918 @ SV918 ) @ SV918 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV385 @ SV918 ) @ SV918 @ SV918 ) @ SV918 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3560,plain,
! [SV1399: $i,SV919: $i,SV386: $i] :
( ( ( c_Relation_Orefl__on @ SV386 @ SV919 @ SV1399 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV386 @ ( c_Relation_Oconverse @ SV919 @ SV1399 @ SV1399 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3561,plain,
! [SV1400: $i,SV920: $i,SV387: $i] :
( ( ( c_Relation_Orefl__on @ SV387 @ ( c_Relation_Oconverse @ SV920 @ SV1400 @ SV1400 ) @ SV1400 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV387 @ SV920 @ SV1400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3562,plain,
! [SV921: $i,SV388: $i] :
( ( ( c_Wellfounded_Owf @ SV388 @ SV921 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV388 @ SV388 @ SV921 @ SV921 @ SV921 ) @ SV921 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3563,plain,
! [SV922: $i,SV389: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV389 @ SV389 @ SV922 @ SV922 @ SV922 ) @ SV922 )
= $false )
| ( ( c_Wellfounded_Owf @ SV389 @ SV922 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3564,plain,
! [SV925: $i,SV392: $i] :
( ( ( c_Relation_Osym @ SV392 @ SV925 )
= $false )
| ( ( ( c_Relation_Oconverse @ SV392 @ SV925 @ SV925 )
= SV392 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3565,plain,
! [SV1732: $i,SV1401: $i,SV927: $i,SV394: $i] :
( ( ! [SY4866: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV394 @ SV927 @ SV1401 @ SV1732 @ SY4866 ) @ SV1401 @ SY4866 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV927 @ SV1732 @ SY4866 ) @ ( c_Relation_Oconverse @ SV394 @ SV1401 @ SV1732 ) @ SY4866 @ SV1732 @ SV1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3566,plain,
! [SV1733: $i,SV1402: $i,SV930: $i,SV397: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SV930 @ SV1402 @ SV1733 ) @ SV1733 )
| ~ ( c_Wellfounded_Owf @ SV397 @ SV1402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3567,plain,
! [SV1734: $i,SV1403: $i,SV931: $i,SV398: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SV931 @ SV1403 @ SV1734 ) @ SV1734 )
| ~ ( c_Relation_Osym @ SV398 @ SV1403 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3568,plain,
! [SV932: $i,SV400: $i] :
( ( ( c_Wellfounded_Owf @ SV400 @ SV932 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV400 @ SV932 ) @ SV932 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3569,plain,
! [SV1735: $i,SV1404: $i,SV933: $i,SV401: $i] :
( ( ! [SY4867: $i,SY4868: $i,SY4869: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SV1404 @ SV1735 @ SY4867 ) @ SY4868 @ SV1404 @ SY4867 @ SY4869 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SY4868 @ SV1735 @ SY4867 @ SY4869 ) @ SV1404 @ SV1735 @ SY4869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3570,plain,
! [SV1736: $i,SV1405: $i,SV934: $i,SV402: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV402 @ SV934 @ SV1405 @ SV1736 ) @ SV1736 @ SV1736 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV402 @ SV1405 @ SV1405 ) @ SV934 @ SV1405 @ SV1736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3571,plain,
! [SV1408: $i,SV940: $i,SV408: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV408 @ SV940 @ SV940 ) @ SV408 @ SV940 @ SV940 @ SV940 )
= SV408 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1408 @ SV408 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3572,plain,
! [SV1409: $i,SV941: $i,SV409: $i] :
( ( ( c_Relation_Orefl__on @ SV409 @ SV941 @ SV1409 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV409 @ SV941 @ SV1409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3573,plain,
! [SV1410: $i,SV942: $i,SV410: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ SV410 @ SV942 @ SV1410 ) @ ( tc_fun @ SV1410 @ tc_bool ) )
= SV410 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV410 @ SV942 @ SV1410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3574,plain,
! [SV1411: $i,SV943: $i,SV411: $i] :
( ( ( c_Relation_Osym @ SV411 @ SV943 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1411 @ SV411 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3575,plain,
! [SV1414: $i,SV946: $i,SV414: $i] :
( ( ( c_Relation_Ototal__on @ SV414 @ SV946 @ SV1414 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV414 @ ( c_Relation_Oconverse @ SV946 @ SV1414 @ SV1414 ) @ SV1414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3576,plain,
! [SV1415: $i,SV947: $i,SV415: $i] :
( ( ( c_Relation_Ototal__on @ SV415 @ ( c_Relation_Oconverse @ SV947 @ SV1415 @ SV1415 ) @ SV1415 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV415 @ SV947 @ SV1415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3577,plain,
! [SV1737: $i,SV1416: $i,SV948: $i,SV416: $i] :
( ( ( SV416 = SV948 )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV948 @ SV1416 @ SV1416 ) @ ( c_Relation_OId__on @ SV1737 @ SV1416 ) @ ( tc_prod @ SV1416 @ SV1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3578,plain,
! [SV1417: $i,SV949: $i,SV417: $i] :
( ( ( SV417 = SV949 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV417 @ SV949 @ SV1417 @ SV1417 ) @ ( c_Relation_OId @ SV1417 ) @ ( tc_prod @ SV1417 @ SV1417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3579,plain,
! [SV1418: $i,SV950: $i,SV418: $i] :
( ( ( c_in @ ( c_Pair @ SV418 @ SV418 @ SV950 @ SV950 ) @ SV1418 @ ( tc_prod @ SV950 @ SV950 ) )
= $true )
| ( ( ~ ( c_Nitpick_Orefl_H @ SV1418 @ SV950 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3580,plain,
! [SV1419: $i,SV951: $i,SV419: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV419 @ SV419 @ SV951 @ SV951 ) @ SV1419 @ ( tc_prod @ SV951 @ SV951 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1419 @ SV951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3581,plain,
! [SV1738: $i,SV1420: $i,SV952: $i,SV420: $i] :
( ( ! [SY4870: $i,SY4871: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SV1738 @ SY4870 @ SY4871 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY4870 @ SV420 ) @ ( hAPP @ SY4870 @ SV952 ) @ SY4871 @ SY4871 ) @ SV1738 @ ( tc_prod @ SY4871 @ SY4871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3582,plain,
! [SV1739: $i,SV1421: $i,SV953: $i,SV421: $i] :
( ( ! [SY4872: $i,SY4873: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SV1739 @ SV1739 ) @ SY4872 @ ( tc_prod @ SV1739 @ SV1739 ) )
| ~ ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SY4873 @ SY4873 ) @ ( c_Relation_Oinv__image @ SY4872 @ SV421 @ SV1739 @ SY4873 ) @ ( tc_prod @ SY4873 @ SY4873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3583,plain,
! [SV1740: $i,SV1422: $i,SV954: $i,SV422: $i] :
( ( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
| ~ ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
| ~ ( c_Relation_Osym @ SV1740 @ SV1422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3584,plain,
! [SV1741: $i,SV1423: $i,SV955: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
| ~ ( c_Relation_Osym @ SV1741 @ SV1423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3585,plain,
! [SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ! [SY4874: $i,SY4875: $i,SY4876: $i,SY4877: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SY4874 @ SY4875 @ SV1424 @ SY4876 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SY4877 @ SV956 @ SY4876 @ SV1742 ) @ SY4875 @ ( tc_prod @ SY4876 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4877 @ SV1424 @ SY4876 ) @ SY4874 @ ( tc_prod @ SV1424 @ SY4876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3586,plain,
! [SV1743: $i,SV1425: $i,SV957: $i,SV425: $i] :
( ( ! [SY4878: $i] :
( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SY4878 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SY4878 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3587,plain,
! [SV1744: $i,SV1426: $i,SV958: $i,SV426: $i] :
( ( ! [SY4879: $i] :
( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SY4879 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SY4879 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3588,plain,
! [SV1745: $i,SV1427: $i,SV961: $i,SV429: $i] :
( ( ! [SY4880: $i,SY4881: $i] :
( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
| ~ ( c_in @ SV961 @ SY4880 @ SY4881 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SY4880 @ SV1427 @ SY4881 @ SV1745 ) @ ( tc_fun @ SY4881 @ SV1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3589,plain,
! [SV1746: $i,SV1428: $i,SV962: $i,SV430: $i] :
( ( ! [SY4882: $i,SY4883: $i] :
( ~ ( c_in @ SV430 @ SV962 @ SV1428 )
| ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SY4882 @ SV430 ) @ SY4883 )
| ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SY4882 @ SV1428 @ SY4883 ) @ ( tc_fun @ SV1428 @ SY4883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3590,plain,
! [SV1747: $i,SV1429: $i,SV963: $i,SV431: $i] :
( ( ! [SY4884: $i,SY4885: $i,SY4886: $i] :
( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SY4884 @ SY4884 ) @ SY4885 @ ( tc_prod @ SY4884 @ SY4884 ) )
| ~ ( c_in @ SV1747 @ SV963 @ SY4884 )
| ~ ( c_in @ SV1429 @ SV431 @ SY4884 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SY4886 @ SY4885 @ SY4884 ) @ ( tc_fun @ SY4884 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY4886 @ SY4885 @ SY4884 ) @ ( tc_fun @ SY4884 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4886 @ SY4885 @ SY4884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3591,plain,
! [SV1748: $i,SV1430: $i,SV964: $i,SV432: $i] :
( ( ! [SY4887: $i,SY4888: $i] :
( ~ ( c_in @ SV432 @ SV964 @ SV1430 )
| ~ ( c_in @ SV1748 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4887 @ SY4888 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SY4887 @ SY4888 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4887 @ SY4888 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SY4888 @ ( tc_prod @ SV1430 @ SV1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3592,plain,
! [SV1749: $i,SV1431: $i,SV965: $i,SV433: $i] :
( ( ( c_in @ SV433 @ SV965 @ SV1431 )
| ~ ( c_in @ SV965 @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) )
| ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3593,plain,
! [SV1750: $i,SV1432: $i,SV966: $i,SV434: $i] :
( ( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
| ~ ( c_in @ SV434 @ SV1750 @ SV1432 )
| ~ ( c_in @ SV1750 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3594,plain,
! [SV1751: $i,SV1433: $i,SV967: $i,SV435: $i] :
( ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SV1751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV435 = SV967 )
| ( SV435 = SV1751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3595,plain,
! [SV1752: $i,SV1434: $i,SV968: $i,SV436: $i] :
( ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SV1752 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV968 = SV1752 )
| ( SV436 = SV1752 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3596,plain,
! [SV1435: $i,SV970: $i,SV438: $i] :
( ( c_in @ ( c_Pair @ SV438 @ SV970 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1435 @ SV438 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3597,plain,
! [SV1753: $i,SV1436: $i,SV971: $i,SV439: $i] :
( ( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1436 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV971 = SV1753 )
| ~ ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1436 @ SV1753 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3598,plain,
! [SV1437: $i,SV972: $i,SV440: $i] :
( ( ( SV440 = SV972 )
= $true )
| ( ( ( SV972 = SV440 )
| ( c_in @ ( c_Pair @ SV440 @ SV972 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1437 @ SV440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3599,plain,
! [SV1438: $i,SV974: $i,SV442: $i] :
( ( c_in @ ( c_Pair @ SV442 @ SV974 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1438 @ SV974 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3600,plain,
! [SV1754: $i,SV1439: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SV1754 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV443 = SV975 )
| ( SV975 = SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3601,plain,
! [SV1755: $i,SV1440: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SV1755 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV444 = SV1755 )
| ( SV976 = SV1755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3602,plain,
! [SV1441: $i,SV977: $i,SV445: $i] :
( ( ( SV445 = SV977 )
= $true )
| ( ( ( SV445 = SV977 )
| ( c_in @ ( c_Pair @ SV445 @ SV977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1441 @ SV977 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3603,plain,
! [SV1756: $i,SV1442: $i,SV978: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1442 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV446 = SV1756 )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1442 @ SV1756 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3604,plain,
! [SV981: $i,SV449: $i] :
( ( ( c_in @ SV449 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ SV449 @ SV981 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3605,plain,
! [SV982: $i,SV450: $i] :
( ( ( c_in @ SV450 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV450 @ SV982 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3606,plain,
! [SV1443: $i,SV983: $i,SV451: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SV983 @ SV1443 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV983 = SV1443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3607,plain,
! [SV1444: $i,SV984: $i,SV454: $i] :
( ( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SV984 @ SV1444 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV984 = SV1444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3608,plain,
! [SV1757: $i,SV1445: $i,SV985: $i,SV455: $i] :
( ( ! [SY4889: $i,SY4890: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SY4889 @ SY4890 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
| ~ ( c_in @ SV985 @ ( hAPP @ SY4890 @ SV455 ) @ SV1757 )
| ~ ( c_in @ SV455 @ SY4889 @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3609,plain,
! [SV1758: $i,SV1446: $i,SV986: $i,SV456: $i] :
( ( ! [SY4891: $i,SY4892: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SY4891 @ SY4892 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
| ~ ( c_in @ SV986 @ ( hAPP @ SY4892 @ SV456 ) @ SV1758 )
| ~ ( c_in @ SV456 @ SY4891 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3610,plain,
! [SV1759: $i,SV1447: $i,SV987: $i,SV457: $i] :
( ( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
| ~ ( c_in @ ( c_Pair @ SV457 @ SV1759 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) )
| ~ ( c_in @ SV1759 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3611,plain,
! [SV1760: $i,SV1448: $i,SV988: $i,SV458: $i] :
( ( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
| ~ ( c_in @ ( c_Pair @ SV458 @ SV1760 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SV1760 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3612,plain,
! [SV1761: $i,SV1449: $i,SV989: $i,SV459: $i] :
( ( ! [SY4893: $i,SY4894: $i] :
( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SY4893 ) @ SY4893 )
| ~ ( c_in @ ( c_Pair @ SY4894 @ SV459 @ SV1761 @ SY4893 ) @ SV989 @ ( tc_prod @ SV1761 @ SY4893 ) )
| ~ ( c_in @ SY4894 @ SV1449 @ SV1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3613,plain,
! [SV1762: $i,SV1450: $i,SV990: $i,SV460: $i] :
( ( ! [SY4895: $i,SY4896: $i] :
( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SY4895 ) @ SY4895 )
| ~ ( c_in @ ( c_Pair @ SY4896 @ SV460 @ SV1762 @ SY4895 ) @ SV990 @ ( tc_prod @ SV1762 @ SY4895 ) )
| ~ ( c_in @ SY4896 @ SV1450 @ SV1762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3614,plain,
! [SV1763: $i,SV1451: $i,SV991: $i,SV461: $i] :
( ( ( c_in @ SV461 @ SV991 @ SV1451 )
| ~ ( c_in @ ( c_Pair @ SV461 @ SV1763 @ SV1451 @ SV1451 ) @ ( c_Relation_OId__on @ SV991 @ SV1451 ) @ ( tc_prod @ SV1451 @ SV1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3615,plain,
! [SV1452: $i,SV992: $i,SV462: $i] :
( ( ( c_in @ ( c_Pair @ SV462 @ SV462 @ SV992 @ SV992 ) @ ( c_Relation_OId__on @ SV1452 @ SV992 ) @ ( tc_prod @ SV992 @ SV992 ) )
= $true )
| ( ( ~ ( c_in @ SV462 @ SV1452 @ SV992 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3616,plain,
! [SV1764: $i,SV1453: $i,SV993: $i,SV463: $i] :
( ( ! [SY4897: $i] :
( ( c_in @ SV463 @ SV993 @ SV1453 )
| ~ ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SY4897 @ ( tc_prod @ SV1453 @ SV1453 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SY4897 @ SV1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3617,plain,
! [SV1765: $i,SV1454: $i,SV994: $i,SV464: $i] :
( ( ! [SY4898: $i] :
( ( c_in @ SV464 @ SV994 @ SV1454 )
| ~ ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SY4898 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SY4898 @ SV1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3618,plain,
! [SV1766: $i,SV1455: $i,SV995: $i,SV465: $i] :
( ( ! [SY4899: $i] :
( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SV1455 @ SV1766 ) @ SV1766 )
| ~ ( c_in @ ( c_Pair @ SY4899 @ SV465 @ SV1455 @ SV1766 ) @ SV995 @ ( tc_prod @ SV1455 @ SV1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3619,plain,
! [SV1767: $i,SV1456: $i,SV996: $i,SV466: $i] :
( ( ! [SY4900: $i] :
( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SV1456 @ SV1767 ) @ SV1767 )
| ~ ( c_in @ ( c_Pair @ SY4900 @ SV466 @ SV1456 @ SV1767 ) @ SV996 @ ( tc_prod @ SV1456 @ SV1767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3620,plain,
! [SV1768: $i,SV1457: $i,SV997: $i,SV467: $i] :
( ( ! [SY4901: $i] :
( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SV1457 @ SV1768 ) @ SV1457 )
| ~ ( c_in @ ( c_Pair @ SV467 @ SY4901 @ SV1457 @ SV1768 ) @ SV997 @ ( tc_prod @ SV1457 @ SV1768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3621,plain,
! [SV1769: $i,SV1458: $i,SV998: $i,SV468: $i] :
( ( ! [SY4902: $i] :
( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SV1458 @ SV1769 ) @ SV1458 )
| ~ ( c_in @ ( c_Pair @ SV468 @ SY4902 @ SV1458 @ SV1769 ) @ SV998 @ ( tc_prod @ SV1458 @ SV1769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3622,plain,
! [SV1770: $i,SV1459: $i,SV999: $i,SV469: $i] :
( ( ! [SY4903: $i,SY4904: $i] :
( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SV1770 )
| ~ ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SY4903 @ SV1770 ) @ ( c_Product__Type_OSigma @ SY4904 @ SV999 @ SY4903 @ SV1770 ) @ ( tc_prod @ SY4903 @ SV1770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3623,plain,
! [SV1771: $i,SV1460: $i,SV1000: $i,SV470: $i] :
( ( ! [SY4905: $i,SY4906: $i] :
( ( c_in @ SV470 @ SV1000 @ SV1460 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SV1771 @ SV1460 @ SY4905 ) @ ( c_Product__Type_OSigma @ SV1000 @ SY4906 @ SV1460 @ SY4905 ) @ ( tc_prod @ SV1460 @ SY4905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3624,plain,
! [SV1772: $i,SV1461: $i,SV1001: $i,SV471: $i] :
( ( ! [SY4907: $i] :
( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SY4907 @ SV1461 )
| ~ ( c_in @ SV1001 @ SY4907 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SY4907 @ SV1772 @ SV1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3625,plain,
! [SV1773: $i,SV1462: $i,SV1002: $i,SV472: $i] :
( ( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
| ~ ( c_in @ SV472 @ SV1773 @ SV1002 )
| ~ ( c_Relation_Orefl__on @ SV1773 @ SV1462 @ SV1002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3626,plain,
! [SV1774: $i,SV1463: $i,SV1003: $i,SV473: $i] :
( ( ! [SY4908: $i] :
( ( c_in @ SV473 @ SV1003 @ SV1463 )
| ~ ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SY4908 @ ( tc_prod @ SV1463 @ SV1463 ) )
| ~ ( c_Relation_Orefl__on @ SV1003 @ SY4908 @ SV1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3627,plain,
! [SV1775: $i,SV1464: $i,SV1004: $i,SV474: $i] :
( ( ! [SY4909: $i] :
( ( c_in @ SV474 @ SV1004 @ SV1464 )
| ~ ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SY4909 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1004 @ SY4909 @ SV1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3628,plain,
! [SV1776: $i,SV1465: $i,SV1005: $i,SV475: $i] :
( ( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
| ~ ( c_in @ SV475 @ SV1776 @ SV1005 )
| ~ ( c_Relation_Orefl__on @ SV1776 @ SV1465 @ SV1005 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3629,plain,
! [SV1777: $i,SV1466: $i,SV1006: $i,SV476: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SV1777 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1466 = SV1777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3630,plain,
! [SV1778: $i,SV1467: $i,SV1007: $i,SV477: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV477 = SV1778 )
| ( SV477 = SV1778 )
| ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3631,plain,
! [SV1779: $i,SV1468: $i,SV1008: $i,SV478: $i] :
( ( ( SV478 = SV1008 )
| ( SV478 = SV1468 )
| ~ ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3632,plain,
! [SV1780: $i,SV1469: $i,SV1009: $i,SV479: $i] :
( ( ! [SY4910: $i] :
( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1009 = SV1780 )
| ( SV479 = SV1780 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SY4910 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SY4910 = SV1780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3633,plain,
! [SV1781: $i,SV1470: $i,SV1010: $i,SV480: $i] :
( ( ( SV480 = SV1010 )
| ~ ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3634,plain,
! [SV1782: $i,SV1471: $i,SV1011: $i,SV481: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1782 = SV481 )
| ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3635,plain,
! [SV1783: $i,SV1472: $i,SV1012: $i,SV482: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1783 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3636,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV483 = SV1013 )
| ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3637,plain,
! [SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ! [SY4911: $i] :
( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SY4911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1785 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SY4911 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SY4911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3638,plain,
! [SV1786: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ! [SY4912: $i] :
( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SY4912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4912 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SY4912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3639,plain,
! [SV1476: $i,SV1016: $i,SV486: $i] :
( ( ( SV486 = SV1016 )
= $true )
| ( ( ( SV1016 = SV486 )
| ~ ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3640,plain,
! [SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ! [SY4913: $i] :
( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SY4913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SY4913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3641,plain,
! [SV1478: $i,SV1018: $i,SV488: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV488 = SV1018 )
| ~ ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3642,plain,
! [SV1788: $i,SV1479: $i,SV1019: $i,SV489: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1788 = SV1019 )
| ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3643,plain,
! [SV1789: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ! [SY4914: $i] :
( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SY4914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1020 = SY4914 )
| ( SV490 = SY4914 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SY4914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3644,plain,
! [SV1790: $i,SV1481: $i,SV1021: $i,SV491: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SV1790 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1481 = SV1790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3645,plain,
! [SV1791: $i,SV1482: $i,SV1022: $i,SV492: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1022 = SV1791 )
| ( SV1791 = SV1022 )
| ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3646,plain,
! [SV1792: $i,SV1483: $i,SV1023: $i,SV493: $i] :
( ( ( SV493 = SV1023 )
| ( SV1483 = SV493 )
| ~ ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3647,plain,
! [SV1793: $i,SV1484: $i,SV1024: $i,SV494: $i] :
( ( ! [SY4915: $i] :
( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV494 = SV1793 )
| ( SV1024 = SV1793 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SY4915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SY4915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3648,plain,
! [SV1794: $i,SV1485: $i,SV1025: $i,SV495: $i] :
( ( ( SV495 = SV1025 )
| ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3649,plain,
! [SV1795: $i,SV1486: $i,SV1026: $i,SV496: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1026 = SV1795 )
| ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3650,plain,
! [SV1796: $i,SV1487: $i,SV1027: $i,SV497: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SV1796 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3651,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV498 = SV1028 )
| ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3652,plain,
! [SV1798: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ! [SY4916: $i] :
( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SY4916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1029 = SY4916 )
| ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SY4916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3653,plain,
! [SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ! [SY4917: $i] :
( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SY4917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SY4917 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SY4917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3654,plain,
! [SV1491: $i,SV1031: $i,SV501: $i] :
( ( ( SV501 = SV1031 )
= $true )
| ( ( ( SV501 = SV1031 )
| ~ ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3655,plain,
! [SV1800: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ! [SY4918: $i] :
( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SY4918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SY4918 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SY4918 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SY4918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3656,plain,
! [SV1493: $i,SV1033: $i,SV503: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV503 = SV1033 )
| ~ ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3657,plain,
! [SV1801: $i,SV1494: $i,SV1034: $i,SV504: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV504 = SV1801 )
| ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3658,plain,
! [SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ! [SY4919: $i] :
( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SY4919 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SV1802 )
| ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SY4919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3659,plain,
! [SV1496: $i,SV1036: $i,SV506: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV506 = SV1036 )
| ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3660,plain,
! [SV1497: $i,SV1037: $i,SV507: $i] :
( ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1037 = SV507 )
| ~ ( c_in @ SV1497 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3661,plain,
! [SV1498: $i,SV1038: $i,SV508: $i] :
( ( ( c_in @ SV508 @ SV1038 @ SV1498 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1038 @ SV508 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3662,plain,
! [SV1499: $i,SV1039: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ SV509 @ SV1039 ) )
= $true )
| ( ( ~ ( c_in @ SV1039 @ SV509 @ SV1499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3663,plain,
! [SV510: $i] :
( ( ( c_in @ SV510 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV510 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3664,plain,
! [SV1500: $i,SV1040: $i,SV511: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3665,plain,
! [SV512: $i,SV1041: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1041 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV512 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SV1041 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3666,plain,
! [SV513: $i,SV1042: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV1042 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV513 @ SV1042 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3667,plain,
! [SV514: $i,SV1043: $i] :
( ( ( class_Lattices_Olattice @ SV1043 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV514 @ SV1043 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3668,plain,
! [SV515: $i,SV1044: $i] :
( ( ( class_Lattices_Olattice @ SV1044 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV515 @ SV1044 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3669,plain,
! [SV516: $i,SV1045: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV1045 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV516 @ SV1045 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3670,plain,
! [SV517: $i,SV1046: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1046 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV517 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SV1046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3671,plain,
! [SV518: $i,SV1047: $i] :
( ( ( class_Orderings_Opreorder @ SV1047 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV518 @ SV1047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3672,plain,
! [SV519: $i,SV1048: $i] :
( ( ( class_Lattices_Olattice @ SV1048 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV519 @ SV1048 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3673,plain,
! [SV520: $i,SV1049: $i] :
( ( ( class_Orderings_Oorder @ SV1049 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV520 @ SV1049 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3674,plain,
! [SV521: $i,SV1050: $i] :
( ( ( class_HOL_Oord @ SV1050 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV521 @ SV1050 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3675,plain,
! [SV1501: $i,SV1052: $i,SV523: $i] :
( ( ( SV523 = SV1052 )
= $true )
| ( ( ~ ( c_fequal @ SV523 @ SV1052 @ SV1501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3676,plain,
! [SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ! [SY4920: $i,SY4921: $i,SY4922: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SY4920 )
!= ( c_Recdef_Ocut @ SY4921 @ SV1053 @ SV1502 @ SV1803 @ SY4920 ) )
| ( ( hAPP @ SV524 @ SY4922 )
= ( hAPP @ SY4921 @ SY4922 ) )
| ~ ( c_in @ ( c_Pair @ SY4922 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3677,plain,
! [SV1503: $i,SV1054: $i,SV525: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV525 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SV1503 @ SV525 )
!= SV1503 )
| ( c_lessequals @ SV1054 @ SV1503 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3678,plain,
! [SV1055: $i,SV526: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 @ SV1055 @ SV1055 )
= SV526 )
= $false )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV526 @ SV1055 @ SV1055 ) @ SV526 @ SV1055 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3679,plain,
! [SV1504: $i,SV1056: $i,SV527: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) )
!= SV1056 )
= $true )
| ( ( c_lessequals @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3219]) ).
thf(3680,plain,
! [SV1505: $i,SV1057: $i,SV528: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV528 ) )
= $true )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SV1505 @ SV528 )
!= SV1057 )
| ( c_lessequals @ SV1057 @ SV1505 @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3681,plain,
! [SV1804: $i,SV1506: $i,SV1058: $i,SV529: $i] :
( ( ! [SY4923: $i,SY4924: $i] :
( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
!= ( c_Product__Type_OSigma @ SY4923 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
| ~ ( c_in @ SY4924 @ SV1058 @ SV1506 )
| ( SV529 = SY4923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3682,plain,
! [SV1805: $i,SV1507: $i,SV1059: $i,SV530: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SV1059 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1059 @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ ( tc_fun @ SV1507 @ tc_bool ) ) )
| ( c_lessequals @ SV1805 @ SV530 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3683,plain,
! [SV1806: $i,SV1508: $i,SV1060: $i,SV531: $i] :
( ( ! [SY4925: $i,SY4926: $i] :
( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SV1806 )
!= ( c_Pair @ SY4925 @ SY4926 @ SV1508 @ SV1806 ) )
| ( SV1060 = SY4926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3684,plain,
! [SV1061: $i,SV532: $i] :
( ( ( ( c_Relation_Oconverse @ SV532 @ SV1061 @ SV1061 )
= SV532 )
= $false )
| ( ( c_Relation_Osym @ SV532 @ SV1061 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3685,plain,
! [SV1807: $i,SV1509: $i,SV1062: $i,SV533: $i] :
( ( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
!= ( c_Set_Oinsert @ SV533 @ SV1807 @ SV1509 ) )
| ( c_in @ SV533 @ SV1807 @ SV1509 )
| ( c_in @ SV533 @ SV1062 @ SV1509 )
| ( SV1062 = SV1807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3686,plain,
! [SV1808: $i,SV1510: $i,SV1063: $i,SV534: $i] :
( ( ! [SY4927: $i,SY4928: $i] :
( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SY4927 @ SY4928 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SY4927 @ SY4928 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SV1808 @ SY4927 @ SY4928 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SV1808 @ SY4927 @ SY4928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3687,plain,
! [SV1809: $i,SV1511: $i,SV1064: $i,SV535: $i] :
( ( ! [SY4929: $i,SY4930: $i] :
( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SV1809 )
!= ( c_Pair @ SY4929 @ SY4930 @ SV1511 @ SV1809 ) )
| ( SV535 = SY4929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3688,plain,
! [SV1512: $i,SV1065: $i,SV539: $i,SV4: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV4 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV539 @ SV1065 @ SV4 ) @ SV1512 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV539 @ SV1512 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1065 @ SV1512 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3689,plain,
! [SV1513: $i,SV1066: $i,SV540: $i,SV5: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV5 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1513 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1066 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1513 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3690,plain,
! [SV1810: $i,SV1516: $i,SV1069: $i,SV543: $i,SV8: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV8 @ SV543 @ ( tc_fun @ SV1069 @ tc_bool ) ) @ SV1516 @ SV1069 @ SV1810 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV8 @ SV1516 @ SV1069 @ SV1810 ) @ ( c_Product__Type_OSigma @ SV543 @ SV1516 @ SV1069 @ SV1810 ) @ ( tc_fun @ ( tc_prod @ SV1069 @ SV1810 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3691,plain,
! [SV1811: $i,SV1517: $i,SV1070: $i,SV544: $i,SV9: $i] :
( ( ! [SY4931: $i] :
( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
| ~ ( c_in @ SV544 @ SV1811 @ SY4931 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SY4931 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3692,plain,
! [SV1812: $i,SV1518: $i,SV1071: $i,SV545: $i,SV10: $i] :
( ( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
| ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SV1812 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1518 @ SV1812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3693,plain,
! [SV1519: $i,SV1072: $i,SV546: $i,SV11: $i] :
( ( ( c_lessequals @ SV11 @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1519 @ SV11 @ SV1072 ) @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3694,plain,
! [SV1520: $i,SV1073: $i,SV547: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SV547 @ SV1073 @ SV1520 ) @ ( tc_fun @ SV1520 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV12 @ SV1073 @ ( tc_fun @ SV1520 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3695,plain,
! [SV1075: $i,SV550: $i,SV15: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV15 )
= $false )
| ( ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SV550 @ SV1075 @ SV15 ) @ SV15 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV550 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1075 @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3696,plain,
! [SV1078: $i,SV556: $i,SV21: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV21 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV556 @ SV1078 @ SV21 ) @ SV21 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV556 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1078 @ SV21 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3697,plain,
! [SV1524: $i,SV1081: $i,SV559: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
= $true )
| ( ( ( SV1081 = SV559 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1081 @ SV24 @ SV1524 ) @ SV559 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3698,plain,
! [SV1813: $i,SV1525: $i,SV1082: $i,SV560: $i,SV25: $i] :
( ( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV25 @ SV560 @ SV1082 @ SV1525 ) @ SV1813 @ ( tc_prod @ SV1082 @ SV1525 ) ) @ SV1082 @ SV1525 )
= ( c_Set_Oinsert @ SV25 @ ( c_Relation_ODomain @ SV1813 @ SV1082 @ SV1525 ) @ SV1082 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3699,plain,
! [SV26: $i,SV1083: $i,SV561: $i] :
( ( ( ~ ( c_Relation_Osym @ SV561 @ SV1083 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV26 @ SV1083 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SV1083 @ SV1083 ) @ tc_bool ) ) @ SV1083 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3700,plain,
! [SV1814: $i,SV1526: $i,SV1084: $i,SV562: $i,SV27: $i] :
( ( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 @ SV562 @ ( tc_fun @ ( tc_prod @ SV1084 @ SV1526 ) @ tc_bool ) ) @ SV1814 @ SV1084 @ SV1526 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV27 @ SV1814 @ SV1084 @ SV1526 ) @ ( c_Relation_OImage @ SV562 @ SV1814 @ SV1084 @ SV1526 ) @ ( tc_fun @ SV1526 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3701,plain,
! [SV1815: $i,SV1527: $i,SV1085: $i,SV563: $i,SV28: $i] :
( ( ( c_Relation_OImage @ SV28 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV563 @ SV1085 @ ( tc_fun @ SV1527 @ tc_bool ) ) @ SV1527 @ SV1815 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV28 @ SV563 @ SV1527 @ SV1815 ) @ ( c_Relation_OImage @ SV28 @ SV1085 @ SV1527 @ SV1815 ) @ ( tc_fun @ SV1815 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3702,plain,
! [SV1529: $i,SV1087: $i,SV565: $i,SV30: $i] :
( ( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV565 @ SV1087 @ ( tc_fun @ ( tc_prod @ SV1529 @ SV1529 ) @ tc_bool ) ) @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) )
= $true )
| ( ( ~ ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SV1087 @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3703,plain,
! [SV1530: $i,SV1088: $i,SV566: $i,SV31: $i] :
( ( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 @ SV1088 @ ( tc_fun @ ( tc_prod @ SV1530 @ SV1530 ) @ tc_bool ) ) @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ~ ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SV566 @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3704,plain,
! [SV1533: $i,SV1091: $i,SV569: $i,SV34: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV34 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ SV1091 @ SV34 ) @ SV1533 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1091 @ SV1533 @ SV34 ) @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3705,plain,
! [SV1534: $i,SV1092: $i,SV570: $i,SV35: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV35 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ SV1534 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ SV1534 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3706,plain,
! [SV1535: $i,SV1093: $i,SV571: $i,SV36: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV36 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ SV1535 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ SV1535 @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3707,plain,
! [SV1536: $i,SV1094: $i,SV572: $i,SV37: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV37 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ SV1094 @ SV37 ) @ SV1536 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1094 @ SV1536 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3708,plain,
! [SV1095: $i,SV574: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV39 @ SV574 @ ( tc_fun @ SV1095 @ tc_bool ) )
= SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3709,plain,
! [SV1096: $i,SV40: $i,SV575: $i] :
( ( ( c_lessequals @ SV575 @ SV40 @ ( tc_fun @ SV1096 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV40 @ SV575 @ ( tc_fun @ SV1096 @ tc_bool ) )
= SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3710,plain,
! [SV1097: $i,SV576: $i,SV41: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV41 )
= $false )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SV1097 @ SV41 )
= SV576 )
| ~ ( c_lessequals @ SV576 @ SV1097 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3711,plain,
! [SV1098: $i,SV577: $i,SV42: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV42 )
= $false )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SV1098 @ SV42 )
= SV1098 )
| ~ ( c_lessequals @ SV1098 @ SV577 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3712,plain,
! [SV1537: $i,SV1099: $i,SV578: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV578 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
| ~ ( c_lessequals @ SV43 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3713,plain,
! [SV1538: $i,SV1102: $i,SV581: $i,SV46: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV581 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
| ~ ( c_lessequals @ SV46 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3264]) ).
thf(3714,plain,
! [SV1539: $i,SV1103: $i,SV582: $i,SV47: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV47 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3715,plain,
! [SV1104: $i,SV583: $i,SV48: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV48 )
= $false )
| ( ( c_lessequals @ SV583 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV583 @ SV1104 @ SV48 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3716,plain,
! [SV1105: $i,SV584: $i,SV49: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV49 )
= $false )
| ( ( c_lessequals @ SV584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1105 @ SV584 @ SV49 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3717,plain,
! [SV1540: $i,SV1106: $i,SV585: $i,SV50: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV50 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3718,plain,
! [SV1541: $i,SV1107: $i,SV586: $i,SV51: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV51 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3719,plain,
! [SV1108: $i,SV587: $i,SV52: $i] :
( ( ( class_Lattices_Olattice @ SV52 )
= $false )
| ( ( c_lessequals @ SV587 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1108 @ SV587 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3720,plain,
! [SV1109: $i,SV588: $i,SV53: $i] :
( ( ( class_Lattices_Olattice @ SV53 )
= $false )
| ( ( c_lessequals @ SV588 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV588 @ SV1109 @ SV53 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3721,plain,
! [SV1111: $i,SV590: $i,SV55: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV55 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV590 @ SV1111 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1111 @ SV590 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3722,plain,
! [SV1112: $i,SV591: $i,SV56: $i] :
( ( ( class_Lattices_Olattice @ SV56 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV591 @ SV1112 @ SV56 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1112 @ SV591 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3723,plain,
! [SV1542: $i,SV1113: $i,SV592: $i,SV57: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV57 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1113 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1542 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1113 @ SV1542 @ SV57 ) @ SV57 ) @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3724,plain,
! [SV1544: $i,SV1115: $i,SV595: $i,SV60: $i] :
( ( ( c_in @ SV60 @ SV595 @ SV1115 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SV1544 @ SV1115 ) @ SV595 @ ( tc_fun @ SV1115 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3725,plain,
! [SV1816: $i,SV1545: $i,SV1116: $i,SV596: $i,SV61: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV596 @ ( tc_fun @ SV1116 @ tc_bool ) ) @ SV1545 @ SV1116 @ SV1816 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV61 @ SV1545 @ SV1116 @ SV1816 ) @ ( c_Product__Type_OSigma @ SV596 @ SV1545 @ SV1116 @ SV1816 ) @ ( tc_fun @ ( tc_prod @ SV1116 @ SV1816 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3726,plain,
! [SV1546: $i,SV1117: $i,SV597: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SV597 @ SV1117 ) @ SV1546 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV597 @ SV1546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3727,plain,
! [SV1817: $i,SV1547: $i,SV1118: $i,SV598: $i,SV63: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) @ SV1817 )
= ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) )
| ~ ( c_in @ SV598 @ SV1118 @ SV1547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3728,plain,
! [SV1548: $i,SV1119: $i,SV599: $i,SV64: $i] :
( ( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SV1119 @ SV1548 ) @ ( tc_fun @ SV1548 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV64 @ SV1119 @ ( tc_fun @ SV1548 @ tc_bool ) )
| ( c_in @ SV599 @ SV64 @ SV1548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3729,plain,
! [SV1549: $i,SV1120: $i,SV600: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SV1120 @ tc_bool ) )
= $true )
| ( ( ( c_in @ SV1549 @ SV65 @ SV1120 )
| ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV1549 @ SV600 @ SV1120 ) @ ( tc_fun @ SV1120 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3730,plain,
! [SV1550: $i,SV1121: $i,SV601: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SV1121 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV66 @ SV1121 @ ( tc_fun @ SV1550 @ tc_bool ) )
| ( c_in @ SV601 @ SV66 @ SV1550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3731,plain,
! [SV1551: $i,SV1122: $i,SV602: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SV1122 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SV1551 @ SV602 @ SV1122 ) @ ( tc_fun @ SV1122 @ tc_bool ) )
| ( c_in @ SV1551 @ SV67 @ SV1122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3732,plain,
! [SV1553: $i,SV1124: $i,SV604: $i,SV69: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Set_Oinsert @ SV604 @ SV1124 @ SV1553 ) @ ( tc_fun @ SV1553 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV1124 @ ( tc_fun @ SV1553 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV604 @ SV69 @ SV1553 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3733,plain,
! [SV1554: $i,SV1125: $i,SV605: $i,SV70: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV70 @ SV605 @ SV1125 ) @ SV1554 @ ( tc_fun @ SV1125 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV605 @ SV1554 @ ( tc_fun @ SV1125 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV70 @ SV1554 @ SV1125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3734,plain,
! [SV1818: $i,SV1555: $i,SV1126: $i,SV606: $i,SV71: $i] :
( ( ! [SY4932: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV606 @ ( tc_fun @ ( tc_prod @ SV1126 @ SV1555 ) @ tc_bool ) ) @ SV1818 @ SV1126 @ SV1555 @ SY4932 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SV1818 @ SV1126 @ SV1555 @ SY4932 ) @ ( c_Relation_Orel__comp @ SV606 @ SV1818 @ SV1126 @ SV1555 @ SY4932 ) @ ( tc_fun @ ( tc_prod @ SV1126 @ SY4932 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3735,plain,
! [SV1819: $i,SV1556: $i,SV1127: $i,SV607: $i,SV72: $i] :
( ( ! [SY4933: $i] :
( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1127 @ ( tc_fun @ ( tc_prod @ SV1556 @ SV1819 ) @ tc_bool ) ) @ SY4933 @ SV1556 @ SV1819 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SV607 @ SY4933 @ SV1556 @ SV1819 ) @ ( c_Relation_Orel__comp @ SV72 @ SV1127 @ SY4933 @ SV1556 @ SV1819 ) @ ( tc_fun @ ( tc_prod @ SY4933 @ SV1819 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3736,plain,
! [SV1557: $i,SV1129: $i,SV610: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) ) @ ( tc_fun @ SV1129 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3737,plain,
! [SV1558: $i,SV1130: $i,SV611: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ SV611 @ ( tc_fun @ SV1130 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV611 @ SV1558 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3738,plain,
! [SV1559: $i,SV1131: $i,SV612: $i,SV77: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV77 ) )
= $true )
| ( ( ( c_lessequals @ SV612 @ SV1131 @ SV77 )
| ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SV1559 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3739,plain,
! [SV1560: $i,SV1132: $i,SV613: $i,SV78: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV78 ) )
= $true )
| ( ( ( c_lessequals @ SV613 @ SV1132 @ SV78 )
| ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1560 @ SV1132 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3740,plain,
! [SV1561: $i,SV1133: $i,SV614: $i,SV79: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV79 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SV1561 @ SV79 )
| ~ ( c_lessequals @ SV614 @ SV1561 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3741,plain,
! [SV1562: $i,SV1134: $i,SV615: $i,SV80: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV80 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SV1562 @ SV80 )
| ~ ( c_lessequals @ SV1134 @ SV1562 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3742,plain,
! [SV1563: $i,SV1135: $i,SV616: $i,SV81: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV81 ) )
= $true )
| ( ( ( c_lessequals @ SV616 @ SV1135 @ SV81 )
| ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SV1563 @ SV81 ) @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3295]) ).
thf(3743,plain,
! [SV1564: $i,SV1136: $i,SV617: $i,SV82: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV82 ) )
= $true )
| ( ( ( c_lessequals @ SV617 @ SV1136 @ SV82 )
| ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1564 @ SV1136 @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3744,plain,
! [SV1138: $i,SV619: $i,SV84: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV619 @ SV1138 @ SV84 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1138 @ SV619 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3745,plain,
! [SV1139: $i,SV620: $i,SV85: $i] :
( ( ( class_Lattices_Olattice @ SV85 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV620 @ SV1139 @ SV85 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1139 @ SV620 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3746,plain,
! [SV1142: $i,SV623: $i,SV88: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) @ SV88 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV623 @ SV1142 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3747,plain,
! [SV1143: $i,SV624: $i,SV89: $i] :
( ( ( class_Lattices_Olattice @ SV89 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) @ SV89 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV624 @ SV1143 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3748,plain,
! [SV1567: $i,SV1146: $i,SV628: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ SV628 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1146 @ SV93 @ ( tc_fun @ SV1567 @ tc_bool ) ) @ SV628 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3749,plain,
! [SV1568: $i,SV1147: $i,SV629: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ SV94 @ SV629 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SV1147 @ ( tc_fun @ SV1568 @ tc_bool ) ) @ SV629 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3750,plain,
! [SV1820: $i,SV1569: $i,SV1148: $i,SV630: $i,SV95: $i] :
( ( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV95 @ SV630 @ SV1148 @ SV1569 ) @ SV1820 @ ( tc_prod @ SV1148 @ SV1569 ) ) @ SV1148 @ SV1569 )
= ( c_Set_Oinsert @ SV630 @ ( c_Relation_ORange @ SV1820 @ SV1148 @ SV1569 ) @ SV1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3751,plain,
! [SV96: $i,SV1149: $i,SV631: $i] :
( ( ( ~ ( c_Relation_Osym @ SV631 @ SV1149 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV96 @ SV1149 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1149 ) @ tc_bool ) ) @ SV1149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3752,plain,
! [SV98: $i,SV1150: $i,SV633: $i] :
( ( ( c_Finite__Set_Ofinite @ SV633 @ SV1150 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV633 @ ( tc_fun @ SV1150 @ tc_bool ) ) @ SV1150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3753,plain,
! [SV634: $i,SV1151: $i,SV99: $i] :
( ( ( c_Finite__Set_Ofinite @ SV99 @ SV1151 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV634 @ ( tc_fun @ SV1151 @ tc_bool ) ) @ SV1151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3754,plain,
! [SV1570: $i,SV1152: $i,SV635: $i,SV100: $i] :
( ( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true )
| ( ( ~ ( c_in @ SV100 @ SV1152 @ SV1570 )
| ~ ( c_in @ SV100 @ SV635 @ SV1570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3755,plain,
! [SV1571: $i,SV1153: $i,SV636: $i,SV101: $i] :
( ( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true )
| ( ( ~ ( c_in @ SV101 @ SV1153 @ SV1571 )
| ~ ( c_in @ SV101 @ SV636 @ SV1571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3312]) ).
thf(3756,plain,
! [SV1572: $i,SV1154: $i,SV637: $i,SV102: $i] :
( ( ( c_in @ SV102 @ ( c_Set_Oinsert @ SV637 @ SV1154 @ SV1572 ) @ SV1572 )
= $true )
| ( ( ~ ( c_in @ SV102 @ SV1154 @ SV1572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3757,plain,
! [SV1573: $i,SV1155: $i,SV638: $i,SV103: $i] :
( ( ( c_in @ SV103 @ ( c_Set_Oinsert @ SV638 @ SV1155 @ SV1573 ) @ SV1573 )
= $true )
| ( ( ~ ( c_in @ SV103 @ SV1155 @ SV1573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3758,plain,
! [SV1574: $i,SV1156: $i,SV639: $i,SV104: $i] :
( ( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1156 @ ( tc_fun @ SV1574 @ tc_bool ) ) @ SV1574 )
= $true )
| ( ( ~ ( c_in @ SV104 @ SV639 @ SV1574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3315]) ).
thf(3759,plain,
! [SV1575: $i,SV1157: $i,SV640: $i,SV105: $i] :
( ( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV640 @ SV1157 @ ( tc_fun @ SV1575 @ tc_bool ) ) @ SV1575 )
= $true )
| ( ( ~ ( c_in @ SV105 @ SV1157 @ SV1575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3316]) ).
thf(3760,plain,
! [SV1576: $i,SV1158: $i,SV641: $i,SV106: $i] :
( ( ( c_in @ SV106 @ SV641 @ SV1158 )
= $true )
| ( ( ( SV106 = SV1576 )
| ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SV1576 @ SV641 @ SV1158 ) @ SV1158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3317]) ).
thf(3761,plain,
! [SV1577: $i,SV1159: $i,SV642: $i,SV107: $i] :
( ( ( c_in @ SV107 @ SV642 @ SV1159 )
= $true )
| ( ( ( c_in @ SV107 @ SV1577 @ SV1159 )
| ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1577 @ SV642 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ SV1159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3762,plain,
! [SV1578: $i,SV1163: $i,SV646: $i,SV111: $i] :
( ( ( c_in @ SV111 @ SV646 @ SV1163 )
= $true )
| ( ( ~ ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1578 @ SV646 @ ( tc_fun @ SV1163 @ tc_bool ) ) @ SV1163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3763,plain,
! [SV1579: $i,SV1164: $i,SV647: $i,SV112: $i] :
( ( ( c_in @ SV112 @ SV647 @ SV1164 )
= $true )
| ( ( ~ ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SV1579 @ ( tc_fun @ SV1164 @ tc_bool ) ) @ SV1164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3320]) ).
thf(3764,plain,
! [SV1165: $i,SV648: $i,SV113: $i] :
( ( ( c_in @ SV113 @ SV648 @ SV1165 )
= $false )
| ( ( ( c_Set_Oinsert @ SV113 @ SV648 @ SV1165 )
= SV648 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3765,plain,
! [SV1821: $i,SV1580: $i,SV1166: $i,SV649: $i,SV114: $i] :
( ( ~ ( c_in @ SV114 @ SV649 @ SV1166 )
| ( c_in @ ( hAPP @ SV1580 @ SV114 ) @ ( c_Set_Oimage @ SV1580 @ SV649 @ SV1166 @ SV1821 ) @ SV1821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3766,plain,
! [SV1822: $i,SV1581: $i,SV1167: $i,SV650: $i,SV115: $i] :
( ( ~ ( c_in @ SV115 @ SV650 @ SV1167 )
| ( c_in @ ( hAPP @ SV1581 @ SV115 ) @ ( c_Set_Oimage @ SV1581 @ SV650 @ SV1167 @ SV1822 ) @ SV1822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3767,plain,
! [SV1823: $i,SV1582: $i,SV1168: $i,SV651: $i,SV116: $i] :
( ( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SV1168 @ SV1582 @ SV1823 ) @ SV1823 )
| ~ ( c_in @ SV651 @ SV1168 @ SV1582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3768,plain,
! [SV1824: $i,SV1583: $i,SV1169: $i,SV652: $i,SV117: $i] :
( ( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SV1169 @ SV1583 @ SV1824 ) @ SV1824 )
| ~ ( c_in @ SV652 @ SV1169 @ SV1583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3769,plain,
! [SV1584: $i,SV1170: $i,SV653: $i,SV118: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SV653 @ SV1170 @ SV1584 ) @ SV1170 @ SV1584 @ SV1584 ) @ SV118 @ ( tc_prod @ SV1584 @ SV1584 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV653 @ SV1170 @ SV1584 @ SV1584 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SV1584 ) @ ( tc_prod @ SV1584 @ SV1584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(3770,plain,
! [SV1825: $i,SV1585: $i,SV1171: $i,SV654: $i,SV119: $i] :
( ( ! [SY4934: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SY4934 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4934 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SY4934 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SY4934 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(3771,plain,
! [SV1172: $i,SV655: $i,SV120: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV655 @ SV1172 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3772,plain,
! [SV1173: $i,SV656: $i,SV121: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV121 @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3773,plain,
! [SV661: $i,SV126: $i,SV1176: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1176 @ SV126 @ SV661 ) @ SV661 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV126 @ SV661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3774,plain,
! [SV127: $i,SV1177: $i,SV662: $i] :
( ( ( c_Finite__Set_Ofinite @ SV662 @ SV1177 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV127 @ SV662 @ SV1177 ) @ SV1177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3775,plain,
! [SV1587: $i,SV1178: $i,SV663: $i,SV128: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SV663 @ SV1178 @ SV1587 ) @ SV1587 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV128 @ SV1178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3776,plain,
! [SV1826: $i,SV1588: $i,SV1179: $i,SV664: $i,SV129: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV129 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV664 @ SV1179 @ ( tc_fun @ SV1588 @ tc_bool ) ) @ SV1588 @ SV1826 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV129 @ SV664 @ SV1588 @ SV1826 ) @ ( c_Set_Oimage @ SV129 @ SV1179 @ SV1588 @ SV1826 ) @ ( tc_fun @ SV1826 @ tc_bool ) ) @ ( tc_fun @ SV1826 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3777,plain,
! [SV130: $i,SV1180: $i,SV665: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV665 @ SV1180 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV130 @ SV1180 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3778,plain,
! [SV131: $i,SV1181: $i,SV666: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV666 @ SV1181 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV131 @ SV1181 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ SV1181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3779,plain,
! [SV1827: $i,SV1589: $i,SV1182: $i,SV667: $i,SV132: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV132 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV667 @ SV1182 @ ( tc_fun @ SV1589 @ tc_bool ) ) @ SV1589 @ SV1827 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV132 @ SV667 @ SV1589 @ SV1827 ) @ ( c_Relation_OImage @ SV132 @ SV1182 @ SV1589 @ SV1827 ) @ ( tc_fun @ SV1827 @ tc_bool ) ) @ ( tc_fun @ SV1827 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3780,plain,
! [SV1590: $i,SV1183: $i,SV668: $i,SV133: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SV668 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV668 @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1590 @ SV133 @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3781,plain,
! [SV1591: $i,SV1184: $i,SV670: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV1184 @ SV670 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1184 @ SV135 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3782,plain,
! [SV1592: $i,SV1185: $i,SV671: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SV671 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SV1592 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV671 @ SV1592 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3783,plain,
! [SV1593: $i,SV1186: $i,SV672: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV672 @ ( tc_fun @ SV1186 @ tc_bool ) ) @ SV1593 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV1593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3784,plain,
! [SV1828: $i,SV1594: $i,SV1187: $i,SV673: $i,SV138: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 @ SV673 @ ( tc_fun @ SV1187 @ tc_bool ) ) @ ( c_COMBK @ SV1594 @ ( tc_fun @ SV1828 @ tc_bool ) @ SV1187 ) @ SV1187 @ SV1828 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV138 @ ( c_COMBK @ SV1594 @ ( tc_fun @ SV1828 @ tc_bool ) @ SV1187 ) @ SV1187 @ SV1828 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1594 @ ( tc_fun @ SV1828 @ tc_bool ) @ SV1187 ) @ SV1187 @ SV1828 ) @ ( tc_fun @ ( tc_prod @ SV1187 @ SV1828 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3785,plain,
! [SV1829: $i,SV1595: $i,SV1188: $i,SV675: $i,SV140: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SV1829 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV675 @ SV1829 @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3786,plain,
! [SV1596: $i,SV1189: $i,SV676: $i,SV141: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV141 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ SV1189 @ SV141 ) @ SV1596 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1189 @ SV1596 @ SV141 ) @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3346]) ).
thf(3787,plain,
! [SV1597: $i,SV1190: $i,SV677: $i,SV142: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV142 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ SV1597 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ SV1597 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3788,plain,
! [SV1598: $i,SV1191: $i,SV678: $i,SV143: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV143 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ SV1598 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ SV1598 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3348]) ).
thf(3789,plain,
! [SV1599: $i,SV1192: $i,SV679: $i,SV144: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV144 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ SV1192 @ SV144 ) @ SV1599 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1192 @ SV1599 @ SV144 ) @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3349]) ).
thf(3790,plain,
! [SV682: $i,SV1195: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV147 @ SV1195 @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV682 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV147 @ SV682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3791,plain,
! [SV683: $i,SV148: $i,SV1196: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1196 @ SV148 @ ( tc_fun @ SV683 @ tc_bool ) ) @ SV683 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV148 @ SV683 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3792,plain,
! [SV1830: $i,SV1602: $i,SV1197: $i,SV684: $i,SV150: $i] :
( ( ! [SY4935: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SV1830 @ SY4935 ) @ ( tc_fun @ SY4935 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4935 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SV1602 @ SV1197 @ SY4935 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV684 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SV1830 @ SY4935 ) @ ( tc_fun @ SY4935 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4935 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ SV1830 @ ( tc_fun @ SY4935 @ tc_bool ) @ SV1197 ) @ SV1197 @ SY4935 ) @ ( tc_fun @ ( tc_prod @ SV1197 @ SY4935 ) @ tc_bool ) ) @ ( tc_prod @ SV1197 @ SY4935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(3793,plain,
! [SV151: $i,SV1198: $i,SV685: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV685 @ SV1198 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV151 @ SV1198 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SV1198 @ SV1198 ) @ tc_bool ) ) @ SV1198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3794,plain,
! [SV1603: $i,SV1199: $i,SV686: $i,SV152: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV152 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1199 @ SV1603 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1199 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1603 @ SV152 ) @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3795,plain,
! [SV1200: $i,SV687: $i,SV153: $i] :
( ( ( class_Lattices_Olattice @ SV153 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV687 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV687 @ SV1200 @ SV153 ) @ SV153 )
= SV687 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3796,plain,
! [SV1201: $i,SV688: $i,SV154: $i] :
( ( ( class_Lattices_Olattice @ SV154 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV688 @ SV1201 @ SV154 ) @ SV154 )
= SV688 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3797,plain,
! [SV1202: $i,SV689: $i,SV155: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV155 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1202 @ SV155 )
= SV689 )
| ~ ( c_lessequals @ SV1202 @ SV689 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3798,plain,
! [SV1203: $i,SV690: $i,SV156: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SV1203 @ SV156 )
= SV1203 )
| ~ ( c_lessequals @ SV690 @ SV1203 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3799,plain,
! [SV1204: $i,SV691: $i,SV157: $i] :
( ( ( c_lessequals @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ SV691 @ ( tc_fun @ SV1204 @ tc_bool ) )
= SV691 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3800,plain,
! [SV1205: $i,SV158: $i,SV692: $i] :
( ( ( c_lessequals @ SV692 @ SV158 @ ( tc_fun @ SV1205 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV692 @ ( tc_fun @ SV1205 @ tc_bool ) )
= SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3362]) ).
thf(3801,plain,
! [SV1831: $i,SV1604: $i,SV1206: $i,SV693: $i,SV159: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SV1831 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV693 @ SV1831 @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3802,plain,
! [SV1605: $i,SV1207: $i,SV694: $i,SV160: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SV694 @ SV1207 @ SV1605 ) @ SV1605 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV694 @ SV1207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3803,plain,
! [SV1606: $i,SV1208: $i,SV695: $i,SV161: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SV695 @ SV1208 ) @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV695 @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) )
= $true )
| ( ( ~ ( c_in @ SV161 @ SV1606 @ SV1208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3804,plain,
! [SV1607: $i,SV1209: $i,SV696: $i,SV162: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SV696 @ SV1209 @ SV1607 ) @ ( tc_fun @ SV1607 @ tc_bool ) )
= ( c_Set_Oinsert @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SV1209 @ ( tc_fun @ SV1607 @ tc_bool ) ) @ SV1607 ) )
= $true )
| ( ( ~ ( c_in @ SV696 @ SV162 @ SV1607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3805,plain,
! [SV1832: $i,SV1608: $i,SV1210: $i,SV697: $i,SV163: $i] :
( ( ( c_Set_Oimage @ SV163 @ ( c_Set_Oinsert @ SV697 @ SV1210 @ SV1608 ) @ SV1608 @ SV1832 )
= ( c_Set_Oinsert @ ( hAPP @ SV163 @ SV697 ) @ ( c_Set_Oimage @ SV163 @ SV1210 @ SV1608 @ SV1832 ) @ SV1832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3806,plain,
! [SV1833: $i,SV1609: $i,SV1211: $i,SV698: $i,SV164: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV698 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3807,plain,
! [SV1213: $i,SV700: $i,SV166: $i] :
( ( ( class_Lattices_Olattice @ SV166 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV700 @ SV1213 @ SV166 ) @ SV700 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3808,plain,
! [SV1214: $i,SV701: $i,SV167: $i] :
( ( ( class_Lattices_Olattice @ SV167 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV701 @ SV1214 @ SV167 ) @ SV1214 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3809,plain,
! [SV1611: $i,SV1215: $i,SV702: $i,SV168: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV168 ) )
= $true )
| ( ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1611 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3810,plain,
! [SV1612: $i,SV1216: $i,SV703: $i,SV169: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV169 ) )
= $true )
| ( ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1612 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3811,plain,
! [SV1613: $i,SV1217: $i,SV704: $i,SV170: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV170 ) )
= $true )
| ( ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1613 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3812,plain,
! [SV1218: $i,SV705: $i,SV171: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV171 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV705 @ SV1218 @ SV171 ) @ SV1218 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3375]) ).
thf(3813,plain,
! [SV1219: $i,SV706: $i,SV172: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV172 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV706 @ SV1219 @ SV172 ) @ SV706 @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3814,plain,
! [SV1614: $i,SV1222: $i,SV709: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) @ ( tc_fun @ SV1614 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SV1614 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3815,plain,
! [SV1615: $i,SV1223: $i,SV710: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ ( tc_fun @ SV1615 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SV1615 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3816,plain,
! [SV1834: $i,SV1616: $i,SV1224: $i,SV711: $i,SV177: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV177 @ SV711 @ ( tc_fun @ SV1224 @ tc_bool ) ) @ ( c_COMBK @ SV1616 @ ( tc_fun @ SV1834 @ tc_bool ) @ SV1224 ) @ SV1224 @ SV1834 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV177 @ ( c_COMBK @ SV1616 @ ( tc_fun @ SV1834 @ tc_bool ) @ SV1224 ) @ SV1224 @ SV1834 ) @ ( c_Product__Type_OSigma @ SV711 @ ( c_COMBK @ SV1616 @ ( tc_fun @ SV1834 @ tc_bool ) @ SV1224 ) @ SV1224 @ SV1834 ) @ ( tc_fun @ ( tc_prod @ SV1224 @ SV1834 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3817,plain,
! [SV1617: $i,SV1225: $i,SV712: $i,SV178: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV178 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV712 @ SV1225 @ SV178 ) @ SV1617 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV712 @ SV1617 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1225 @ SV1617 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3818,plain,
! [SV1618: $i,SV1226: $i,SV713: $i,SV179: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV179 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1226 @ SV1618 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1226 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1618 @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3819,plain,
! [SV1621: $i,SV1230: $i,SV717: $i,SV183: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV717 @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
| ~ ( c_in @ SV183 @ SV1621 @ SV1230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3820,plain,
! [SV1231: $i,SV718: $i,SV184: $i] :
( ( ( class_Lattices_Olattice @ SV184 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) @ SV184 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV718 @ SV1231 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3821,plain,
! [SV1232: $i,SV719: $i,SV185: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV185 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) @ SV185 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV719 @ SV1232 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3822,plain,
! [SV721: $i,SV1234: $i,SV187: $i] :
( ( ( c_lessequals @ SV187 @ SV1234 @ ( tc_fun @ ( tc_prod @ SV721 @ SV721 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OField @ SV187 @ SV721 ) @ ( c_Relation_OField @ SV1234 @ SV721 ) @ ( tc_fun @ SV721 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3823,plain,
! [SV723: $i,SV1236: $i,SV189: $i] :
( ( ( c_Wellfounded_Owf @ SV189 @ SV1236 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV723 @ ( tc_fun @ ( tc_prod @ SV1236 @ SV1236 ) @ tc_bool ) ) @ SV1236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3824,plain,
! [SV190: $i,SV1237: $i,SV724: $i] :
( ( ( c_Wellfounded_Owf @ SV724 @ SV1237 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV190 @ SV724 @ ( tc_fun @ ( tc_prod @ SV1237 @ SV1237 ) @ tc_bool ) ) @ SV1237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3825,plain,
! [SV1623: $i,SV1238: $i,SV728: $i,SV194: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV194 ) )
= $true )
| ( ( ( c_lessequals @ SV728 @ SV1238 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1623 @ SV728 @ SV194 ) @ SV1238 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3826,plain,
! [SV1624: $i,SV1239: $i,SV729: $i,SV195: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV195 ) )
= $true )
| ( ( ( c_lessequals @ SV729 @ SV1239 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SV1624 @ SV195 ) @ SV1239 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3827,plain,
! [SV1625: $i,SV1240: $i,SV730: $i,SV196: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV196 ) )
= $true )
| ( ( ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SV1625 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SV730 @ SV1625 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3828,plain,
! [SV1626: $i,SV1241: $i,SV731: $i,SV197: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV197 ) )
= $true )
| ( ( ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SV1626 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV731 @ SV1241 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3829,plain,
! [SV1627: $i,SV1242: $i,SV732: $i,SV198: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV198 ) )
= $true )
| ( ( ( c_lessequals @ SV732 @ SV1242 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1627 @ SV732 @ SV198 ) @ SV1242 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3830,plain,
! [SV1628: $i,SV1243: $i,SV733: $i,SV199: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV199 ) )
= $true )
| ( ( ( c_lessequals @ SV733 @ SV1243 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV1628 @ SV199 ) @ SV1243 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3831,plain,
! [SV1629: $i,SV1244: $i,SV734: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV1629 @ ( tc_fun @ SV1244 @ tc_bool ) ) @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3832,plain,
! [SV1630: $i,SV1245: $i,SV735: $i,SV201: $i] :
( ( ( c_lessequals @ SV201 @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1630 @ SV201 @ ( tc_fun @ SV1245 @ tc_bool ) ) @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3833,plain,
! [SV202: $i,SV736: $i,SV1246: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1246 @ SV736 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV202 @ SV1246 @ ( tc_fun @ SV736 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3834,plain,
! [SV737: $i,SV1247: $i,SV203: $i] :
( ( ( ~ ( c_lessequals @ SV203 @ SV1247 @ ( tc_fun @ SV737 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1247 @ SV737 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3401]) ).
thf(3835,plain,
! [SV1835: $i,SV1631: $i,SV1248: $i,SV738: $i,SV204: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV738 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3836,plain,
! [SV1632: $i,SV1249: $i,SV739: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV1632 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV739 @ SV1632 ) )
| ~ ( hBOOL @ ( hAPP @ SV205 @ SV1632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3837,plain,
! [SV1836: $i,SV1633: $i,SV1250: $i,SV740: $i,SV206: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SV1250 @ SV1633 ) @ ( c_Set_Oimage @ SV206 @ SV1836 @ SV1250 @ SV1633 ) @ ( tc_fun @ SV1633 @ tc_bool ) )
| ~ ( c_lessequals @ SV740 @ SV1836 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3838,plain,
! [SV1837: $i,SV1634: $i,SV1251: $i,SV741: $i,SV207: $i] :
( ( ~ ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SV1251 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SV1634 @ SV207 @ SV1251 @ SV1837 ) @ ( c_Set_Oimage @ SV1634 @ SV741 @ SV1251 @ SV1837 ) @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3839,plain,
! [SV1635: $i,SV1252: $i,SV742: $i,SV208: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SV742 @ SV1252 ) @ ( c_Set_Oinsert @ SV208 @ SV1635 @ SV1252 ) @ ( tc_fun @ SV1252 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV742 @ SV1635 @ ( tc_fun @ SV1252 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3840,plain,
! [SV743: $i,SV209: $i,SV1253: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1253 @ SV209 @ SV743 )
= $false )
| ( ( c_Relation_Otrans @ SV209 @ SV743 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3841,plain,
! [SV1838: $i,SV1636: $i,SV1254: $i,SV744: $i,SV210: $i] :
( ( ( c_Set_Oimage @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV744 @ SV1254 @ ( tc_fun @ SV1636 @ tc_bool ) ) @ SV1636 @ SV1838 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV210 @ SV744 @ SV1636 @ SV1838 ) @ ( c_Set_Oimage @ SV210 @ SV1254 @ SV1636 @ SV1838 ) @ ( tc_fun @ SV1838 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3842,plain,
! [SV1839: $i,SV1637: $i,SV1255: $i,SV745: $i,SV211: $i] :
( ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(3843,plain,
! [SV1840: $i,SV1638: $i,SV1256: $i,SV746: $i,SV212: $i] :
( ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3844,plain,
! [SV1639: $i,SV1257: $i,SV747: $i,SV213: $i] :
( ( ( c_Wellfounded_Owf @ SV213 @ SV747 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1257 @ SV1639 @ SV747 @ SV747 ) @ SV213 @ ( tc_prod @ SV747 @ SV747 ) ) @ SV747 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3411]) ).
thf(3845,plain,
! [SV748: $i,SV1258: $i,SV214: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV214 @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV214 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( c_Relation_Orel__comp @ SV1258 @ SV214 @ SV748 @ SV748 @ SV748 ) @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV1258 @ ( tc_fun @ ( tc_prod @ SV748 @ SV748 ) @ tc_bool ) ) @ SV748 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3846,plain,
! [SV749: $i,SV1259: $i,SV215: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV215 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( c_Relation_Orel__comp @ SV749 @ SV215 @ SV1259 @ SV1259 @ SV1259 ) @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV749 @ ( tc_fun @ ( tc_prod @ SV1259 @ SV1259 ) @ tc_bool ) ) @ SV1259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3847,plain,
! [SV217: $i,SV751: $i,SV1260: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV751 ) )
= $true )
| ( ( ~ ( c_in @ SV1260 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3414]) ).
thf(3848,plain,
! [SV1640: $i,SV1262: $i,SV757: $i,SV223: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV223 @ SV757 @ SV1262 @ SV1262 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1262 ) @ ( tc_prod @ SV1262 @ SV1262 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SV1262 @ SV1262 ) @ SV1640 @ ( tc_prod @ SV1262 @ SV1262 ) ) @ SV1262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3415]) ).
thf(3849,plain,
! [SV1641: $i,SV1263: $i,SV758: $i,SV224: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SV1263 @ SV1263 ) @ SV1641 @ ( tc_prod @ SV1263 @ SV1263 ) ) @ SV1263 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV758 @ SV224 @ SV1263 @ SV1263 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1263 ) @ ( tc_prod @ SV1263 @ SV1263 ) )
| ~ ( c_Wellfounded_Owf @ SV1641 @ SV1263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(3850,plain,
! [SV1642: $i,SV1264: $i,SV759: $i,SV225: $i] :
( ( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV759 @ SV225 @ SV1264 @ SV1642 ) @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV225 @ SV1264 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(3851,plain,
! [SV1841: $i,SV1643: $i,SV1265: $i,SV760: $i,SV226: $i] :
( ( ! [SY4936: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SV1841 @ SY4936 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SY4936 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
| ~ ( c_lessequals @ SV226 @ SV1841 @ ( tc_fun @ SV1265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3852,plain,
! [SV1842: $i,SV1644: $i,SV1266: $i,SV761: $i,SV227: $i] :
( ( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SV1266 @ ( tc_fun @ SV1644 @ tc_bool ) @ SV1842 ) @ SV1842 @ SV1644 ) @ ( tc_fun @ SV1842 @ SV1644 ) )
| ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SV1266 @ SV227 @ SV1842 @ SV1644 ) ) @ SV1266 @ SV1644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3853,plain,
! [SV1843: $i,SV1645: $i,SV1267: $i,SV762: $i,SV228: $i] :
( ( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SV762 @ ( c_COMBK @ SV1267 @ ( tc_fun @ SV1645 @ tc_bool ) @ SV1843 ) @ SV1843 @ SV1645 ) @ ( tc_fun @ SV1843 @ SV1645 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV762 @ SV1267 @ SV228 @ SV1843 @ SV1645 ) @ SV762 @ SV1843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3854,plain,
! [SV1844: $i,SV1646: $i,SV1268: $i,SV763: $i,SV229: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SV1268 @ SV1646 ) @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) )
| ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) @ SV1268 ) @ SV1268 @ SV1646 ) @ ( tc_fun @ SV1268 @ SV1646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3855,plain,
! [SV1269: $i,SV765: $i,SV231: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(3856,plain,
! [SV766: $i,SV232: $i] :
( ( ( c_Relation_Otrans @ SV232 @ SV766 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV232 @ SV766 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SV766 @ SV766 ) @ SV232 @ SV766 @ SV766 @ SV766 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SV766 @ SV766 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3857,plain,
! [SV1647: $i,SV1270: $i,SV767: $i,SV233: $i] :
( ( ( c_Wellfounded_Owf @ SV233 @ SV767 )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1270 @ SV1647 @ SV233 @ SV767 ) @ SV1647 @ SV767 )
| ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SV1270 @ ( c_COMBK @ SV1647 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3858,plain,
! [SV1648: $i,SV1271: $i,SV768: $i,SV234: $i] :
( ( ( c_Wellfounded_Owf @ SV234 @ SV768 )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1271 @ SV1648 @ SV234 @ SV768 ) @ SV1271 @ SV768 )
| ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SV1271 @ ( c_COMBK @ SV1648 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(3859,plain,
! [SV1272: $i,SV769: $i,SV235: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SV769 @ SV1272 ) @ SV235 @ SV1272 )
= $true )
| ( ( ~ ( c_lessequals @ SV769 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SV1272 @ tc_bool ) @ SV1272 ) @ SV1272 @ SV1272 ) @ ( tc_fun @ ( tc_prod @ SV1272 @ SV1272 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV235 @ SV769 @ SV1272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3860,plain,
! [SV1273: $i,SV770: $i,SV236: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SV770 @ SV1273 ) @ SV236 @ SV1273 )
= $true )
| ( ( ~ ( c_lessequals @ SV770 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SV1273 @ tc_bool ) @ SV1273 ) @ SV1273 @ SV1273 ) @ ( tc_fun @ ( tc_prod @ SV1273 @ SV1273 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV236 @ SV770 @ SV1273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(3861,plain,
! [SV1649: $i,SV1274: $i,SV771: $i,SV237: $i] :
( ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true )
| ( ( ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
| ~ ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3428]) ).
thf(3862,plain,
! [SV1275: $i,SV772: $i,SV238: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ SV1275 @ SV1275 ) @ SV772 @ ( tc_prod @ SV1275 @ SV1275 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SV1275 @ tc_bool ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ ( tc_prod @ SV1275 @ SV1275 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SV1275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3429]) ).
thf(3863,plain,
! [SV1276: $i,SV773: $i,SV239: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ SV1276 @ SV1276 ) @ SV773 @ ( tc_prod @ SV1276 @ SV1276 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SV1276 @ tc_bool ) @ SV1276 ) @ SV1276 @ SV1276 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1276 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SV1276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3430]) ).
thf(3864,plain,
! [SV1650: $i,SV1277: $i,SV774: $i,SV240: $i] :
( ( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Otrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
= $true )
| ( ( ( SV240 = SV774 )
| ~ ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Ortrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(3865,plain,
! [SV1651: $i,SV1278: $i,SV775: $i,SV241: $i] :
( ( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Otrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
= $true )
| ( ( ( SV241 = SV775 )
| ~ ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Ortrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3866,plain,
! [SV1652: $i,SV1279: $i,SV776: $i,SV242: $i] :
( ( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Ortrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Otrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
| ( SV242 = SV776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3433]) ).
thf(3867,plain,
! [SV1653: $i,SV1280: $i,SV777: $i,SV243: $i] :
( ( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SV1280 @ SV1653 ) @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
| ~ ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SV1653 ) @ ( tc_prod @ SV1653 @ SV1653 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3434]) ).
thf(3868,plain,
! [SV1845: $i,SV1654: $i,SV1281: $i,SV778: $i,SV244: $i] :
( ( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SV1845 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SV1845 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3869,plain,
! [SV1846: $i,SV1655: $i,SV1282: $i,SV779: $i,SV245: $i] :
( ( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV1846 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SV1846 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(3870,plain,
! [SV780: $i,SV246: $i,SV1283: $i] :
( ( ( c_in @ SV1283 @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV246 @ ( tc_fun @ SV780 @ tc_bool ) ) @ SV1283 @ ( tc_fun @ SV780 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3871,plain,
! [SV1284: $i,SV783: $i,SV249: $i] :
( ( ( c_in @ SV249 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ SV249 @ SV783 @ SV1284 ) @ SV1284 )
= $false )
| ( ( c_in @ SV249 @ ( c_Complete__Lattice_OInf__class_OInf @ SV783 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3872,plain,
! [SV1656: $i,SV1285: $i,SV784: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SV1285 @ SV1656 ) @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 )
| ~ ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(3873,plain,
! [SV1286: $i,SV251: $i,SV785: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV785 @ SV251 @ SV1286 ) @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 )
= $false )
| ( ( c_in @ SV251 @ ( c_Wellfounded_Oacc @ SV785 @ SV1286 ) @ SV1286 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3874,plain,
! [SV786: $i,SV1287: $i,SV252: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SV1287 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SV1287 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(3875,plain,
! [SV1657: $i,SV1288: $i,SV787: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SV1657 ) ) )
| ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SV1657 ) @ SV1657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3876,plain,
! [SV1289: $i,SV788: $i,SV254: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV254 @ SV788 @ SV1289 ) @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 )
= $false )
| ( ( c_in @ SV788 @ ( c_Wellfounded_Oacc @ SV254 @ SV1289 ) @ SV1289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3877,plain,
! [SV1658: $i,SV1290: $i,SV789: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SV1290 @ SV1658 ) @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 )
| ~ ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3444]) ).
thf(3878,plain,
! [SV790: $i,SV1291: $i,SV256: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SV1291 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SV1291 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(3879,plain,
! [SV1659: $i,SV1292: $i,SV791: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SV1659 ) ) )
| ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SV1659 ) @ SV1659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3880,plain,
! [SV1293: $i,SV792: $i,SV258: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false )
| ( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SV1293 @ SV258 )
| ~ ( c_in @ SV1293 @ SV792 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3881,plain,
! [SV1294: $i,SV793: $i,SV259: $i] :
( ( ( c_in @ SV259 @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV259 @ ( c_Complete__Lattice_OSup__class_OSup @ SV793 @ ( tc_fun @ SV1294 @ tc_bool ) ) @ ( tc_fun @ SV1294 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3882,plain,
! [SV1660: $i,SV1295: $i,SV794: $i,SV260: $i] :
( ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1660 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) )
| ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV1660 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3883,plain,
! [SV1847: $i,SV1661: $i,SV1296: $i,SV795: $i,SV261: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SV1296 @ SV1661 @ SV1847 ) @ SV261 @ SV1661 )
| ~ ( c_in @ SV795 @ ( c_Relation_OImage @ SV1296 @ SV261 @ SV1661 @ SV1847 ) @ SV1847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(3884,plain,
! [SV1848: $i,SV1662: $i,SV1297: $i,SV796: $i,SV262: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SV1297 @ SV1662 @ SV1848 ) @ SV262 @ SV1662 )
| ~ ( c_in @ SV796 @ ( c_Relation_OImage @ SV1297 @ SV262 @ SV1662 @ SV1848 ) @ SV1848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(3885,plain,
! [SV1663: $i,SV1298: $i,SV797: $i,SV263: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
= $true )
| ( ( ~ ( c_in @ SV1663 @ SV263 @ SV1298 )
| ~ ( c_Wellfounded_Owf @ SV797 @ SV1298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3452]) ).
thf(3886,plain,
! [SV1664: $i,SV1299: $i,SV798: $i,SV264: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
= $true )
| ( ( ~ ( c_in @ SV1664 @ SV264 @ SV1299 )
| ~ ( c_Wellfounded_Owf @ SV798 @ SV1299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(3887,plain,
! [SV1300: $i,SV799: $i,SV265: $i] :
( ( ( c_in @ SV265 @ ( c_Complete__Lattice_OSup__class_OSup @ SV799 @ ( tc_fun @ SV1300 @ tc_bool ) ) @ SV1300 )
= $false )
| ( ( c_in @ SV265 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV265 @ SV799 @ SV1300 ) @ SV1300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3888,plain,
! [SV1301: $i,SV800: $i,SV266: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
= $false )
| ( ( ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1301 @ SV266 ) @ SV266 )
| ~ ( c_in @ SV800 @ SV1301 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3889,plain,
! [SV1849: $i,SV1665: $i,SV1302: $i,SV801: $i,SV267: $i] :
( ( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SV1849 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SV1849 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3890,plain,
! [SV1850: $i,SV1666: $i,SV1303: $i,SV802: $i,SV268: $i] :
( ( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SV1850 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SV1850 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3891,plain,
! [SV1851: $i,SV1667: $i,SV1304: $i,SV803: $i,SV269: $i] :
( ( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SV1851 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SV1851 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3892,plain,
! [SV1668: $i,SV1307: $i,SV806: $i,SV272: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SV806 @ SV1307 @ SV1668 ) @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV806 @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3893,plain,
! [SV1308: $i,SV807: $i,SV273: $i] :
( ( ( class_Orderings_Olinorder @ SV273 )
= $false )
| ( ( ( c_lessequals @ SV807 @ SV1308 @ SV273 )
| ( c_lessequals @ SV1308 @ SV807 @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3894,plain,
! [SV1309: $i,SV275: $i,SV809: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV809 @ SV275 @ SV1309 )
= $false )
| ( ( c_lessequals @ SV275 @ ( c_Product__Type_OSigma @ SV809 @ ( c_COMBK @ SV809 @ ( tc_fun @ SV1309 @ tc_bool ) @ SV1309 ) @ SV1309 @ SV1309 ) @ ( tc_fun @ ( tc_prod @ SV1309 @ SV1309 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3895,plain,
! [SV1852: $i,SV1669: $i,SV1310: $i,SV811: $i,SV277: $i] :
( ( ! [SY4937: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SY4937 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
| ~ ( c_lessequals @ SV811 @ SY4937 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3896,plain,
! [SV1670: $i,SV1311: $i,SV812: $i,SV278: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SV812 @ SV1311 ) @ ( c_Relation_ODomain @ SV1670 @ SV812 @ SV1311 ) @ ( tc_fun @ SV812 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV278 @ SV1670 @ ( tc_fun @ ( tc_prod @ SV812 @ SV1311 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3463]) ).
thf(3897,plain,
! [SV1671: $i,SV1312: $i,SV813: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SV1671 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3464]) ).
thf(3898,plain,
! [SV816: $i,SV1313: $i,SV282: $i] :
( ( ( ~ ( c_lessequals @ SV282 @ SV1313 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1313 @ SV816 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV282 @ SV816 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(3899,plain,
! [SV1672: $i,SV1314: $i,SV817: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) )
| ~ ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SV1672 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3468]) ).
thf(3900,plain,
! [SV1673: $i,SV1315: $i,SV818: $i,SV284: $i] :
( ( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1673 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
| ~ ( c_lessequals @ SV284 @ SV1673 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(3901,plain,
! [SV1674: $i,SV1316: $i,SV821: $i,SV287: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV287 ) )
= $true )
| ( ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3902,plain,
! [SV1675: $i,SV1317: $i,SV822: $i,SV288: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV288 ) )
= $true )
| ( ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
| ~ ( c_lessequals @ SV822 @ SV1675 @ SV288 )
| ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(3903,plain,
! [SV824: $i,SV1318: $i,SV290: $i] :
( ( ( c_lessequals @ SV290 @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV290 @ SV824 ) @ ( c_Transitive__Closure_Ortrancl @ SV1318 @ SV824 ) @ ( tc_fun @ ( tc_prod @ SV824 @ SV824 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3904,plain,
! [SV825: $i,SV1319: $i,SV291: $i] :
( ( ( c_lessequals @ SV291 @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV291 @ SV825 ) @ ( c_Product__Type_OSigma @ SV1319 @ ( c_COMBK @ SV1319 @ ( tc_fun @ SV825 @ tc_bool ) @ SV825 ) @ SV825 @ SV825 ) @ ( tc_fun @ ( tc_prod @ SV825 @ SV825 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3905,plain,
! [SV1320: $i,SV826: $i,SV292: $i] :
( ( ( class_Orderings_Oorder @ SV292 )
= $false )
| ( ( ( SV826 = SV1320 )
| ~ ( c_lessequals @ SV826 @ SV1320 @ SV292 )
| ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3906,plain,
! [SV1321: $i,SV827: $i,SV293: $i] :
( ( ( class_Orderings_Oorder @ SV293 )
= $false )
| ( ( ( SV827 = SV1321 )
| ~ ( c_lessequals @ SV1321 @ SV827 @ SV293 )
| ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3907,plain,
! [SV1322: $i,SV828: $i,SV294: $i] :
( ( ( class_Orderings_Oorder @ SV294 )
= $false )
| ( ( ( SV828 = SV1322 )
| ~ ( c_lessequals @ SV1322 @ SV828 @ SV294 )
| ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3908,plain,
! [SV1323: $i,SV295: $i,SV829: $i] :
( ( ( ~ ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true )
| ( ( SV295 = SV829 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3477]) ).
thf(3909,plain,
! [SV1324: $i,SV296: $i,SV830: $i] :
( ( ( ~ ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true )
| ( ( SV296 = SV830 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3478]) ).
thf(3910,plain,
! [SV1853: $i,SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ! [SY4938: $i,SY4939: $i,SY4940: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SY4938 @ ( c_COMBK @ SY4939 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY4940 @ ( c_COMBK @ SY4939 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SY4938 @ ( c_COMBK @ SY4940 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3911,plain,
! [SV833: $i,SV1326: $i,SV299: $i] :
( ( ( c_lessequals @ SV299 @ SV1326 @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV299 @ SV833 ) @ ( c_Transitive__Closure_Ortrancl @ SV1326 @ SV833 ) @ ( tc_fun @ ( tc_prod @ SV833 @ SV833 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3912,plain,
! [SV1854: $i,SV1677: $i,SV1327: $i,SV836: $i,SV302: $i] :
( ( ! [SY4941: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) )
| ~ ( c_in @ SY4941 @ SV836 @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3913,plain,
! [SV1855: $i,SV1678: $i,SV1328: $i,SV837: $i,SV303: $i] :
( ( ! [SY4942: $i] :
( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) )
| ~ ( c_in @ SY4942 @ SV1678 @ SV1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(3914,plain,
! [SV1329: $i,SV305: $i,SV839: $i] :
( ( ( c_Relation_Orefl__on @ SV839 @ SV305 @ SV1329 )
= $false )
| ( ( c_lessequals @ SV305 @ ( c_Product__Type_OSigma @ SV839 @ ( c_COMBK @ SV839 @ ( tc_fun @ SV1329 @ tc_bool ) @ SV1329 ) @ SV1329 @ SV1329 ) @ ( tc_fun @ ( tc_prod @ SV1329 @ SV1329 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3915,plain,
! [SV1856: $i,SV1679: $i,SV1330: $i,SV840: $i,SV306: $i] :
( ( ! [SY4943: $i,SY4944: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SY4943 @ SY4944 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SY4944 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SY4943 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3916,plain,
! [SV1857: $i,SV1681: $i,SV1332: $i,SV842: $i,SV308: $i] :
( ( ! [SY4945: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SV1681 ) @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SY4945 @ ( c_COMBK @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) @ SV1332 ) @ SV1332 @ SV1681 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1681 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(3917,plain,
! [SV844: $i,SV1333: $i,SV310: $i] :
( ( ( ~ ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1333 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3918,plain,
! [SV1858: $i,SV1682: $i,SV1334: $i,SV845: $i,SV311: $i] :
( ( ( c_in @ SV311 @ SV845 @ SV1334 )
| ( SV311 = SV1682 )
| ~ ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3919,plain,
! [SV846: $i,SV312: $i,SV1335: $i] :
( ( ( c_lessequals @ SV1335 @ SV312 @ ( tc_fun @ ( tc_prod @ SV846 @ SV846 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV312 @ SV846 ) @ ( c_Wellfounded_Oacc @ SV1335 @ SV846 ) @ ( tc_fun @ SV846 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3920,plain,
! [SV1859: $i,SV1683: $i,SV1336: $i,SV847: $i,SV313: $i] :
( ( ~ ( class_HOL_Oord @ SV313 )
| ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SV1859 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(3921,plain,
! [SV1684: $i,SV1337: $i,SV848: $i,SV314: $i] :
( ( ( c_in @ SV314 @ SV848 @ SV1337 )
= $true )
| ( ( ~ ( c_in @ SV314 @ SV1684 @ SV1337 )
| ~ ( c_lessequals @ SV1684 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3922,plain,
! [SV1685: $i,SV1338: $i,SV849: $i,SV315: $i] :
( ( ( c_in @ SV315 @ SV849 @ SV1338 )
= $true )
| ( ( ~ ( c_lessequals @ SV1685 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) )
| ~ ( c_in @ SV315 @ SV1685 @ SV1338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3923,plain,
! [SV1686: $i,SV1339: $i,SV850: $i,SV316: $i] :
( ( ( c_in @ SV316 @ SV850 @ SV1339 )
= $true )
| ( ( ~ ( c_in @ SV316 @ SV1686 @ SV1339 )
| ~ ( c_lessequals @ SV1686 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(3924,plain,
! [SV1687: $i,SV1340: $i,SV851: $i,SV317: $i] :
( ( ( c_in @ SV317 @ SV851 @ SV1340 )
= $true )
| ( ( ~ ( c_in @ SV317 @ SV1687 @ SV1340 )
| ~ ( c_lessequals @ SV1687 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(3925,plain,
! [SV1341: $i,SV852: $i,SV318: $i] :
( ( ( c_in @ SV318 @ SV852 @ ( tc_prod @ SV1341 @ SV1341 ) )
= $false )
| ( ( c_in @ SV318 @ ( c_Transitive__Closure_Ortrancl @ SV852 @ SV1341 ) @ ( tc_prod @ SV1341 @ SV1341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3926,plain,
! [SV1688: $i,SV1342: $i,SV853: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Ortrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Otrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(3927,plain,
! [SV1860: $i,SV1689: $i,SV1343: $i,SV854: $i,SV320: $i] :
( ( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SV1860 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SV1860 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(3928,plain,
! [SV1861: $i,SV1690: $i,SV1344: $i,SV855: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SV1861 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV1861 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3929,plain,
! [SV1691: $i,SV1345: $i,SV856: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV856 @ SV322 @ SV1345 @ SV1691 ) @ SV1691 @ SV1691 ) @ SV856 @ ( tc_prod @ SV1691 @ SV1691 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV322 @ SV1345 @ SV1691 @ SV1691 ) @ ( c_Transitive__Closure_Otrancl @ SV856 @ SV1691 ) @ ( tc_prod @ SV1691 @ SV1691 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3930,plain,
! [SV1692: $i,SV1346: $i,SV857: $i,SV323: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SV1346 @ SV1692 ) @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ SV323 @ ( tc_prod @ SV1692 @ SV1692 ) )
| ~ ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(3931,plain,
! [SV1347: $i,SV858: $i,SV324: $i] :
( ( ( c_in @ ( c_Pair @ SV324 @ SV324 @ SV858 @ SV858 ) @ SV1347 @ ( tc_prod @ SV858 @ SV858 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1347 @ SV858 ) @ SV858 @ SV858 ) @ ( c_Transitive__Closure_Otrancl @ SV1347 @ SV858 ) @ ( tc_prod @ SV858 @ SV858 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3932,plain,
! [SV1348: $i,SV859: $i,SV325: $i] :
( ( ( c_in @ SV325 @ ( c_Complete__Lattice_OSup__class_OSup @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SV1348 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ SV325 @ SV859 @ SV1348 ) @ SV859 @ ( tc_fun @ SV1348 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3933,plain,
! [SV1693: $i,SV1349: $i,SV860: $i,SV326: $i] :
( ( ( c_in @ ( c_Pair @ SV326 @ SV860 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1693 @ SV1349 @ SV1349 ) @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV860 @ SV326 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3504]) ).
thf(3934,plain,
! [SV1694: $i,SV1350: $i,SV861: $i,SV327: $i] :
( ( ( c_in @ ( c_Pair @ SV327 @ SV861 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV861 @ SV327 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1694 @ SV1350 @ SV1350 ) @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(3935,plain,
! [SV1862: $i,SV1695: $i,SV1351: $i,SV862: $i,SV328: $i] :
( ( ! [SY4946: $i,SY4947: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SV1862 @ SY4946 @ SY4947 ) @ SV1862 @ SY4947 ) @ SV1351 @ ( tc_prod @ SV1862 @ SY4947 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SV1862 @ SY4946 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SV1862 @ SY4947 @ SY4946 ) @ ( tc_prod @ SV1862 @ SY4946 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(3936,plain,
! [SV1863: $i,SV1696: $i,SV1352: $i,SV863: $i,SV329: $i] :
( ( ! [SY4948: $i,SY4949: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SV1863 @ SY4948 @ SY4949 ) @ SV863 @ SY4949 @ SY4948 ) @ SV1696 @ ( tc_prod @ SY4949 @ SY4948 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SV1863 @ SY4948 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SV1863 @ SY4949 @ SY4948 ) @ ( tc_prod @ SV1863 @ SY4948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3937,plain,
! [SV1864: $i,SV1697: $i,SV1353: $i,SV864: $i,SV330: $i] :
( ( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SV1353 @ SV1697 @ SV1864 ) @ ( tc_fun @ SV1697 @ SV1864 ) )
| ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ ( hAPP @ SV1353 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ SV1864 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3938,plain,
! [SV1865: $i,SV1698: $i,SV1354: $i,SV865: $i,SV331: $i] :
( ( ! [SY4950: $i] :
( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
| ~ ( c_in @ SV865 @ SV1865 @ SY4950 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SY4950 ) @ SY4950 @ SV1698 ) @ ( tc_fun @ SY4950 @ SV1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(3939,plain,
! [SV1866: $i,SV1699: $i,SV1355: $i,SV866: $i,SV332: $i] :
( ( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SV1355 @ SV1699 @ SV1866 ) @ ( tc_fun @ SV1699 @ SV1866 ) )
| ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ ( hAPP @ SV1355 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ SV1866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(3940,plain,
! [SV1867: $i,SV1700: $i,SV1356: $i,SV867: $i,SV333: $i] :
( ( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV867 @ SV1356 @ SV1700 @ SV1867 ) @ ( tc_fun @ SV1700 @ SV1867 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV867 @ SV1356 @ SV333 @ SV1700 @ SV1867 ) @ SV867 @ SV1700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(3941,plain,
! [SV1868: $i,SV1701: $i,SV1357: $i,SV868: $i,SV334: $i] :
( ( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SV868 @ SV1357 @ SV1701 @ SV1868 ) @ ( tc_fun @ SV1701 @ SV1868 ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV868 @ SV1357 @ SV334 @ SV1701 @ SV1868 ) @ SV868 @ SV1701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(3942,plain,
! [SV1702: $i,SV1358: $i,SV869: $i,SV335: $i] :
( ( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SV869 @ SV1358 @ SV1702 ) @ SV335 @ SV1702 )
= $true )
| ( ( ~ ( c_in @ SV869 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SV1358 @ SV1702 ) @ ( tc_fun @ SV1702 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3943,plain,
! [SV1360: $i,SV340: $i,SV874: $i] :
( ( ( c_in @ SV874 @ ( c_Relation_OId__on @ SV340 @ SV1360 ) @ ( tc_prod @ SV1360 @ SV1360 ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV340 @ SV874 @ SV1360 ) @ SV340 @ SV1360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3944,plain,
! [SV1361: $i,SV875: $i,SV341: $i] :
( ( ( c_in @ SV341 @ ( c_Relation_OId__on @ SV875 @ SV1361 ) @ ( tc_prod @ SV1361 @ SV1361 ) )
= $false )
| ( ( SV341
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV875 @ SV341 @ SV1361 ) @ SV1361 @ SV1361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3945,plain,
! [SV1869: $i,SV1703: $i,SV1362: $i,SV876: $i,SV342: $i] :
( ( ! [SY4951: $i] :
( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SV1362 @ SV1703 @ SV1869 )
= ( c_Recdef_Ocut @ SY4951 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SY4951 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) @ SV1362 @ SV1703 @ SV1703 ) @ SV876 @ ( tc_prod @ SV1703 @ SV1703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(3946,plain,
! [SV877: $i,SV343: $i,SV1363: $i] :
( ( ( c_Relation_Orefl__on @ SV1363 @ SV343 @ SV877 )
= $false )
| ( ( c_lessequals @ SV343 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV343 @ SV877 @ SV877 ) @ SV343 @ SV877 @ SV877 @ SV877 ) @ ( tc_fun @ ( tc_prod @ SV877 @ SV877 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3947,plain,
! [SV1870: $i,SV1704: $i,SV1364: $i,SV879: $i,SV345: $i] :
( ( ~ ( c_in @ SV345 @ SV879 @ SV1364 )
| ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_in @ SV1870 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(3948,plain,
! [SV1871: $i,SV1705: $i,SV1365: $i,SV880: $i,SV346: $i] :
( ( ~ ( c_in @ SV346 @ SV880 @ SV1365 )
| ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
| ~ ( c_in @ SV1871 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3949,plain,
! [SV1872: $i,SV1706: $i,SV1366: $i,SV881: $i,SV347: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SV1366 @ SV1706 @ SV1872 ) @ SV881 @ SV1706 @ SV1872 ) @ SV1366 @ ( tc_prod @ SV1706 @ SV1872 ) )
| ~ ( c_in @ SV881 @ ( c_Relation_OImage @ SV1366 @ SV347 @ SV1706 @ SV1872 ) @ SV1872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(3950,plain,
! [SV1873: $i,SV1707: $i,SV1367: $i,SV882: $i,SV348: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SV1367 @ SV1707 @ SV1873 ) @ SV882 @ SV1707 @ SV1873 ) @ SV1367 @ ( tc_prod @ SV1707 @ SV1873 ) )
| ~ ( c_in @ SV882 @ ( c_Relation_OImage @ SV1367 @ SV348 @ SV1707 @ SV1873 ) @ SV1873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3951,plain,
! [SV1708: $i,SV1368: $i,SV883: $i,SV349: $i] :
( ( ( SV349 = SV883 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV349 @ SV883 @ SV1368 @ SV1368 ) @ ( c_Transitive__Closure_Ortrancl @ SV1708 @ SV1368 ) @ ( tc_prod @ SV1368 @ SV1368 ) )
| ( c_in @ SV349 @ ( c_Relation_ODomain @ SV1708 @ SV1368 @ SV1368 ) @ SV1368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3952,plain,
! [SV1709: $i,SV1369: $i,SV884: $i,SV350: $i] :
( ( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SV884 @ SV1369 @ SV1709 ) @ SV1369 @ SV1709 ) @ SV884 @ ( tc_prod @ SV1369 @ SV1709 ) )
= $true )
| ( ( ~ ( c_in @ SV350 @ ( c_Relation_ODomain @ SV884 @ SV1369 @ SV1709 ) @ SV1369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(3953,plain,
! [SV1710: $i,SV1370: $i,SV885: $i,SV351: $i] :
( ( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SV885 @ SV1370 @ SV1710 ) @ SV1370 @ SV1710 ) @ SV885 @ ( tc_prod @ SV1370 @ SV1710 ) )
= $true )
| ( ( ~ ( c_in @ SV351 @ ( c_Relation_ODomain @ SV885 @ SV1370 @ SV1710 ) @ SV1370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3954,plain,
! [SV1874: $i,SV1711: $i,SV1372: $i,SV887: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
| ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
| ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(3955,plain,
! [SV1712: $i,SV1373: $i,SV888: $i,SV354: $i] :
( ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
= $true )
| ( ( ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3956,plain,
! [SV1713: $i,SV1374: $i,SV889: $i,SV355: $i] :
( ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
| ~ ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(3957,plain,
! [SV1714: $i,SV1375: $i,SV890: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
= $true )
| ( ( ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(3958,plain,
! [SV1715: $i,SV1376: $i,SV891: $i,SV357: $i] :
( ( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV357 @ SV1715 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
| ~ ( c_in @ SV1715 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(3959,plain,
! [SV1716: $i,SV1377: $i,SV892: $i,SV358: $i] :
( ( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $true )
| ( ( ~ ( c_in @ SV1716 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
| ~ ( c_in @ ( c_Pair @ SV358 @ SV1716 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(3960,plain,
! [SV1717: $i,SV1379: $i,SV894: $i,SV360: $i] :
( ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
| ~ ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(3961,plain,
! [SV1875: $i,SV1718: $i,SV1380: $i,SV895: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
| ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
| ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3962,plain,
! [SV1719: $i,SV1382: $i,SV897: $i,SV363: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SV897 @ SV1382 @ SV1719 ) @ SV363 @ SV1719 @ SV1382 ) @ SV897 @ ( tc_prod @ SV1719 @ SV1382 ) )
= $true )
| ( ( ~ ( c_in @ SV363 @ ( c_Relation_ORange @ SV897 @ SV1719 @ SV1382 ) @ SV1382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3963,plain,
! [SV1720: $i,SV1383: $i,SV898: $i,SV364: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SV898 @ SV1383 @ SV1720 ) @ SV364 @ SV1720 @ SV1383 ) @ SV898 @ ( tc_prod @ SV1720 @ SV1383 ) )
= $true )
| ( ( ~ ( c_in @ SV364 @ ( c_Relation_ORange @ SV898 @ SV1720 @ SV1383 ) @ SV1383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(3964,plain,
! [SV1721: $i,SV1384: $i,SV899: $i,SV365: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_Wellfounded_Owf @ SV1721 @ SV1384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(3965,plain,
! [SV1722: $i,SV1385: $i,SV900: $i,SV366: $i] :
( ( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1722 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ SV1722 @ ( tc_prod @ SV1385 @ SV1385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3966,plain,
! [SV1876: $i,SV1723: $i,SV1386: $i,SV901: $i,SV367: $i] :
( ( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV1876 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SV1876 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(3967,plain,
! [SV1877: $i,SV1724: $i,SV1387: $i,SV902: $i,SV368: $i] :
( ( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV1877 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SV1877 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(3968,plain,
! [SV1878: $i,SV1725: $i,SV1388: $i,SV903: $i,SV369: $i] :
( ( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SV1388 @ SV1725 ) @ SV1878 @ ( tc_prod @ SV1388 @ SV1725 ) )
| ~ ( c_in @ ( c_Pair @ SV903 @ SV369 @ SV1725 @ SV1388 ) @ ( c_Relation_Oconverse @ SV1878 @ SV1388 @ SV1725 ) @ ( tc_prod @ SV1725 @ SV1388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3969,plain,
! [SV1879: $i,SV1726: $i,SV1389: $i,SV904: $i,SV370: $i] :
( ( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SV1389 @ SV1726 ) @ ( c_Relation_Oconverse @ SV1879 @ SV1726 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1726 ) )
| ~ ( c_in @ ( c_Pair @ SV904 @ SV370 @ SV1726 @ SV1389 ) @ SV1879 @ ( tc_prod @ SV1726 @ SV1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(3970,plain,
! [SV1880: $i,SV1727: $i,SV1390: $i,SV905: $i,SV371: $i] :
( ( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SV1390 @ SV1727 ) @ ( c_Relation_Oconverse @ SV1880 @ SV1727 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1727 ) )
| ~ ( c_in @ ( c_Pair @ SV905 @ SV371 @ SV1727 @ SV1390 ) @ SV1880 @ ( tc_prod @ SV1727 @ SV1390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(3971,plain,
! [SV1881: $i,SV1728: $i,SV1391: $i,SV906: $i,SV372: $i] :
( ( ! [SY4952: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SV1728 @ SV1881 ) @ SY4952 )
= ( hAPP @ SV372 @ SY4952 ) )
| ~ ( c_in @ ( c_Pair @ SY4952 @ SV1391 @ SV1728 @ SV1728 ) @ SV906 @ ( tc_prod @ SV1728 @ SV1728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3972,plain,
! [SV1882: $i,SV1729: $i,SV1392: $i,SV907: $i,SV373: $i] :
( ( ! [SY4953: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SV1729 @ SV1882 ) @ SY4953 )
= ( hAPP @ SV373 @ SY4953 ) )
| ~ ( c_in @ ( c_Pair @ SY4953 @ SV1392 @ SV1729 @ SV1729 ) @ SV907 @ ( tc_prod @ SV1729 @ SV1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(3973,plain,
! [SV1393: $i,SV908: $i,SV374: $i] :
( ( ( c_in @ SV374 @ SV908 @ ( tc_prod @ SV1393 @ SV1393 ) )
= $false )
| ( ( c_in @ SV374 @ ( c_Transitive__Closure_Otrancl @ SV908 @ SV1393 ) @ ( tc_prod @ SV1393 @ SV1393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3974,plain,
! [SV1730: $i,SV1394: $i,SV909: $i,SV375: $i] :
( ( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1730 @ SV1394 ) @ SV1394 @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1730 @ SV1394 @ SV1394 ) @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3975,plain,
! [SV1731: $i,SV1395: $i,SV910: $i,SV376: $i] :
( ( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1731 @ SV1395 @ SV1395 ) @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1731 @ SV1395 ) @ SV1395 @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3976,plain,
! [SV377: $i,SV1396: $i,SV911: $i] :
( ( ( c_Wellfounded_Owf @ SV911 @ SV1396 )
= $false )
| ( ( c_in @ SV377 @ ( c_Wellfounded_Oacc @ SV911 @ SV1396 ) @ SV1396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3977,plain,
! [SV1399: $i,SV919: $i,SV386: $i] :
( ( ( c_Relation_Orefl__on @ SV386 @ ( c_Relation_Oconverse @ SV919 @ SV1399 @ SV1399 ) @ SV1399 )
= $false )
| ( ( c_Relation_Orefl__on @ SV386 @ SV919 @ SV1399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3560]) ).
thf(3978,plain,
! [SV1400: $i,SV920: $i,SV387: $i] :
( ( ( c_Relation_Orefl__on @ SV387 @ SV920 @ SV1400 )
= $false )
| ( ( c_Relation_Orefl__on @ SV387 @ ( c_Relation_Oconverse @ SV920 @ SV1400 @ SV1400 ) @ SV1400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3561]) ).
thf(3979,plain,
! [SV1883: $i,SV1732: $i,SV1401: $i,SV927: $i,SV394: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV394 @ SV927 @ SV1401 @ SV1732 @ SV1883 ) @ SV1401 @ SV1883 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV927 @ SV1732 @ SV1883 ) @ ( c_Relation_Oconverse @ SV394 @ SV1401 @ SV1732 ) @ SV1883 @ SV1732 @ SV1401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(3980,plain,
! [SV1733: $i,SV1402: $i,SV930: $i,SV397: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SV930 @ SV1402 @ SV1733 ) @ SV1733 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV397 @ SV1402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3981,plain,
! [SV1734: $i,SV1403: $i,SV931: $i,SV398: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SV931 @ SV1403 @ SV1734 ) @ SV1734 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV398 @ SV1403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(3982,plain,
! [SV1884: $i,SV1735: $i,SV1404: $i,SV933: $i,SV401: $i] :
( ( ! [SY4954: $i,SY4955: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SV1404 @ SV1735 @ SV1884 ) @ SY4954 @ SV1404 @ SV1884 @ SY4955 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SY4954 @ SV1735 @ SV1884 @ SY4955 ) @ SV1404 @ SV1735 @ SY4955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3983,plain,
! [SV940: $i,SV408: $i,SV1408: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1408 @ SV408 @ SV940 )
= $false )
| ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV408 @ SV940 @ SV940 ) @ SV408 @ SV940 @ SV940 @ SV940 )
= SV408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3984,plain,
! [SV1409: $i,SV941: $i,SV409: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV409 @ SV941 @ SV1409 )
= $false )
| ( ( c_Relation_Orefl__on @ SV409 @ SV941 @ SV1409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3985,plain,
! [SV1410: $i,SV942: $i,SV410: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV410 @ SV942 @ SV1410 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ SV410 @ SV942 @ SV1410 ) @ ( tc_fun @ SV1410 @ tc_bool ) )
= SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3986,plain,
! [SV943: $i,SV411: $i,SV1411: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1411 @ SV411 @ SV943 )
= $false )
| ( ( c_Relation_Osym @ SV411 @ SV943 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3987,plain,
! [SV1414: $i,SV946: $i,SV414: $i] :
( ( ( c_Relation_Ototal__on @ SV414 @ ( c_Relation_Oconverse @ SV946 @ SV1414 @ SV1414 ) @ SV1414 )
= $false )
| ( ( c_Relation_Ototal__on @ SV414 @ SV946 @ SV1414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3988,plain,
! [SV1415: $i,SV947: $i,SV415: $i] :
( ( ( c_Relation_Ototal__on @ SV415 @ SV947 @ SV1415 )
= $false )
| ( ( c_Relation_Ototal__on @ SV415 @ ( c_Relation_Oconverse @ SV947 @ SV1415 @ SV1415 ) @ SV1415 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3989,plain,
! [SV1737: $i,SV1416: $i,SV948: $i,SV416: $i] :
( ( ( SV416 = SV948 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV416 @ SV948 @ SV1416 @ SV1416 ) @ ( c_Relation_OId__on @ SV1737 @ SV1416 ) @ ( tc_prod @ SV1416 @ SV1416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3577]) ).
thf(3990,plain,
! [SV1417: $i,SV949: $i,SV417: $i] :
( ( ( c_in @ ( c_Pair @ SV417 @ SV949 @ SV1417 @ SV1417 ) @ ( c_Relation_OId @ SV1417 ) @ ( tc_prod @ SV1417 @ SV1417 ) )
= $false )
| ( ( SV417 = SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3991,plain,
! [SV418: $i,SV950: $i,SV1418: $i] :
( ( ( c_Nitpick_Orefl_H @ SV1418 @ SV950 )
= $false )
| ( ( c_in @ ( c_Pair @ SV418 @ SV418 @ SV950 @ SV950 ) @ SV1418 @ ( tc_prod @ SV950 @ SV950 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3992,plain,
! [SV1419: $i,SV951: $i,SV419: $i] :
( ( ( c_in @ ( c_Pair @ SV419 @ SV419 @ SV951 @ SV951 ) @ SV1419 @ ( tc_prod @ SV951 @ SV951 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1419 @ SV951 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3580]) ).
thf(3993,plain,
! [SV1885: $i,SV1738: $i,SV1420: $i,SV952: $i,SV420: $i] :
( ( ! [SY4956: $i] :
( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SV1738 @ SV1885 @ SY4956 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1885 @ SV420 ) @ ( hAPP @ SV1885 @ SV952 ) @ SY4956 @ SY4956 ) @ SV1738 @ ( tc_prod @ SY4956 @ SY4956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(3994,plain,
! [SV1886: $i,SV1739: $i,SV1421: $i,SV953: $i,SV421: $i] :
( ( ! [SY4957: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SV1739 @ SV1739 ) @ SV1886 @ ( tc_prod @ SV1739 @ SV1739 ) )
| ~ ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SY4957 @ SY4957 ) @ ( c_Relation_Oinv__image @ SV1886 @ SV421 @ SV1739 @ SY4957 ) @ ( tc_prod @ SY4957 @ SY4957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(3995,plain,
! [SV1740: $i,SV1422: $i,SV954: $i,SV422: $i] :
( ( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
| ~ ( c_Relation_Osym @ SV1740 @ SV1422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3996,plain,
! [SV1741: $i,SV1423: $i,SV955: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
| ~ ( c_Relation_Osym @ SV1741 @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(3997,plain,
! [SV1887: $i,SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ! [SY4958: $i,SY4959: $i,SY4960: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SY4958 @ SV1424 @ SY4959 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SY4960 @ SV956 @ SY4959 @ SV1742 ) @ SY4958 @ ( tc_prod @ SY4959 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4960 @ SV1424 @ SY4959 ) @ SV1887 @ ( tc_prod @ SV1424 @ SY4959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3998,plain,
! [SV1888: $i,SV1743: $i,SV1425: $i,SV957: $i,SV425: $i] :
( ( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SV1888 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SV1888 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3999,plain,
! [SV1889: $i,SV1744: $i,SV1426: $i,SV958: $i,SV426: $i] :
( ( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SV1889 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SV1889 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4000,plain,
! [SV1890: $i,SV1745: $i,SV1427: $i,SV961: $i,SV429: $i] :
( ( ! [SY4961: $i] :
( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
| ~ ( c_in @ SV961 @ SV1890 @ SY4961 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SY4961 @ SV1745 ) @ ( tc_fun @ SY4961 @ SV1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(4001,plain,
! [SV1891: $i,SV1746: $i,SV1428: $i,SV962: $i,SV430: $i] :
( ( ! [SY4962: $i] :
( ~ ( c_in @ SV430 @ SV962 @ SV1428 )
| ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SY4962 )
| ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SY4962 ) @ ( tc_fun @ SV1428 @ SY4962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4002,plain,
! [SV1892: $i,SV1747: $i,SV1429: $i,SV963: $i,SV431: $i] :
( ( ! [SY4963: $i,SY4964: $i] :
( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SY4963 @ ( tc_prod @ SV1892 @ SV1892 ) )
| ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SY4964 @ SY4963 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY4964 @ SY4963 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4964 @ SY4963 @ SV1892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4003,plain,
! [SV1893: $i,SV1748: $i,SV1430: $i,SV964: $i,SV432: $i] :
( ( ! [SY4965: $i] :
( ~ ( c_in @ SV432 @ SV964 @ SV1430 )
| ~ ( c_in @ SV1748 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SY4965 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SY4965 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SY4965 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SY4965 @ ( tc_prod @ SV1430 @ SV1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(4004,plain,
! [SV1749: $i,SV1431: $i,SV965: $i,SV433: $i] :
( ( ( c_in @ SV433 @ SV965 @ SV1431 )
= $true )
| ( ( ~ ( c_in @ SV965 @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) )
| ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3592]) ).
thf(4005,plain,
! [SV1750: $i,SV1432: $i,SV966: $i,SV434: $i] :
( ( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
= $true )
| ( ( ~ ( c_in @ SV434 @ SV1750 @ SV1432 )
| ~ ( c_in @ SV1750 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(4006,plain,
! [SV1751: $i,SV1433: $i,SV967: $i,SV435: $i] :
( ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SV1751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV435 = SV967 )
| ( SV435 = SV1751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4007,plain,
! [SV1752: $i,SV1434: $i,SV968: $i,SV436: $i] :
( ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SV1752 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV968 = SV1752 )
| ( SV436 = SV1752 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4008,plain,
! [SV1753: $i,SV1436: $i,SV971: $i,SV439: $i] :
( ( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1436 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( SV971 = SV1753 )
| ~ ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1436 @ SV1753 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4009,plain,
! [SV1437: $i,SV440: $i,SV972: $i] :
( ( ( SV972 = SV440 )
= $true )
| ( ( c_in @ ( c_Pair @ SV440 @ SV972 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1437 @ SV440 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV440 = SV972 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4010,plain,
! [SV1754: $i,SV1439: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SV1754 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV443 = SV975 )
| ( SV975 = SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(4011,plain,
! [SV1755: $i,SV1440: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SV1755 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV444 = SV1755 )
| ( SV976 = SV1755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(4012,plain,
! [SV1441: $i,SV977: $i,SV445: $i] :
( ( ( SV445 = SV977 )
= $true )
| ( ( c_in @ ( c_Pair @ SV445 @ SV977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1441 @ SV977 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV445 = SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(4013,plain,
! [SV1756: $i,SV1442: $i,SV978: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1442 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( SV446 = SV1756 )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1442 @ SV1756 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(4014,plain,
! [SV1443: $i,SV983: $i,SV451: $i] :
( ( ( ~ ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV983 = SV1443 )
= $true )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SV983 @ SV1443 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(4015,plain,
! [SV1444: $i,SV984: $i,SV454: $i] :
( ( ( ~ ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV984 = SV1444 )
= $true )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SV984 @ SV1444 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(4016,plain,
! [SV1894: $i,SV1757: $i,SV1445: $i,SV985: $i,SV455: $i] :
( ( ! [SY4966: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SY4966 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
| ~ ( c_in @ SV985 @ ( hAPP @ SY4966 @ SV455 ) @ SV1757 )
| ~ ( c_in @ SV455 @ SV1894 @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4017,plain,
! [SV1895: $i,SV1758: $i,SV1446: $i,SV986: $i,SV456: $i] :
( ( ! [SY4967: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SY4967 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
| ~ ( c_in @ SV986 @ ( hAPP @ SY4967 @ SV456 ) @ SV1758 )
| ~ ( c_in @ SV456 @ SV1895 @ SV1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4018,plain,
! [SV1759: $i,SV1447: $i,SV987: $i,SV457: $i] :
( ( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV457 @ SV1759 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) )
| ~ ( c_in @ SV1759 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3610]) ).
thf(4019,plain,
! [SV1760: $i,SV1448: $i,SV988: $i,SV458: $i] :
( ( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV458 @ SV1760 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) )
| ~ ( c_in @ SV1760 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3611]) ).
thf(4020,plain,
! [SV1896: $i,SV1761: $i,SV1449: $i,SV989: $i,SV459: $i] :
( ( ! [SY4968: $i] :
( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
| ~ ( c_in @ ( c_Pair @ SY4968 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) )
| ~ ( c_in @ SY4968 @ SV1449 @ SV1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4021,plain,
! [SV1897: $i,SV1762: $i,SV1450: $i,SV990: $i,SV460: $i] :
( ( ! [SY4969: $i] :
( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
| ~ ( c_in @ ( c_Pair @ SY4969 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) )
| ~ ( c_in @ SY4969 @ SV1450 @ SV1762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4022,plain,
! [SV1763: $i,SV1451: $i,SV991: $i,SV461: $i] :
( ( ( c_in @ SV461 @ SV991 @ SV1451 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV461 @ SV1763 @ SV1451 @ SV1451 ) @ ( c_Relation_OId__on @ SV991 @ SV1451 ) @ ( tc_prod @ SV1451 @ SV1451 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(4023,plain,
! [SV992: $i,SV1452: $i,SV462: $i] :
( ( ( c_in @ SV462 @ SV1452 @ SV992 )
= $false )
| ( ( c_in @ ( c_Pair @ SV462 @ SV462 @ SV992 @ SV992 ) @ ( c_Relation_OId__on @ SV1452 @ SV992 ) @ ( tc_prod @ SV992 @ SV992 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(4024,plain,
! [SV1898: $i,SV1764: $i,SV1453: $i,SV993: $i,SV463: $i] :
( ( ( c_in @ SV463 @ SV993 @ SV1453 )
| ~ ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SV1898 @ ( tc_prod @ SV1453 @ SV1453 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SV1898 @ SV1453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4025,plain,
! [SV1899: $i,SV1765: $i,SV1454: $i,SV994: $i,SV464: $i] :
( ( ( c_in @ SV464 @ SV994 @ SV1454 )
| ~ ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SV1899 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SV1899 @ SV1454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4026,plain,
! [SV1900: $i,SV1766: $i,SV1455: $i,SV995: $i,SV465: $i] :
( ( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SV1455 @ SV1766 ) @ SV1766 )
| ~ ( c_in @ ( c_Pair @ SV1900 @ SV465 @ SV1455 @ SV1766 ) @ SV995 @ ( tc_prod @ SV1455 @ SV1766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4027,plain,
! [SV1901: $i,SV1767: $i,SV1456: $i,SV996: $i,SV466: $i] :
( ( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SV1456 @ SV1767 ) @ SV1767 )
| ~ ( c_in @ ( c_Pair @ SV1901 @ SV466 @ SV1456 @ SV1767 ) @ SV996 @ ( tc_prod @ SV1456 @ SV1767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4028,plain,
! [SV1902: $i,SV1768: $i,SV1457: $i,SV997: $i,SV467: $i] :
( ( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SV1457 @ SV1768 ) @ SV1457 )
| ~ ( c_in @ ( c_Pair @ SV467 @ SV1902 @ SV1457 @ SV1768 ) @ SV997 @ ( tc_prod @ SV1457 @ SV1768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4029,plain,
! [SV1903: $i,SV1769: $i,SV1458: $i,SV998: $i,SV468: $i] :
( ( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SV1458 @ SV1769 ) @ SV1458 )
| ~ ( c_in @ ( c_Pair @ SV468 @ SV1903 @ SV1458 @ SV1769 ) @ SV998 @ ( tc_prod @ SV1458 @ SV1769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4030,plain,
! [SV1904: $i,SV1770: $i,SV1459: $i,SV999: $i,SV469: $i] :
( ( ! [SY4970: $i] :
( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SV1770 )
| ~ ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SV1904 @ SV1770 ) @ ( c_Product__Type_OSigma @ SY4970 @ SV999 @ SV1904 @ SV1770 ) @ ( tc_prod @ SV1904 @ SV1770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4031,plain,
! [SV1905: $i,SV1771: $i,SV1460: $i,SV1000: $i,SV470: $i] :
( ( ! [SY4971: $i] :
( ( c_in @ SV470 @ SV1000 @ SV1460 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SV1771 @ SV1460 @ SV1905 ) @ ( c_Product__Type_OSigma @ SV1000 @ SY4971 @ SV1460 @ SV1905 ) @ ( tc_prod @ SV1460 @ SV1905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4032,plain,
! [SV1906: $i,SV1772: $i,SV1461: $i,SV1001: $i,SV471: $i] :
( ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SV1906 @ SV1461 )
| ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4033,plain,
! [SV1773: $i,SV1462: $i,SV1002: $i,SV472: $i] :
( ( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
= $true )
| ( ( ~ ( c_in @ SV472 @ SV1773 @ SV1002 )
| ~ ( c_Relation_Orefl__on @ SV1773 @ SV1462 @ SV1002 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3625]) ).
thf(4034,plain,
! [SV1907: $i,SV1774: $i,SV1463: $i,SV1003: $i,SV473: $i] :
( ( ( c_in @ SV473 @ SV1003 @ SV1463 )
| ~ ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SV1907 @ ( tc_prod @ SV1463 @ SV1463 ) )
| ~ ( c_Relation_Orefl__on @ SV1003 @ SV1907 @ SV1463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4035,plain,
! [SV1908: $i,SV1775: $i,SV1464: $i,SV1004: $i,SV474: $i] :
( ( ( c_in @ SV474 @ SV1004 @ SV1464 )
| ~ ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SV1908 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1004 @ SV1908 @ SV1464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4036,plain,
! [SV1776: $i,SV1465: $i,SV1005: $i,SV475: $i] :
( ( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
= $true )
| ( ( ~ ( c_in @ SV475 @ SV1776 @ SV1005 )
| ~ ( c_Relation_Orefl__on @ SV1776 @ SV1465 @ SV1005 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(4037,plain,
! [SV1777: $i,SV1466: $i,SV1006: $i,SV476: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SV1777 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1466 = SV1777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(4038,plain,
! [SV1778: $i,SV1467: $i,SV1007: $i,SV477: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV477 = SV1778 )
| ( SV477 = SV1778 )
| ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4039,plain,
! [SV1779: $i,SV1468: $i,SV1008: $i,SV478: $i] :
( ( ( SV478 = SV1008 )
= $true )
| ( ( ( SV478 = SV1468 )
| ~ ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(4040,plain,
! [SV1909: $i,SV1780: $i,SV1469: $i,SV1009: $i,SV479: $i] :
( ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1009 = SV1780 )
| ( SV479 = SV1780 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4041,plain,
! [SV1781: $i,SV1470: $i,SV1010: $i,SV480: $i] :
( ( ( SV480 = SV1010 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(4042,plain,
! [SV1782: $i,SV1471: $i,SV1011: $i,SV481: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1782 = SV481 )
| ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(4043,plain,
! [SV1783: $i,SV1472: $i,SV1012: $i,SV482: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1783 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(4044,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV483 = SV1013 )
| ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(4045,plain,
! [SV1910: $i,SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1785 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4046,plain,
! [SV1911: $i,SV1786: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4047,plain,
! [SV1476: $i,SV486: $i,SV1016: $i] :
( ( ( SV1016 = SV486 )
= $true )
| ( ( ~ ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV486 = SV1016 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(4048,plain,
! [SV1912: $i,SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4049,plain,
! [SV1478: $i,SV1018: $i,SV488: $i] :
( ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV488 = SV1018 )
| ~ ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(4050,plain,
! [SV1788: $i,SV1479: $i,SV1019: $i,SV489: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1788 = SV1019 )
| ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3642]) ).
thf(4051,plain,
! [SV1913: $i,SV1789: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1020 = SV1913 )
| ( SV490 = SV1913 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4052,plain,
! [SV1790: $i,SV1481: $i,SV1021: $i,SV491: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SV1790 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1481 = SV1790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(4053,plain,
! [SV1791: $i,SV1482: $i,SV1022: $i,SV492: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1022 = SV1791 )
| ( SV1791 = SV1022 )
| ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(4054,plain,
! [SV1792: $i,SV1483: $i,SV1023: $i,SV493: $i] :
( ( ( SV493 = SV1023 )
= $true )
| ( ( ( SV1483 = SV493 )
| ~ ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3646]) ).
thf(4055,plain,
! [SV1914: $i,SV1793: $i,SV1484: $i,SV1024: $i,SV494: $i] :
( ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV494 = SV1793 )
| ( SV1024 = SV1793 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4056,plain,
! [SV1794: $i,SV1485: $i,SV1025: $i,SV495: $i] :
( ( ( SV495 = SV1025 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4057,plain,
! [SV1795: $i,SV1486: $i,SV1026: $i,SV496: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1026 = SV1795 )
| ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4058,plain,
! [SV1796: $i,SV1487: $i,SV1027: $i,SV497: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SV1796 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(4059,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV498 = SV1028 )
| ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(4060,plain,
! [SV1915: $i,SV1798: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1029 = SV1915 )
| ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4061,plain,
! [SV1916: $i,SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4062,plain,
! [SV1491: $i,SV1031: $i,SV501: $i] :
( ( ( SV501 = SV1031 )
= $true )
| ( ( ~ ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV501 = SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(4063,plain,
! [SV1917: $i,SV1800: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4064,plain,
! [SV1493: $i,SV1033: $i,SV503: $i] :
( ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV503 = SV1033 )
| ~ ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(4065,plain,
! [SV1801: $i,SV1494: $i,SV1034: $i,SV504: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV504 = SV1801 )
| ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(4066,plain,
! [SV1918: $i,SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SV1802 )
| ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4067,plain,
! [SV1496: $i,SV1036: $i,SV506: $i] :
( ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV506 = SV1036 )
| ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(4068,plain,
! [SV1497: $i,SV507: $i,SV1037: $i] :
( ( ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( SV1037 = SV507 )
| ~ ( c_in @ SV1497 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(4069,plain,
! [SV1498: $i,SV508: $i,SV1038: $i] :
( ( ( hBOOL @ ( hAPP @ SV1038 @ SV508 ) )
= $false )
| ( ( c_in @ SV508 @ SV1038 @ SV1498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(4070,plain,
! [SV1499: $i,SV509: $i,SV1039: $i] :
( ( ( c_in @ SV1039 @ SV509 @ SV1499 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV509 @ SV1039 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(4071,plain,
! [SV510: $i] :
( ( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV510 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ SV510 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(4072,plain,
! [SV1500: $i,SV1040: $i,SV511: $i] :
( ( ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(4073,plain,
! [SV512: $i,SV1041: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV1041 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV512 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SV1041 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(4074,plain,
! [SV517: $i,SV1046: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV1046 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV517 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SV1046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(4075,plain,
! [SV1501: $i,SV1052: $i,SV523: $i] :
( ( ( c_fequal @ SV523 @ SV1052 @ SV1501 )
= $false )
| ( ( SV523 = SV1052 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3675]) ).
thf(4076,plain,
! [SV1919: $i,SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ! [SY4972: $i,SY4973: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
!= ( c_Recdef_Ocut @ SY4972 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
| ( ( hAPP @ SV524 @ SY4973 )
= ( hAPP @ SY4972 @ SY4973 ) )
| ~ ( c_in @ ( c_Pair @ SY4973 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4077,plain,
! [SV1503: $i,SV1054: $i,SV525: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV525 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SV1503 @ SV525 )
!= SV1503 )
| ( c_lessequals @ SV1054 @ SV1503 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(4078,plain,
! [SV1504: $i,SV1056: $i,SV527: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) )
= SV1056 )
= $false )
| ( ( c_lessequals @ SV527 @ SV1056 @ ( tc_fun @ SV1504 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(4079,plain,
! [SV1505: $i,SV1057: $i,SV528: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV528 )
= $false )
| ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SV1505 @ SV528 )
!= SV1057 )
| ( c_lessequals @ SV1057 @ SV1505 @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(4080,plain,
! [SV1920: $i,SV1804: $i,SV1506: $i,SV1058: $i,SV529: $i] :
( ( ! [SY4974: $i] :
( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
!= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
| ~ ( c_in @ SY4974 @ SV1058 @ SV1506 )
| ( SV529 = SV1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(4081,plain,
! [SV1805: $i,SV1507: $i,SV1059: $i,SV530: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SV1059 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1059 @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1805 @ SV530 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(4082,plain,
! [SV1921: $i,SV1806: $i,SV1508: $i,SV1060: $i,SV531: $i] :
( ( ! [SY4975: $i] :
( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SV1806 )
!= ( c_Pair @ SV1921 @ SY4975 @ SV1508 @ SV1806 ) )
| ( SV1060 = SY4975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4083,plain,
! [SV1807: $i,SV1509: $i,SV1062: $i,SV533: $i] :
( ( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
!= ( c_Set_Oinsert @ SV533 @ SV1807 @ SV1509 ) )
= $true )
| ( ( ( c_in @ SV533 @ SV1807 @ SV1509 )
| ( c_in @ SV533 @ SV1062 @ SV1509 )
| ( SV1062 = SV1807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(4084,plain,
! [SV1922: $i,SV1808: $i,SV1510: $i,SV1063: $i,SV534: $i] :
( ( ! [SY4976: $i] :
( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SY4976 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SY4976 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SV1808 @ SV1922 @ SY4976 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SY4976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4085,plain,
! [SV1923: $i,SV1809: $i,SV1511: $i,SV1064: $i,SV535: $i] :
( ( ! [SY4977: $i] :
( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SV1809 )
!= ( c_Pair @ SV1923 @ SY4977 @ SV1511 @ SV1809 ) )
| ( SV535 = SV1923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4086,plain,
! [SV1512: $i,SV1065: $i,SV539: $i,SV4: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV4 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV539 @ SV1065 @ SV4 ) @ SV1512 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV539 @ SV1512 @ SV4 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1065 @ SV1512 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(4087,plain,
! [SV1513: $i,SV1066: $i,SV540: $i,SV5: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV5 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1513 @ SV5 ) @ SV5 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1066 @ SV5 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1513 @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(4088,plain,
! [SV1924: $i,SV1811: $i,SV1517: $i,SV1070: $i,SV544: $i,SV9: $i] :
( ( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
| ~ ( c_in @ SV544 @ SV1811 @ SV1924 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SV1924 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4089,plain,
! [SV1812: $i,SV1518: $i,SV1071: $i,SV545: $i,SV10: $i] :
( ( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SV1812 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1518 @ SV1812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(4090,plain,
! [SV546: $i,SV1072: $i,SV11: $i,SV1519: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV1519 @ SV11 @ SV1072 ) @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV11 @ SV546 @ ( tc_fun @ SV1072 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(4091,plain,
! [SV547: $i,SV1520: $i,SV1073: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ SV1073 @ ( tc_fun @ SV1520 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV12 @ ( c_Set_Oinsert @ SV547 @ SV1073 @ SV1520 ) @ ( tc_fun @ SV1520 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(4092,plain,
! [SV1524: $i,SV24: $i,SV559: $i,SV1081: $i] :
( ( ( SV1081 = SV559 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1081 @ SV24 @ SV1524 ) @ SV559 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(4093,plain,
! [SV26: $i,SV1083: $i,SV561: $i] :
( ( ( c_Relation_Osym @ SV561 @ SV1083 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV26 @ SV1083 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SV1083 @ SV1083 ) @ tc_bool ) ) @ SV1083 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(4094,plain,
! [SV565: $i,SV1529: $i,SV1087: $i,SV30: $i] :
( ( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ SV1087 @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) )
= $false )
| ( ( c_in @ SV30 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV565 @ SV1087 @ ( tc_fun @ ( tc_prod @ SV1529 @ SV1529 ) @ tc_bool ) ) @ SV1529 ) @ ( tc_prod @ SV1529 @ SV1529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(4095,plain,
! [SV1088: $i,SV1530: $i,SV566: $i,SV31: $i] :
( ( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ SV566 @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) )
= $false )
| ( ( c_in @ SV31 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 @ SV1088 @ ( tc_fun @ ( tc_prod @ SV1530 @ SV1530 ) @ tc_bool ) ) @ SV1530 ) @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(4096,plain,
! [SV1533: $i,SV1091: $i,SV569: $i,SV34: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV34 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ SV1091 @ SV34 ) @ SV1533 @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1091 @ SV1533 @ SV34 ) @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(4097,plain,
! [SV1534: $i,SV1092: $i,SV570: $i,SV35: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV35 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ SV1534 @ SV35 ) @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1092 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV570 @ SV1534 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(4098,plain,
! [SV1535: $i,SV1093: $i,SV571: $i,SV36: $i] :
( ( ( class_Lattices_Olattice @ SV36 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ SV1535 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1093 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV571 @ SV1535 @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(4099,plain,
! [SV1536: $i,SV1094: $i,SV572: $i,SV37: $i] :
( ( ( class_Lattices_Olattice @ SV37 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ SV1094 @ SV37 ) @ SV1536 @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV572 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1094 @ SV1536 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4100,plain,
! [SV41: $i,SV1097: $i,SV576: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SV1097 @ SV41 )
= SV576 )
= $true )
| ( ( ~ ( c_lessequals @ SV576 @ SV1097 @ SV41 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(4101,plain,
! [SV42: $i,SV1098: $i,SV577: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SV1098 @ SV42 )
= SV1098 )
= $true )
| ( ( ~ ( c_lessequals @ SV1098 @ SV577 @ SV42 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3711]) ).
thf(4102,plain,
! [SV43: $i,SV1099: $i,SV1537: $i,SV578: $i] :
( ( ( ~ ( c_lessequals @ SV578 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV43 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(4103,plain,
! [SV46: $i,SV1102: $i,SV1538: $i,SV581: $i] :
( ( ( ~ ( c_lessequals @ SV581 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV46 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(4104,plain,
! [SV1539: $i,SV1103: $i,SV582: $i,SV47: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV47 )
= $false )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(4105,plain,
! [SV1540: $i,SV1106: $i,SV585: $i,SV50: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV50 )
= $false )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(4106,plain,
! [SV1541: $i,SV1107: $i,SV586: $i,SV51: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV51 )
= $false )
| ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(4107,plain,
! [SV1542: $i,SV1113: $i,SV592: $i,SV57: $i] :
( ( ( class_Lattices_Olattice @ SV57 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1113 @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ SV1542 @ SV57 ) @ SV57 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1113 @ SV1542 @ SV57 ) @ SV57 ) @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(4108,plain,
! [SV595: $i,SV1115: $i,SV1544: $i,SV60: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV60 @ SV1544 @ SV1115 ) @ SV595 @ ( tc_fun @ SV1115 @ tc_bool ) )
= $false )
| ( ( c_in @ SV60 @ SV595 @ SV1115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(4109,plain,
! [SV1117: $i,SV62: $i,SV1546: $i,SV597: $i] :
( ( ( hBOOL @ ( hAPP @ SV597 @ SV1546 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV62 @ SV597 @ SV1117 ) @ SV1546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(4110,plain,
! [SV1817: $i,SV1547: $i,SV1118: $i,SV598: $i,SV63: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) @ SV1817 )
= ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) )
= $true )
| ( ( ~ ( c_in @ SV598 @ SV1118 @ SV1547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(4111,plain,
! [SV599: $i,SV1548: $i,SV1119: $i,SV64: $i] :
( ( ( ~ ( c_lessequals @ SV64 @ SV1119 @ ( tc_fun @ SV1548 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV599 @ SV64 @ SV1548 )
= $true )
| ( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SV1119 @ SV1548 ) @ ( tc_fun @ SV1548 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(4112,plain,
! [SV600: $i,SV1120: $i,SV65: $i,SV1549: $i] :
( ( ( c_in @ SV1549 @ SV65 @ SV1120 )
= $true )
| ( ( ~ ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV1549 @ SV600 @ SV1120 ) @ ( tc_fun @ SV1120 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SV1120 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(4113,plain,
! [SV601: $i,SV1550: $i,SV1121: $i,SV66: $i] :
( ( ( ~ ( c_lessequals @ SV66 @ SV1121 @ ( tc_fun @ SV1550 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV601 @ SV66 @ SV1550 )
= $true )
| ( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SV1121 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(4114,plain,
! [SV1122: $i,SV602: $i,SV1551: $i,SV67: $i] :
( ( ( ~ ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SV1551 @ SV602 @ SV1122 ) @ ( tc_fun @ SV1122 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV1551 @ SV67 @ SV1122 )
= $true )
| ( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SV1122 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4115,plain,
! [SV1925: $i,SV1818: $i,SV1555: $i,SV1126: $i,SV606: $i,SV71: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV606 @ ( tc_fun @ ( tc_prod @ SV1126 @ SV1555 ) @ tc_bool ) ) @ SV1818 @ SV1126 @ SV1555 @ SV1925 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV71 @ SV1818 @ SV1126 @ SV1555 @ SV1925 ) @ ( c_Relation_Orel__comp @ SV606 @ SV1818 @ SV1126 @ SV1555 @ SV1925 ) @ ( tc_fun @ ( tc_prod @ SV1126 @ SV1925 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4116,plain,
! [SV1926: $i,SV1819: $i,SV1556: $i,SV1127: $i,SV607: $i,SV72: $i] :
( ( ( c_Relation_Orel__comp @ SV72 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV607 @ SV1127 @ ( tc_fun @ ( tc_prod @ SV1556 @ SV1819 ) @ tc_bool ) ) @ SV1926 @ SV1556 @ SV1819 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV72 @ SV607 @ SV1926 @ SV1556 @ SV1819 ) @ ( c_Relation_Orel__comp @ SV72 @ SV1127 @ SV1926 @ SV1556 @ SV1819 ) @ ( tc_fun @ ( tc_prod @ SV1926 @ SV1819 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4117,plain,
! [SV1129: $i,SV610: $i,SV1557: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) ) @ ( tc_fun @ SV1129 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV75 @ SV610 @ ( tc_fun @ SV1129 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(4118,plain,
! [SV1130: $i,SV1558: $i,SV611: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV611 @ SV1558 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV76 @ SV611 @ ( tc_fun @ SV1130 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3737]) ).
thf(4119,plain,
! [SV1559: $i,SV1131: $i,SV612: $i,SV77: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false )
| ( ( ( c_lessequals @ SV612 @ SV1131 @ SV77 )
| ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SV1559 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(4120,plain,
! [SV1560: $i,SV1132: $i,SV613: $i,SV78: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false )
| ( ( ( c_lessequals @ SV613 @ SV1132 @ SV78 )
| ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1560 @ SV1132 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(4121,plain,
! [SV1561: $i,SV1133: $i,SV614: $i,SV79: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false )
| ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SV1561 @ SV79 )
| ~ ( c_lessequals @ SV614 @ SV1561 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(4122,plain,
! [SV1562: $i,SV1134: $i,SV615: $i,SV80: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV80 )
= $false )
| ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SV1562 @ SV80 )
| ~ ( c_lessequals @ SV1134 @ SV1562 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(4123,plain,
! [SV1563: $i,SV1135: $i,SV616: $i,SV81: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV81 )
= $false )
| ( ( ( c_lessequals @ SV616 @ SV1135 @ SV81 )
| ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SV1563 @ SV81 ) @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(4124,plain,
! [SV1564: $i,SV1136: $i,SV617: $i,SV82: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV82 )
= $false )
| ( ( ( c_lessequals @ SV617 @ SV1136 @ SV82 )
| ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1564 @ SV1136 @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(4125,plain,
! [SV628: $i,SV1567: $i,SV93: $i,SV1146: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1146 @ SV93 @ ( tc_fun @ SV1567 @ tc_bool ) ) @ SV628 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV93 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(4126,plain,
! [SV629: $i,SV1568: $i,SV1147: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ SV1147 @ ( tc_fun @ SV1568 @ tc_bool ) ) @ SV629 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV94 @ SV629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(4127,plain,
! [SV96: $i,SV1149: $i,SV631: $i] :
( ( ( c_Relation_Osym @ SV631 @ SV1149 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV96 @ SV1149 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1149 ) @ tc_bool ) ) @ SV1149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(4128,plain,
! [SV635: $i,SV1570: $i,SV1152: $i,SV100: $i] :
( ( ( ~ ( c_in @ SV100 @ SV1152 @ SV1570 ) )
= $true )
| ( ( ~ ( c_in @ SV100 @ SV635 @ SV1570 ) )
= $true )
| ( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(4129,plain,
! [SV636: $i,SV1571: $i,SV1153: $i,SV101: $i] :
( ( ( ~ ( c_in @ SV101 @ SV1153 @ SV1571 ) )
= $true )
| ( ( ~ ( c_in @ SV101 @ SV636 @ SV1571 ) )
= $true )
| ( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(4130,plain,
! [SV637: $i,SV1572: $i,SV1154: $i,SV102: $i] :
( ( ( c_in @ SV102 @ SV1154 @ SV1572 )
= $false )
| ( ( c_in @ SV102 @ ( c_Set_Oinsert @ SV637 @ SV1154 @ SV1572 ) @ SV1572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(4131,plain,
! [SV638: $i,SV1573: $i,SV1155: $i,SV103: $i] :
( ( ( c_in @ SV103 @ SV1155 @ SV1573 )
= $false )
| ( ( c_in @ SV103 @ ( c_Set_Oinsert @ SV638 @ SV1155 @ SV1573 ) @ SV1573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(4132,plain,
! [SV1156: $i,SV1574: $i,SV639: $i,SV104: $i] :
( ( ( c_in @ SV104 @ SV639 @ SV1574 )
= $false )
| ( ( c_in @ SV104 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1156 @ ( tc_fun @ SV1574 @ tc_bool ) ) @ SV1574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(4133,plain,
! [SV640: $i,SV1575: $i,SV1157: $i,SV105: $i] :
( ( ( c_in @ SV105 @ SV1157 @ SV1575 )
= $false )
| ( ( c_in @ SV105 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV640 @ SV1157 @ ( tc_fun @ SV1575 @ tc_bool ) ) @ SV1575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(4134,plain,
! [SV1158: $i,SV641: $i,SV1576: $i,SV106: $i] :
( ( ( SV106 = SV1576 )
= $true )
| ( ( ~ ( c_in @ SV106 @ ( c_Set_Oinsert @ SV1576 @ SV641 @ SV1158 ) @ SV1158 ) )
= $true )
| ( ( c_in @ SV106 @ SV641 @ SV1158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3760]) ).
thf(4135,plain,
! [SV642: $i,SV1159: $i,SV1577: $i,SV107: $i] :
( ( ( c_in @ SV107 @ SV1577 @ SV1159 )
= $true )
| ( ( ~ ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1577 @ SV642 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ SV1159 ) )
= $true )
| ( ( c_in @ SV107 @ SV642 @ SV1159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3761]) ).
thf(4136,plain,
! [SV1163: $i,SV646: $i,SV1578: $i,SV111: $i] :
( ( ( c_in @ SV111 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1578 @ SV646 @ ( tc_fun @ SV1163 @ tc_bool ) ) @ SV1163 )
= $false )
| ( ( c_in @ SV111 @ SV646 @ SV1163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(4137,plain,
! [SV1164: $i,SV1579: $i,SV647: $i,SV112: $i] :
( ( ( c_in @ SV112 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV647 @ SV1579 @ ( tc_fun @ SV1164 @ tc_bool ) ) @ SV1164 )
= $false )
| ( ( c_in @ SV112 @ SV647 @ SV1164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(4138,plain,
! [SV1821: $i,SV1580: $i,SV1166: $i,SV649: $i,SV114: $i] :
( ( ( ~ ( c_in @ SV114 @ SV649 @ SV1166 ) )
= $true )
| ( ( c_in @ ( hAPP @ SV1580 @ SV114 ) @ ( c_Set_Oimage @ SV1580 @ SV649 @ SV1166 @ SV1821 ) @ SV1821 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(4139,plain,
! [SV1822: $i,SV1581: $i,SV1167: $i,SV650: $i,SV115: $i] :
( ( ( ~ ( c_in @ SV115 @ SV650 @ SV1167 ) )
= $true )
| ( ( c_in @ ( hAPP @ SV1581 @ SV115 ) @ ( c_Set_Oimage @ SV1581 @ SV650 @ SV1167 @ SV1822 ) @ SV1822 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(4140,plain,
! [SV1823: $i,SV1582: $i,SV1168: $i,SV651: $i,SV116: $i] :
( ( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SV1168 @ SV1582 @ SV1823 ) @ SV1823 )
= $true )
| ( ( ~ ( c_in @ SV651 @ SV1168 @ SV1582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3767]) ).
thf(4141,plain,
! [SV1824: $i,SV1583: $i,SV1169: $i,SV652: $i,SV117: $i] :
( ( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SV1169 @ SV1583 @ SV1824 ) @ SV1824 )
= $true )
| ( ( ~ ( c_in @ SV652 @ SV1169 @ SV1583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(4142,plain,
! [SV118: $i,SV1584: $i,SV1170: $i,SV653: $i] :
( ( ( c_in @ ( c_Pair @ SV653 @ SV1170 @ SV1584 @ SV1584 ) @ ( c_Transitive__Closure_Otrancl @ SV118 @ SV1584 ) @ ( tc_prod @ SV1584 @ SV1584 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV118 @ SV653 @ SV1170 @ SV1584 ) @ SV1170 @ SV1584 @ SV1584 ) @ SV118 @ ( tc_prod @ SV1584 @ SV1584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4143,plain,
! [SV1927: $i,SV1825: $i,SV1585: $i,SV1171: $i,SV654: $i,SV119: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SV1927 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SV1927 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(4144,plain,
! [SV1172: $i,SV655: $i,SV120: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV655 @ SV1172 )
| ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(4145,plain,
! [SV1173: $i,SV656: $i,SV121: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV121 @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(4146,plain,
! [SV1587: $i,SV663: $i,SV1178: $i,SV128: $i] :
( ( ( c_Relation_Otrans @ SV128 @ SV1178 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV128 @ SV663 @ SV1178 @ SV1587 ) @ SV1587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(4147,plain,
! [SV130: $i,SV1180: $i,SV665: $i] :
( ( ( c_Finite__Set_Ofinite @ SV665 @ SV1180 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV130 @ SV1180 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(4148,plain,
! [SV131: $i,SV1181: $i,SV666: $i] :
( ( ( c_Finite__Set_Ofinite @ SV666 @ SV1181 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV131 @ SV1181 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ SV1181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(4149,plain,
! [SV668: $i,SV1183: $i,SV133: $i,SV1590: $i] :
( ( ( c_lessequals @ SV1590 @ SV133 @ ( tc_fun @ SV1183 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ SV668 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV668 @ SV1590 @ ( tc_fun @ SV1183 @ tc_bool ) ) @ ( tc_fun @ SV1183 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(4150,plain,
! [SV1591: $i,SV135: $i,SV670: $i,SV1184: $i] :
( ( ( hBOOL @ ( hAPP @ SV1184 @ SV670 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1184 @ SV135 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(4151,plain,
! [SV1185: $i,SV136: $i,SV1592: $i,SV671: $i] :
( ( ( hBOOL @ ( hAPP @ SV671 @ SV1592 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV136 @ SV671 @ ( tc_fun @ SV1185 @ tc_bool ) ) @ SV1592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(4152,plain,
! [SV1186: $i,SV672: $i,SV1593: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ SV137 @ SV1593 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ SV672 @ ( tc_fun @ SV1186 @ tc_bool ) ) @ SV1593 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(4153,plain,
! [SV1829: $i,SV1595: $i,SV1188: $i,SV675: $i,SV140: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SV1829 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV675 @ SV1829 @ SV1188 )
| ~ ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(4154,plain,
! [SV1596: $i,SV1189: $i,SV676: $i,SV141: $i] :
( ( ( class_Lattices_Olattice @ SV141 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ SV1189 @ SV141 ) @ SV1596 @ SV141 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1189 @ SV1596 @ SV141 ) @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(4155,plain,
! [SV1597: $i,SV1190: $i,SV677: $i,SV142: $i] :
( ( ( class_Lattices_Olattice @ SV142 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ SV1597 @ SV142 ) @ SV142 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1190 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV677 @ SV1597 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(4156,plain,
! [SV1598: $i,SV1191: $i,SV678: $i,SV143: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV143 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ SV1598 @ SV143 ) @ SV143 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1191 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV678 @ SV1598 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(4157,plain,
! [SV1599: $i,SV1192: $i,SV679: $i,SV144: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV144 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ SV1192 @ SV144 ) @ SV1599 @ SV144 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1192 @ SV1599 @ SV144 ) @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(4158,plain,
! [SV1928: $i,SV1830: $i,SV1602: $i,SV1197: $i,SV684: $i,SV150: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SV1830 @ SV1928 ) @ ( tc_fun @ SV1928 @ tc_bool ) @ SV1197 ) @ SV1197 @ SV1928 )
= ( c_Set_Oinsert @ ( c_Pair @ SV150 @ SV1602 @ SV1197 @ SV1928 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV684 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1602 @ SV1830 @ SV1928 ) @ ( tc_fun @ SV1928 @ tc_bool ) @ SV1197 ) @ SV1197 @ SV1928 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV150 @ SV684 @ SV1197 ) @ ( c_COMBK @ SV1830 @ ( tc_fun @ SV1928 @ tc_bool ) @ SV1197 ) @ SV1197 @ SV1928 ) @ ( tc_fun @ ( tc_prod @ SV1197 @ SV1928 ) @ tc_bool ) ) @ ( tc_prod @ SV1197 @ SV1928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(4159,plain,
! [SV151: $i,SV1198: $i,SV685: $i] :
( ( ( c_Relation_Otrans @ SV685 @ SV1198 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV151 @ SV1198 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SV1198 @ SV1198 ) @ tc_bool ) ) @ SV1198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(4160,plain,
! [SV1603: $i,SV1199: $i,SV686: $i,SV152: $i] :
( ( ( class_Lattices_Olattice @ SV152 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1199 @ SV1603 @ SV152 ) @ SV152 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1199 @ SV152 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1603 @ SV152 ) @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3794]) ).
thf(4161,plain,
! [SV155: $i,SV1202: $i,SV689: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1202 @ SV155 )
= SV689 )
= $true )
| ( ( ~ ( c_lessequals @ SV1202 @ SV689 @ SV155 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(4162,plain,
! [SV156: $i,SV1203: $i,SV690: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SV1203 @ SV156 )
= SV1203 )
= $true )
| ( ( ~ ( c_lessequals @ SV690 @ SV1203 @ SV156 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(4163,plain,
! [SV1831: $i,SV1604: $i,SV1206: $i,SV693: $i,SV159: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SV1831 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV693 @ SV1831 @ SV1206 )
| ~ ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(4164,plain,
! [SV1605: $i,SV160: $i,SV1207: $i,SV694: $i] :
( ( ( c_Finite__Set_Ofinite @ SV694 @ SV1207 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV160 @ SV694 @ SV1207 @ SV1605 ) @ SV1605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(4165,plain,
! [SV695: $i,SV1208: $i,SV1606: $i,SV161: $i] :
( ( ( c_in @ SV161 @ SV1606 @ SV1208 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV161 @ SV695 @ SV1208 ) @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) )
= ( c_Set_Oinsert @ SV161 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV695 @ SV1606 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(4166,plain,
! [SV1209: $i,SV1607: $i,SV162: $i,SV696: $i] :
( ( ( c_in @ SV696 @ SV162 @ SV1607 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ ( c_Set_Oinsert @ SV696 @ SV1209 @ SV1607 ) @ ( tc_fun @ SV1607 @ tc_bool ) )
= ( c_Set_Oinsert @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV162 @ SV1209 @ ( tc_fun @ SV1607 @ tc_bool ) ) @ SV1607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(4167,plain,
! [SV1833: $i,SV1609: $i,SV1211: $i,SV698: $i,SV164: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV698 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) )
| ~ ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(4168,plain,
! [SV1611: $i,SV1215: $i,SV702: $i,SV168: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV168 )
= $false )
| ( ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1611 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(4169,plain,
! [SV1612: $i,SV1216: $i,SV703: $i,SV169: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV169 )
= $false )
| ( ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1612 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(4170,plain,
! [SV1613: $i,SV1217: $i,SV704: $i,SV170: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV170 )
= $false )
| ( ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1613 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(4171,plain,
! [SV709: $i,SV1614: $i,SV1222: $i,SV175: $i] :
( ( ( ~ ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SV1614 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) @ ( tc_fun @ SV1614 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4172,plain,
! [SV710: $i,SV1615: $i,SV1223: $i,SV176: $i] :
( ( ( ~ ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SV1615 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ ( tc_fun @ SV1615 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4173,plain,
! [SV1617: $i,SV1225: $i,SV712: $i,SV178: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV178 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV712 @ SV1225 @ SV178 ) @ SV1617 @ SV178 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV712 @ SV1617 @ SV178 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1225 @ SV1617 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3817]) ).
thf(4174,plain,
! [SV1618: $i,SV1226: $i,SV713: $i,SV179: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV179 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1226 @ SV1618 @ SV179 ) @ SV179 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1226 @ SV179 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV713 @ SV1618 @ SV179 ) @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(4175,plain,
! [SV183: $i,SV1230: $i,SV1621: $i,SV717: $i] :
( ( ( ~ ( c_lessequals @ SV717 @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV183 @ SV1621 @ SV1230 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(4176,plain,
! [SV1623: $i,SV1238: $i,SV728: $i,SV194: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV194 )
= $false )
| ( ( ( c_lessequals @ SV728 @ SV1238 @ SV194 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1623 @ SV728 @ SV194 ) @ SV1238 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(4177,plain,
! [SV1624: $i,SV1239: $i,SV729: $i,SV195: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV195 )
= $false )
| ( ( ( c_lessequals @ SV729 @ SV1239 @ SV195 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SV1624 @ SV195 ) @ SV1239 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(4178,plain,
! [SV1625: $i,SV1240: $i,SV730: $i,SV196: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV196 )
= $false )
| ( ( ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SV1625 @ SV196 ) @ SV196 )
| ~ ( c_lessequals @ SV730 @ SV1625 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(4179,plain,
! [SV1626: $i,SV1241: $i,SV731: $i,SV197: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV197 )
= $false )
| ( ( ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SV1626 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV731 @ SV1241 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(4180,plain,
! [SV1627: $i,SV1242: $i,SV732: $i,SV198: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV198 )
= $false )
| ( ( ( c_lessequals @ SV732 @ SV1242 @ SV198 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1627 @ SV732 @ SV198 ) @ SV1242 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(4181,plain,
! [SV1628: $i,SV1243: $i,SV733: $i,SV199: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV199 )
= $false )
| ( ( ( c_lessequals @ SV733 @ SV1243 @ SV199 )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV1628 @ SV199 ) @ SV1243 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(4182,plain,
! [SV734: $i,SV1244: $i,SV1629: $i,SV200: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV1629 @ ( tc_fun @ SV1244 @ tc_bool ) ) @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV200 @ SV734 @ ( tc_fun @ SV1244 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(4183,plain,
! [SV735: $i,SV1245: $i,SV201: $i,SV1630: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1630 @ SV201 @ ( tc_fun @ SV1245 @ tc_bool ) ) @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV201 @ SV735 @ ( tc_fun @ SV1245 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(4184,plain,
! [SV202: $i,SV736: $i,SV1246: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1246 @ SV736 )
= $false )
| ( ( ~ ( c_lessequals @ SV202 @ SV1246 @ ( tc_fun @ SV736 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3833]) ).
thf(4185,plain,
! [SV737: $i,SV1247: $i,SV203: $i] :
( ( ( c_lessequals @ SV203 @ SV1247 @ ( tc_fun @ SV737 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1247 @ SV737 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4186,plain,
! [SV1835: $i,SV1631: $i,SV1248: $i,SV738: $i,SV204: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV738 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(4187,plain,
! [SV1249: $i,SV205: $i,SV1632: $i,SV739: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV739 @ SV1632 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV205 @ SV1632 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV1632 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4188,plain,
! [SV1836: $i,SV1633: $i,SV1250: $i,SV740: $i,SV206: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SV1250 @ SV1633 ) @ ( c_Set_Oimage @ SV206 @ SV1836 @ SV1250 @ SV1633 ) @ ( tc_fun @ SV1633 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV740 @ SV1836 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4189,plain,
! [SV1837: $i,SV1634: $i,SV1251: $i,SV741: $i,SV207: $i] :
( ( ( ~ ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV1634 @ SV207 @ SV1251 @ SV1837 ) @ ( c_Set_Oimage @ SV1634 @ SV741 @ SV1251 @ SV1837 ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3838]) ).
thf(4190,plain,
! [SV208: $i,SV1252: $i,SV1635: $i,SV742: $i] :
( ( ( c_lessequals @ SV742 @ SV1635 @ ( tc_fun @ SV1252 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV208 @ SV742 @ SV1252 ) @ ( c_Set_Oinsert @ SV208 @ SV1635 @ SV1252 ) @ ( tc_fun @ SV1252 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(4191,plain,
! [SV1839: $i,SV1637: $i,SV1255: $i,SV745: $i,SV211: $i] :
( ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4192,plain,
! [SV1840: $i,SV1638: $i,SV1256: $i,SV746: $i,SV212: $i] :
( ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(4193,plain,
! [SV213: $i,SV747: $i,SV1639: $i,SV1257: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1257 @ SV1639 @ SV747 @ SV747 ) @ SV213 @ ( tc_prod @ SV747 @ SV747 ) ) @ SV747 )
= $false )
| ( ( c_Wellfounded_Owf @ SV213 @ SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4194,plain,
! [SV217: $i,SV751: $i,SV1260: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1260 @ SV751 )
= $false )
| ( ( ~ ( c_in @ SV1260 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4195,plain,
! [SV1640: $i,SV1262: $i,SV757: $i,SV223: $i] :
( ( ( c_in @ ( c_Pair @ SV223 @ SV757 @ SV1262 @ SV1262 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1262 ) @ ( tc_prod @ SV1262 @ SV1262 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SV1262 @ SV1262 ) @ SV1640 @ ( tc_prod @ SV1262 @ SV1262 ) ) @ SV1262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3848]) ).
thf(4196,plain,
! [SV1641: $i,SV1263: $i,SV224: $i,SV758: $i] :
( ( ( c_in @ ( c_Pair @ SV758 @ SV224 @ SV1263 @ SV1263 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1263 ) @ ( tc_prod @ SV1263 @ SV1263 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1641 @ SV1263 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SV1263 @ SV1263 ) @ SV1641 @ ( tc_prod @ SV1263 @ SV1263 ) ) @ SV1263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(4197,plain,
! [SV759: $i,SV1642: $i,SV1264: $i,SV225: $i] :
( ( ( c_in @ ( c_Pair @ SV225 @ SV1264 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV225 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV759 @ SV225 @ SV1264 @ SV1642 ) @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV759 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(4198,plain,
! [SV1929: $i,SV1841: $i,SV1643: $i,SV1265: $i,SV760: $i,SV226: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SV1841 @ SV1929 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SV1929 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
| ~ ( c_lessequals @ SV226 @ SV1841 @ ( tc_fun @ SV1265 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4199,plain,
! [SV1842: $i,SV1644: $i,SV1266: $i,SV761: $i,SV227: $i] :
( ( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SV1266 @ ( tc_fun @ SV1644 @ tc_bool ) @ SV1842 ) @ SV1842 @ SV1644 ) @ ( tc_fun @ SV1842 @ SV1644 ) )
= $true )
| ( ( ~ ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SV1266 @ SV227 @ SV1842 @ SV1644 ) ) @ SV1266 @ SV1644 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4200,plain,
! [SV1843: $i,SV1645: $i,SV1267: $i,SV762: $i,SV228: $i] :
( ( ( c_in @ SV228 @ ( c_FuncSet_OPi @ SV762 @ ( c_COMBK @ SV1267 @ ( tc_fun @ SV1645 @ tc_bool ) @ SV1843 ) @ SV1843 @ SV1645 ) @ ( tc_fun @ SV1843 @ SV1645 ) )
= $true )
| ( ( c_in @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV762 @ SV1267 @ SV228 @ SV1843 @ SV1645 ) @ SV762 @ SV1843 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4201,plain,
! [SV1844: $i,SV1646: $i,SV1268: $i,SV763: $i,SV229: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SV1268 @ SV1646 ) @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) @ SV1268 ) @ SV1268 @ SV1646 ) @ ( tc_fun @ SV1268 @ SV1646 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3854]) ).
thf(4202,plain,
! [SV1269: $i,SV765: $i,SV231: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3855]) ).
thf(4203,plain,
! [SV766: $i,SV232: $i] :
( ( ( c_Relation_Osym @ SV232 @ SV766 )
= $false )
| ( ( c_Relation_Otrans @ SV232 @ SV766 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV232 @ SV766 @ SV766 ) @ SV232 @ SV766 @ SV766 @ SV766 ) @ SV232 @ ( tc_fun @ ( tc_prod @ SV766 @ SV766 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(4204,plain,
! [SV767: $i,SV233: $i,SV1647: $i,SV1270: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1270 @ SV1647 @ SV233 @ SV767 ) @ SV1647 @ SV767 )
= $true )
| ( ( ~ ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SV1270 @ ( c_COMBK @ SV1647 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV233 @ SV767 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(4205,plain,
! [SV768: $i,SV234: $i,SV1648: $i,SV1271: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1271 @ SV1648 @ SV234 @ SV768 ) @ SV1271 @ SV768 )
= $true )
| ( ( ~ ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SV1271 @ ( c_COMBK @ SV1648 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV234 @ SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4206,plain,
! [SV1272: $i,SV235: $i,SV769: $i] :
( ( ( c_lessequals @ SV769 @ ( c_Product__Type_OSigma @ SV235 @ ( c_COMBK @ SV235 @ ( tc_fun @ SV1272 @ tc_bool ) @ SV1272 ) @ SV1272 @ SV1272 ) @ ( tc_fun @ ( tc_prod @ SV1272 @ SV1272 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV235 @ SV769 @ SV1272 ) @ SV235 @ SV1272 )
= $true )
| ( ( c_Relation_Orefl__on @ SV235 @ SV769 @ SV1272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(4207,plain,
! [SV1273: $i,SV236: $i,SV770: $i] :
( ( ( c_lessequals @ SV770 @ ( c_Product__Type_OSigma @ SV236 @ ( c_COMBK @ SV236 @ ( tc_fun @ SV1273 @ tc_bool ) @ SV1273 ) @ SV1273 @ SV1273 ) @ ( tc_fun @ ( tc_prod @ SV1273 @ SV1273 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV236 @ SV770 @ SV1273 ) @ SV236 @ SV1273 )
= $true )
| ( ( c_Relation_Orefl__on @ SV236 @ SV770 @ SV1273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4208,plain,
! [SV771: $i,SV1649: $i,SV1274: $i,SV237: $i] :
( ( ( ~ ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4209,plain,
! [SV1275: $i,SV772: $i,SV238: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ SV1275 @ SV1275 ) @ SV772 @ ( tc_prod @ SV1275 @ SV1275 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SV1275 @ tc_bool ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ ( tc_prod @ SV1275 @ SV1275 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SV1275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4210,plain,
! [SV1276: $i,SV773: $i,SV239: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ SV1276 @ SV1276 ) @ SV773 @ ( tc_prod @ SV1276 @ SV1276 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SV1276 @ tc_bool ) @ SV1276 ) @ SV1276 @ SV1276 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1276 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SV1276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(4211,plain,
! [SV1650: $i,SV1277: $i,SV774: $i,SV240: $i] :
( ( ( SV240 = SV774 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Ortrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Otrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4212,plain,
! [SV1651: $i,SV1278: $i,SV775: $i,SV241: $i] :
( ( ( SV241 = SV775 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Ortrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Otrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(4213,plain,
! [SV1652: $i,SV1279: $i,SV776: $i,SV242: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Otrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) ) )
= $true )
| ( ( SV242 = SV776 )
= $true )
| ( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Ortrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(4214,plain,
! [SV777: $i,SV1653: $i,SV1280: $i,SV243: $i] :
( ( ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SV1653 ) @ ( tc_prod @ SV1653 @ SV1653 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SV1280 @ SV1653 ) @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(4215,plain,
! [SV1845: $i,SV1654: $i,SV1281: $i,SV778: $i,SV244: $i] :
( ( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1845 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) )
| ~ ( c_in @ ( c_Pair @ SV244 @ SV1845 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4216,plain,
! [SV1846: $i,SV1655: $i,SV1282: $i,SV779: $i,SV245: $i] :
( ( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1846 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
| ~ ( c_in @ ( c_Pair @ SV245 @ SV1846 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4217,plain,
! [SV784: $i,SV1656: $i,SV1285: $i,SV250: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SV1285 @ SV1656 ) @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 )
= $true )
| ( ( ~ ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4218,plain,
! [SV786: $i,SV1287: $i,SV252: $i] :
( ( ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SV1287 ) ) )
= $false )
| ( ( ~ ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SV1287 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(4219,plain,
! [SV787: $i,SV1657: $i,SV1288: $i,SV253: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SV1657 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SV1657 ) @ SV1657 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4220,plain,
! [SV789: $i,SV1658: $i,SV1290: $i,SV255: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SV1290 @ SV1658 ) @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 )
= $true )
| ( ( ~ ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(4221,plain,
! [SV790: $i,SV1291: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SV1291 ) ) )
= $false )
| ( ( ~ ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SV1291 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(4222,plain,
! [SV791: $i,SV1659: $i,SV1292: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SV1659 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SV1659 ) @ SV1659 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4223,plain,
! [SV1293: $i,SV258: $i,SV792: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SV1293 @ SV258 )
= $true )
| ( ( ~ ( c_in @ SV1293 @ SV792 @ SV258 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4224,plain,
! [SV260: $i,SV1295: $i,SV794: $i,SV1660: $i] :
( ( ( ~ ( c_lessequals @ SV1660 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV1660 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) ) )
= $true )
| ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4225,plain,
! [SV1847: $i,SV1661: $i,SV1296: $i,SV795: $i,SV261: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SV1296 @ SV1661 @ SV1847 ) @ SV261 @ SV1661 )
= $true )
| ( ( ~ ( c_in @ SV795 @ ( c_Relation_OImage @ SV1296 @ SV261 @ SV1661 @ SV1847 ) @ SV1847 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4226,plain,
! [SV1848: $i,SV1662: $i,SV1297: $i,SV796: $i,SV262: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SV1297 @ SV1662 @ SV1848 ) @ SV262 @ SV1662 )
= $true )
| ( ( ~ ( c_in @ SV796 @ ( c_Relation_OImage @ SV1297 @ SV262 @ SV1662 @ SV1848 ) @ SV1848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(4227,plain,
! [SV797: $i,SV1298: $i,SV263: $i,SV1663: $i] :
( ( ( ~ ( c_in @ SV1663 @ SV263 @ SV1298 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV797 @ SV1298 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3885]) ).
thf(4228,plain,
! [SV798: $i,SV1299: $i,SV264: $i,SV1664: $i] :
( ( ( ~ ( c_in @ SV1664 @ SV264 @ SV1299 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV798 @ SV1299 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3886]) ).
thf(4229,plain,
! [SV266: $i,SV1301: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1301 @ SV266 ) @ SV266 )
= $true )
| ( ( ~ ( c_in @ SV800 @ SV1301 @ SV266 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(4230,plain,
! [SV1849: $i,SV1665: $i,SV1302: $i,SV801: $i,SV267: $i] :
( ( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1849 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) )
| ~ ( c_in @ ( c_Pair @ SV267 @ SV1849 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4231,plain,
! [SV1850: $i,SV1666: $i,SV1303: $i,SV802: $i,SV268: $i] :
( ( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1850 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
| ~ ( c_in @ ( c_Pair @ SV268 @ SV1850 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4232,plain,
! [SV1851: $i,SV1667: $i,SV1304: $i,SV803: $i,SV269: $i] :
( ( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1851 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
| ~ ( c_in @ ( c_Pair @ SV269 @ SV1851 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3891]) ).
thf(4233,plain,
! [SV272: $i,SV1668: $i,SV1307: $i,SV806: $i] :
( ( ( c_in @ ( c_Pair @ SV806 @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Otrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV272 @ SV806 @ SV1307 @ SV1668 ) @ SV1307 @ SV1668 @ SV1668 ) @ ( c_Transitive__Closure_Ortrancl @ SV272 @ SV1668 ) @ ( tc_prod @ SV1668 @ SV1668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4234,plain,
! [SV273: $i,SV1308: $i,SV807: $i] :
( ( ( c_lessequals @ SV807 @ SV1308 @ SV273 )
= $true )
| ( ( c_lessequals @ SV1308 @ SV807 @ SV273 )
= $true )
| ( ( class_Orderings_Olinorder @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4235,plain,
! [SV1930: $i,SV1852: $i,SV1669: $i,SV1310: $i,SV811: $i,SV277: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SV1930 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
| ~ ( c_lessequals @ SV811 @ SV1930 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4236,plain,
! [SV1311: $i,SV812: $i,SV1670: $i,SV278: $i] :
( ( ( c_lessequals @ SV278 @ SV1670 @ ( tc_fun @ ( tc_prod @ SV812 @ SV1311 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_ODomain @ SV278 @ SV812 @ SV1311 ) @ ( c_Relation_ODomain @ SV1670 @ SV812 @ SV1311 ) @ ( tc_fun @ SV812 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3896]) ).
thf(4237,plain,
! [SV813: $i,SV1671: $i,SV279: $i,SV1312: $i] :
( ( ( ~ ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SV1671 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3897]) ).
thf(4238,plain,
! [SV816: $i,SV1313: $i,SV282: $i] :
( ( ( c_lessequals @ SV282 @ SV1313 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1313 @ SV816 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV282 @ SV816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(4239,plain,
! [SV1672: $i,SV283: $i,SV817: $i,SV1314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SV1672 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4240,plain,
! [SV284: $i,SV1315: $i,SV818: $i,SV1673: $i] :
( ( ( ~ ( c_lessequals @ SV1673 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV284 @ SV1673 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3900]) ).
thf(4241,plain,
! [SV1674: $i,SV1316: $i,SV821: $i,SV287: $i] :
( ( ( class_Orderings_Opreorder @ SV287 )
= $false )
| ( ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3901]) ).
thf(4242,plain,
! [SV1675: $i,SV1317: $i,SV822: $i,SV288: $i] :
( ( ( class_Orderings_Oorder @ SV288 )
= $false )
| ( ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
| ~ ( c_lessequals @ SV822 @ SV1675 @ SV288 )
| ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4243,plain,
! [SV292: $i,SV1320: $i,SV826: $i] :
( ( ( SV826 = SV1320 )
= $true )
| ( ( ~ ( c_lessequals @ SV826 @ SV1320 @ SV292 )
| ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4244,plain,
! [SV293: $i,SV1321: $i,SV827: $i] :
( ( ( SV827 = SV1321 )
= $true )
| ( ( ~ ( c_lessequals @ SV1321 @ SV827 @ SV293 )
| ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4245,plain,
! [SV294: $i,SV1322: $i,SV828: $i] :
( ( ( SV828 = SV1322 )
= $true )
| ( ( ~ ( c_lessequals @ SV1322 @ SV828 @ SV294 )
| ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(4246,plain,
! [SV1323: $i,SV295: $i,SV829: $i] :
( ( ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SV1323 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true )
| ( ( SV295 = SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4247,plain,
! [SV1324: $i,SV296: $i,SV830: $i] :
( ( ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true )
| ( ( SV296 = SV830 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4248,plain,
! [SV1931: $i,SV1853: $i,SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ! [SY4978: $i,SY4979: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SY4978 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY4979 @ ( c_COMBK @ SY4978 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SY4979 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4249,plain,
! [SV1932: $i,SV1854: $i,SV1677: $i,SV1327: $i,SV836: $i,SV302: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) )
| ~ ( c_in @ SV1932 @ SV836 @ SV1327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4250,plain,
! [SV1933: $i,SV1855: $i,SV1678: $i,SV1328: $i,SV837: $i,SV303: $i] :
( ( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) )
| ~ ( c_in @ SV1933 @ SV1678 @ SV1855 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4251,plain,
! [SV1934: $i,SV1856: $i,SV1679: $i,SV1330: $i,SV840: $i,SV306: $i] :
( ( ! [SY4980: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SY4980 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SY4980 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4252,plain,
! [SV1935: $i,SV1857: $i,SV1681: $i,SV1332: $i,SV842: $i,SV308: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SV1681 ) @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) )
| ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SV1935 @ ( c_COMBK @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) @ SV1332 ) @ SV1332 @ SV1681 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1681 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4253,plain,
! [SV844: $i,SV1333: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1333 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4254,plain,
! [SV1858: $i,SV1682: $i,SV1334: $i,SV845: $i,SV311: $i] :
( ( ( c_in @ SV311 @ SV845 @ SV1334 )
= $true )
| ( ( ( SV311 = SV1682 )
| ~ ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3918]) ).
thf(4255,plain,
! [SV1859: $i,SV1683: $i,SV1336: $i,SV847: $i,SV313: $i] :
( ( ( ~ ( class_HOL_Oord @ SV313 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SV1859 @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4256,plain,
! [SV848: $i,SV1337: $i,SV1684: $i,SV314: $i] :
( ( ( ~ ( c_in @ SV314 @ SV1684 @ SV1337 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1684 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV314 @ SV848 @ SV1337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4257,plain,
! [SV315: $i,SV1338: $i,SV849: $i,SV1685: $i] :
( ( ( ~ ( c_lessequals @ SV1685 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV315 @ SV1685 @ SV1338 ) )
= $true )
| ( ( c_in @ SV315 @ SV849 @ SV1338 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(4258,plain,
! [SV850: $i,SV1339: $i,SV1686: $i,SV316: $i] :
( ( ( ~ ( c_in @ SV316 @ SV1686 @ SV1339 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1686 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV316 @ SV850 @ SV1339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3923]) ).
thf(4259,plain,
! [SV851: $i,SV1340: $i,SV1687: $i,SV317: $i] :
( ( ( ~ ( c_in @ SV317 @ SV1687 @ SV1340 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1687 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV317 @ SV851 @ SV1340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4260,plain,
! [SV1688: $i,SV1342: $i,SV853: $i,SV319: $i] :
( ( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Otrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV319 @ SV853 @ SV1342 @ SV1342 ) @ ( c_Transitive__Closure_Ortrancl @ SV1688 @ SV1342 ) @ ( tc_prod @ SV1342 @ SV1342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3926]) ).
thf(4261,plain,
! [SV1860: $i,SV1689: $i,SV1343: $i,SV854: $i,SV320: $i] :
( ( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1860 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
| ~ ( c_in @ ( c_Pair @ SV320 @ SV1860 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4262,plain,
! [SV1861: $i,SV1690: $i,SV1344: $i,SV855: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1861 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
| ~ ( c_in @ ( c_Pair @ SV321 @ SV1861 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4263,plain,
! [SV856: $i,SV1691: $i,SV1345: $i,SV322: $i] :
( ( ( c_in @ ( c_Pair @ SV322 @ SV1345 @ SV1691 @ SV1691 ) @ ( c_Transitive__Closure_Otrancl @ SV856 @ SV1691 ) @ ( tc_prod @ SV1691 @ SV1691 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV322 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV856 @ SV322 @ SV1345 @ SV1691 ) @ SV1691 @ SV1691 ) @ SV856 @ ( tc_prod @ SV1691 @ SV1691 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3929]) ).
thf(4264,plain,
! [SV323: $i,SV1692: $i,SV1346: $i,SV857: $i] :
( ( ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ SV323 @ ( tc_prod @ SV1692 @ SV1692 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SV1346 @ SV1692 ) @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4265,plain,
! [SV1693: $i,SV1349: $i,SV326: $i,SV860: $i] :
( ( ( c_in @ ( c_Pair @ SV860 @ SV326 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ SV1693 @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV326 @ SV860 @ SV1349 @ SV1349 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1693 @ SV1349 @ SV1349 ) @ SV1349 ) @ ( tc_prod @ SV1349 @ SV1349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3933]) ).
thf(4266,plain,
! [SV1694: $i,SV1350: $i,SV327: $i,SV861: $i] :
( ( ( c_in @ ( c_Pair @ SV861 @ SV327 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1694 @ SV1350 @ SV1350 ) @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV327 @ SV861 @ SV1350 @ SV1350 ) @ ( c_Transitive__Closure_Ortrancl @ SV1694 @ SV1350 ) @ ( tc_prod @ SV1350 @ SV1350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3934]) ).
thf(4267,plain,
! [SV1936: $i,SV1862: $i,SV1695: $i,SV1351: $i,SV862: $i,SV328: $i] :
( ( ! [SY4981: $i] :
( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SV1862 @ SV1936 @ SY4981 ) @ SV1862 @ SY4981 ) @ SV1351 @ ( tc_prod @ SV1862 @ SY4981 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SV1862 @ SV1936 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SV1862 @ SY4981 @ SV1936 ) @ ( tc_prod @ SV1862 @ SV1936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4268,plain,
! [SV1937: $i,SV1863: $i,SV1696: $i,SV1352: $i,SV863: $i,SV329: $i] :
( ( ! [SY4982: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SV1863 @ SV1937 @ SY4982 ) @ SV863 @ SY4982 @ SV1937 ) @ SV1696 @ ( tc_prod @ SY4982 @ SV1937 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SV1863 @ SV1937 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SV1863 @ SY4982 @ SV1937 ) @ ( tc_prod @ SV1863 @ SV1937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4269,plain,
! [SV1864: $i,SV1697: $i,SV1353: $i,SV864: $i,SV330: $i] :
( ( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SV1353 @ SV1697 @ SV1864 ) @ ( tc_fun @ SV1697 @ SV1864 ) )
= $true )
| ( ( ~ ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ ( hAPP @ SV1353 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ SV1864 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4270,plain,
! [SV1938: $i,SV1865: $i,SV1698: $i,SV1354: $i,SV865: $i,SV331: $i] :
( ( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
| ~ ( c_in @ SV865 @ SV1865 @ SV1938 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1938 ) @ SV1938 @ SV1698 ) @ ( tc_fun @ SV1938 @ SV1698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4271,plain,
! [SV1866: $i,SV1699: $i,SV1355: $i,SV866: $i,SV332: $i] :
( ( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SV1355 @ SV1699 @ SV1866 ) @ ( tc_fun @ SV1699 @ SV1866 ) )
= $true )
| ( ( ~ ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ ( hAPP @ SV1355 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ SV1866 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3939]) ).
thf(4272,plain,
! [SV1867: $i,SV1700: $i,SV1356: $i,SV867: $i,SV333: $i] :
( ( ( c_in @ SV333 @ ( c_FuncSet_OPi @ SV867 @ SV1356 @ SV1700 @ SV1867 ) @ ( tc_fun @ SV1700 @ SV1867 ) )
= $true )
| ( ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV867 @ SV1356 @ SV333 @ SV1700 @ SV1867 ) @ SV867 @ SV1700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4273,plain,
! [SV1868: $i,SV1701: $i,SV1357: $i,SV868: $i,SV334: $i] :
( ( ( c_in @ SV334 @ ( c_FuncSet_OPi @ SV868 @ SV1357 @ SV1701 @ SV1868 ) @ ( tc_fun @ SV1701 @ SV1868 ) )
= $true )
| ( ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV868 @ SV1357 @ SV334 @ SV1701 @ SV1868 ) @ SV868 @ SV1701 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4274,plain,
! [SV1702: $i,SV1358: $i,SV335: $i,SV869: $i] :
( ( ( c_in @ SV869 @ ( c_Equiv__Relations_Oquotient @ SV335 @ SV1358 @ SV1702 ) @ ( tc_fun @ SV1702 @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ SV335 @ SV869 @ SV1358 @ SV1702 ) @ SV335 @ SV1702 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4275,plain,
! [SV1939: $i,SV1869: $i,SV1703: $i,SV1362: $i,SV876: $i,SV342: $i] :
( ( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SV1362 @ SV1703 @ SV1869 )
= ( c_Recdef_Ocut @ SV1939 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SV1939 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) @ SV1362 @ SV1703 @ SV1703 ) @ SV876 @ ( tc_prod @ SV1703 @ SV1703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4276,plain,
! [SV1870: $i,SV1704: $i,SV1364: $i,SV879: $i,SV345: $i] :
( ( ( ~ ( c_in @ SV345 @ SV879 @ SV1364 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_in @ SV1870 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4277,plain,
! [SV1871: $i,SV1705: $i,SV1365: $i,SV880: $i,SV346: $i] :
( ( ( ~ ( c_in @ SV346 @ SV880 @ SV1365 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
| ~ ( c_in @ SV1871 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4278,plain,
! [SV1872: $i,SV1706: $i,SV1366: $i,SV881: $i,SV347: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SV1366 @ SV1706 @ SV1872 ) @ SV881 @ SV1706 @ SV1872 ) @ SV1366 @ ( tc_prod @ SV1706 @ SV1872 ) )
= $true )
| ( ( ~ ( c_in @ SV881 @ ( c_Relation_OImage @ SV1366 @ SV347 @ SV1706 @ SV1872 ) @ SV1872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3949]) ).
thf(4279,plain,
! [SV1873: $i,SV1707: $i,SV1367: $i,SV882: $i,SV348: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SV1367 @ SV1707 @ SV1873 ) @ SV882 @ SV1707 @ SV1873 ) @ SV1367 @ ( tc_prod @ SV1707 @ SV1873 ) )
= $true )
| ( ( ~ ( c_in @ SV882 @ ( c_Relation_OImage @ SV1367 @ SV348 @ SV1707 @ SV1873 ) @ SV1873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4280,plain,
! [SV1708: $i,SV1368: $i,SV883: $i,SV349: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV349 @ SV883 @ SV1368 @ SV1368 ) @ ( c_Transitive__Closure_Ortrancl @ SV1708 @ SV1368 ) @ ( tc_prod @ SV1368 @ SV1368 ) ) )
= $true )
| ( ( c_in @ SV349 @ ( c_Relation_ODomain @ SV1708 @ SV1368 @ SV1368 ) @ SV1368 )
= $true )
| ( ( SV349 = SV883 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4281,plain,
! [SV1709: $i,SV1369: $i,SV884: $i,SV350: $i] :
( ( ( c_in @ SV350 @ ( c_Relation_ODomain @ SV884 @ SV1369 @ SV1709 ) @ SV1369 )
= $false )
| ( ( c_in @ ( c_Pair @ SV350 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV350 @ SV884 @ SV1369 @ SV1709 ) @ SV1369 @ SV1709 ) @ SV884 @ ( tc_prod @ SV1369 @ SV1709 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4282,plain,
! [SV1710: $i,SV1370: $i,SV885: $i,SV351: $i] :
( ( ( c_in @ SV351 @ ( c_Relation_ODomain @ SV885 @ SV1370 @ SV1710 ) @ SV1370 )
= $false )
| ( ( c_in @ ( c_Pair @ SV351 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV351 @ SV885 @ SV1370 @ SV1710 ) @ SV1370 @ SV1710 ) @ SV885 @ ( tc_prod @ SV1370 @ SV1710 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4283,plain,
! [SV1874: $i,SV1711: $i,SV1372: $i,SV887: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
| ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3954]) ).
thf(4284,plain,
! [SV888: $i,SV354: $i,SV1712: $i,SV1373: $i] :
( ( ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3955]) ).
thf(4285,plain,
! [SV889: $i,SV1713: $i,SV1374: $i,SV355: $i] :
( ( ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(4286,plain,
! [SV890: $i,SV356: $i,SV1714: $i,SV1375: $i] :
( ( ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4287,plain,
! [SV891: $i,SV1376: $i,SV1715: $i,SV357: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV357 @ SV1715 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1715 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 ) )
= $true )
| ( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(4288,plain,
! [SV358: $i,SV1377: $i,SV892: $i,SV1716: $i] :
( ( ( ~ ( c_in @ SV1716 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV358 @ SV1716 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) ) )
= $true )
| ( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4289,plain,
! [SV894: $i,SV1717: $i,SV1379: $i,SV360: $i] :
( ( ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4290,plain,
! [SV1875: $i,SV1718: $i,SV1380: $i,SV895: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
| ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4291,plain,
! [SV1382: $i,SV1719: $i,SV897: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Relation_ORange @ SV897 @ SV1719 @ SV1382 ) @ SV1382 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV363 @ SV897 @ SV1382 @ SV1719 ) @ SV363 @ SV1719 @ SV1382 ) @ SV897 @ ( tc_prod @ SV1719 @ SV1382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4292,plain,
! [SV1383: $i,SV1720: $i,SV898: $i,SV364: $i] :
( ( ( c_in @ SV364 @ ( c_Relation_ORange @ SV898 @ SV1720 @ SV1383 ) @ SV1383 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV364 @ SV898 @ SV1383 @ SV1720 ) @ SV364 @ SV1720 @ SV1383 ) @ SV898 @ ( tc_prod @ SV1720 @ SV1383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3963]) ).
thf(4293,plain,
! [SV1721: $i,SV1384: $i,SV899: $i,SV365: $i] :
( ( ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
| ~ ( c_Wellfounded_Owf @ SV1721 @ SV1384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4294,plain,
! [SV1722: $i,SV1385: $i,SV900: $i,SV366: $i] :
( ( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ SV1722 @ ( tc_prod @ SV1385 @ SV1385 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV366 @ SV900 @ SV1385 @ SV1385 ) @ ( c_Transitive__Closure_Otrancl @ SV1722 @ SV1385 ) @ ( tc_prod @ SV1385 @ SV1385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4295,plain,
! [SV1876: $i,SV1723: $i,SV1386: $i,SV901: $i,SV367: $i] :
( ( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1876 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
| ~ ( c_in @ ( c_Pair @ SV367 @ SV1876 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4296,plain,
! [SV1877: $i,SV1724: $i,SV1387: $i,SV902: $i,SV368: $i] :
( ( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1877 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) )
| ~ ( c_in @ ( c_Pair @ SV368 @ SV1877 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4297,plain,
! [SV1878: $i,SV1725: $i,SV1388: $i,SV903: $i,SV369: $i] :
( ( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SV1388 @ SV1725 ) @ SV1878 @ ( tc_prod @ SV1388 @ SV1725 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV903 @ SV369 @ SV1725 @ SV1388 ) @ ( c_Relation_Oconverse @ SV1878 @ SV1388 @ SV1725 ) @ ( tc_prod @ SV1725 @ SV1388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4298,plain,
! [SV1879: $i,SV1726: $i,SV1389: $i,SV904: $i,SV370: $i] :
( ( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SV1389 @ SV1726 ) @ ( c_Relation_Oconverse @ SV1879 @ SV1726 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1726 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV904 @ SV370 @ SV1726 @ SV1389 ) @ SV1879 @ ( tc_prod @ SV1726 @ SV1389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4299,plain,
! [SV1880: $i,SV1727: $i,SV1390: $i,SV905: $i,SV371: $i] :
( ( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SV1390 @ SV1727 ) @ ( c_Relation_Oconverse @ SV1880 @ SV1727 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1727 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV905 @ SV371 @ SV1727 @ SV1390 ) @ SV1880 @ ( tc_prod @ SV1727 @ SV1390 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4300,plain,
! [SV1940: $i,SV1881: $i,SV1728: $i,SV1391: $i,SV906: $i,SV372: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SV1728 @ SV1881 ) @ SV1940 )
= ( hAPP @ SV372 @ SV1940 ) )
| ~ ( c_in @ ( c_Pair @ SV1940 @ SV1391 @ SV1728 @ SV1728 ) @ SV906 @ ( tc_prod @ SV1728 @ SV1728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4301,plain,
! [SV1941: $i,SV1882: $i,SV1729: $i,SV1392: $i,SV907: $i,SV373: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SV1729 @ SV1882 ) @ SV1941 )
= ( hAPP @ SV373 @ SV1941 ) )
| ~ ( c_in @ ( c_Pair @ SV1941 @ SV1392 @ SV1729 @ SV1729 ) @ SV907 @ ( tc_prod @ SV1729 @ SV1729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4302,plain,
! [SV1730: $i,SV1394: $i,SV909: $i,SV375: $i] :
( ( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1730 @ SV1394 @ SV1394 ) @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV375 @ SV909 @ SV1394 @ SV1394 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1730 @ SV1394 ) @ SV1394 @ SV1394 ) @ ( tc_prod @ SV1394 @ SV1394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4303,plain,
! [SV1731: $i,SV1395: $i,SV910: $i,SV376: $i] :
( ( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1731 @ SV1395 ) @ SV1395 @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV376 @ SV910 @ SV1395 @ SV1395 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1731 @ SV1395 @ SV1395 ) @ SV1395 ) @ ( tc_prod @ SV1395 @ SV1395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3975]) ).
thf(4304,plain,
! [SV1733: $i,SV930: $i,SV1402: $i,SV397: $i] :
( ( ( c_Wellfounded_Owf @ SV397 @ SV1402 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV397 @ SV930 @ SV1402 @ SV1733 ) @ SV1733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4305,plain,
! [SV1734: $i,SV931: $i,SV1403: $i,SV398: $i] :
( ( ( c_Relation_Osym @ SV398 @ SV1403 )
= $false )
| ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV398 @ SV931 @ SV1403 @ SV1734 ) @ SV1734 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4306,plain,
! [SV1942: $i,SV1884: $i,SV1735: $i,SV1404: $i,SV933: $i,SV401: $i] :
( ( ! [SY4983: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SV1404 @ SV1735 @ SV1884 ) @ SV1942 @ SV1404 @ SV1884 @ SY4983 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SV1942 @ SV1735 @ SV1884 @ SY4983 ) @ SV1404 @ SV1735 @ SY4983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4307,plain,
! [SV1737: $i,SV1416: $i,SV948: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ SV416 @ SV948 @ SV1416 @ SV1416 ) @ ( c_Relation_OId__on @ SV1737 @ SV1416 ) @ ( tc_prod @ SV1416 @ SV1416 ) )
= $false )
| ( ( SV416 = SV948 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4308,plain,
! [SV419: $i,SV951: $i,SV1419: $i] :
( ( ( c_Wellfounded_Owf @ SV1419 @ SV951 )
= $false )
| ( ( c_in @ ( c_Pair @ SV419 @ SV419 @ SV951 @ SV951 ) @ SV1419 @ ( tc_prod @ SV951 @ SV951 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4309,plain,
! [SV1943: $i,SV1885: $i,SV1738: $i,SV1420: $i,SV952: $i,SV420: $i] :
( ( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SV1738 @ SV1885 @ SV1943 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1885 @ SV420 ) @ ( hAPP @ SV1885 @ SV952 ) @ SV1943 @ SV1943 ) @ SV1738 @ ( tc_prod @ SV1943 @ SV1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4310,plain,
! [SV1944: $i,SV1886: $i,SV1739: $i,SV1421: $i,SV953: $i,SV421: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SV1739 @ SV1739 ) @ SV1886 @ ( tc_prod @ SV1739 @ SV1739 ) )
| ~ ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SV1944 @ SV1944 ) @ ( c_Relation_Oinv__image @ SV1886 @ SV421 @ SV1739 @ SV1944 ) @ ( tc_prod @ SV1944 @ SV1944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4311,plain,
! [SV1740: $i,SV1422: $i,SV422: $i,SV954: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1740 @ SV1422 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4312,plain,
! [SV1741: $i,SV1423: $i,SV423: $i,SV955: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1741 @ SV1423 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4313,plain,
! [SV1945: $i,SV1887: $i,SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ! [SY4984: $i,SY4985: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SY4984 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SY4985 @ SV956 @ SY4984 @ SV1742 ) @ SV1945 @ ( tc_prod @ SY4984 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4985 @ SV1424 @ SY4984 ) @ SV1887 @ ( tc_prod @ SV1424 @ SY4984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4314,plain,
! [SV1888: $i,SV1743: $i,SV1425: $i,SV957: $i,SV425: $i] :
( ( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1888 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
| ~ ( c_in @ ( c_Pair @ SV425 @ SV1888 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3998]) ).
thf(4315,plain,
! [SV1889: $i,SV1744: $i,SV1426: $i,SV958: $i,SV426: $i] :
( ( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1889 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
| ~ ( c_in @ ( c_Pair @ SV426 @ SV1889 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3999]) ).
thf(4316,plain,
! [SV1946: $i,SV1890: $i,SV1745: $i,SV1427: $i,SV961: $i,SV429: $i] :
( ( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
| ~ ( c_in @ SV961 @ SV1890 @ SV1946 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SV1946 @ SV1745 ) @ ( tc_fun @ SV1946 @ SV1745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4317,plain,
! [SV1947: $i,SV1891: $i,SV1746: $i,SV1428: $i,SV962: $i,SV430: $i] :
( ( ~ ( c_in @ SV430 @ SV962 @ SV1428 )
| ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SV1947 )
| ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SV1947 ) @ ( tc_fun @ SV1428 @ SV1947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(4318,plain,
! [SV1948: $i,SV1892: $i,SV1747: $i,SV1429: $i,SV963: $i,SV431: $i] :
( ( ! [SY4986: $i] :
( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
| ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SY4986 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SY4986 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4986 @ SV1948 @ SV1892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4319,plain,
! [SV1949: $i,SV1893: $i,SV1748: $i,SV1430: $i,SV964: $i,SV432: $i] :
( ( ~ ( c_in @ SV432 @ SV964 @ SV1430 )
| ~ ( c_in @ SV1748 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4320,plain,
! [SV433: $i,SV1431: $i,SV1749: $i,SV965: $i] :
( ( ( ~ ( c_in @ SV965 @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 ) )
= $true )
| ( ( c_in @ SV433 @ SV965 @ SV1431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4004]) ).
thf(4321,plain,
! [SV966: $i,SV1432: $i,SV1750: $i,SV434: $i] :
( ( ( ~ ( c_in @ SV434 @ SV1750 @ SV1432 ) )
= $true )
| ( ( ~ ( c_in @ SV1750 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4322,plain,
! [SV1751: $i,SV1433: $i,SV967: $i,SV435: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV435 = SV967 )
| ( SV435 = SV1751 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SV1751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4323,plain,
! [SV1752: $i,SV1434: $i,SV968: $i,SV436: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV968 = SV1752 )
| ( SV436 = SV1752 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SV1752 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4324,plain,
! [SV1436: $i,SV439: $i,SV1753: $i,SV971: $i] :
( ( ( SV971 = SV1753 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1436 @ SV1753 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1436 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4325,plain,
! [SV1754: $i,SV1439: $i,SV975: $i,SV443: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV443 = SV975 )
| ( SV975 = SV1754 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SV1754 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4326,plain,
! [SV1755: $i,SV1440: $i,SV976: $i,SV444: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV444 = SV1755 )
| ( SV976 = SV1755 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SV1755 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4011]) ).
thf(4327,plain,
! [SV1442: $i,SV978: $i,SV1756: $i,SV446: $i] :
( ( ( SV446 = SV1756 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1442 @ SV1756 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1442 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4328,plain,
! [SV1443: $i,SV983: $i,SV451: $i] :
( ( ( c_in @ SV451 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV983 = SV1443 )
= $true )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ SV451 @ SV983 @ SV1443 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4329,plain,
! [SV1444: $i,SV984: $i,SV454: $i] :
( ( ( c_in @ SV454 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV984 = SV1444 )
= $true )
| ( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ SV454 @ SV984 @ SV1444 ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4330,plain,
! [SV1950: $i,SV1894: $i,SV1757: $i,SV1445: $i,SV985: $i,SV455: $i] :
( ( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SV1950 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
| ~ ( c_in @ SV985 @ ( hAPP @ SV1950 @ SV455 ) @ SV1757 )
| ~ ( c_in @ SV455 @ SV1894 @ SV1445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4331,plain,
! [SV1951: $i,SV1895: $i,SV1758: $i,SV1446: $i,SV986: $i,SV456: $i] :
( ( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SV1951 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
| ~ ( c_in @ SV986 @ ( hAPP @ SV1951 @ SV456 ) @ SV1758 )
| ~ ( c_in @ SV456 @ SV1895 @ SV1446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4332,plain,
! [SV987: $i,SV1447: $i,SV1759: $i,SV457: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV457 @ SV1759 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1759 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 ) )
= $true )
| ( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4018]) ).
thf(4333,plain,
! [SV988: $i,SV1448: $i,SV1760: $i,SV458: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV458 @ SV1760 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1760 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 ) )
= $true )
| ( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4334,plain,
! [SV1952: $i,SV1896: $i,SV1761: $i,SV1449: $i,SV989: $i,SV459: $i] :
( ( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
| ~ ( c_in @ ( c_Pair @ SV1952 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) )
| ~ ( c_in @ SV1952 @ SV1449 @ SV1761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4335,plain,
! [SV1953: $i,SV1897: $i,SV1762: $i,SV1450: $i,SV990: $i,SV460: $i] :
( ( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
| ~ ( c_in @ ( c_Pair @ SV1953 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) )
| ~ ( c_in @ SV1953 @ SV1450 @ SV1762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4336,plain,
! [SV991: $i,SV1451: $i,SV1763: $i,SV461: $i] :
( ( ( c_in @ ( c_Pair @ SV461 @ SV1763 @ SV1451 @ SV1451 ) @ ( c_Relation_OId__on @ SV991 @ SV1451 ) @ ( tc_prod @ SV1451 @ SV1451 ) )
= $false )
| ( ( c_in @ SV461 @ SV991 @ SV1451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4337,plain,
! [SV1898: $i,SV1764: $i,SV1453: $i,SV993: $i,SV463: $i] :
( ( ( c_in @ SV463 @ SV993 @ SV1453 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SV1898 @ ( tc_prod @ SV1453 @ SV1453 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SV1898 @ SV1453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4024]) ).
thf(4338,plain,
! [SV1899: $i,SV1765: $i,SV1454: $i,SV994: $i,SV464: $i] :
( ( ( c_in @ SV464 @ SV994 @ SV1454 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SV1899 @ ( tc_prod @ SV1454 @ SV1454 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SV1899 @ SV1454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4025]) ).
thf(4339,plain,
! [SV1900: $i,SV1766: $i,SV1455: $i,SV995: $i,SV465: $i] :
( ( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SV1455 @ SV1766 ) @ SV1766 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1900 @ SV465 @ SV1455 @ SV1766 ) @ SV995 @ ( tc_prod @ SV1455 @ SV1766 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4340,plain,
! [SV1901: $i,SV1767: $i,SV1456: $i,SV996: $i,SV466: $i] :
( ( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SV1456 @ SV1767 ) @ SV1767 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1901 @ SV466 @ SV1456 @ SV1767 ) @ SV996 @ ( tc_prod @ SV1456 @ SV1767 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4341,plain,
! [SV1902: $i,SV1768: $i,SV1457: $i,SV997: $i,SV467: $i] :
( ( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SV1457 @ SV1768 ) @ SV1457 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV467 @ SV1902 @ SV1457 @ SV1768 ) @ SV997 @ ( tc_prod @ SV1457 @ SV1768 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4342,plain,
! [SV1903: $i,SV1769: $i,SV1458: $i,SV998: $i,SV468: $i] :
( ( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SV1458 @ SV1769 ) @ SV1458 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV468 @ SV1903 @ SV1458 @ SV1769 ) @ SV998 @ ( tc_prod @ SV1458 @ SV1769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4343,plain,
! [SV1954: $i,SV1904: $i,SV1770: $i,SV1459: $i,SV999: $i,SV469: $i] :
( ( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SV1770 )
| ~ ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SV1904 @ SV1770 ) @ ( c_Product__Type_OSigma @ SV1954 @ SV999 @ SV1904 @ SV1770 ) @ ( tc_prod @ SV1904 @ SV1770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4344,plain,
! [SV1955: $i,SV1905: $i,SV1771: $i,SV1460: $i,SV1000: $i,SV470: $i] :
( ( ( c_in @ SV470 @ SV1000 @ SV1460 )
| ~ ( c_in @ ( c_Pair @ SV470 @ SV1771 @ SV1460 @ SV1905 ) @ ( c_Product__Type_OSigma @ SV1000 @ SV1955 @ SV1460 @ SV1905 ) @ ( tc_prod @ SV1460 @ SV1905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4031]) ).
thf(4345,plain,
! [SV1906: $i,SV1772: $i,SV1461: $i,SV1001: $i,SV471: $i] :
( ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
| ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SV1906 @ SV1461 )
| ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4346,plain,
! [SV1462: $i,SV1002: $i,SV1773: $i,SV472: $i] :
( ( ( ~ ( c_in @ SV472 @ SV1773 @ SV1002 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1773 @ SV1462 @ SV1002 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4033]) ).
thf(4347,plain,
! [SV1907: $i,SV1774: $i,SV1463: $i,SV1003: $i,SV473: $i] :
( ( ( c_in @ SV473 @ SV1003 @ SV1463 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SV1907 @ ( tc_prod @ SV1463 @ SV1463 ) )
| ~ ( c_Relation_Orefl__on @ SV1003 @ SV1907 @ SV1463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4034]) ).
thf(4348,plain,
! [SV1908: $i,SV1775: $i,SV1464: $i,SV1004: $i,SV474: $i] :
( ( ( c_in @ SV474 @ SV1004 @ SV1464 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SV1908 @ ( tc_prod @ SV1464 @ SV1464 ) )
| ~ ( c_Relation_Orefl__on @ SV1004 @ SV1908 @ SV1464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4349,plain,
! [SV1465: $i,SV1005: $i,SV1776: $i,SV475: $i] :
( ( ( ~ ( c_in @ SV475 @ SV1776 @ SV1005 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1776 @ SV1465 @ SV1005 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4036]) ).
thf(4350,plain,
! [SV1777: $i,SV1466: $i,SV1006: $i,SV476: $i] :
( ( ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SV1777 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1466 = SV1777 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4351,plain,
! [SV1778: $i,SV1467: $i,SV1007: $i,SV477: $i] :
( ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV477 = SV1778 )
| ( SV477 = SV1778 )
| ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4352,plain,
! [SV1008: $i,SV1779: $i,SV1468: $i,SV478: $i] :
( ( ( SV478 = SV1468 )
= $true )
| ( ( ~ ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4039]) ).
thf(4353,plain,
! [SV1909: $i,SV1780: $i,SV1469: $i,SV1009: $i,SV479: $i] :
( ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( SV1009 = SV1780 )
| ( SV479 = SV1780 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4354,plain,
! [SV1781: $i,SV1470: $i,SV1010: $i,SV480: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4355,plain,
! [SV1782: $i,SV1471: $i,SV1011: $i,SV481: $i] :
( ( ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1782 = SV481 )
| ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4356,plain,
! [SV1783: $i,SV1472: $i,SV1012: $i,SV482: $i] :
( ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1783 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4357,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV483 = SV1013 )
| ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4358,plain,
! [SV1910: $i,SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1785 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4045]) ).
thf(4359,plain,
! [SV1911: $i,SV1786: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4046]) ).
thf(4360,plain,
! [SV486: $i,SV1016: $i,SV1476: $i] :
( ( ( ~ ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1016 = SV486 )
= $true )
| ( ( SV486 = SV1016 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4047]) ).
thf(4361,plain,
! [SV1912: $i,SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4362,plain,
! [SV1478: $i,SV1018: $i,SV488: $i] :
( ( ( SV488 = SV1018 )
= $true )
| ( ( ~ ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4049]) ).
thf(4363,plain,
! [SV1788: $i,SV1479: $i,SV1019: $i,SV489: $i] :
( ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1788 = SV1019 )
| ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4364,plain,
! [SV1913: $i,SV1789: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1020 = SV1913 )
| ( SV490 = SV1913 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4051]) ).
thf(4365,plain,
! [SV1790: $i,SV1481: $i,SV1021: $i,SV491: $i] :
( ( ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SV1790 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1481 = SV1790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4366,plain,
! [SV1791: $i,SV1482: $i,SV1022: $i,SV492: $i] :
( ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1022 = SV1791 )
| ( SV1791 = SV1022 )
| ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4367,plain,
! [SV1023: $i,SV1792: $i,SV493: $i,SV1483: $i] :
( ( ( SV1483 = SV493 )
= $true )
| ( ( ~ ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4054]) ).
thf(4368,plain,
! [SV1914: $i,SV1793: $i,SV1484: $i,SV1024: $i,SV494: $i] :
( ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ( SV494 = SV1793 )
| ( SV1024 = SV1793 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4369,plain,
! [SV1794: $i,SV1485: $i,SV495: $i,SV1025: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4370,plain,
! [SV1795: $i,SV1486: $i,SV1026: $i,SV496: $i] :
( ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1026 = SV1795 )
| ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4371,plain,
! [SV1796: $i,SV1487: $i,SV1027: $i,SV497: $i] :
( ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV497 = SV1796 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4372,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV498 = SV1028 )
| ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4059]) ).
thf(4373,plain,
! [SV1915: $i,SV1798: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1029 = SV1915 )
| ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4374,plain,
! [SV1916: $i,SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4375,plain,
! [SV1031: $i,SV501: $i,SV1491: $i] :
( ( ( ~ ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV501 = SV1031 )
= $true )
| ( ( SV501 = SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4376,plain,
! [SV1917: $i,SV1800: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4377,plain,
! [SV1493: $i,SV1033: $i,SV503: $i] :
( ( ( SV503 = SV1033 )
= $true )
| ( ( ~ ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4378,plain,
! [SV1801: $i,SV1494: $i,SV1034: $i,SV504: $i] :
( ( ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV504 = SV1801 )
| ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4065]) ).
thf(4379,plain,
! [SV1918: $i,SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV505 = SV1802 )
| ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4380,plain,
! [SV1496: $i,SV506: $i,SV1036: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV506 = SV1036 )
| ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4381,plain,
! [SV1497: $i,SV507: $i,SV1037: $i] :
( ( ( SV1037 = SV507 )
= $true )
| ( ( ~ ( c_in @ SV1497 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4382,plain,
! [SV1500: $i,SV511: $i,SV1040: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4383,plain,
! [SV1041: $i,SV512: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV512 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV1041 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ SV512 @ SV1041 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4384,plain,
! [SV1046: $i,SV517: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV517 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV1046 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV517 @ SV1046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4385,plain,
! [SV1956: $i,SV1919: $i,SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ! [SY4987: $i] :
( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
!= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
| ( ( hAPP @ SV524 @ SY4987 )
= ( hAPP @ SV1956 @ SY4987 ) )
| ~ ( c_in @ ( c_Pair @ SY4987 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4386,plain,
! [SV525: $i,SV1503: $i,SV1054: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SV1503 @ SV525 )
!= SV1503 )
= $true )
| ( ( c_lessequals @ SV1054 @ SV1503 @ SV525 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4387,plain,
! [SV528: $i,SV1505: $i,SV1057: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SV1505 @ SV528 )
!= SV1057 )
= $true )
| ( ( c_lessequals @ SV1057 @ SV1505 @ SV528 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV528 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4388,plain,
! [SV1957: $i,SV1920: $i,SV1804: $i,SV1506: $i,SV1058: $i,SV529: $i] :
( ( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
!= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
| ~ ( c_in @ SV1957 @ SV1058 @ SV1506 )
| ( SV529 = SV1920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4389,plain,
! [SV1805: $i,SV1507: $i,SV1059: $i,SV530: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ SV1059 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV530 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1059 @ SV1805 @ ( tc_fun @ SV1507 @ tc_bool ) ) @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $false )
| ( ( c_lessequals @ SV1805 @ SV530 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4390,plain,
! [SV1958: $i,SV1921: $i,SV1806: $i,SV1508: $i,SV1060: $i,SV531: $i] :
( ( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SV1806 )
!= ( c_Pair @ SV1921 @ SV1958 @ SV1508 @ SV1806 ) )
| ( SV1060 = SV1958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4391,plain,
! [SV1807: $i,SV1509: $i,SV1062: $i,SV533: $i] :
( ( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
= ( c_Set_Oinsert @ SV533 @ SV1807 @ SV1509 ) )
= $false )
| ( ( ( c_in @ SV533 @ SV1807 @ SV1509 )
| ( c_in @ SV533 @ SV1062 @ SV1509 )
| ( SV1062 = SV1807 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4392,plain,
! [SV1959: $i,SV1922: $i,SV1808: $i,SV1510: $i,SV1063: $i,SV534: $i] :
( ( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) ) )
| ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SV1808 @ SV1922 @ SV1959 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(4393,plain,
! [SV1960: $i,SV1923: $i,SV1809: $i,SV1511: $i,SV1064: $i,SV535: $i] :
( ( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SV1809 )
!= ( c_Pair @ SV1923 @ SV1960 @ SV1511 @ SV1809 ) )
| ( SV535 = SV1923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4394,plain,
! [SV1924: $i,SV1811: $i,SV1517: $i,SV1070: $i,SV544: $i,SV9: $i] :
( ( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
= $true )
| ( ( ~ ( c_in @ SV544 @ SV1811 @ SV1924 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SV1924 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4395,plain,
! [SV545: $i,SV1812: $i,SV1518: $i,SV1071: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SV1812 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1518 @ SV1812 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4089]) ).
thf(4396,plain,
! [SV559: $i,SV1524: $i,SV24: $i,SV1081: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1081 @ SV24 @ SV1524 ) @ SV559 ) )
= $false )
| ( ( SV1081 = SV559 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV24 @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4397,plain,
! [SV561: $i,SV1083: $i,SV26: $i] :
( ( ( c_Relation_Osym @ SV26 @ SV1083 )
= $false )
| ( ( c_Relation_Osym @ SV561 @ SV1083 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV26 @ SV561 @ ( tc_fun @ ( tc_prod @ SV1083 @ SV1083 ) @ tc_bool ) ) @ SV1083 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4398,plain,
! [SV41: $i,SV1097: $i,SV576: $i] :
( ( ( c_lessequals @ SV576 @ SV1097 @ SV41 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV576 @ SV1097 @ SV41 )
= SV576 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4399,plain,
! [SV42: $i,SV577: $i,SV1098: $i] :
( ( ( c_lessequals @ SV1098 @ SV577 @ SV42 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV577 @ SV1098 @ SV42 )
= SV1098 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4400,plain,
! [SV43: $i,SV1099: $i,SV1537: $i,SV578: $i] :
( ( ( c_lessequals @ SV578 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV43 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4401,plain,
! [SV46: $i,SV1102: $i,SV1538: $i,SV581: $i] :
( ( ( c_lessequals @ SV581 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV46 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4402,plain,
! [SV1539: $i,SV47: $i,SV1103: $i,SV582: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
= $true )
| ( ( ~ ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
| ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4403,plain,
! [SV1540: $i,SV50: $i,SV1106: $i,SV585: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
= $true )
| ( ( ~ ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
| ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4404,plain,
! [SV1541: $i,SV51: $i,SV1107: $i,SV586: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
= $true )
| ( ( ~ ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
| ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4106]) ).
thf(4405,plain,
! [SV1817: $i,SV63: $i,SV1547: $i,SV1118: $i,SV598: $i] :
( ( ( c_in @ SV598 @ SV1118 @ SV1547 )
= $false )
| ( ( ( c_Set_Oinsert @ ( hAPP @ SV63 @ SV598 ) @ ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) @ SV1817 )
= ( c_Set_Oimage @ SV63 @ SV1118 @ SV1547 @ SV1817 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4406,plain,
! [SV599: $i,SV1548: $i,SV1119: $i,SV64: $i] :
( ( ( c_lessequals @ SV64 @ SV1119 @ ( tc_fun @ SV1548 @ tc_bool ) )
= $false )
| ( ( c_in @ SV599 @ SV64 @ SV1548 )
= $true )
| ( ( c_lessequals @ SV64 @ ( c_Set_Oinsert @ SV599 @ SV1119 @ SV1548 ) @ ( tc_fun @ SV1548 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4111]) ).
thf(4407,plain,
! [SV1120: $i,SV600: $i,SV1549: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV1549 @ SV600 @ SV1120 ) @ ( tc_fun @ SV1120 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1549 @ SV65 @ SV1120 )
= $true )
| ( ( c_lessequals @ SV65 @ SV600 @ ( tc_fun @ SV1120 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4408,plain,
! [SV601: $i,SV1550: $i,SV1121: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ SV1121 @ ( tc_fun @ SV1550 @ tc_bool ) )
= $false )
| ( ( c_in @ SV601 @ SV66 @ SV1550 )
= $true )
| ( ( c_lessequals @ SV66 @ ( c_Set_Oinsert @ SV601 @ SV1121 @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4409,plain,
! [SV1122: $i,SV602: $i,SV1551: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ ( c_Set_Oinsert @ SV1551 @ SV602 @ SV1122 ) @ ( tc_fun @ SV1122 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1551 @ SV67 @ SV1122 )
= $true )
| ( ( c_lessequals @ SV67 @ SV602 @ ( tc_fun @ SV1122 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4410,plain,
! [SV1559: $i,SV77: $i,SV1131: $i,SV612: $i] :
( ( ( c_lessequals @ SV612 @ SV1131 @ SV77 )
= $true )
| ( ( ~ ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SV1559 @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4411,plain,
! [SV1560: $i,SV78: $i,SV1132: $i,SV613: $i] :
( ( ( c_lessequals @ SV613 @ SV1132 @ SV78 )
= $true )
| ( ( ~ ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1560 @ SV1132 @ SV78 ) @ SV78 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4412,plain,
! [SV1561: $i,SV79: $i,SV1133: $i,SV614: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SV1561 @ SV79 )
= $true )
| ( ( ~ ( c_lessequals @ SV614 @ SV1561 @ SV79 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4413,plain,
! [SV1562: $i,SV80: $i,SV1134: $i,SV615: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SV1562 @ SV80 )
= $true )
| ( ( ~ ( c_lessequals @ SV1134 @ SV1562 @ SV80 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4414,plain,
! [SV1563: $i,SV81: $i,SV1135: $i,SV616: $i] :
( ( ( c_lessequals @ SV616 @ SV1135 @ SV81 )
= $true )
| ( ( ~ ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SV1563 @ SV81 ) @ SV81 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4415,plain,
! [SV1564: $i,SV82: $i,SV1136: $i,SV617: $i] :
( ( ( c_lessequals @ SV617 @ SV1136 @ SV82 )
= $true )
| ( ( ~ ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1564 @ SV1136 @ SV82 ) @ SV82 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4416,plain,
! [SV631: $i,SV1149: $i,SV96: $i] :
( ( ( c_Relation_Osym @ SV96 @ SV1149 )
= $false )
| ( ( c_Relation_Osym @ SV631 @ SV1149 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV96 @ SV631 @ ( tc_fun @ ( tc_prod @ SV1149 @ SV1149 ) @ tc_bool ) ) @ SV1149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4417,plain,
! [SV635: $i,SV1570: $i,SV1152: $i,SV100: $i] :
( ( ( c_in @ SV100 @ SV1152 @ SV1570 )
= $false )
| ( ( ~ ( c_in @ SV100 @ SV635 @ SV1570 ) )
= $true )
| ( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4128]) ).
thf(4418,plain,
! [SV636: $i,SV1571: $i,SV1153: $i,SV101: $i] :
( ( ( c_in @ SV101 @ SV1153 @ SV1571 )
= $false )
| ( ( ~ ( c_in @ SV101 @ SV636 @ SV1571 ) )
= $true )
| ( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4129]) ).
thf(4419,plain,
! [SV1158: $i,SV641: $i,SV1576: $i,SV106: $i] :
( ( ( c_in @ SV106 @ ( c_Set_Oinsert @ SV1576 @ SV641 @ SV1158 ) @ SV1158 )
= $false )
| ( ( SV106 = SV1576 )
= $true )
| ( ( c_in @ SV106 @ SV641 @ SV1158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4420,plain,
! [SV1159: $i,SV642: $i,SV1577: $i,SV107: $i] :
( ( ( c_in @ SV107 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1577 @ SV642 @ ( tc_fun @ SV1159 @ tc_bool ) ) @ SV1159 )
= $false )
| ( ( c_in @ SV107 @ SV1577 @ SV1159 )
= $true )
| ( ( c_in @ SV107 @ SV642 @ SV1159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4421,plain,
! [SV1821: $i,SV1580: $i,SV1166: $i,SV649: $i,SV114: $i] :
( ( ( c_in @ SV114 @ SV649 @ SV1166 )
= $false )
| ( ( c_in @ ( hAPP @ SV1580 @ SV114 ) @ ( c_Set_Oimage @ SV1580 @ SV649 @ SV1166 @ SV1821 ) @ SV1821 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4422,plain,
! [SV1822: $i,SV1581: $i,SV1167: $i,SV650: $i,SV115: $i] :
( ( ( c_in @ SV115 @ SV650 @ SV1167 )
= $false )
| ( ( c_in @ ( hAPP @ SV1581 @ SV115 ) @ ( c_Set_Oimage @ SV1581 @ SV650 @ SV1167 @ SV1822 ) @ SV1822 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4139]) ).
thf(4423,plain,
! [SV1823: $i,SV116: $i,SV1582: $i,SV1168: $i,SV651: $i] :
( ( ( c_in @ SV651 @ SV1168 @ SV1582 )
= $false )
| ( ( c_in @ ( hAPP @ SV116 @ SV651 ) @ ( c_Set_Oimage @ SV116 @ SV1168 @ SV1582 @ SV1823 ) @ SV1823 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4424,plain,
! [SV1824: $i,SV117: $i,SV1583: $i,SV1169: $i,SV652: $i] :
( ( ( c_in @ SV652 @ SV1169 @ SV1583 )
= $false )
| ( ( c_in @ ( hAPP @ SV117 @ SV652 ) @ ( c_Set_Oimage @ SV117 @ SV1169 @ SV1583 @ SV1824 ) @ SV1824 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4141]) ).
thf(4425,plain,
! [SV1927: $i,SV1825: $i,SV1585: $i,SV1171: $i,SV654: $i,SV119: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SV1927 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SV1927 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
| ~ ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4143]) ).
thf(4426,plain,
! [SV120: $i,SV1172: $i,SV655: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV655 @ SV1172 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4144]) ).
thf(4427,plain,
! [SV656: $i,SV1173: $i,SV121: $i] :
( ( ( c_lessequals @ SV121 @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) ) @ SV121 @ SV656 @ SV656 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV121 @ SV656 ) @ SV1173 @ ( tc_fun @ ( tc_prod @ SV656 @ SV656 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4428,plain,
! [SV665: $i,SV1180: $i,SV130: $i] :
( ( ( c_Finite__Set_Ofinite @ SV130 @ SV1180 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV665 @ SV1180 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV665 @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4429,plain,
! [SV666: $i,SV1181: $i,SV131: $i] :
( ( ( c_Finite__Set_Ofinite @ SV131 @ SV1181 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV666 @ SV1181 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 @ SV666 @ ( tc_fun @ SV1181 @ tc_bool ) ) @ SV1181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4430,plain,
! [SV670: $i,SV1591: $i,SV135: $i,SV1184: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1184 @ SV135 @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV670 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1184 @ SV670 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV135 @ SV670 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4431,plain,
! [SV1595: $i,SV140: $i,SV1188: $i,SV1829: $i,SV675: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV675 @ SV1829 @ SV1188 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SV1829 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4432,plain,
! [SV685: $i,SV1198: $i,SV151: $i] :
( ( ( c_Relation_Otrans @ SV151 @ SV1198 )
= $false )
| ( ( c_Relation_Otrans @ SV685 @ SV1198 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV151 @ SV685 @ ( tc_fun @ ( tc_prod @ SV1198 @ SV1198 ) @ tc_bool ) ) @ SV1198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4433,plain,
! [SV155: $i,SV689: $i,SV1202: $i] :
( ( ( c_lessequals @ SV1202 @ SV689 @ SV155 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1202 @ SV155 )
= SV689 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4434,plain,
! [SV156: $i,SV1203: $i,SV690: $i] :
( ( ( c_lessequals @ SV690 @ SV1203 @ SV156 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV690 @ SV1203 @ SV156 )
= SV1203 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4162]) ).
thf(4435,plain,
! [SV1604: $i,SV159: $i,SV1206: $i,SV1831: $i,SV693: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV693 @ SV1831 @ SV1206 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SV1831 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4163]) ).
thf(4436,plain,
! [SV1609: $i,SV164: $i,SV1211: $i,SV1833: $i,SV698: $i] :
( ( ( ~ ( c_lessequals @ SV698 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4437,plain,
! [SV168: $i,SV1611: $i,SV1215: $i,SV702: $i] :
( ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( c_lessequals @ SV702 @ SV1611 @ SV168 )
| ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4438,plain,
! [SV169: $i,SV1612: $i,SV1216: $i,SV703: $i] :
( ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
= $true )
| ( ( ~ ( c_lessequals @ SV703 @ SV1612 @ SV169 )
| ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4439,plain,
! [SV170: $i,SV1613: $i,SV1217: $i,SV704: $i] :
( ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
= $true )
| ( ( ~ ( c_lessequals @ SV704 @ SV1613 @ SV170 )
| ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4440,plain,
! [SV709: $i,SV1614: $i,SV1222: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SV1614 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) @ ( tc_fun @ SV1614 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4441,plain,
! [SV710: $i,SV1615: $i,SV1223: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SV1615 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ ( tc_fun @ SV1615 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4442,plain,
! [SV183: $i,SV1230: $i,SV1621: $i,SV717: $i] :
( ( ( c_lessequals @ SV717 @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV183 @ SV1621 @ SV1230 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4443,plain,
! [SV1623: $i,SV194: $i,SV1238: $i,SV728: $i] :
( ( ( c_lessequals @ SV728 @ SV1238 @ SV194 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1623 @ SV728 @ SV194 ) @ SV1238 @ SV194 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4444,plain,
! [SV1624: $i,SV195: $i,SV1239: $i,SV729: $i] :
( ( ( c_lessequals @ SV729 @ SV1239 @ SV195 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SV1624 @ SV195 ) @ SV1239 @ SV195 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4177]) ).
thf(4445,plain,
! [SV196: $i,SV1625: $i,SV1240: $i,SV730: $i] :
( ( ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SV1625 @ SV196 ) @ SV196 )
= $true )
| ( ( ~ ( c_lessequals @ SV730 @ SV1625 @ SV196 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4178]) ).
thf(4446,plain,
! [SV197: $i,SV1626: $i,SV1241: $i,SV731: $i] :
( ( ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SV1626 @ SV197 ) @ SV197 )
= $true )
| ( ( ~ ( c_lessequals @ SV731 @ SV1241 @ SV197 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4179]) ).
thf(4447,plain,
! [SV1627: $i,SV198: $i,SV1242: $i,SV732: $i] :
( ( ( c_lessequals @ SV732 @ SV1242 @ SV198 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1627 @ SV732 @ SV198 ) @ SV1242 @ SV198 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4448,plain,
! [SV1628: $i,SV199: $i,SV1243: $i,SV733: $i] :
( ( ( c_lessequals @ SV733 @ SV1243 @ SV199 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV1628 @ SV199 ) @ SV1243 @ SV199 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4181]) ).
thf(4449,plain,
! [SV736: $i,SV1246: $i,SV202: $i] :
( ( ( c_lessequals @ SV202 @ SV1246 @ ( tc_fun @ SV736 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1246 @ SV736 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV202 @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4450,plain,
! [SV203: $i,SV737: $i,SV1247: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1247 @ SV737 )
= $false )
| ( ( c_lessequals @ SV203 @ SV1247 @ ( tc_fun @ SV737 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV203 @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4451,plain,
! [SV1631: $i,SV204: $i,SV1248: $i,SV1835: $i,SV738: $i] :
( ( ( ~ ( c_lessequals @ SV738 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4452,plain,
! [SV1249: $i,SV205: $i,SV1632: $i,SV739: $i] :
( ( ( hBOOL @ ( hAPP @ SV739 @ SV1632 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV205 @ SV1632 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV1632 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4453,plain,
! [SV1633: $i,SV206: $i,SV1250: $i,SV1836: $i,SV740: $i] :
( ( ( c_lessequals @ SV740 @ SV1836 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV206 @ SV740 @ SV1250 @ SV1633 ) @ ( c_Set_Oimage @ SV206 @ SV1836 @ SV1250 @ SV1633 ) @ ( tc_fun @ SV1633 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4188]) ).
thf(4454,plain,
! [SV1837: $i,SV1634: $i,SV1251: $i,SV741: $i,SV207: $i] :
( ( ( c_lessequals @ SV207 @ SV741 @ ( tc_fun @ SV1251 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV1634 @ SV207 @ SV1251 @ SV1837 ) @ ( c_Set_Oimage @ SV1634 @ SV741 @ SV1251 @ SV1837 ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4189]) ).
thf(4455,plain,
! [SV211: $i,SV1637: $i,SV1255: $i,SV745: $i,SV1839: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4456,plain,
! [SV212: $i,SV1638: $i,SV1256: $i,SV746: $i,SV1840: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4192]) ).
thf(4457,plain,
! [SV751: $i,SV217: $i,SV1260: $i] :
( ( ( c_in @ SV1260 @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1260 @ SV751 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ SV217 @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4458,plain,
! [SV1640: $i,SV1262: $i,SV223: $i,SV757: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV757 @ SV223 @ SV1262 @ SV1262 ) @ SV1640 @ ( tc_prod @ SV1262 @ SV1262 ) ) @ SV1262 )
= $false )
| ( ( c_in @ ( c_Pair @ SV223 @ SV757 @ SV1262 @ SV1262 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1262 ) @ ( tc_prod @ SV1262 @ SV1262 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4195]) ).
thf(4459,plain,
! [SV224: $i,SV758: $i,SV1263: $i,SV1641: $i] :
( ( ( c_Wellfounded_Owf @ SV1641 @ SV1263 )
= $false )
| ( ( c_in @ ( c_Pair @ SV758 @ SV224 @ SV1263 @ SV1263 ) @ ( c_Transitive__Closure_Ortrancl @ SV1641 @ SV1263 ) @ ( tc_prod @ SV1263 @ SV1263 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV224 @ SV758 @ SV1263 @ SV1263 ) @ SV1641 @ ( tc_prod @ SV1263 @ SV1263 ) ) @ SV1263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4460,plain,
! [SV1929: $i,SV1841: $i,SV1643: $i,SV1265: $i,SV760: $i,SV226: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SV1841 @ SV1929 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
= $true )
| ( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SV1929 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
| ~ ( c_lessequals @ SV226 @ SV1841 @ ( tc_fun @ SV1265 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(4461,plain,
! [SV1644: $i,SV1842: $i,SV1266: $i,SV761: $i,SV227: $i] :
( ( ( c_in @ ( hAPP @ SV227 @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ SV761 @ SV1266 @ SV227 @ SV1842 @ SV1644 ) ) @ SV1266 @ SV1644 )
= $false )
| ( ( c_in @ SV227 @ ( c_FuncSet_OPi @ SV761 @ ( c_COMBK @ SV1266 @ ( tc_fun @ SV1644 @ tc_bool ) @ SV1842 ) @ SV1842 @ SV1644 ) @ ( tc_fun @ SV1842 @ SV1644 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4462,plain,
! [SV1268: $i,SV1646: $i,SV1844: $i,SV763: $i,SV229: $i] :
( ( ( c_in @ SV229 @ ( c_FuncSet_OPi @ SV763 @ ( c_COMBK @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) @ SV1268 ) @ SV1268 @ SV1646 ) @ ( tc_fun @ SV1268 @ SV1646 ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV229 @ SV763 @ SV1268 @ SV1646 ) @ SV1844 @ ( tc_fun @ SV1646 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4463,plain,
! [SV231: $i,SV1269: $i,SV765: $i] :
( ( ( c_lessequals @ ( c_Relation_OId @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) ) @ SV231 @ SV765 @ SV765 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV231 @ SV765 ) @ SV1269 @ ( tc_fun @ ( tc_prod @ SV765 @ SV765 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4464,plain,
! [SV767: $i,SV1647: $i,SV1270: $i,SV233: $i] :
( ( ( c_lessequals @ SV233 @ ( c_Product__Type_OSigma @ SV1270 @ ( c_COMBK @ SV1647 @ ( tc_fun @ SV767 @ tc_bool ) @ SV767 ) @ SV767 @ SV767 ) @ ( tc_fun @ ( tc_prod @ SV767 @ SV767 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1270 @ SV1647 @ SV233 @ SV767 ) @ SV1647 @ SV767 )
= $true )
| ( ( c_Wellfounded_Owf @ SV233 @ SV767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4465,plain,
! [SV768: $i,SV1648: $i,SV1271: $i,SV234: $i] :
( ( ( c_lessequals @ SV234 @ ( c_Product__Type_OSigma @ SV1271 @ ( c_COMBK @ SV1648 @ ( tc_fun @ SV768 @ tc_bool ) @ SV768 ) @ SV768 @ SV768 ) @ ( tc_fun @ ( tc_prod @ SV768 @ SV768 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ SV1271 @ SV1648 @ SV234 @ SV768 ) @ SV1271 @ SV768 )
= $true )
| ( ( c_Wellfounded_Owf @ SV234 @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4466,plain,
! [SV771: $i,SV1649: $i,SV1274: $i,SV237: $i] :
( ( ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4467,plain,
! [SV1275: $i,SV238: $i,SV772: $i] :
( ( ( c_lessequals @ SV772 @ ( c_Product__Type_OSigma @ SV238 @ ( c_COMBK @ SV238 @ ( tc_fun @ SV1275 @ tc_bool ) @ SV1275 ) @ SV1275 @ SV1275 ) @ ( tc_fun @ ( tc_prod @ SV1275 @ SV1275 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ SV238 @ SV772 @ SV1275 ) @ SV1275 @ SV1275 ) @ SV772 @ ( tc_prod @ SV1275 @ SV1275 ) )
= $false )
| ( ( c_Relation_Orefl__on @ SV238 @ SV772 @ SV1275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4209]) ).
thf(4468,plain,
! [SV1276: $i,SV239: $i,SV773: $i] :
( ( ( c_lessequals @ SV773 @ ( c_Product__Type_OSigma @ SV239 @ ( c_COMBK @ SV239 @ ( tc_fun @ SV1276 @ tc_bool ) @ SV1276 ) @ SV1276 @ SV1276 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1276 ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ SV239 @ SV773 @ SV1276 ) @ SV1276 @ SV1276 ) @ SV773 @ ( tc_prod @ SV1276 @ SV1276 ) )
= $false )
| ( ( c_Relation_Orefl__on @ SV239 @ SV773 @ SV1276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4210]) ).
thf(4469,plain,
! [SV1650: $i,SV1277: $i,SV774: $i,SV240: $i] :
( ( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Ortrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
= $false )
| ( ( SV240 = SV774 )
= $true )
| ( ( c_in @ ( c_Pair @ SV240 @ SV774 @ SV1277 @ SV1277 ) @ ( c_Transitive__Closure_Otrancl @ SV1650 @ SV1277 ) @ ( tc_prod @ SV1277 @ SV1277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4211]) ).
thf(4470,plain,
! [SV1651: $i,SV1278: $i,SV775: $i,SV241: $i] :
( ( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Ortrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
= $false )
| ( ( SV241 = SV775 )
= $true )
| ( ( c_in @ ( c_Pair @ SV241 @ SV775 @ SV1278 @ SV1278 ) @ ( c_Transitive__Closure_Otrancl @ SV1651 @ SV1278 ) @ ( tc_prod @ SV1278 @ SV1278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4471,plain,
! [SV1652: $i,SV1279: $i,SV776: $i,SV242: $i] :
( ( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Otrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
= $false )
| ( ( SV242 = SV776 )
= $true )
| ( ( c_in @ ( c_Pair @ SV242 @ SV776 @ SV1279 @ SV1279 ) @ ( c_Transitive__Closure_Ortrancl @ SV1652 @ SV1279 ) @ ( tc_prod @ SV1279 @ SV1279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4472,plain,
! [SV777: $i,SV1653: $i,SV1280: $i,SV243: $i] :
( ( ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ ( c_Transitive__Closure_Otrancl @ SV777 @ SV1653 ) @ ( tc_prod @ SV1653 @ SV1653 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV243 @ SV1280 @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV243 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV777 @ SV243 @ SV1280 @ SV1653 ) @ SV1653 @ SV1653 ) @ SV777 @ ( tc_prod @ SV1653 @ SV1653 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4473,plain,
! [SV244: $i,SV1654: $i,SV1281: $i,SV778: $i,SV1845: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1845 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV244 @ SV1845 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4215]) ).
thf(4474,plain,
! [SV245: $i,SV1655: $i,SV1282: $i,SV779: $i,SV1846: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1846 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV245 @ SV1846 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4216]) ).
thf(4475,plain,
! [SV250: $i,SV1656: $i,SV1285: $i,SV784: $i] :
( ( ( c_in @ SV784 @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV250 @ SV1285 @ SV1656 ) @ ( c_Wellfounded_Oacc @ SV1285 @ SV1656 ) @ SV1656 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV250 @ SV784 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4476,plain,
! [SV252: $i,SV1287: $i,SV786: $i] :
( ( ( c_in @ SV786 @ ( c_Wellfounded_Oacc @ SV1287 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV252 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV252 @ SV1287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV252 @ SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4477,plain,
! [SV787: $i,SV1657: $i,SV1288: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SV1657 ) ) )
= $false )
| ( ( ~ ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SV1657 ) @ SV1657 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4478,plain,
! [SV255: $i,SV1658: $i,SV1290: $i,SV789: $i] :
( ( ( c_in @ SV789 @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV255 @ SV1290 @ SV1658 ) @ ( c_Wellfounded_Oacc @ SV1290 @ SV1658 ) @ SV1658 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ SV789 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4220]) ).
thf(4479,plain,
! [SV256: $i,SV1291: $i,SV790: $i] :
( ( ( c_in @ SV790 @ ( c_Wellfounded_Oacc @ SV1291 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV256 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV256 @ SV1291 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV256 @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4480,plain,
! [SV791: $i,SV1659: $i,SV1292: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SV1659 ) ) )
= $false )
| ( ( ~ ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SV1659 ) @ SV1659 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4481,plain,
! [SV258: $i,SV792: $i,SV1293: $i] :
( ( ( c_in @ SV1293 @ SV792 @ SV258 )
= $false )
| ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV792 @ SV258 ) @ SV1293 @ SV258 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4482,plain,
! [SV260: $i,SV1295: $i,SV794: $i,SV1660: $i] :
( ( ( c_lessequals @ SV1660 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV1660 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) ) )
= $true )
| ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(4483,plain,
! [SV1847: $i,SV1661: $i,SV261: $i,SV1296: $i,SV795: $i] :
( ( ( c_in @ SV795 @ ( c_Relation_OImage @ SV1296 @ SV261 @ SV1661 @ SV1847 ) @ SV1847 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV261 @ SV795 @ SV1296 @ SV1661 @ SV1847 ) @ SV261 @ SV1661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4484,plain,
! [SV1848: $i,SV1662: $i,SV262: $i,SV1297: $i,SV796: $i] :
( ( ( c_in @ SV796 @ ( c_Relation_OImage @ SV1297 @ SV262 @ SV1662 @ SV1848 ) @ SV1848 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV262 @ SV796 @ SV1297 @ SV1662 @ SV1848 ) @ SV262 @ SV1662 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4485,plain,
! [SV797: $i,SV1298: $i,SV263: $i,SV1663: $i] :
( ( ( c_in @ SV1663 @ SV263 @ SV1298 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV797 @ SV1298 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4486,plain,
! [SV798: $i,SV1299: $i,SV264: $i,SV1664: $i] :
( ( ( c_in @ SV1664 @ SV264 @ SV1299 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV798 @ SV1299 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4487,plain,
! [SV266: $i,SV1301: $i,SV800: $i] :
( ( ( c_in @ SV800 @ SV1301 @ SV266 )
= $false )
| ( ( c_lessequals @ SV800 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1301 @ SV266 ) @ SV266 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4488,plain,
! [SV267: $i,SV1665: $i,SV1302: $i,SV801: $i,SV1849: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1849 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV267 @ SV1849 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4489,plain,
! [SV268: $i,SV1666: $i,SV1303: $i,SV802: $i,SV1850: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1850 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV268 @ SV1850 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4231]) ).
thf(4490,plain,
! [SV269: $i,SV1667: $i,SV1304: $i,SV803: $i,SV1851: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1851 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV269 @ SV1851 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4232]) ).
thf(4491,plain,
! [SV1930: $i,SV1852: $i,SV1669: $i,SV1310: $i,SV811: $i,SV277: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SV1930 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV811 @ SV1930 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4492,plain,
! [SV813: $i,SV1671: $i,SV279: $i,SV1312: $i] :
( ( ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SV1671 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4493,plain,
! [SV282: $i,SV816: $i,SV1313: $i] :
( ( ( c_Wellfounded_Owf @ SV1313 @ SV816 )
= $false )
| ( ( c_lessequals @ SV282 @ SV1313 @ ( tc_fun @ ( tc_prod @ SV816 @ SV816 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV282 @ SV816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4494,plain,
! [SV1672: $i,SV283: $i,SV817: $i,SV1314: $i] :
( ( ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SV1672 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4495,plain,
! [SV284: $i,SV1315: $i,SV818: $i,SV1673: $i] :
( ( ( c_lessequals @ SV1673 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV284 @ SV1673 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4496,plain,
! [SV1674: $i,SV287: $i,SV1316: $i,SV821: $i] :
( ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
= $true )
| ( ( ~ ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
| ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4241]) ).
thf(4497,plain,
! [SV1675: $i,SV288: $i,SV1317: $i,SV822: $i] :
( ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
= $true )
| ( ( ~ ( c_lessequals @ SV822 @ SV1675 @ SV288 )
| ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4242]) ).
thf(4498,plain,
! [SV292: $i,SV1320: $i,SV826: $i] :
( ( ( ~ ( c_lessequals @ SV826 @ SV1320 @ SV292 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true )
| ( ( SV826 = SV1320 )
= $true )
| ( ( class_Orderings_Oorder @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4499,plain,
! [SV293: $i,SV827: $i,SV1321: $i] :
( ( ( ~ ( c_lessequals @ SV1321 @ SV827 @ SV293 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true )
| ( ( SV827 = SV1321 )
= $true )
| ( ( class_Orderings_Oorder @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4500,plain,
! [SV294: $i,SV828: $i,SV1322: $i] :
( ( ( ~ ( c_lessequals @ SV1322 @ SV828 @ SV294 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true )
| ( ( SV828 = SV1322 )
= $true )
| ( ( class_Orderings_Oorder @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4501,plain,
! [SV1323: $i,SV829: $i,SV295: $i] :
( ( ( c_lessequals @ SV295 @ SV829 @ ( tc_fun @ SV1323 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV829 @ SV295 @ ( tc_fun @ SV1323 @ tc_bool ) )
= $false )
| ( ( SV295 = SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4502,plain,
! [SV1324: $i,SV830: $i,SV296: $i] :
( ( ( c_lessequals @ SV296 @ SV830 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV830 @ SV296 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $false )
| ( ( SV296 = SV830 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4503,plain,
! [SV1961: $i,SV1931: $i,SV1853: $i,SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ! [SY4988: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SY4988 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SY4988 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4504,plain,
! [SV1932: $i,SV1854: $i,SV1677: $i,SV1327: $i,SV836: $i,SV302: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) )
| ~ ( c_in @ SV1932 @ SV836 @ SV1327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4249]) ).
thf(4505,plain,
! [SV1933: $i,SV1855: $i,SV1678: $i,SV1328: $i,SV837: $i,SV303: $i] :
( ( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) )
| ~ ( c_in @ SV1933 @ SV1678 @ SV1855 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4506,plain,
! [SV1962: $i,SV1934: $i,SV1856: $i,SV1679: $i,SV1330: $i,SV840: $i,SV306: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SV1962 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV840 @ SV1962 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4507,plain,
! [SV1935: $i,SV1857: $i,SV1681: $i,SV1332: $i,SV842: $i,SV308: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SV1681 ) @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SV1935 @ ( c_COMBK @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) @ SV1332 ) @ SV1332 @ SV1681 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1681 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4508,plain,
! [SV844: $i,SV310: $i,SV1333: $i] :
( ( ( c_lessequals @ SV1333 @ SV310 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV310 @ ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
= $false )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV310 @ SV844 )
= ( c_Transitive__Closure_Ortrancl @ SV1333 @ SV844 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4509,plain,
! [SV1334: $i,SV845: $i,SV1858: $i,SV1682: $i,SV311: $i] :
( ( ( SV311 = SV1682 )
= $true )
| ( ( ~ ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) )
= $true )
| ( ( c_in @ SV311 @ SV845 @ SV1334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4254]) ).
thf(4510,plain,
! [SV1859: $i,SV1683: $i,SV1336: $i,SV847: $i,SV313: $i] :
( ( ( class_HOL_Oord @ SV313 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
| ~ ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SV1859 @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4511,plain,
! [SV848: $i,SV1337: $i,SV1684: $i,SV314: $i] :
( ( ( c_in @ SV314 @ SV1684 @ SV1337 )
= $false )
| ( ( ~ ( c_lessequals @ SV1684 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV314 @ SV848 @ SV1337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4256]) ).
thf(4512,plain,
! [SV315: $i,SV1338: $i,SV849: $i,SV1685: $i] :
( ( ( c_lessequals @ SV1685 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV315 @ SV1685 @ SV1338 ) )
= $true )
| ( ( c_in @ SV315 @ SV849 @ SV1338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4257]) ).
thf(4513,plain,
! [SV850: $i,SV1339: $i,SV1686: $i,SV316: $i] :
( ( ( c_in @ SV316 @ SV1686 @ SV1339 )
= $false )
| ( ( ~ ( c_lessequals @ SV1686 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV316 @ SV850 @ SV1339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4514,plain,
! [SV851: $i,SV1340: $i,SV1687: $i,SV317: $i] :
( ( ( c_in @ SV317 @ SV1687 @ SV1340 )
= $false )
| ( ( ~ ( c_lessequals @ SV1687 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV317 @ SV851 @ SV1340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4515,plain,
! [SV320: $i,SV1689: $i,SV1343: $i,SV854: $i,SV1860: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1860 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV320 @ SV1860 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4516,plain,
! [SV321: $i,SV1690: $i,SV1344: $i,SV855: $i,SV1861: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1861 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV321 @ SV1861 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4517,plain,
! [SV323: $i,SV1692: $i,SV1346: $i,SV857: $i] :
( ( ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV857 @ SV1346 @ SV1692 @ SV1692 ) @ SV323 @ ( tc_prod @ SV1692 @ SV1692 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV323 @ SV857 @ SV1346 @ SV1692 ) @ SV1346 @ SV1692 @ SV1692 ) @ ( c_Transitive__Closure_Otrancl @ SV323 @ SV1692 ) @ ( tc_prod @ SV1692 @ SV1692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4264]) ).
thf(4518,plain,
! [SV1963: $i,SV1936: $i,SV1862: $i,SV1695: $i,SV1351: $i,SV862: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SV1862 @ SV1936 @ SV1963 ) @ SV1862 @ SV1963 ) @ SV1351 @ ( tc_prod @ SV1862 @ SV1963 ) )
| ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SV1862 @ SV1936 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SV1862 @ SV1963 @ SV1936 ) @ ( tc_prod @ SV1862 @ SV1936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(4519,plain,
! [SV1964: $i,SV1937: $i,SV1863: $i,SV1696: $i,SV1352: $i,SV863: $i,SV329: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SV1863 @ SV1937 @ SV1964 ) @ SV863 @ SV1964 @ SV1937 ) @ SV1696 @ ( tc_prod @ SV1964 @ SV1937 ) )
| ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SV1863 @ SV1937 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SV1863 @ SV1964 @ SV1937 ) @ ( tc_prod @ SV1863 @ SV1937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4520,plain,
! [SV1864: $i,SV1697: $i,SV1353: $i,SV864: $i,SV330: $i] :
( ( ( c_in @ ( hAPP @ SV330 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ ( hAPP @ SV1353 @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ SV864 @ SV1353 @ SV330 @ SV1697 @ SV1864 ) ) @ SV1864 )
= $false )
| ( ( c_in @ SV330 @ ( c_FuncSet_OPi @ SV864 @ SV1353 @ SV1697 @ SV1864 ) @ ( tc_fun @ SV1697 @ SV1864 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4269]) ).
thf(4521,plain,
! [SV1938: $i,SV1865: $i,SV1698: $i,SV1354: $i,SV865: $i,SV331: $i] :
( ( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
= $true )
| ( ( ~ ( c_in @ SV865 @ SV1865 @ SV1938 )
| ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1938 ) @ SV1938 @ SV1698 ) @ ( tc_fun @ SV1938 @ SV1698 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4522,plain,
! [SV1866: $i,SV1699: $i,SV1355: $i,SV866: $i,SV332: $i] :
( ( ( c_in @ ( hAPP @ SV332 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ ( hAPP @ SV1355 @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ SV866 @ SV1355 @ SV332 @ SV1699 @ SV1866 ) ) @ SV1866 )
= $false )
| ( ( c_in @ SV332 @ ( c_FuncSet_OPi @ SV866 @ SV1355 @ SV1699 @ SV1866 ) @ ( tc_fun @ SV1699 @ SV1866 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4523,plain,
! [SV1939: $i,SV1869: $i,SV1703: $i,SV1362: $i,SV876: $i,SV342: $i] :
( ( ( ( c_Recdef_Ocut @ SV342 @ SV876 @ SV1362 @ SV1703 @ SV1869 )
= ( c_Recdef_Ocut @ SV1939 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV342 @ SV1939 @ SV876 @ SV1362 @ SV1703 @ SV1869 ) @ SV1362 @ SV1703 @ SV1703 ) @ SV876 @ ( tc_prod @ SV1703 @ SV1703 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4524,plain,
! [SV1870: $i,SV1704: $i,SV1364: $i,SV879: $i,SV345: $i] :
( ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
| ~ ( c_in @ SV1870 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4525,plain,
! [SV1871: $i,SV1705: $i,SV1365: $i,SV880: $i,SV346: $i] :
( ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
| ~ ( c_in @ SV1871 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4526,plain,
! [SV1872: $i,SV1706: $i,SV347: $i,SV1366: $i,SV881: $i] :
( ( ( c_in @ SV881 @ ( c_Relation_OImage @ SV1366 @ SV347 @ SV1706 @ SV1872 ) @ SV1872 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV347 @ SV881 @ SV1366 @ SV1706 @ SV1872 ) @ SV881 @ SV1706 @ SV1872 ) @ SV1366 @ ( tc_prod @ SV1706 @ SV1872 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4527,plain,
! [SV1873: $i,SV1707: $i,SV348: $i,SV1367: $i,SV882: $i] :
( ( ( c_in @ SV882 @ ( c_Relation_OImage @ SV1367 @ SV348 @ SV1707 @ SV1873 ) @ SV1873 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV348 @ SV882 @ SV1367 @ SV1707 @ SV1873 ) @ SV882 @ SV1707 @ SV1873 ) @ SV1367 @ ( tc_prod @ SV1707 @ SV1873 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4279]) ).
thf(4528,plain,
! [SV1708: $i,SV1368: $i,SV883: $i,SV349: $i] :
( ( ( c_in @ ( c_Pair @ SV349 @ SV883 @ SV1368 @ SV1368 ) @ ( c_Transitive__Closure_Ortrancl @ SV1708 @ SV1368 ) @ ( tc_prod @ SV1368 @ SV1368 ) )
= $false )
| ( ( c_in @ SV349 @ ( c_Relation_ODomain @ SV1708 @ SV1368 @ SV1368 ) @ SV1368 )
= $true )
| ( ( SV349 = SV883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4280]) ).
thf(4529,plain,
! [SV887: $i,SV1874: $i,SV1711: $i,SV1372: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) )
| ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4530,plain,
! [SV888: $i,SV1712: $i,SV354: $i,SV1373: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(4531,plain,
! [SV889: $i,SV1713: $i,SV355: $i,SV1374: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4285]) ).
thf(4532,plain,
! [SV890: $i,SV1714: $i,SV356: $i,SV1375: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4286]) ).
thf(4533,plain,
! [SV891: $i,SV1376: $i,SV1715: $i,SV357: $i] :
( ( ( c_in @ ( c_Pair @ SV357 @ SV1715 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
= $false )
| ( ( ~ ( c_in @ SV1715 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 ) )
= $true )
| ( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4534,plain,
! [SV358: $i,SV1377: $i,SV892: $i,SV1716: $i] :
( ( ( c_in @ SV1716 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV358 @ SV1716 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) ) )
= $true )
| ( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4288]) ).
thf(4535,plain,
! [SV894: $i,SV1717: $i,SV360: $i,SV1379: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4289]) ).
thf(4536,plain,
! [SV895: $i,SV1875: $i,SV1718: $i,SV1380: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) )
| ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4537,plain,
! [SV1721: $i,SV1384: $i,SV365: $i,SV899: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1721 @ SV1384 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4538,plain,
! [SV367: $i,SV1723: $i,SV1386: $i,SV901: $i,SV1876: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1876 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV367 @ SV1876 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4295]) ).
thf(4539,plain,
! [SV368: $i,SV1724: $i,SV1387: $i,SV902: $i,SV1877: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1877 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV368 @ SV1877 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4296]) ).
thf(4540,plain,
! [SV1878: $i,SV1388: $i,SV1725: $i,SV369: $i,SV903: $i] :
( ( ( c_in @ ( c_Pair @ SV903 @ SV369 @ SV1725 @ SV1388 ) @ ( c_Relation_Oconverse @ SV1878 @ SV1388 @ SV1725 ) @ ( tc_prod @ SV1725 @ SV1388 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV369 @ SV903 @ SV1388 @ SV1725 ) @ SV1878 @ ( tc_prod @ SV1388 @ SV1725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4541,plain,
! [SV1879: $i,SV1389: $i,SV1726: $i,SV370: $i,SV904: $i] :
( ( ( c_in @ ( c_Pair @ SV904 @ SV370 @ SV1726 @ SV1389 ) @ SV1879 @ ( tc_prod @ SV1726 @ SV1389 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV370 @ SV904 @ SV1389 @ SV1726 ) @ ( c_Relation_Oconverse @ SV1879 @ SV1726 @ SV1389 ) @ ( tc_prod @ SV1389 @ SV1726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4542,plain,
! [SV1880: $i,SV1390: $i,SV1727: $i,SV371: $i,SV905: $i] :
( ( ( c_in @ ( c_Pair @ SV905 @ SV371 @ SV1727 @ SV1390 ) @ SV1880 @ ( tc_prod @ SV1727 @ SV1390 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV371 @ SV905 @ SV1390 @ SV1727 ) @ ( c_Relation_Oconverse @ SV1880 @ SV1727 @ SV1390 ) @ ( tc_prod @ SV1390 @ SV1727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4543,plain,
! [SV1940: $i,SV1881: $i,SV1728: $i,SV1391: $i,SV906: $i,SV372: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SV1728 @ SV1881 ) @ SV1940 )
= ( hAPP @ SV372 @ SV1940 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1940 @ SV1391 @ SV1728 @ SV1728 ) @ SV906 @ ( tc_prod @ SV1728 @ SV1728 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4544,plain,
! [SV1941: $i,SV1882: $i,SV1729: $i,SV1392: $i,SV907: $i,SV373: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SV1729 @ SV1882 ) @ SV1941 )
= ( hAPP @ SV373 @ SV1941 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1941 @ SV1392 @ SV1729 @ SV1729 ) @ SV907 @ ( tc_prod @ SV1729 @ SV1729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(4545,plain,
! [SV1965: $i,SV1942: $i,SV1884: $i,SV1735: $i,SV1404: $i,SV933: $i,SV401: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV401 @ SV933 @ SV1404 @ SV1735 @ SV1884 ) @ SV1942 @ SV1404 @ SV1884 @ SV1965 )
= ( c_Relation_Orel__comp @ SV401 @ ( c_Relation_Orel__comp @ SV933 @ SV1942 @ SV1735 @ SV1884 @ SV1965 ) @ SV1404 @ SV1735 @ SV1965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4546,plain,
! [SV1943: $i,SV1885: $i,SV1738: $i,SV1420: $i,SV952: $i,SV420: $i] :
( ( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SV1738 @ SV1885 @ SV1943 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( hAPP @ SV1885 @ SV420 ) @ ( hAPP @ SV1885 @ SV952 ) @ SV1943 @ SV1943 ) @ SV1738 @ ( tc_prod @ SV1943 @ SV1943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4547,plain,
! [SV1944: $i,SV1886: $i,SV1739: $i,SV1421: $i,SV953: $i,SV421: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SV1739 @ SV1739 ) @ SV1886 @ ( tc_prod @ SV1739 @ SV1739 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SV1944 @ SV1944 ) @ ( c_Relation_Oinv__image @ SV1886 @ SV421 @ SV1739 @ SV1944 ) @ ( tc_prod @ SV1944 @ SV1944 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4548,plain,
! [SV1740: $i,SV1422: $i,SV422: $i,SV954: $i] :
( ( ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1740 @ SV1422 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4549,plain,
! [SV1741: $i,SV1423: $i,SV423: $i,SV955: $i] :
( ( ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1741 @ SV1423 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4550,plain,
! [SV1966: $i,SV1945: $i,SV1887: $i,SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ! [SY4989: $i] :
( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SY4989 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SY4989 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4551,plain,
! [SV425: $i,SV1743: $i,SV1425: $i,SV957: $i,SV1888: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1888 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV425 @ SV1888 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4552,plain,
! [SV426: $i,SV1744: $i,SV1426: $i,SV958: $i,SV1889: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1889 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV426 @ SV1889 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4553,plain,
! [SV1946: $i,SV1890: $i,SV1745: $i,SV1427: $i,SV961: $i,SV429: $i] :
( ( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
= $true )
| ( ( ~ ( c_in @ SV961 @ SV1890 @ SV1946 )
| ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SV1946 @ SV1745 ) @ ( tc_fun @ SV1946 @ SV1745 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(4554,plain,
! [SV1947: $i,SV1891: $i,SV1746: $i,SV1428: $i,SV962: $i,SV430: $i] :
( ( ( ~ ( c_in @ SV430 @ SV962 @ SV1428 ) )
= $true )
| ( ( ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SV1947 )
| ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SV1947 ) @ ( tc_fun @ SV1428 @ SV1947 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4555,plain,
! [SV1967: $i,SV1948: $i,SV1892: $i,SV1747: $i,SV1429: $i,SV963: $i,SV431: $i] :
( ( ( SV431 = SV963 )
| ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
| ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4556,plain,
! [SV1949: $i,SV1893: $i,SV1748: $i,SV1430: $i,SV964: $i,SV432: $i] :
( ( ( ~ ( c_in @ SV432 @ SV964 @ SV1430 ) )
= $true )
| ( ( ~ ( c_in @ SV1748 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4557,plain,
! [SV433: $i,SV1431: $i,SV1749: $i,SV965: $i] :
( ( ( c_in @ SV965 @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 ) )
= $true )
| ( ( c_in @ SV433 @ SV965 @ SV1431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4558,plain,
! [SV966: $i,SV1432: $i,SV1750: $i,SV434: $i] :
( ( ( c_in @ SV434 @ SV1750 @ SV1432 )
= $false )
| ( ( ~ ( c_in @ SV1750 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4559,plain,
! [SV1751: $i,SV1433: $i,SV967: $i,SV435: $i] :
( ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV435 = SV967 )
| ( SV435 = SV1751 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SV1751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4560,plain,
! [SV1752: $i,SV1434: $i,SV968: $i,SV436: $i] :
( ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV968 = SV1752 )
| ( SV436 = SV1752 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SV1752 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4561,plain,
! [SV1753: $i,SV1436: $i,SV971: $i,SV439: $i] :
( ( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1436 @ SV1753 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV971 = SV1753 )
= $true )
| ( ( c_in @ ( c_Pair @ SV439 @ SV971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1436 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4324]) ).
thf(4562,plain,
! [SV1754: $i,SV1439: $i,SV975: $i,SV443: $i] :
( ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV443 = SV975 )
| ( SV975 = SV1754 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SV1754 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4325]) ).
thf(4563,plain,
! [SV1755: $i,SV1440: $i,SV976: $i,SV444: $i] :
( ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV444 = SV1755 )
| ( SV976 = SV1755 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SV1755 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4564,plain,
! [SV1756: $i,SV1442: $i,SV978: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1442 @ SV1756 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV446 = SV1756 )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV978 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1442 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4565,plain,
! [SV1950: $i,SV1894: $i,SV1757: $i,SV1445: $i,SV985: $i,SV455: $i] :
( ( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SV1950 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
= $true )
| ( ( ~ ( c_in @ SV985 @ ( hAPP @ SV1950 @ SV455 ) @ SV1757 )
| ~ ( c_in @ SV455 @ SV1894 @ SV1445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4566,plain,
! [SV1951: $i,SV1895: $i,SV1758: $i,SV1446: $i,SV986: $i,SV456: $i] :
( ( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SV1951 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
= $true )
| ( ( ~ ( c_in @ SV986 @ ( hAPP @ SV1951 @ SV456 ) @ SV1758 )
| ~ ( c_in @ SV456 @ SV1895 @ SV1446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4331]) ).
thf(4567,plain,
! [SV987: $i,SV1447: $i,SV1759: $i,SV457: $i] :
( ( ( c_in @ ( c_Pair @ SV457 @ SV1759 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) )
= $false )
| ( ( ~ ( c_in @ SV1759 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 ) )
= $true )
| ( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4568,plain,
! [SV988: $i,SV1448: $i,SV1760: $i,SV458: $i] :
( ( ( c_in @ ( c_Pair @ SV458 @ SV1760 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) )
= $false )
| ( ( ~ ( c_in @ SV1760 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 ) )
= $true )
| ( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4333]) ).
thf(4569,plain,
! [SV1952: $i,SV1896: $i,SV1761: $i,SV1449: $i,SV989: $i,SV459: $i] :
( ( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1952 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) )
| ~ ( c_in @ SV1952 @ SV1449 @ SV1761 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4334]) ).
thf(4570,plain,
! [SV1953: $i,SV1897: $i,SV1762: $i,SV1450: $i,SV990: $i,SV460: $i] :
( ( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1953 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) )
| ~ ( c_in @ SV1953 @ SV1450 @ SV1762 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4571,plain,
! [SV993: $i,SV1898: $i,SV1453: $i,SV463: $i,SV1764: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SV1898 @ ( tc_prod @ SV1453 @ SV1453 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SV1898 @ SV1453 ) )
= $true )
| ( ( c_in @ SV463 @ SV993 @ SV1453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4337]) ).
thf(4572,plain,
! [SV994: $i,SV1899: $i,SV1454: $i,SV1765: $i,SV464: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SV1899 @ ( tc_prod @ SV1454 @ SV1454 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SV1899 @ SV1454 ) )
= $true )
| ( ( c_in @ SV464 @ SV994 @ SV1454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4338]) ).
thf(4573,plain,
! [SV995: $i,SV1766: $i,SV1455: $i,SV465: $i,SV1900: $i] :
( ( ( c_in @ ( c_Pair @ SV1900 @ SV465 @ SV1455 @ SV1766 ) @ SV995 @ ( tc_prod @ SV1455 @ SV1766 ) )
= $false )
| ( ( c_in @ SV465 @ ( c_Relation_ORange @ SV995 @ SV1455 @ SV1766 ) @ SV1766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(4574,plain,
! [SV996: $i,SV1767: $i,SV1456: $i,SV466: $i,SV1901: $i] :
( ( ( c_in @ ( c_Pair @ SV1901 @ SV466 @ SV1456 @ SV1767 ) @ SV996 @ ( tc_prod @ SV1456 @ SV1767 ) )
= $false )
| ( ( c_in @ SV466 @ ( c_Relation_ORange @ SV996 @ SV1456 @ SV1767 ) @ SV1767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4575,plain,
! [SV997: $i,SV1768: $i,SV1457: $i,SV1902: $i,SV467: $i] :
( ( ( c_in @ ( c_Pair @ SV467 @ SV1902 @ SV1457 @ SV1768 ) @ SV997 @ ( tc_prod @ SV1457 @ SV1768 ) )
= $false )
| ( ( c_in @ SV467 @ ( c_Relation_ODomain @ SV997 @ SV1457 @ SV1768 ) @ SV1457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4341]) ).
thf(4576,plain,
! [SV998: $i,SV1769: $i,SV1458: $i,SV1903: $i,SV468: $i] :
( ( ( c_in @ ( c_Pair @ SV468 @ SV1903 @ SV1458 @ SV1769 ) @ SV998 @ ( tc_prod @ SV1458 @ SV1769 ) )
= $false )
| ( ( c_in @ SV468 @ ( c_Relation_ODomain @ SV998 @ SV1458 @ SV1769 ) @ SV1458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4577,plain,
! [SV1954: $i,SV1904: $i,SV1770: $i,SV1459: $i,SV999: $i,SV469: $i] :
( ( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SV1770 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SV1904 @ SV1770 ) @ ( c_Product__Type_OSigma @ SV1954 @ SV999 @ SV1904 @ SV1770 ) @ ( tc_prod @ SV1904 @ SV1770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(4578,plain,
! [SV1955: $i,SV1905: $i,SV1771: $i,SV1460: $i,SV1000: $i,SV470: $i] :
( ( ( c_in @ SV470 @ SV1000 @ SV1460 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV470 @ SV1771 @ SV1460 @ SV1905 ) @ ( c_Product__Type_OSigma @ SV1000 @ SV1955 @ SV1460 @ SV1905 ) @ ( tc_prod @ SV1460 @ SV1905 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4344]) ).
thf(4579,plain,
! [SV1906: $i,SV1772: $i,SV1461: $i,SV471: $i,SV1001: $i] :
( ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( ( SV1001 = SV471 )
| ~ ( c_in @ SV471 @ SV1906 @ SV1461 )
| ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4580,plain,
! [SV1462: $i,SV1002: $i,SV1773: $i,SV472: $i] :
( ( ( c_in @ SV472 @ SV1773 @ SV1002 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1773 @ SV1462 @ SV1002 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4581,plain,
! [SV1003: $i,SV1907: $i,SV1463: $i,SV473: $i,SV1774: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SV1907 @ ( tc_prod @ SV1463 @ SV1463 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1003 @ SV1907 @ SV1463 ) )
= $true )
| ( ( c_in @ SV473 @ SV1003 @ SV1463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4582,plain,
! [SV1004: $i,SV1908: $i,SV1464: $i,SV1775: $i,SV474: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SV1908 @ ( tc_prod @ SV1464 @ SV1464 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1004 @ SV1908 @ SV1464 ) )
= $true )
| ( ( c_in @ SV474 @ SV1004 @ SV1464 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4348]) ).
thf(4583,plain,
! [SV1465: $i,SV1005: $i,SV1776: $i,SV475: $i] :
( ( ( c_in @ SV475 @ SV1776 @ SV1005 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1776 @ SV1465 @ SV1005 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4584,plain,
! [SV476: $i,SV1777: $i,SV1466: $i,SV1006: $i] :
( ( ( ~ ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1466 = SV1777 )
= $true )
| ( ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SV1777 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4585,plain,
! [SV1007: $i,SV1467: $i,SV1778: $i,SV477: $i] :
( ( ( SV477 = SV1778 )
= $true )
| ( ( ( SV477 = SV1778 )
| ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4586,plain,
! [SV1468: $i,SV1008: $i,SV478: $i,SV1779: $i] :
( ( ( ~ ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV478 = SV1468 )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4587,plain,
! [SV1909: $i,SV1469: $i,SV479: $i,SV1780: $i,SV1009: $i] :
( ( ( SV1009 = SV1780 )
= $true )
| ( ( ( SV479 = SV1780 )
| ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4353]) ).
thf(4588,plain,
! [SV1781: $i,SV1470: $i,SV1010: $i,SV480: $i] :
( ( ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4589,plain,
! [SV1011: $i,SV481: $i,SV1782: $i,SV1471: $i] :
( ( ( ~ ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1782 = SV481 )
| ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4355]) ).
thf(4590,plain,
! [SV1012: $i,SV1472: $i,SV482: $i,SV1783: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1783 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4591,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ( SV483 = SV1013 )
= $true )
| ( ( ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4592,plain,
! [SV1910: $i,SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV484 = SV1785 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4358]) ).
thf(4593,plain,
! [SV1786: $i,SV1911: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4359]) ).
thf(4594,plain,
! [SV486: $i,SV1016: $i,SV1476: $i] :
( ( ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1016 = SV486 )
| ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1016 = SV486 )
= $true )
| ( ( SV486 = SV1016 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4595,plain,
! [SV1912: $i,SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4361]) ).
thf(4596,plain,
! [SV1018: $i,SV488: $i,SV1478: $i] :
( ( ( ~ ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV488 = SV1018 )
= $true )
| ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4362]) ).
thf(4597,plain,
! [SV489: $i,SV1479: $i,SV1019: $i,SV1788: $i] :
( ( ( SV1788 = SV1019 )
= $true )
| ( ( ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4598,plain,
! [SV1789: $i,SV1913: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1020 = SV1913 )
| ( SV490 = SV1913 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4599,plain,
! [SV491: $i,SV1790: $i,SV1481: $i,SV1021: $i] :
( ( ( ~ ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1481 = SV1790 )
= $true )
| ( ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SV1790 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4600,plain,
! [SV492: $i,SV1482: $i,SV1791: $i,SV1022: $i] :
( ( ( SV1022 = SV1791 )
= $true )
| ( ( ( SV1791 = SV1022 )
| ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4601,plain,
! [SV1483: $i,SV493: $i,SV1023: $i,SV1792: $i] :
( ( ( ~ ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1483 = SV493 )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4602,plain,
! [SV1914: $i,SV1484: $i,SV1024: $i,SV1793: $i,SV494: $i] :
( ( ( SV494 = SV1793 )
= $true )
| ( ( ( SV1024 = SV1793 )
| ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4368]) ).
thf(4603,plain,
! [SV1794: $i,SV1485: $i,SV495: $i,SV1025: $i] :
( ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4369]) ).
thf(4604,plain,
! [SV496: $i,SV1795: $i,SV1026: $i,SV1486: $i] :
( ( ( ~ ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1026 = SV1795 )
| ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4370]) ).
thf(4605,plain,
! [SV497: $i,SV1487: $i,SV1796: $i,SV1027: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV497 = SV1796 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(4606,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ( SV498 = SV1028 )
= $true )
| ( ( ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4372]) ).
thf(4607,plain,
! [SV1798: $i,SV1915: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1029 = SV1915 )
| ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4608,plain,
! [SV1916: $i,SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4374]) ).
thf(4609,plain,
! [SV1031: $i,SV501: $i,SV1491: $i] :
( ( ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV501 = SV1031 )
| ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV501 = SV1031 )
= $true )
| ( ( SV501 = SV1031 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4610,plain,
! [SV1800: $i,SV1917: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4376]) ).
thf(4611,plain,
! [SV1033: $i,SV503: $i,SV1493: $i] :
( ( ( ~ ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV503 = SV1033 )
= $true )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4377]) ).
thf(4612,plain,
! [SV1034: $i,SV1494: $i,SV1801: $i,SV504: $i] :
( ( ( SV504 = SV1801 )
= $true )
| ( ( ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4378]) ).
thf(4613,plain,
! [SV1918: $i,SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV505 = SV1802 )
| ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4379]) ).
thf(4614,plain,
! [SV1496: $i,SV506: $i,SV1036: $i] :
( ( ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV506 = SV1036 )
| ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4615,plain,
! [SV507: $i,SV1037: $i,SV1497: $i] :
( ( ( c_in @ SV1497 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1037 = SV507 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1037 @ SV507 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV507 @ SV1037 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1497 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4616,plain,
! [SV1500: $i,SV511: $i,SV1040: $i] :
( ( ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4382]) ).
thf(4617,plain,
! [SV1968: $i,SV1956: $i,SV1919: $i,SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
!= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
| ( ( hAPP @ SV524 @ SV1968 )
= ( hAPP @ SV1956 @ SV1968 ) )
| ~ ( c_in @ ( c_Pair @ SV1968 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4618,plain,
! [SV525: $i,SV1503: $i,SV1054: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1054 @ SV1503 @ SV525 )
= SV1503 )
= $false )
| ( ( c_lessequals @ SV1054 @ SV1503 @ SV525 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4619,plain,
! [SV528: $i,SV1505: $i,SV1057: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1057 @ SV1505 @ SV528 )
= SV1057 )
= $false )
| ( ( c_lessequals @ SV1057 @ SV1505 @ SV528 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV528 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4620,plain,
! [SV1957: $i,SV1920: $i,SV1804: $i,SV1506: $i,SV1058: $i,SV529: $i] :
( ( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
!= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
= $true )
| ( ( ~ ( c_in @ SV1957 @ SV1058 @ SV1506 )
| ( SV529 = SV1920 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4388]) ).
thf(4621,plain,
! [SV1958: $i,SV1921: $i,SV1806: $i,SV1508: $i,SV1060: $i,SV531: $i] :
( ( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SV1806 )
!= ( c_Pair @ SV1921 @ SV1958 @ SV1508 @ SV1806 ) )
= $true )
| ( ( SV1060 = SV1958 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4622,plain,
! [SV1062: $i,SV1509: $i,SV1807: $i,SV533: $i] :
( ( ( c_in @ SV533 @ SV1807 @ SV1509 )
= $true )
| ( ( ( c_in @ SV533 @ SV1062 @ SV1509 )
| ( SV1062 = SV1807 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
= ( c_Set_Oinsert @ SV533 @ SV1807 @ SV1509 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4391]) ).
thf(4623,plain,
! [SV1959: $i,SV1922: $i,SV1808: $i,SV1510: $i,SV1063: $i,SV534: $i] :
( ( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) )
!= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SV1808 @ SV1922 @ SV1959 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4392]) ).
thf(4624,plain,
! [SV1960: $i,SV1923: $i,SV1809: $i,SV1511: $i,SV1064: $i,SV535: $i] :
( ( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SV1809 )
!= ( c_Pair @ SV1923 @ SV1960 @ SV1511 @ SV1809 ) )
= $true )
| ( ( SV535 = SV1923 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4625,plain,
! [SV1070: $i,SV1517: $i,SV9: $i,SV1924: $i,SV1811: $i,SV544: $i] :
( ( ( ~ ( c_in @ SV544 @ SV1811 @ SV1924 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SV1924 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4394]) ).
thf(4626,plain,
! [SV545: $i,SV1812: $i,SV1518: $i,SV1071: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SV1812 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1518 @ SV1812 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4395]) ).
thf(4627,plain,
! [SV578: $i,SV1099: $i,SV1537: $i,SV43: $i] :
( ( ( c_lessequals @ SV43 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV578 @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV43 @ SV578 @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1537 @ ( tc_fun @ SV1099 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4628,plain,
! [SV581: $i,SV1102: $i,SV1538: $i,SV46: $i] :
( ( ( c_lessequals @ SV46 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV581 @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV581 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1538 @ ( tc_fun @ SV1102 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4629,plain,
! [SV582: $i,SV47: $i,SV1539: $i,SV1103: $i] :
( ( ( ~ ( c_lessequals @ SV1103 @ SV1539 @ SV47 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(4630,plain,
! [SV585: $i,SV50: $i,SV1540: $i,SV1106: $i] :
( ( ( ~ ( c_lessequals @ SV1106 @ SV1540 @ SV50 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4403]) ).
thf(4631,plain,
! [SV586: $i,SV51: $i,SV1541: $i,SV1107: $i] :
( ( ( ~ ( c_lessequals @ SV1107 @ SV1541 @ SV51 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4404]) ).
thf(4632,plain,
! [SV77: $i,SV1559: $i,SV1131: $i,SV612: $i] :
( ( ( c_lessequals @ SV612 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1131 @ SV1559 @ SV77 ) @ SV77 )
= $false )
| ( ( c_lessequals @ SV612 @ SV1131 @ SV77 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4633,plain,
! [SV78: $i,SV1132: $i,SV1560: $i,SV613: $i] :
( ( ( c_lessequals @ SV613 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1560 @ SV1132 @ SV78 ) @ SV78 )
= $false )
| ( ( c_lessequals @ SV613 @ SV1132 @ SV78 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4634,plain,
! [SV1133: $i,SV79: $i,SV1561: $i,SV614: $i] :
( ( ( c_lessequals @ SV614 @ SV1561 @ SV79 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV614 @ SV1133 @ SV79 ) @ SV1561 @ SV79 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4412]) ).
thf(4635,plain,
! [SV615: $i,SV80: $i,SV1562: $i,SV1134: $i] :
( ( ( c_lessequals @ SV1134 @ SV1562 @ SV80 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV615 @ SV1134 @ SV80 ) @ SV1562 @ SV80 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4413]) ).
thf(4636,plain,
! [SV81: $i,SV1563: $i,SV1135: $i,SV616: $i] :
( ( ( c_lessequals @ SV616 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1135 @ SV1563 @ SV81 ) @ SV81 )
= $false )
| ( ( c_lessequals @ SV616 @ SV1135 @ SV81 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4414]) ).
thf(4637,plain,
! [SV82: $i,SV1136: $i,SV1564: $i,SV617: $i] :
( ( ( c_lessequals @ SV617 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1564 @ SV1136 @ SV82 ) @ SV82 )
= $false )
| ( ( c_lessequals @ SV617 @ SV1136 @ SV82 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(4638,plain,
! [SV1152: $i,SV1570: $i,SV635: $i,SV100: $i] :
( ( ( c_in @ SV100 @ SV635 @ SV1570 )
= $false )
| ( ( c_in @ SV100 @ SV1152 @ SV1570 )
= $false )
| ( ( c_in @ SV100 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV635 @ SV1152 @ ( tc_fun @ SV1570 @ tc_bool ) ) @ SV1570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(4639,plain,
! [SV1153: $i,SV1571: $i,SV636: $i,SV101: $i] :
( ( ( c_in @ SV101 @ SV636 @ SV1571 )
= $false )
| ( ( c_in @ SV101 @ SV1153 @ SV1571 )
= $false )
| ( ( c_in @ SV101 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV636 @ SV1153 @ ( tc_fun @ SV1571 @ tc_bool ) ) @ SV1571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4640,plain,
! [SV1825: $i,SV1585: $i,SV1171: $i,SV1927: $i,SV119: $i,SV654: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SV1927 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SV1927 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(4641,plain,
! [SV120: $i,SV1172: $i,SV655: $i] :
( ( ( c_Wellfounded_Owf @ SV655 @ SV1172 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV120 @ SV1172 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(4642,plain,
! [SV1595: $i,SV140: $i,SV1188: $i,SV1829: $i,SV675: $i] :
( ( ( c_Relation_Orefl__on @ SV675 @ SV1829 @ SV1188 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SV1829 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(4643,plain,
! [SV1604: $i,SV159: $i,SV1206: $i,SV1831: $i,SV693: $i] :
( ( ( c_Relation_Orefl__on @ SV693 @ SV1831 @ SV1206 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SV1831 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(4644,plain,
! [SV1609: $i,SV164: $i,SV1211: $i,SV1833: $i,SV698: $i] :
( ( ( c_lessequals @ SV698 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(4645,plain,
! [SV1215: $i,SV168: $i,SV1611: $i,SV702: $i] :
( ( ( ~ ( c_lessequals @ SV702 @ SV1611 @ SV168 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true )
| ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4646,plain,
! [SV1216: $i,SV169: $i,SV1612: $i,SV703: $i] :
( ( ( ~ ( c_lessequals @ SV703 @ SV1612 @ SV169 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true )
| ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(4647,plain,
! [SV1217: $i,SV170: $i,SV1613: $i,SV704: $i] :
( ( ( ~ ( c_lessequals @ SV704 @ SV1613 @ SV170 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true )
| ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(4648,plain,
! [SV1222: $i,SV1614: $i,SV709: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ SV709 @ ( tc_fun @ SV1614 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV175 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV175 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV709 @ SV1222 @ ( tc_fun @ SV1614 @ tc_bool ) ) @ ( tc_fun @ SV1614 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4440]) ).
thf(4649,plain,
! [SV1223: $i,SV1615: $i,SV710: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ SV710 @ ( tc_fun @ SV1615 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV176 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV176 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV710 @ SV1223 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ ( tc_fun @ SV1615 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4441]) ).
thf(4650,plain,
! [SV717: $i,SV1230: $i,SV1621: $i,SV183: $i] :
( ( ( c_in @ SV183 @ SV1621 @ SV1230 )
= $false )
| ( ( c_lessequals @ SV717 @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV183 @ SV717 @ SV1230 ) @ SV1621 @ ( tc_fun @ SV1230 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4442]) ).
thf(4651,plain,
! [SV1238: $i,SV194: $i,SV728: $i,SV1623: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1623 @ SV728 @ SV194 ) @ SV1238 @ SV194 )
= $false )
| ( ( c_lessequals @ SV728 @ SV1238 @ SV194 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4443]) ).
thf(4652,plain,
! [SV1239: $i,SV195: $i,SV1624: $i,SV729: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV729 @ SV1624 @ SV195 ) @ SV1239 @ SV195 )
= $false )
| ( ( c_lessequals @ SV729 @ SV1239 @ SV195 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4653,plain,
! [SV1240: $i,SV196: $i,SV1625: $i,SV730: $i] :
( ( ( c_lessequals @ SV730 @ SV1625 @ SV196 )
= $false )
| ( ( c_lessequals @ SV730 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1240 @ SV1625 @ SV196 ) @ SV196 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4654,plain,
! [SV1626: $i,SV197: $i,SV1241: $i,SV731: $i] :
( ( ( c_lessequals @ SV731 @ SV1241 @ SV197 )
= $false )
| ( ( c_lessequals @ SV731 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1241 @ SV1626 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4446]) ).
thf(4655,plain,
! [SV1242: $i,SV198: $i,SV732: $i,SV1627: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1627 @ SV732 @ SV198 ) @ SV1242 @ SV198 )
= $false )
| ( ( c_lessequals @ SV732 @ SV1242 @ SV198 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(4656,plain,
! [SV1243: $i,SV199: $i,SV1628: $i,SV733: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV1628 @ SV199 ) @ SV1243 @ SV199 )
= $false )
| ( ( c_lessequals @ SV733 @ SV1243 @ SV199 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4657,plain,
! [SV1631: $i,SV204: $i,SV1248: $i,SV1835: $i,SV738: $i] :
( ( ( c_lessequals @ SV738 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4658,plain,
! [SV1249: $i,SV739: $i,SV1632: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ SV205 @ SV1632 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV739 @ SV1632 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV205 @ SV739 @ ( tc_fun @ SV1249 @ tc_bool ) ) @ SV1632 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4452]) ).
thf(4659,plain,
! [SV211: $i,SV1637: $i,SV1255: $i,SV745: $i,SV1839: $i] :
( ( ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
| ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4455]) ).
thf(4660,plain,
! [SV212: $i,SV1638: $i,SV1256: $i,SV746: $i,SV1840: $i] :
( ( ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
| ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4661,plain,
! [SV1841: $i,SV1643: $i,SV1265: $i,SV1929: $i,SV760: $i,SV226: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SV1929 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
= $true )
| ( ( ~ ( c_lessequals @ SV226 @ SV1841 @ ( tc_fun @ SV1265 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SV1841 @ SV1929 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(4662,plain,
! [SV237: $i,SV771: $i,SV1274: $i,SV1649: $i] :
( ( ( ~ ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true )
| ( ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4663,plain,
! [SV244: $i,SV1654: $i,SV1281: $i,SV778: $i,SV1845: $i] :
( ( ( c_in @ ( c_Pair @ SV1845 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV244 @ SV1845 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4664,plain,
! [SV245: $i,SV1655: $i,SV1282: $i,SV779: $i,SV1846: $i] :
( ( ( c_in @ ( c_Pair @ SV1846 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV245 @ SV1846 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4474]) ).
thf(4665,plain,
! [SV253: $i,SV1657: $i,SV1288: $i,SV787: $i] :
( ( ( c_in @ SV787 @ ( c_Wellfounded_Oacc @ SV1288 @ SV1657 ) @ SV1657 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV253 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV253 @ SV1288 @ SV1657 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV253 @ SV787 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4666,plain,
! [SV257: $i,SV1659: $i,SV1292: $i,SV791: $i] :
( ( ( c_in @ SV791 @ ( c_Wellfounded_Oacc @ SV1292 @ SV1659 ) @ SV1659 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV257 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV257 @ SV1292 @ SV1659 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV257 @ SV791 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4480]) ).
thf(4667,plain,
! [SV794: $i,SV1295: $i,SV1660: $i,SV260: $i] :
( ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV1660 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
= $false )
| ( ( c_lessequals @ SV1660 @ SV794 @ ( tc_fun @ ( tc_prod @ SV1295 @ SV1295 ) @ tc_bool ) )
= $false )
| ( ( c_in @ SV260 @ ( c_Transitive__Closure_Otrancl @ SV794 @ SV1295 ) @ ( tc_prod @ SV1295 @ SV1295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4668,plain,
! [SV263: $i,SV1663: $i,SV1298: $i,SV797: $i] :
( ( ( c_Wellfounded_Owf @ SV797 @ SV1298 )
= $false )
| ( ( c_in @ SV1663 @ SV263 @ SV1298 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV263 @ SV797 @ SV1298 ) @ SV263 @ SV1298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4669,plain,
! [SV264: $i,SV1664: $i,SV1299: $i,SV798: $i] :
( ( ( c_Wellfounded_Owf @ SV798 @ SV1299 )
= $false )
| ( ( c_in @ SV1664 @ SV264 @ SV1299 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV264 @ SV798 @ SV1299 ) @ SV264 @ SV1299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4670,plain,
! [SV267: $i,SV1665: $i,SV1302: $i,SV801: $i,SV1849: $i] :
( ( ( c_in @ ( c_Pair @ SV1849 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV267 @ SV1849 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4671,plain,
! [SV268: $i,SV1666: $i,SV1303: $i,SV802: $i,SV1850: $i] :
( ( ( c_in @ ( c_Pair @ SV1850 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV268 @ SV1850 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4672,plain,
! [SV269: $i,SV1667: $i,SV1304: $i,SV803: $i,SV1851: $i] :
( ( ( c_in @ ( c_Pair @ SV1851 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV269 @ SV1851 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(4673,plain,
! [SV1669: $i,SV1852: $i,SV277: $i,SV1310: $i,SV1930: $i,SV811: $i] :
( ( ( ~ ( c_lessequals @ SV811 @ SV1930 @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SV1930 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4491]) ).
thf(4674,plain,
! [SV1671: $i,SV279: $i,SV813: $i,SV1312: $i] :
( ( ( hBOOL @ ( hAPP @ SV1312 @ SV813 ) )
= $false )
| ( ( c_lessequals @ SV1312 @ SV279 @ ( tc_fun @ SV1671 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV279 @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4492]) ).
thf(4675,plain,
! [SV817: $i,SV1672: $i,SV283: $i,SV1314: $i] :
( ( ( c_lessequals @ SV1314 @ SV283 @ ( tc_fun @ SV1672 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1314 @ SV817 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV283 @ SV817 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4676,plain,
! [SV818: $i,SV1315: $i,SV1673: $i,SV284: $i] :
( ( ( c_lessequals @ SV284 @ SV1673 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1673 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV284 @ SV818 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4677,plain,
! [SV821: $i,SV287: $i,SV1316: $i,SV1674: $i] :
( ( ( ~ ( c_lessequals @ SV1674 @ SV1316 @ SV287 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true )
| ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
= $true )
| ( ( class_Orderings_Opreorder @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(4678,plain,
! [SV1317: $i,SV288: $i,SV1675: $i,SV822: $i] :
( ( ( ~ ( c_lessequals @ SV822 @ SV1675 @ SV288 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true )
| ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
= $true )
| ( ( class_Orderings_Oorder @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(4679,plain,
! [SV292: $i,SV1320: $i,SV826: $i] :
( ( ( c_lessequals @ SV826 @ SV1320 @ SV292 )
= $false )
| ( ( ~ ( c_lessequals @ SV1320 @ SV826 @ SV292 ) )
= $true )
| ( ( SV826 = SV1320 )
= $true )
| ( ( class_Orderings_Oorder @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4680,plain,
! [SV293: $i,SV827: $i,SV1321: $i] :
( ( ( c_lessequals @ SV1321 @ SV827 @ SV293 )
= $false )
| ( ( ~ ( c_lessequals @ SV827 @ SV1321 @ SV293 ) )
= $true )
| ( ( SV827 = SV1321 )
= $true )
| ( ( class_Orderings_Oorder @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4681,plain,
! [SV294: $i,SV828: $i,SV1322: $i] :
( ( ( c_lessequals @ SV1322 @ SV828 @ SV294 )
= $false )
| ( ( ~ ( c_lessequals @ SV828 @ SV1322 @ SV294 ) )
= $true )
| ( ( SV828 = SV1322 )
= $true )
| ( ( class_Orderings_Oorder @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4682,plain,
! [SV1969: $i,SV1961: $i,SV1931: $i,SV1853: $i,SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1969 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(4683,plain,
! [SV1327: $i,SV836: $i,SV1932: $i,SV1677: $i,SV1854: $i,SV302: $i] :
( ( ( ~ ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV1932 @ SV836 @ SV1327 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4684,plain,
! [SV1933: $i,SV837: $i,SV1328: $i,SV1855: $i,SV1678: $i,SV303: $i] :
( ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV1933 @ SV1678 @ SV1855 ) )
= $true )
| ( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4685,plain,
! [SV1962: $i,SV1934: $i,SV1856: $i,SV1679: $i,SV1330: $i,SV840: $i,SV306: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SV1962 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV840 @ SV1962 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(4686,plain,
! [SV842: $i,SV1332: $i,SV1681: $i,SV1857: $i,SV1935: $i,SV308: $i] :
( ( ( c_lessequals @ SV308 @ ( c_Product__Type_OSigma @ SV1935 @ ( c_COMBK @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) @ SV1332 ) @ SV1332 @ SV1681 ) @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1681 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV308 @ SV842 @ SV1332 @ SV1681 ) @ SV1857 @ ( tc_fun @ SV1681 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(4687,plain,
! [SV1682: $i,SV311: $i,SV1334: $i,SV845: $i,SV1858: $i] :
( ( ( ~ ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) )
= $true )
| ( ( SV311 = SV1682 )
= $true )
| ( ( c_in @ SV311 @ SV845 @ SV1334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4688,plain,
! [SV1859: $i,SV313: $i,SV1683: $i,SV1336: $i,SV847: $i] :
( ( ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
= $true )
| ( ( ~ ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SV1859 @ SV313 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(4689,plain,
! [SV314: $i,SV1337: $i,SV848: $i,SV1684: $i] :
( ( ( c_lessequals @ SV1684 @ SV848 @ ( tc_fun @ SV1337 @ tc_bool ) )
= $false )
| ( ( c_in @ SV314 @ SV1684 @ SV1337 )
= $false )
| ( ( c_in @ SV314 @ SV848 @ SV1337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4690,plain,
! [SV849: $i,SV1338: $i,SV1685: $i,SV315: $i] :
( ( ( c_in @ SV315 @ SV1685 @ SV1338 )
= $false )
| ( ( c_lessequals @ SV1685 @ SV849 @ ( tc_fun @ SV1338 @ tc_bool ) )
= $false )
| ( ( c_in @ SV315 @ SV849 @ SV1338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(4691,plain,
! [SV316: $i,SV1339: $i,SV850: $i,SV1686: $i] :
( ( ( c_lessequals @ SV1686 @ SV850 @ ( tc_fun @ SV1339 @ tc_bool ) )
= $false )
| ( ( c_in @ SV316 @ SV1686 @ SV1339 )
= $false )
| ( ( c_in @ SV316 @ SV850 @ SV1339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(4692,plain,
! [SV317: $i,SV1340: $i,SV851: $i,SV1687: $i] :
( ( ( c_lessequals @ SV1687 @ SV851 @ ( tc_fun @ SV1340 @ tc_bool ) )
= $false )
| ( ( c_in @ SV317 @ SV1687 @ SV1340 )
= $false )
| ( ( c_in @ SV317 @ SV851 @ SV1340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(4693,plain,
! [SV320: $i,SV1689: $i,SV1343: $i,SV854: $i,SV1860: $i] :
( ( ( c_in @ ( c_Pair @ SV1860 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV320 @ SV1860 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(4694,plain,
! [SV321: $i,SV1690: $i,SV1344: $i,SV855: $i,SV1861: $i] :
( ( ( c_in @ ( c_Pair @ SV1861 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV321 @ SV1861 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4516]) ).
thf(4695,plain,
! [SV1963: $i,SV1936: $i,SV1862: $i,SV1695: $i,SV1351: $i,SV862: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SV1862 @ SV1936 @ SV1963 ) @ SV1862 @ SV1963 ) @ SV1351 @ ( tc_prod @ SV1862 @ SV1963 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV328 @ SV862 @ SV1862 @ SV1936 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SV1862 @ SV1963 @ SV1936 ) @ ( tc_prod @ SV1862 @ SV1936 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4696,plain,
! [SV1964: $i,SV1937: $i,SV1863: $i,SV1696: $i,SV1352: $i,SV863: $i,SV329: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SV1863 @ SV1937 @ SV1964 ) @ SV863 @ SV1964 @ SV1937 ) @ SV1696 @ ( tc_prod @ SV1964 @ SV1937 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV329 @ SV863 @ SV1863 @ SV1937 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SV1863 @ SV1964 @ SV1937 ) @ ( tc_prod @ SV1863 @ SV1937 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4697,plain,
! [SV1698: $i,SV1354: $i,SV331: $i,SV1938: $i,SV1865: $i,SV865: $i] :
( ( ( ~ ( c_in @ SV865 @ SV1865 @ SV1938 ) )
= $true )
| ( ( ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1938 ) @ SV1938 @ SV1698 ) @ ( tc_fun @ SV1938 @ SV1698 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(4698,plain,
! [SV1870: $i,SV1364: $i,SV1704: $i,SV879: $i,SV345: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1870 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true )
| ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4699,plain,
! [SV1871: $i,SV1365: $i,SV1705: $i,SV880: $i,SV346: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1871 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true )
| ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4700,plain,
! [SV887: $i,SV1874: $i,SV1711: $i,SV353: $i,SV1372: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) ) )
= $true )
| ( ( ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(4701,plain,
! [SV888: $i,SV1712: $i,SV354: $i,SV1373: $i] :
( ( ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(4702,plain,
! [SV889: $i,SV1713: $i,SV355: $i,SV1374: $i] :
( ( ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4531]) ).
thf(4703,plain,
! [SV890: $i,SV1714: $i,SV356: $i,SV1375: $i] :
( ( ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4704,plain,
! [SV357: $i,SV1376: $i,SV891: $i,SV1715: $i] :
( ( ( c_in @ SV1715 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
= $false )
| ( ( c_in @ ( c_Pair @ SV357 @ SV1715 @ SV1376 @ SV1376 ) @ ( c_Transitive__Closure_Ortrancl @ SV891 @ SV1376 ) @ ( tc_prod @ SV1376 @ SV1376 ) )
= $false )
| ( ( c_in @ SV357 @ ( c_Wellfounded_Oacc @ SV891 @ SV1376 ) @ SV1376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4705,plain,
! [SV892: $i,SV1377: $i,SV1716: $i,SV358: $i] :
( ( ( c_in @ ( c_Pair @ SV358 @ SV1716 @ SV1377 @ SV1377 ) @ ( c_Transitive__Closure_Ortrancl @ SV892 @ SV1377 ) @ ( tc_prod @ SV1377 @ SV1377 ) )
= $false )
| ( ( c_in @ SV1716 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $false )
| ( ( c_in @ SV358 @ ( c_Wellfounded_Oacc @ SV892 @ SV1377 ) @ SV1377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4706,plain,
! [SV894: $i,SV1717: $i,SV360: $i,SV1379: $i] :
( ( ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4707,plain,
! [SV895: $i,SV1875: $i,SV1718: $i,SV361: $i,SV1380: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) ) )
= $true )
| ( ( ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(4708,plain,
! [SV1721: $i,SV1384: $i,SV365: $i,SV899: $i] :
( ( ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1721 @ SV1384 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(4709,plain,
! [SV367: $i,SV1723: $i,SV1386: $i,SV901: $i,SV1876: $i] :
( ( ( c_in @ ( c_Pair @ SV1876 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV367 @ SV1876 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(4710,plain,
! [SV368: $i,SV1724: $i,SV1387: $i,SV902: $i,SV1877: $i] :
( ( ( c_in @ ( c_Pair @ SV1877 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV368 @ SV1877 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4711,plain,
! [SV1881: $i,SV372: $i,SV906: $i,SV1728: $i,SV1391: $i,SV1940: $i] :
( ( ( c_in @ ( c_Pair @ SV1940 @ SV1391 @ SV1728 @ SV1728 ) @ SV906 @ ( tc_prod @ SV1728 @ SV1728 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV372 @ SV906 @ SV1391 @ SV1728 @ SV1881 ) @ SV1940 )
= ( hAPP @ SV372 @ SV1940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4712,plain,
! [SV1882: $i,SV373: $i,SV907: $i,SV1729: $i,SV1392: $i,SV1941: $i] :
( ( ( c_in @ ( c_Pair @ SV1941 @ SV1392 @ SV1729 @ SV1729 ) @ SV907 @ ( tc_prod @ SV1729 @ SV1729 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV373 @ SV907 @ SV1392 @ SV1729 @ SV1882 ) @ SV1941 )
= ( hAPP @ SV373 @ SV1941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(4713,plain,
! [SV1420: $i,SV1738: $i,SV1943: $i,SV952: $i,SV420: $i,SV1885: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV1885 @ SV420 ) @ ( hAPP @ SV1885 @ SV952 ) @ SV1943 @ SV1943 ) @ SV1738 @ ( tc_prod @ SV1943 @ SV1943 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV420 @ SV952 @ SV1420 @ SV1420 ) @ ( c_Relation_Oinv__image @ SV1738 @ SV1885 @ SV1943 @ SV1420 ) @ ( tc_prod @ SV1420 @ SV1420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4714,plain,
! [SV1739: $i,SV421: $i,SV1886: $i,SV1944: $i,SV1421: $i,SV953: $i] :
( ( ( c_in @ ( c_Pair @ SV953 @ SV1421 @ SV1944 @ SV1944 ) @ ( c_Relation_Oinv__image @ SV1886 @ SV421 @ SV1739 @ SV1944 ) @ ( tc_prod @ SV1944 @ SV1944 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( hAPP @ SV421 @ SV953 ) @ ( hAPP @ SV421 @ SV1421 ) @ SV1739 @ SV1739 ) @ SV1886 @ ( tc_prod @ SV1739 @ SV1739 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4715,plain,
! [SV422: $i,SV954: $i,SV1422: $i,SV1740: $i] :
( ( ( c_Relation_Osym @ SV1740 @ SV1422 )
= $false )
| ( ( c_in @ ( c_Pair @ SV954 @ SV422 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV422 @ SV954 @ SV1422 @ SV1422 ) @ SV1740 @ ( tc_prod @ SV1422 @ SV1422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(4716,plain,
! [SV423: $i,SV955: $i,SV1423: $i,SV1741: $i] :
( ( ( c_Relation_Osym @ SV1741 @ SV1423 )
= $false )
| ( ( c_in @ ( c_Pair @ SV955 @ SV423 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV423 @ SV955 @ SV1423 @ SV1423 ) @ SV1741 @ ( tc_prod @ SV1423 @ SV1423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4549]) ).
thf(4717,plain,
! [SV1970: $i,SV1966: $i,SV1945: $i,SV1887: $i,SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV1970 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SV1970 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4550]) ).
thf(4718,plain,
! [SV425: $i,SV1743: $i,SV1425: $i,SV957: $i,SV1888: $i] :
( ( ( c_in @ ( c_Pair @ SV1888 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV425 @ SV1888 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4719,plain,
! [SV426: $i,SV1744: $i,SV1426: $i,SV958: $i,SV1889: $i] :
( ( ( c_in @ ( c_Pair @ SV1889 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV426 @ SV1889 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4720,plain,
! [SV1745: $i,SV1427: $i,SV429: $i,SV1946: $i,SV1890: $i,SV961: $i] :
( ( ( ~ ( c_in @ SV961 @ SV1890 @ SV1946 ) )
= $true )
| ( ( ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SV1946 @ SV1745 ) @ ( tc_fun @ SV1946 @ SV1745 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4553]) ).
thf(4721,plain,
! [SV1947: $i,SV1891: $i,SV1746: $i,SV1428: $i,SV962: $i,SV430: $i] :
( ( ( c_in @ SV430 @ SV962 @ SV1428 )
= $false )
| ( ( ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SV1947 )
| ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SV1947 ) @ ( tc_fun @ SV1428 @ SV1947 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4722,plain,
! [SV1967: $i,SV1948: $i,SV1892: $i,SV1747: $i,SV1429: $i,SV963: $i,SV431: $i] :
( ( ( SV431 = SV963 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
| ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4555]) ).
thf(4723,plain,
! [SV1949: $i,SV1893: $i,SV1748: $i,SV1430: $i,SV964: $i,SV432: $i] :
( ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false )
| ( ( ~ ( c_in @ SV1748 @ SV964 @ SV1430 )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4556]) ).
thf(4724,plain,
! [SV965: $i,SV1431: $i,SV1749: $i,SV433: $i] :
( ( ( c_in @ SV433 @ ( c_Complete__Lattice_OInf__class_OInf @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) ) @ SV1431 )
= $false )
| ( ( c_in @ SV965 @ SV1749 @ ( tc_fun @ SV1431 @ tc_bool ) )
= $false )
| ( ( c_in @ SV433 @ SV965 @ SV1431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4725,plain,
! [SV434: $i,SV1432: $i,SV966: $i,SV1750: $i] :
( ( ( c_in @ SV1750 @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) )
= $false )
| ( ( c_in @ SV434 @ SV1750 @ SV1432 )
= $false )
| ( ( c_in @ SV434 @ ( c_Complete__Lattice_OSup__class_OSup @ SV966 @ ( tc_fun @ SV1432 @ tc_bool ) ) @ SV1432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4558]) ).
thf(4726,plain,
! [SV1433: $i,SV1751: $i,SV967: $i,SV435: $i] :
( ( ( SV435 = SV967 )
= $true )
| ( ( SV435 = SV1751 )
= $true )
| ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1433 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV435 @ SV967 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1433 @ SV1751 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4727,plain,
! [SV1434: $i,SV436: $i,SV1752: $i,SV968: $i] :
( ( ( SV968 = SV1752 )
= $true )
| ( ( SV436 = SV1752 )
= $true )
| ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1434 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV436 @ SV968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ SV1434 @ SV1752 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(4728,plain,
! [SV1439: $i,SV1754: $i,SV975: $i,SV443: $i] :
( ( ( SV443 = SV975 )
= $true )
| ( ( SV975 = SV1754 )
= $true )
| ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1439 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV443 @ SV975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1439 @ SV1754 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(4729,plain,
! [SV1440: $i,SV976: $i,SV1755: $i,SV444: $i] :
( ( ( SV444 = SV1755 )
= $true )
| ( ( SV976 = SV1755 )
= $true )
| ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1440 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV444 @ SV976 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ SV1440 @ SV1755 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(4730,plain,
! [SV1445: $i,SV1894: $i,SV1757: $i,SV455: $i,SV1950: $i,SV985: $i] :
( ( ( ~ ( c_in @ SV985 @ ( hAPP @ SV1950 @ SV455 ) @ SV1757 ) )
= $true )
| ( ( ~ ( c_in @ SV455 @ SV1894 @ SV1445 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SV1950 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(4731,plain,
! [SV1446: $i,SV1895: $i,SV1758: $i,SV456: $i,SV1951: $i,SV986: $i] :
( ( ( ~ ( c_in @ SV986 @ ( hAPP @ SV1951 @ SV456 ) @ SV1758 ) )
= $true )
| ( ( ~ ( c_in @ SV456 @ SV1895 @ SV1446 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SV1951 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(4732,plain,
! [SV457: $i,SV1447: $i,SV987: $i,SV1759: $i] :
( ( ( c_in @ SV1759 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
= $false )
| ( ( c_in @ ( c_Pair @ SV457 @ SV1759 @ SV1447 @ SV1447 ) @ SV987 @ ( tc_prod @ SV1447 @ SV1447 ) )
= $false )
| ( ( c_in @ SV457 @ ( c_Wellfounded_Oacc @ SV987 @ SV1447 ) @ SV1447 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(4733,plain,
! [SV458: $i,SV1448: $i,SV988: $i,SV1760: $i] :
( ( ( c_in @ SV1760 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
= $false )
| ( ( c_in @ ( c_Pair @ SV458 @ SV1760 @ SV1448 @ SV1448 ) @ SV988 @ ( tc_prod @ SV1448 @ SV1448 ) )
= $false )
| ( ( c_in @ SV458 @ ( c_Wellfounded_Oacc @ SV988 @ SV1448 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4734,plain,
! [SV1449: $i,SV989: $i,SV1896: $i,SV1761: $i,SV459: $i,SV1952: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1952 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1952 @ SV1449 @ SV1761 ) )
= $true )
| ( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4735,plain,
! [SV1450: $i,SV990: $i,SV1897: $i,SV1762: $i,SV460: $i,SV1953: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1953 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1953 @ SV1450 @ SV1762 ) )
= $true )
| ( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(4736,plain,
! [SV993: $i,SV1898: $i,SV1453: $i,SV463: $i,SV1764: $i] :
( ( ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SV1898 @ ( tc_prod @ SV1453 @ SV1453 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV993 @ SV1898 @ SV1453 ) )
= $true )
| ( ( c_in @ SV463 @ SV993 @ SV1453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4737,plain,
! [SV994: $i,SV1899: $i,SV1454: $i,SV1765: $i,SV464: $i] :
( ( ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SV1899 @ ( tc_prod @ SV1454 @ SV1454 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV994 @ SV1899 @ SV1454 ) )
= $true )
| ( ( c_in @ SV464 @ SV994 @ SV1454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4738,plain,
! [SV999: $i,SV1954: $i,SV1770: $i,SV1904: $i,SV469: $i,SV1459: $i] :
( ( ( c_in @ ( c_Pair @ SV1459 @ SV469 @ SV1904 @ SV1770 ) @ ( c_Product__Type_OSigma @ SV1954 @ SV999 @ SV1904 @ SV1770 ) @ ( tc_prod @ SV1904 @ SV1770 ) )
= $false )
| ( ( c_in @ SV469 @ ( hAPP @ SV999 @ SV1459 ) @ SV1770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4577]) ).
thf(4739,plain,
! [SV1955: $i,SV1000: $i,SV1905: $i,SV1460: $i,SV1771: $i,SV470: $i] :
( ( ( c_in @ ( c_Pair @ SV470 @ SV1771 @ SV1460 @ SV1905 ) @ ( c_Product__Type_OSigma @ SV1000 @ SV1955 @ SV1460 @ SV1905 ) @ ( tc_prod @ SV1460 @ SV1905 ) )
= $false )
| ( ( c_in @ SV470 @ SV1000 @ SV1460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(4740,plain,
! [SV1772: $i,SV1461: $i,SV1906: $i,SV471: $i,SV1001: $i] :
( ( ( SV1001 = SV471 )
= $true )
| ( ( ~ ( c_in @ SV471 @ SV1906 @ SV1461 )
| ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(4741,plain,
! [SV472: $i,SV1002: $i,SV1462: $i,SV1773: $i] :
( ( ( c_Relation_Orefl__on @ SV1773 @ SV1462 @ SV1002 )
= $false )
| ( ( c_in @ SV472 @ SV1773 @ SV1002 )
= $false )
| ( ( c_in @ ( c_Pair @ SV472 @ SV472 @ SV1002 @ SV1002 ) @ SV1462 @ ( tc_prod @ SV1002 @ SV1002 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4742,plain,
! [SV1003: $i,SV1907: $i,SV1463: $i,SV473: $i,SV1774: $i] :
( ( ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SV1907 @ ( tc_prod @ SV1463 @ SV1463 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1003 @ SV1907 @ SV1463 ) )
= $true )
| ( ( c_in @ SV473 @ SV1003 @ SV1463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4743,plain,
! [SV1004: $i,SV1908: $i,SV1464: $i,SV1775: $i,SV474: $i] :
( ( ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SV1908 @ ( tc_prod @ SV1464 @ SV1464 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1004 @ SV1908 @ SV1464 ) )
= $true )
| ( ( c_in @ SV474 @ SV1004 @ SV1464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4744,plain,
! [SV475: $i,SV1005: $i,SV1465: $i,SV1776: $i] :
( ( ( c_Relation_Orefl__on @ SV1776 @ SV1465 @ SV1005 )
= $false )
| ( ( c_in @ SV475 @ SV1776 @ SV1005 )
= $false )
| ( ( c_in @ ( c_Pair @ SV475 @ SV475 @ SV1005 @ SV1005 ) @ SV1465 @ ( tc_prod @ SV1005 @ SV1005 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4583]) ).
thf(4745,plain,
! [SV476: $i,SV1777: $i,SV1466: $i,SV1006: $i] :
( ( ( c_in @ SV1006 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1466 = SV1777 )
= $true )
| ( ( c_in @ ( c_Pair @ SV476 @ SV476 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1006 @ SV1466 @ SV1777 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4746,plain,
! [SV1007: $i,SV1467: $i,SV1778: $i,SV477: $i] :
( ( ( SV477 = SV1778 )
= $true )
| ( ( ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(4747,plain,
! [SV1468: $i,SV1008: $i,SV478: $i,SV1779: $i] :
( ( ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV478 = SV1008 )
| ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV478 = SV1468 )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4748,plain,
! [SV1909: $i,SV1469: $i,SV1009: $i,SV1780: $i,SV479: $i] :
( ( ( SV479 = SV1780 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true )
| ( ( SV1009 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4587]) ).
thf(4749,plain,
! [SV480: $i,SV1010: $i,SV1781: $i,SV1470: $i] :
( ( ( ~ ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(4750,plain,
! [SV1011: $i,SV481: $i,SV1782: $i,SV1471: $i] :
( ( ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1782 = SV481 )
| ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4751,plain,
! [SV1012: $i,SV1472: $i,SV482: $i,SV1783: $i] :
( ( ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1783 = SV1012 )
| ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(4752,plain,
! [SV483: $i,SV1013: $i,SV1784: $i,SV1473: $i] :
( ( ( ~ ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV483 = SV1013 )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4591]) ).
thf(4753,plain,
! [SV1910: $i,SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV484 = SV1785 )
| ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4592]) ).
thf(4754,plain,
! [SV1786: $i,SV1911: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4593]) ).
thf(4755,plain,
! [SV1476: $i,SV486: $i,SV1016: $i] :
( ( ( SV1016 = SV486 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1016 @ SV486 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1476 @ SV1016 @ SV486 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1476 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1016 = SV486 )
= $true )
| ( ( SV486 = SV1016 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4594]) ).
thf(4756,plain,
! [SV1912: $i,SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4595]) ).
thf(4757,plain,
! [SV1018: $i,SV488: $i,SV1478: $i] :
( ( ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV488 = SV1018 )
| ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV488 = SV1018 )
= $true )
| ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4596]) ).
thf(4758,plain,
! [SV1019: $i,SV1788: $i,SV489: $i,SV1479: $i] :
( ( ( ~ ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1788 = SV1019 )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4597]) ).
thf(4759,plain,
! [SV1789: $i,SV1913: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1020 = SV1913 )
| ( SV490 = SV1913 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4598]) ).
thf(4760,plain,
! [SV491: $i,SV1790: $i,SV1481: $i,SV1021: $i] :
( ( ( c_in @ SV1021 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1481 = SV1790 )
= $true )
| ( ( c_in @ ( c_Pair @ SV491 @ SV491 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1021 @ SV1481 @ SV1790 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4599]) ).
thf(4761,plain,
! [SV492: $i,SV1482: $i,SV1022: $i,SV1791: $i] :
( ( ( SV1791 = SV1022 )
= $true )
| ( ( ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1022 = SV1791 )
= $true )
| ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4600]) ).
thf(4762,plain,
! [SV1483: $i,SV493: $i,SV1023: $i,SV1792: $i] :
( ( ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1023 = SV493 )
| ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1483 = SV493 )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(4763,plain,
! [SV1914: $i,SV1484: $i,SV494: $i,SV1793: $i,SV1024: $i] :
( ( ( SV1024 = SV1793 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true )
| ( ( SV494 = SV1793 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(4764,plain,
! [SV495: $i,SV1794: $i,SV1025: $i,SV1485: $i] :
( ( ( ~ ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(4765,plain,
! [SV496: $i,SV1795: $i,SV1026: $i,SV1486: $i] :
( ( ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1026 = SV1795 )
| ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(4766,plain,
! [SV497: $i,SV1487: $i,SV1796: $i,SV1027: $i] :
( ( ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV497 = SV1796 )
| ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4605]) ).
thf(4767,plain,
! [SV1028: $i,SV1797: $i,SV498: $i,SV1488: $i] :
( ( ( ~ ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV498 = SV1028 )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4606]) ).
thf(4768,plain,
! [SV1798: $i,SV1915: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1029 = SV1915 )
| ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4607]) ).
thf(4769,plain,
! [SV1916: $i,SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(4770,plain,
! [SV1491: $i,SV1031: $i,SV501: $i] :
( ( ( SV501 = SV1031 )
= $true )
| ( ( c_in @ ( c_Pair @ SV501 @ SV1031 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1491 @ SV501 @ SV1031 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1491 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV501 = SV1031 )
= $true )
| ( ( SV501 = SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4609]) ).
thf(4771,plain,
! [SV1800: $i,SV1917: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(4772,plain,
! [SV1033: $i,SV503: $i,SV1493: $i] :
( ( ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV503 = SV1033 )
| ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV503 = SV1033 )
= $true )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(4773,plain,
! [SV504: $i,SV1034: $i,SV1801: $i,SV1494: $i] :
( ( ( ~ ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV504 = SV1801 )
= $true )
| ( ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(4774,plain,
! [SV1918: $i,SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV505 = SV1802 )
| ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(4775,plain,
! [SV1496: $i,SV1036: $i,SV506: $i] :
( ( ( SV506 = SV1036 )
= $true )
| ( ( ~ ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(4776,plain,
! [SV511: $i,SV1040: $i,SV1500: $i] :
( ( ( c_in @ SV1500 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1040 @ SV511 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV511 @ SV1040 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1500 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(4777,plain,
! [SV1968: $i,SV1956: $i,SV1919: $i,SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
!= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
= $true )
| ( ( ( ( hAPP @ SV524 @ SV1968 )
= ( hAPP @ SV1956 @ SV1968 ) )
| ~ ( c_in @ ( c_Pair @ SV1968 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(4778,plain,
! [SV1957: $i,SV1920: $i,SV1804: $i,SV1506: $i,SV1058: $i,SV529: $i] :
( ( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
= $false )
| ( ( ~ ( c_in @ SV1957 @ SV1058 @ SV1506 )
| ( SV529 = SV1920 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4779,plain,
! [SV1958: $i,SV1921: $i,SV1806: $i,SV1508: $i,SV1060: $i,SV531: $i] :
( ( ( ( c_Pair @ SV531 @ SV1060 @ SV1508 @ SV1806 )
= ( c_Pair @ SV1921 @ SV1958 @ SV1508 @ SV1806 ) )
= $false )
| ( ( SV1060 = SV1958 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(4780,plain,
! [SV1807: $i,SV1509: $i,SV1062: $i,SV533: $i] :
( ( ( c_in @ SV533 @ SV1062 @ SV1509 )
= $true )
| ( ( SV1062 = SV1807 )
= $true )
| ( ( c_in @ SV533 @ SV1807 @ SV1509 )
= $true )
| ( ( ( c_Set_Oinsert @ SV533 @ SV1062 @ SV1509 )
= ( c_Set_Oinsert @ SV533 @ SV1807 @ SV1509 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(4781,plain,
! [SV1959: $i,SV1922: $i,SV1808: $i,SV1510: $i,SV1063: $i,SV534: $i] :
( ( ( ( hAPP @ SV534 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) )
= ( hAPP @ SV1063 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV534 @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV534 @ SV1510 @ SV1808 @ SV1922 @ SV1959 )
= ( c_Recdef_Ocut @ SV1063 @ SV1510 @ SV1808 @ SV1922 @ SV1959 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(4782,plain,
! [SV1960: $i,SV1923: $i,SV1809: $i,SV1511: $i,SV1064: $i,SV535: $i] :
( ( ( ( c_Pair @ SV535 @ SV1064 @ SV1511 @ SV1809 )
= ( c_Pair @ SV1923 @ SV1960 @ SV1511 @ SV1809 ) )
= $false )
| ( ( SV535 = SV1923 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(4783,plain,
! [SV1070: $i,SV1517: $i,SV9: $i,SV1924: $i,SV1811: $i,SV544: $i] :
( ( ( c_in @ SV544 @ SV1811 @ SV1924 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SV1924 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(4784,plain,
! [SV545: $i,SV1071: $i,SV10: $i,SV1812: $i,SV1518: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1518 @ SV1812 )
= $false )
| ( ( c_lessequals @ SV10 @ ( c_Set_Oimage @ SV1071 @ SV1518 @ SV1812 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV10 @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(4785,plain,
! [SV582: $i,SV47: $i,SV1539: $i,SV1103: $i] :
( ( ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
= $false )
| ( ( ~ ( c_lessequals @ SV582 @ SV1539 @ SV47 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4786,plain,
! [SV585: $i,SV50: $i,SV1540: $i,SV1106: $i] :
( ( ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
= $false )
| ( ( ~ ( c_lessequals @ SV585 @ SV1540 @ SV50 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4787,plain,
! [SV586: $i,SV51: $i,SV1541: $i,SV1107: $i] :
( ( ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
= $false )
| ( ( ~ ( c_lessequals @ SV586 @ SV1541 @ SV51 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4631]) ).
thf(4788,plain,
! [SV1825: $i,SV1585: $i,SV1171: $i,SV1927: $i,SV119: $i,SV654: $i] :
( ( ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SV1927 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SV1927 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4640]) ).
thf(4789,plain,
! [SV655: $i,SV1172: $i,SV120: $i] :
( ( ( c_Wellfounded_Owf @ SV120 @ SV1172 )
= $false )
| ( ( c_Wellfounded_Owf @ SV655 @ SV1172 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV120 @ SV655 @ SV1172 @ SV1172 @ SV1172 ) @ SV120 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV655 @ ( tc_fun @ ( tc_prod @ SV1172 @ SV1172 ) @ tc_bool ) ) @ SV1172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4641]) ).
thf(4790,plain,
! [SV1829: $i,SV675: $i,SV1188: $i,SV1595: $i,SV140: $i] :
( ( ( c_Relation_Orefl__on @ SV140 @ SV1595 @ SV1188 )
= $false )
| ( ( c_Relation_Orefl__on @ SV675 @ SV1829 @ SV1188 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV140 @ SV675 @ ( tc_fun @ SV1188 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1595 @ SV1829 @ ( tc_fun @ ( tc_prod @ SV1188 @ SV1188 ) @ tc_bool ) ) @ SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4642]) ).
thf(4791,plain,
! [SV1831: $i,SV693: $i,SV1206: $i,SV1604: $i,SV159: $i] :
( ( ( c_Relation_Orefl__on @ SV159 @ SV1604 @ SV1206 )
= $false )
| ( ( c_Relation_Orefl__on @ SV693 @ SV1831 @ SV1206 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV159 @ SV693 @ ( tc_fun @ SV1206 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1604 @ SV1831 @ ( tc_fun @ ( tc_prod @ SV1206 @ SV1206 ) @ tc_bool ) ) @ SV1206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4643]) ).
thf(4792,plain,
! [SV1833: $i,SV698: $i,SV1211: $i,SV1609: $i,SV164: $i] :
( ( ( c_lessequals @ SV164 @ SV1609 @ ( tc_fun @ SV1211 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV698 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV698 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1609 @ SV1833 @ ( tc_fun @ SV1211 @ tc_bool ) ) @ ( tc_fun @ SV1211 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4644]) ).
thf(4793,plain,
! [SV1215: $i,SV168: $i,SV1611: $i,SV702: $i] :
( ( ( c_lessequals @ SV702 @ SV1611 @ SV168 )
= $false )
| ( ( ~ ( c_lessequals @ SV702 @ SV1215 @ SV168 ) )
= $true )
| ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(4794,plain,
! [SV1216: $i,SV169: $i,SV1612: $i,SV703: $i] :
( ( ( c_lessequals @ SV703 @ SV1612 @ SV169 )
= $false )
| ( ( ~ ( c_lessequals @ SV703 @ SV1216 @ SV169 ) )
= $true )
| ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(4795,plain,
! [SV1217: $i,SV170: $i,SV1613: $i,SV704: $i] :
( ( ( c_lessequals @ SV704 @ SV1613 @ SV170 )
= $false )
| ( ( ~ ( c_lessequals @ SV704 @ SV1217 @ SV170 ) )
= $true )
| ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4647]) ).
thf(4796,plain,
! [SV1835: $i,SV738: $i,SV1248: $i,SV1631: $i,SV204: $i] :
( ( ( c_lessequals @ SV204 @ SV1631 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV738 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV204 @ SV738 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1631 @ SV1835 @ ( tc_fun @ SV1248 @ tc_bool ) ) @ ( tc_fun @ SV1248 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4797,plain,
! [SV745: $i,SV1637: $i,SV1255: $i,SV1839: $i,SV211: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4659]) ).
thf(4798,plain,
! [SV746: $i,SV1638: $i,SV1256: $i,SV1840: $i,SV212: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(4799,plain,
! [SV1643: $i,SV1929: $i,SV760: $i,SV1265: $i,SV1841: $i,SV226: $i] :
( ( ( c_lessequals @ SV226 @ SV1841 @ ( tc_fun @ SV1265 @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV226 @ SV760 @ SV1929 @ SV1265 @ SV1643 ) @ SV226 @ SV1265 )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV226 @ SV760 @ SV1265 @ SV1643 ) @ ( c_Product__Type_OSigma @ SV1841 @ SV1929 @ SV1265 @ SV1643 ) @ ( tc_fun @ ( tc_prod @ SV1265 @ SV1643 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4800,plain,
! [SV237: $i,SV771: $i,SV1274: $i,SV1649: $i] :
( ( ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1274 @ SV771 ) )
= $true )
| ( ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(4801,plain,
! [SV778: $i,SV1654: $i,SV1281: $i,SV1845: $i,SV244: $i] :
( ( ( c_in @ ( c_Pair @ SV244 @ SV1845 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Ortrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1845 @ SV778 @ SV1281 @ SV1281 ) @ SV1654 @ ( tc_prod @ SV1281 @ SV1281 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV244 @ SV778 @ SV1281 @ SV1281 ) @ ( c_Transitive__Closure_Otrancl @ SV1654 @ SV1281 ) @ ( tc_prod @ SV1281 @ SV1281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4663]) ).
thf(4802,plain,
! [SV779: $i,SV1655: $i,SV1282: $i,SV1846: $i,SV245: $i] :
( ( ( c_in @ ( c_Pair @ SV245 @ SV1846 @ SV1282 @ SV1282 ) @ SV1655 @ ( tc_prod @ SV1282 @ SV1282 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1846 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Ortrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV245 @ SV779 @ SV1282 @ SV1282 ) @ ( c_Transitive__Closure_Otrancl @ SV1655 @ SV1282 ) @ ( tc_prod @ SV1282 @ SV1282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4664]) ).
thf(4803,plain,
! [SV801: $i,SV1665: $i,SV1302: $i,SV1849: $i,SV267: $i] :
( ( ( c_in @ ( c_Pair @ SV267 @ SV1849 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1849 @ SV801 @ SV1302 @ SV1302 ) @ SV1665 @ ( tc_prod @ SV1302 @ SV1302 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV267 @ SV801 @ SV1302 @ SV1302 ) @ ( c_Transitive__Closure_Ortrancl @ SV1665 @ SV1302 ) @ ( tc_prod @ SV1302 @ SV1302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4670]) ).
thf(4804,plain,
! [SV802: $i,SV1666: $i,SV1303: $i,SV1850: $i,SV268: $i] :
( ( ( c_in @ ( c_Pair @ SV268 @ SV1850 @ SV1303 @ SV1303 ) @ SV1666 @ ( tc_prod @ SV1303 @ SV1303 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1850 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV268 @ SV802 @ SV1303 @ SV1303 ) @ ( c_Transitive__Closure_Ortrancl @ SV1666 @ SV1303 ) @ ( tc_prod @ SV1303 @ SV1303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4671]) ).
thf(4805,plain,
! [SV803: $i,SV1667: $i,SV1304: $i,SV1851: $i,SV269: $i] :
( ( ( c_in @ ( c_Pair @ SV269 @ SV1851 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1851 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV269 @ SV803 @ SV1304 @ SV1304 ) @ ( c_Transitive__Closure_Ortrancl @ SV1667 @ SV1304 ) @ ( tc_prod @ SV1304 @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4672]) ).
thf(4806,plain,
! [SV1669: $i,SV1852: $i,SV277: $i,SV1310: $i,SV1930: $i,SV811: $i] :
( ( ( c_lessequals @ SV811 @ SV1930 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SV1930 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4807,plain,
! [SV821: $i,SV287: $i,SV1316: $i,SV1674: $i] :
( ( ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
= $false )
| ( ( ~ ( c_lessequals @ SV821 @ SV1674 @ SV287 ) )
= $true )
| ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
= $true )
| ( ( class_Orderings_Opreorder @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4677]) ).
thf(4808,plain,
! [SV1317: $i,SV288: $i,SV1675: $i,SV822: $i] :
( ( ( c_lessequals @ SV822 @ SV1675 @ SV288 )
= $false )
| ( ( ~ ( c_lessequals @ SV1675 @ SV1317 @ SV288 ) )
= $true )
| ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
= $true )
| ( ( class_Orderings_Oorder @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(4809,plain,
! [SV292: $i,SV826: $i,SV1320: $i] :
( ( ( c_lessequals @ SV1320 @ SV826 @ SV292 )
= $false )
| ( ( c_lessequals @ SV826 @ SV1320 @ SV292 )
= $false )
| ( ( SV826 = SV1320 )
= $true )
| ( ( class_Orderings_Oorder @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(4810,plain,
! [SV293: $i,SV1321: $i,SV827: $i] :
( ( ( c_lessequals @ SV827 @ SV1321 @ SV293 )
= $false )
| ( ( c_lessequals @ SV1321 @ SV827 @ SV293 )
= $false )
| ( ( SV827 = SV1321 )
= $true )
| ( ( class_Orderings_Oorder @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4811,plain,
! [SV294: $i,SV1322: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ SV1322 @ SV294 )
= $false )
| ( ( c_lessequals @ SV1322 @ SV828 @ SV294 )
= $false )
| ( ( SV828 = SV1322 )
= $true )
| ( ( class_Orderings_Oorder @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4812,plain,
! [SV1969: $i,SV1961: $i,SV1931: $i,SV1853: $i,SV1676: $i,SV1325: $i,SV832: $i,SV298: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1969 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4682]) ).
thf(4813,plain,
! [SV1327: $i,SV836: $i,SV1932: $i,SV1677: $i,SV1854: $i,SV302: $i] :
( ( ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV1932 @ SV836 @ SV1327 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4683]) ).
thf(4814,plain,
! [SV1933: $i,SV837: $i,SV1328: $i,SV1855: $i,SV1678: $i,SV303: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV1933 @ SV1678 @ SV1855 ) )
= $true )
| ( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4815,plain,
! [SV1330: $i,SV1934: $i,SV306: $i,SV1856: $i,SV1679: $i,SV1962: $i,SV840: $i] :
( ( ( ~ ( c_lessequals @ SV840 @ SV1962 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SV1962 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(4816,plain,
! [SV1682: $i,SV311: $i,SV1334: $i,SV845: $i,SV1858: $i] :
( ( ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) ) )
= $true )
| ( ( SV311 = SV1682 )
= $true )
| ( ( c_in @ SV311 @ SV845 @ SV1334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(4817,plain,
! [SV1336: $i,SV313: $i,SV1859: $i,SV1683: $i,SV847: $i] :
( ( ( c_lessequals @ SV847 @ SV1683 @ ( tc_fun @ SV1859 @ SV313 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV847 @ SV1336 ) @ ( hAPP @ SV1683 @ SV1336 ) @ SV313 )
= $true )
| ( ( class_HOL_Oord @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4818,plain,
! [SV854: $i,SV1689: $i,SV1343: $i,SV1860: $i,SV320: $i] :
( ( ( c_in @ ( c_Pair @ SV320 @ SV1860 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1860 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Ortrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV320 @ SV854 @ SV1343 @ SV1343 ) @ ( c_Transitive__Closure_Otrancl @ SV1689 @ SV1343 ) @ ( tc_prod @ SV1343 @ SV1343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(4819,plain,
! [SV855: $i,SV1690: $i,SV1344: $i,SV1861: $i,SV321: $i] :
( ( ( c_in @ ( c_Pair @ SV321 @ SV1861 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Ortrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1861 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV321 @ SV855 @ SV1344 @ SV1344 ) @ ( c_Transitive__Closure_Otrancl @ SV1690 @ SV1344 ) @ ( tc_prod @ SV1344 @ SV1344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(4820,plain,
! [SV1963: $i,SV1695: $i,SV1351: $i,SV1936: $i,SV1862: $i,SV862: $i,SV328: $i] :
( ( ( c_in @ ( c_Pair @ SV328 @ SV862 @ SV1862 @ SV1936 ) @ ( c_Relation_Orel__comp @ SV1351 @ SV1695 @ SV1862 @ SV1963 @ SV1936 ) @ ( tc_prod @ SV1862 @ SV1936 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV328 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV328 @ SV862 @ SV1351 @ SV1695 @ SV1862 @ SV1936 @ SV1963 ) @ SV1862 @ SV1963 ) @ SV1351 @ ( tc_prod @ SV1862 @ SV1963 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(4821,plain,
! [SV1964: $i,SV1696: $i,SV1352: $i,SV1937: $i,SV1863: $i,SV863: $i,SV329: $i] :
( ( ( c_in @ ( c_Pair @ SV329 @ SV863 @ SV1863 @ SV1937 ) @ ( c_Relation_Orel__comp @ SV1352 @ SV1696 @ SV1863 @ SV1964 @ SV1937 ) @ ( tc_prod @ SV1863 @ SV1937 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV329 @ SV863 @ SV1352 @ SV1696 @ SV1863 @ SV1937 @ SV1964 ) @ SV863 @ SV1964 @ SV1937 ) @ SV1696 @ ( tc_prod @ SV1964 @ SV1937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4822,plain,
! [SV1698: $i,SV1354: $i,SV331: $i,SV1938: $i,SV1865: $i,SV865: $i] :
( ( ( c_in @ SV865 @ SV1865 @ SV1938 )
= $false )
| ( ( ~ ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1938 ) @ SV1938 @ SV1698 ) @ ( tc_fun @ SV1938 @ SV1698 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(4823,plain,
! [SV1870: $i,SV1364: $i,SV1704: $i,SV879: $i,SV345: $i] :
( ( ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false )
| ( ( ~ ( c_in @ SV1870 @ SV879 @ SV1364 )
| ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true )
| ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4698]) ).
thf(4824,plain,
! [SV1871: $i,SV1365: $i,SV1705: $i,SV880: $i,SV346: $i] :
( ( ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
= $false )
| ( ( ~ ( c_in @ SV1871 @ SV880 @ SV1365 )
| ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true )
| ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4825,plain,
! [SV887: $i,SV1874: $i,SV1711: $i,SV353: $i,SV1372: $i] :
( ( ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) )
= $false )
| ( ( ~ ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4700]) ).
thf(4826,plain,
! [SV354: $i,SV1373: $i,SV1712: $i,SV888: $i] :
( ( ( c_in @ SV888 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1373 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV354 @ SV1712 ) @ t_a @ t_a ) @ SV1712 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1373 @ ( c_Wellfounded_Oacc @ SV1712 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV354 @ SV888 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4701]) ).
thf(4827,plain,
! [SV355: $i,SV1374: $i,SV1713: $i,SV889: $i] :
( ( ( c_in @ SV889 @ ( c_Wellfounded_Oacc @ SV1713 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1374 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV355 @ SV1713 ) @ t_a @ t_a ) @ SV1713 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV1374 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV355 @ SV889 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4702]) ).
thf(4828,plain,
! [SV356: $i,SV1375: $i,SV1714: $i,SV890: $i] :
( ( ( c_in @ SV890 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1375 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV356 @ SV1714 ) @ t_a @ t_a ) @ SV1714 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1375 @ ( c_Wellfounded_Oacc @ SV1714 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV356 @ SV890 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(4829,plain,
! [SV360: $i,SV1379: $i,SV1717: $i,SV894: $i] :
( ( ( c_in @ SV894 @ ( c_Wellfounded_Oacc @ SV1717 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1379 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV360 @ SV1717 ) @ t_a @ t_a ) @ SV1717 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV1379 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ SV894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(4830,plain,
! [SV895: $i,SV1875: $i,SV1718: $i,SV361: $i,SV1380: $i] :
( ( ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) )
= $false )
| ( ( ~ ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(4831,plain,
! [SV365: $i,SV899: $i,SV1384: $i,SV1721: $i] :
( ( ( c_Wellfounded_Owf @ SV1721 @ SV1384 )
= $false )
| ( ( c_in @ ( c_Pair @ SV899 @ SV365 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV365 @ SV899 @ SV1384 @ SV1384 ) @ SV1721 @ ( tc_prod @ SV1384 @ SV1384 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4708]) ).
thf(4832,plain,
! [SV901: $i,SV1723: $i,SV1386: $i,SV1876: $i,SV367: $i] :
( ( ( c_in @ ( c_Pair @ SV367 @ SV1876 @ SV1386 @ SV1386 ) @ SV1723 @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1876 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV367 @ SV901 @ SV1386 @ SV1386 ) @ ( c_Transitive__Closure_Otrancl @ SV1723 @ SV1386 ) @ ( tc_prod @ SV1386 @ SV1386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(4833,plain,
! [SV902: $i,SV1724: $i,SV1387: $i,SV1877: $i,SV368: $i] :
( ( ( c_in @ ( c_Pair @ SV368 @ SV1877 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1877 @ SV902 @ SV1387 @ SV1387 ) @ SV1724 @ ( tc_prod @ SV1387 @ SV1387 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV368 @ SV902 @ SV1387 @ SV1387 ) @ ( c_Transitive__Closure_Otrancl @ SV1724 @ SV1387 ) @ ( tc_prod @ SV1387 @ SV1387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(4834,plain,
! [SV1970: $i,SV1966: $i,SV1945: $i,SV1887: $i,SV1742: $i,SV1424: $i,SV956: $i,SV424: $i] :
( ( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1970 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) )
| ~ ( c_in @ ( c_Pair @ SV424 @ SV1970 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(4835,plain,
! [SV957: $i,SV1743: $i,SV1425: $i,SV1888: $i,SV425: $i] :
( ( ( c_in @ ( c_Pair @ SV425 @ SV1888 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1888 @ SV957 @ SV1425 @ SV1425 ) @ SV1743 @ ( tc_prod @ SV1425 @ SV1425 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV425 @ SV957 @ SV1425 @ SV1425 ) @ ( c_Transitive__Closure_Otrancl @ SV1743 @ SV1425 ) @ ( tc_prod @ SV1425 @ SV1425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4718]) ).
thf(4836,plain,
! [SV958: $i,SV1744: $i,SV1426: $i,SV1889: $i,SV426: $i] :
( ( ( c_in @ ( c_Pair @ SV426 @ SV1889 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1889 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV426 @ SV958 @ SV1426 @ SV1426 ) @ ( c_Transitive__Closure_Otrancl @ SV1744 @ SV1426 ) @ ( tc_prod @ SV1426 @ SV1426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(4837,plain,
! [SV1745: $i,SV1427: $i,SV429: $i,SV1946: $i,SV1890: $i,SV961: $i] :
( ( ( c_in @ SV961 @ SV1890 @ SV1946 )
= $false )
| ( ( ~ ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SV1946 @ SV1745 ) @ ( tc_fun @ SV1946 @ SV1745 ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(4838,plain,
! [SV1428: $i,SV962: $i,SV1947: $i,SV1891: $i,SV430: $i,SV1746: $i] :
( ( ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SV1947 )
= $true )
| ( ( ~ ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SV1947 ) @ ( tc_fun @ SV1428 @ SV1947 ) ) )
= $true )
| ( ( c_in @ SV430 @ SV962 @ SV1428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4721]) ).
thf(4839,plain,
! [SV1967: $i,SV431: $i,SV963: $i,SV1948: $i,SV1892: $i,SV1747: $i,SV1429: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4722]) ).
thf(4840,plain,
! [SV432: $i,SV1949: $i,SV1893: $i,SV1430: $i,SV964: $i,SV1748: $i] :
( ( ( ~ ( c_in @ SV1748 @ SV964 @ SV1430 ) )
= $true )
| ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(4841,plain,
! [SV1445: $i,SV1894: $i,SV1757: $i,SV455: $i,SV1950: $i,SV985: $i] :
( ( ( c_in @ SV985 @ ( hAPP @ SV1950 @ SV455 ) @ SV1757 )
= $false )
| ( ( ~ ( c_in @ SV455 @ SV1894 @ SV1445 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SV1950 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4730]) ).
thf(4842,plain,
! [SV1446: $i,SV1895: $i,SV1758: $i,SV456: $i,SV1951: $i,SV986: $i] :
( ( ( c_in @ SV986 @ ( hAPP @ SV1951 @ SV456 ) @ SV1758 )
= $false )
| ( ( ~ ( c_in @ SV456 @ SV1895 @ SV1446 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SV1951 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4843,plain,
! [SV1449: $i,SV989: $i,SV1896: $i,SV1761: $i,SV459: $i,SV1952: $i] :
( ( ( c_in @ ( c_Pair @ SV1952 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) )
= $false )
| ( ( ~ ( c_in @ SV1952 @ SV1449 @ SV1761 ) )
= $true )
| ( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(4844,plain,
! [SV1450: $i,SV990: $i,SV1897: $i,SV1762: $i,SV460: $i,SV1953: $i] :
( ( ( c_in @ ( c_Pair @ SV1953 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) )
= $false )
| ( ( ~ ( c_in @ SV1953 @ SV1450 @ SV1762 ) )
= $true )
| ( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4735]) ).
thf(4845,plain,
! [SV463: $i,SV1764: $i,SV1453: $i,SV1898: $i,SV993: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV993 @ SV1898 @ SV1453 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1764 @ SV463 @ SV1453 @ SV1453 ) @ SV1898 @ ( tc_prod @ SV1453 @ SV1453 ) )
= $false )
| ( ( c_in @ SV463 @ SV993 @ SV1453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4736]) ).
thf(4846,plain,
! [SV1765: $i,SV464: $i,SV1454: $i,SV1899: $i,SV994: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV994 @ SV1899 @ SV1454 )
= $false )
| ( ( c_in @ ( c_Pair @ SV464 @ SV1765 @ SV1454 @ SV1454 ) @ SV1899 @ ( tc_prod @ SV1454 @ SV1454 ) )
= $false )
| ( ( c_in @ SV464 @ SV994 @ SV1454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4737]) ).
thf(4847,plain,
! [SV1772: $i,SV1001: $i,SV1461: $i,SV1906: $i,SV471: $i] :
( ( ( ~ ( c_in @ SV471 @ SV1906 @ SV1461 ) )
= $true )
| ( ( ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( SV1001 = SV471 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4740]) ).
thf(4848,plain,
! [SV473: $i,SV1774: $i,SV1463: $i,SV1907: $i,SV1003: $i] :
( ( ( c_Relation_Orefl__on @ SV1003 @ SV1907 @ SV1463 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1774 @ SV473 @ SV1463 @ SV1463 ) @ SV1907 @ ( tc_prod @ SV1463 @ SV1463 ) )
= $false )
| ( ( c_in @ SV473 @ SV1003 @ SV1463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4742]) ).
thf(4849,plain,
! [SV1775: $i,SV474: $i,SV1464: $i,SV1908: $i,SV1004: $i] :
( ( ( c_Relation_Orefl__on @ SV1004 @ SV1908 @ SV1464 )
= $false )
| ( ( c_in @ ( c_Pair @ SV474 @ SV1775 @ SV1464 @ SV1464 ) @ SV1908 @ ( tc_prod @ SV1464 @ SV1464 ) )
= $false )
| ( ( c_in @ SV474 @ SV1004 @ SV1464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4743]) ).
thf(4850,plain,
! [SV477: $i,SV1778: $i,SV1007: $i,SV1467: $i] :
( ( ( ~ ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(4851,plain,
! [SV1779: $i,SV1468: $i,SV1008: $i,SV478: $i] :
( ( ( SV478 = SV1008 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV478 = SV1468 )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4747]) ).
thf(4852,plain,
! [SV1780: $i,SV1909: $i,SV1469: $i,SV1009: $i,SV479: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true )
| ( ( SV479 = SV1780 )
= $true )
| ( ( SV1009 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(4853,plain,
! [SV480: $i,SV1010: $i,SV1781: $i,SV1470: $i] :
( ( ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1781 = SV1010 )
| ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(4854,plain,
! [SV1471: $i,SV1011: $i,SV481: $i,SV1782: $i] :
( ( ( SV1782 = SV481 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1782 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1471 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1471 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV481 @ SV1011 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1471 @ SV1782 @ SV481 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(4855,plain,
! [SV482: $i,SV1472: $i,SV1012: $i,SV1783: $i] :
( ( ( SV1783 = SV1012 )
= $true )
| ( ( ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(4856,plain,
! [SV483: $i,SV1013: $i,SV1784: $i,SV1473: $i] :
( ( ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1784 = SV1013 )
| ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV483 = SV1013 )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(4857,plain,
! [SV1014: $i,SV1474: $i,SV1910: $i,SV1785: $i,SV484: $i] :
( ( ( SV484 = SV1785 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(4858,plain,
! [SV485: $i,SV1786: $i,SV1475: $i,SV1015: $i,SV1911: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(4859,plain,
! [SV1912: $i,SV1017: $i,SV1477: $i,SV1787: $i,SV487: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(4860,plain,
! [SV1478: $i,SV1018: $i,SV488: $i] :
( ( ( SV488 = SV1018 )
= $true )
| ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1478 @ SV488 @ SV1018 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1478 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV488 = SV1018 )
= $true )
| ( ( c_in @ ( c_Pair @ SV488 @ SV1018 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1478 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(4861,plain,
! [SV1019: $i,SV1788: $i,SV489: $i,SV1479: $i] :
( ( ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV489 = SV1788 )
| ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1788 = SV1019 )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(4862,plain,
! [SV1789: $i,SV1480: $i,SV490: $i,SV1913: $i,SV1020: $i] :
( ( ( SV1020 = SV1913 )
= $true )
| ( ( ( SV490 = SV1913 )
| ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(4863,plain,
! [SV1022: $i,SV492: $i,SV1791: $i,SV1482: $i] :
( ( ( ~ ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1791 = SV1022 )
= $true )
| ( ( SV1022 = SV1791 )
= $true )
| ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(4864,plain,
! [SV1792: $i,SV1483: $i,SV493: $i,SV1023: $i] :
( ( ( SV1023 = SV493 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1483 = SV493 )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(4865,plain,
! [SV1914: $i,SV1793: $i,SV1484: $i,SV1024: $i,SV494: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true )
| ( ( SV1024 = SV1793 )
= $true )
| ( ( SV494 = SV1793 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4763]) ).
thf(4866,plain,
! [SV495: $i,SV1794: $i,SV1025: $i,SV1485: $i] :
( ( ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1025 = SV1794 )
| ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(4867,plain,
! [SV1486: $i,SV496: $i,SV1795: $i,SV1026: $i] :
( ( ( SV1026 = SV1795 )
= $true )
| ( ( c_in @ ( c_Pair @ SV496 @ SV1795 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1486 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1486 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV496 @ SV1026 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1486 @ SV1026 @ SV1795 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(4868,plain,
! [SV1027: $i,SV1487: $i,SV1796: $i,SV497: $i] :
( ( ( SV497 = SV1796 )
= $true )
| ( ( ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(4869,plain,
! [SV1028: $i,SV1797: $i,SV498: $i,SV1488: $i] :
( ( ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV498 = SV1797 )
| ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV498 = SV1028 )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(4870,plain,
! [SV499: $i,SV1489: $i,SV1798: $i,SV1915: $i,SV1029: $i] :
( ( ( SV1029 = SV1915 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4768]) ).
thf(4871,plain,
! [SV1030: $i,SV1916: $i,SV1490: $i,SV1799: $i,SV500: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4769]) ).
thf(4872,plain,
! [SV1800: $i,SV502: $i,SV1492: $i,SV1032: $i,SV1917: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4771]) ).
thf(4873,plain,
! [SV1493: $i,SV1033: $i,SV503: $i] :
( ( ( SV503 = SV1033 )
= $true )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1493 @ SV503 @ SV1033 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1493 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV503 = SV1033 )
= $true )
| ( ( c_in @ ( c_Pair @ SV503 @ SV1033 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1493 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4772]) ).
thf(4874,plain,
! [SV504: $i,SV1034: $i,SV1801: $i,SV1494: $i] :
( ( ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1801 = SV1034 )
| ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV504 = SV1801 )
= $true )
| ( ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(4875,plain,
! [SV1918: $i,SV1495: $i,SV1035: $i,SV1802: $i,SV505: $i] :
( ( ( SV505 = SV1802 )
= $true )
| ( ( ( SV1035 = SV1802 )
| ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(4876,plain,
! [SV1036: $i,SV506: $i,SV1496: $i] :
( ( ( c_in @ SV1496 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV506 = SV1036 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1036 @ SV506 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV506 @ SV1036 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1496 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4877,plain,
! [SV1968: $i,SV1956: $i,SV1919: $i,SV1803: $i,SV1502: $i,SV1053: $i,SV524: $i] :
( ( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
= $false )
| ( ( ( ( hAPP @ SV524 @ SV1968 )
= ( hAPP @ SV1956 @ SV1968 ) )
| ~ ( c_in @ ( c_Pair @ SV1968 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4878,plain,
! [SV1804: $i,SV1920: $i,SV529: $i,SV1506: $i,SV1058: $i,SV1957: $i] :
( ( ( ~ ( c_in @ SV1957 @ SV1058 @ SV1506 ) )
= $true )
| ( ( SV529 = SV1920 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(4879,plain,
! [SV544: $i,SV1070: $i,SV1517: $i,SV1924: $i,SV1811: $i,SV9: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV9 @ SV1811 @ SV1924 @ SV1517 ) @ SV1070 @ ( tc_fun @ SV1517 @ tc_bool ) )
= $false )
| ( ( c_in @ SV544 @ SV1811 @ SV1924 )
= $false )
| ( ( c_in @ ( hAPP @ SV9 @ SV544 ) @ SV1070 @ SV1517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4783]) ).
thf(4880,plain,
! [SV1103: $i,SV47: $i,SV1539: $i,SV582: $i] :
( ( ( c_lessequals @ SV582 @ SV1539 @ SV47 )
= $false )
| ( ( c_lessequals @ SV1103 @ SV1539 @ SV47 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV582 @ SV1103 @ SV47 ) @ SV1539 @ SV47 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4785]) ).
thf(4881,plain,
! [SV1106: $i,SV50: $i,SV1540: $i,SV585: $i] :
( ( ( c_lessequals @ SV585 @ SV1540 @ SV50 )
= $false )
| ( ( c_lessequals @ SV1106 @ SV1540 @ SV50 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV585 @ SV1106 @ SV50 ) @ SV1540 @ SV50 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(4882,plain,
! [SV1107: $i,SV51: $i,SV1541: $i,SV586: $i] :
( ( ( c_lessequals @ SV586 @ SV1541 @ SV51 )
= $false )
| ( ( c_lessequals @ SV1107 @ SV1541 @ SV51 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV1107 @ SV51 ) @ SV1541 @ SV51 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(4883,plain,
! [SV1585: $i,SV1927: $i,SV654: $i,SV1171: $i,SV1825: $i,SV119: $i] :
( ( ( c_lessequals @ SV119 @ SV1825 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV654 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( hAPP @ SV1927 @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ SV119 @ SV654 @ SV1927 @ SV1171 @ SV1585 ) ) @ ( tc_fun @ SV1585 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV119 @ SV654 @ SV1171 @ SV1585 ) @ ( c_Product__Type_OSigma @ SV1825 @ SV1927 @ SV1171 @ SV1585 ) @ ( tc_fun @ ( tc_prod @ SV1171 @ SV1585 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4788]) ).
thf(4884,plain,
! [SV1611: $i,SV168: $i,SV1215: $i,SV702: $i] :
( ( ( c_lessequals @ SV702 @ SV1215 @ SV168 )
= $false )
| ( ( c_lessequals @ SV702 @ SV1611 @ SV168 )
= $false )
| ( ( c_lessequals @ SV702 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1215 @ SV1611 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4885,plain,
! [SV1612: $i,SV169: $i,SV1216: $i,SV703: $i] :
( ( ( c_lessequals @ SV703 @ SV1216 @ SV169 )
= $false )
| ( ( c_lessequals @ SV703 @ SV1612 @ SV169 )
= $false )
| ( ( c_lessequals @ SV703 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1216 @ SV1612 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4794]) ).
thf(4886,plain,
! [SV1613: $i,SV170: $i,SV1217: $i,SV704: $i] :
( ( ( c_lessequals @ SV704 @ SV1217 @ SV170 )
= $false )
| ( ( c_lessequals @ SV704 @ SV1613 @ SV170 )
= $false )
| ( ( c_lessequals @ SV704 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1217 @ SV1613 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(4887,plain,
! [SV745: $i,SV1637: $i,SV1255: $i,SV1839: $i,SV211: $i] :
( ( ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1637 @ SV1255 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4888,plain,
! [SV746: $i,SV1638: $i,SV1256: $i,SV1840: $i,SV212: $i] :
( ( ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1638 @ SV1256 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(4889,plain,
! [SV237: $i,SV1649: $i,SV771: $i,SV1274: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1274 @ SV771 )
= $false )
| ( ( c_lessequals @ SV1649 @ ( c_Product__Type_OSigma @ SV1274 @ ( c_COMBK @ SV1274 @ ( tc_fun @ SV771 @ tc_bool ) @ SV771 ) @ SV771 @ SV771 ) @ ( tc_fun @ ( tc_prod @ SV771 @ SV771 ) @ tc_bool ) )
= $false )
| ( ( c_in @ SV237 @ ( c_Equiv__Relations_Oquotient @ SV1274 @ SV1649 @ SV771 ) @ ( tc_fun @ SV771 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV237 @ SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(4890,plain,
! [SV1930: $i,SV811: $i,SV1669: $i,SV1310: $i,SV1852: $i,SV277: $i] :
( ( ( c_lessequals @ SV277 @ SV1852 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1669 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV811 @ SV1930 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV277 @ SV811 @ SV1310 @ SV1669 ) @ ( c_Relation_OImage @ SV1852 @ SV1930 @ SV1310 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(4891,plain,
! [SV1316: $i,SV287: $i,SV1674: $i,SV821: $i] :
( ( ( c_lessequals @ SV821 @ SV1674 @ SV287 )
= $false )
| ( ( c_lessequals @ SV1674 @ SV1316 @ SV287 )
= $false )
| ( ( c_lessequals @ SV821 @ SV1316 @ SV287 )
= $true )
| ( ( class_Orderings_Opreorder @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4892,plain,
! [SV822: $i,SV288: $i,SV1317: $i,SV1675: $i] :
( ( ( c_lessequals @ SV1675 @ SV1317 @ SV288 )
= $false )
| ( ( c_lessequals @ SV822 @ SV1675 @ SV288 )
= $false )
| ( ( c_lessequals @ SV822 @ SV1317 @ SV288 )
= $true )
| ( ( class_Orderings_Oorder @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4808]) ).
thf(4893,plain,
! [SV1325: $i,SV1931: $i,SV298: $i,SV1676: $i,SV1853: $i,SV1961: $i,SV1969: $i,SV832: $i] :
( ( ( ~ ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1969 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(4894,plain,
! [SV1677: $i,SV1854: $i,SV302: $i,SV1327: $i,SV836: $i,SV1932: $i] :
( ( ( c_in @ SV1932 @ SV836 @ SV1327 )
= $false )
| ( ( c_lessequals @ SV302 @ SV1854 @ ( tc_fun @ SV1677 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV302 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( c_Product__Type_OSigma @ SV1854 @ ( c_COMBK @ SV836 @ ( tc_fun @ SV1327 @ tc_bool ) @ SV1677 ) @ SV1677 @ SV1327 ) @ ( tc_fun @ ( tc_prod @ SV1677 @ SV1327 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(4895,plain,
! [SV837: $i,SV1328: $i,SV303: $i,SV1855: $i,SV1678: $i,SV1933: $i] :
( ( ( c_in @ SV1933 @ SV1678 @ SV1855 )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV303 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( c_Product__Type_OSigma @ SV837 @ ( c_COMBK @ SV1678 @ ( tc_fun @ SV1855 @ tc_bool ) @ SV1328 ) @ SV1328 @ SV1855 ) @ ( tc_fun @ ( tc_prod @ SV1328 @ SV1855 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV303 @ SV837 @ ( tc_fun @ SV1328 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4896,plain,
! [SV1330: $i,SV1934: $i,SV306: $i,SV1856: $i,SV1679: $i,SV1962: $i,SV840: $i] :
( ( ( c_lessequals @ SV840 @ SV1962 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SV1962 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4815]) ).
thf(4897,plain,
! [SV845: $i,SV1858: $i,SV1334: $i,SV1682: $i,SV311: $i] :
( ( ( c_in @ ( c_Pair @ SV311 @ SV1682 @ SV1334 @ SV1334 ) @ ( c_Transitive__Closure_Ortrancl @ SV1858 @ SV1334 ) @ ( tc_prod @ SV1334 @ SV1334 ) )
= $false )
| ( ( c_lessequals @ SV1858 @ ( c_Product__Type_OSigma @ SV845 @ ( c_COMBK @ SV845 @ ( tc_fun @ SV1334 @ tc_bool ) @ SV1334 ) @ SV1334 @ SV1334 ) @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) )
= $false )
| ( ( SV311 = SV1682 )
= $true )
| ( ( c_in @ SV311 @ SV845 @ SV1334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(4898,plain,
! [SV865: $i,SV1938: $i,SV1698: $i,SV1354: $i,SV1865: $i,SV331: $i] :
( ( ( c_in @ SV331 @ ( c_FuncSet_OPi @ SV1865 @ ( c_COMBK @ SV1354 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1938 ) @ SV1938 @ SV1698 ) @ ( tc_fun @ SV1938 @ SV1698 ) )
= $false )
| ( ( c_in @ SV865 @ SV1865 @ SV1938 )
= $false )
| ( ( c_in @ ( hAPP @ SV331 @ SV865 ) @ SV1354 @ SV1698 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(4899,plain,
! [SV345: $i,SV1704: $i,SV1364: $i,SV879: $i,SV1870: $i] :
( ( ( ~ ( c_in @ SV1870 @ SV879 @ SV1364 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false )
| ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4823]) ).
thf(4900,plain,
! [SV346: $i,SV1705: $i,SV1365: $i,SV880: $i,SV1871: $i] :
( ( ( ~ ( c_in @ SV1871 @ SV880 @ SV1365 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
= $false )
| ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4824]) ).
thf(4901,plain,
! [SV353: $i,SV1372: $i,SV1874: $i,SV1711: $i,SV887: $i] :
( ( ( c_in @ SV887 @ ( c_Wellfounded_Oacc @ SV1711 @ SV1874 ) @ SV1874 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1372 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV353 @ SV1711 @ SV1874 ) @ SV1874 @ SV1874 ) @ SV1711 @ ( tc_prod @ SV1874 @ SV1874 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV1372 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV353 @ SV887 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4902,plain,
! [SV361: $i,SV1380: $i,SV1875: $i,SV1718: $i,SV895: $i] :
( ( ( c_in @ SV895 @ ( c_Wellfounded_Oacc @ SV1718 @ SV1875 ) @ SV1875 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1380 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV361 @ SV1718 @ SV1875 ) @ SV1875 @ SV1875 ) @ SV1718 @ ( tc_prod @ SV1875 @ SV1875 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV1380 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(4903,plain,
! [SV1887: $i,SV1424: $i,SV424: $i,SV1945: $i,SV1742: $i,SV1966: $i,SV956: $i,SV1970: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1970 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV424 @ SV1970 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4834]) ).
thf(4904,plain,
! [SV961: $i,SV1745: $i,SV1946: $i,SV1427: $i,SV1890: $i,SV429: $i] :
( ( ( c_in @ SV429 @ ( c_FuncSet_OPi @ SV1890 @ SV1427 @ SV1946 @ SV1745 ) @ ( tc_fun @ SV1946 @ SV1745 ) )
= $false )
| ( ( c_in @ SV961 @ SV1890 @ SV1946 )
= $false )
| ( ( c_in @ ( hAPP @ SV429 @ SV961 ) @ ( hAPP @ SV1427 @ SV961 ) @ SV1745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(4905,plain,
! [SV430: $i,SV1947: $i,SV1428: $i,SV1891: $i,SV962: $i,SV1746: $i] :
( ( ( c_in @ SV1746 @ ( c_FuncSet_OPi @ SV962 @ SV1891 @ SV1428 @ SV1947 ) @ ( tc_fun @ SV1428 @ SV1947 ) )
= $false )
| ( ( c_in @ ( hAPP @ SV1746 @ SV430 ) @ ( hAPP @ SV1891 @ SV430 ) @ SV1947 )
= $true )
| ( ( c_in @ SV430 @ SV962 @ SV1428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(4906,plain,
! [SV1967: $i,SV431: $i,SV963: $i,SV1948: $i,SV1892: $i,SV1747: $i,SV1429: $i] :
( ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( ~ ( c_in @ SV1747 @ SV963 @ SV1892 )
| ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4839]) ).
thf(4907,plain,
! [SV432: $i,SV1949: $i,SV1893: $i,SV1430: $i,SV964: $i,SV1748: $i] :
( ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4840]) ).
thf(4908,plain,
! [SV1757: $i,SV1950: $i,SV985: $i,SV1445: $i,SV1894: $i,SV455: $i] :
( ( ( c_in @ SV455 @ SV1894 @ SV1445 )
= $false )
| ( ( c_in @ SV985 @ ( hAPP @ SV1950 @ SV455 ) @ SV1757 )
= $false )
| ( ( c_in @ ( c_Pair @ SV455 @ SV985 @ SV1445 @ SV1757 ) @ ( c_Product__Type_OSigma @ SV1894 @ SV1950 @ SV1445 @ SV1757 ) @ ( tc_prod @ SV1445 @ SV1757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4909,plain,
! [SV1758: $i,SV1951: $i,SV986: $i,SV1446: $i,SV1895: $i,SV456: $i] :
( ( ( c_in @ SV456 @ SV1895 @ SV1446 )
= $false )
| ( ( c_in @ SV986 @ ( hAPP @ SV1951 @ SV456 ) @ SV1758 )
= $false )
| ( ( c_in @ ( c_Pair @ SV456 @ SV986 @ SV1446 @ SV1758 ) @ ( c_Product__Type_OSigma @ SV1895 @ SV1951 @ SV1446 @ SV1758 ) @ ( tc_prod @ SV1446 @ SV1758 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4842]) ).
thf(4910,plain,
! [SV989: $i,SV1896: $i,SV459: $i,SV1761: $i,SV1449: $i,SV1952: $i] :
( ( ( c_in @ SV1952 @ SV1449 @ SV1761 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1952 @ SV459 @ SV1761 @ SV1896 ) @ SV989 @ ( tc_prod @ SV1761 @ SV1896 ) )
= $false )
| ( ( c_in @ SV459 @ ( c_Relation_OImage @ SV989 @ SV1449 @ SV1761 @ SV1896 ) @ SV1896 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4911,plain,
! [SV990: $i,SV1897: $i,SV460: $i,SV1762: $i,SV1450: $i,SV1953: $i] :
( ( ( c_in @ SV1953 @ SV1450 @ SV1762 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1953 @ SV460 @ SV1762 @ SV1897 ) @ SV990 @ ( tc_prod @ SV1762 @ SV1897 ) )
= $false )
| ( ( c_in @ SV460 @ ( c_Relation_OImage @ SV990 @ SV1450 @ SV1762 @ SV1897 ) @ SV1897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4844]) ).
thf(4912,plain,
! [SV1772: $i,SV1001: $i,SV1461: $i,SV1906: $i,SV471: $i] :
( ( ( c_in @ SV471 @ SV1906 @ SV1461 )
= $false )
| ( ( ~ ( c_in @ SV1001 @ SV1906 @ SV1461 )
| ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( SV1001 = SV471 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(4913,plain,
! [SV477: $i,SV1778: $i,SV1007: $i,SV1467: $i] :
( ( ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1007 = SV1778 )
| ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(4914,plain,
! [SV1008: $i,SV1779: $i,SV1468: $i,SV478: $i] :
( ( ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV478 = SV1008 )
= $true )
| ( ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV478 = SV1468 )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4851]) ).
thf(4915,plain,
! [SV1780: $i,SV1909: $i,SV1469: $i,SV1009: $i,SV479: $i] :
( ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1909 = SV1780 ) )
= $true )
| ( ( SV479 = SV1780 )
= $true )
| ( ( SV1009 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4916,plain,
! [SV1470: $i,SV480: $i,SV1010: $i,SV1781: $i] :
( ( ( SV1781 = SV1010 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV480 = SV1781 ) )
= $true )
| ( ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(4917,plain,
! [SV1012: $i,SV482: $i,SV1783: $i,SV1472: $i] :
( ( ( ~ ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1783 = SV1012 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(4918,plain,
! [SV1473: $i,SV483: $i,SV1013: $i,SV1784: $i] :
( ( ( SV1784 = SV1013 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV483 = SV1013 )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4856]) ).
thf(4919,plain,
! [SV1785: $i,SV1014: $i,SV1474: $i,SV1910: $i,SV484: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( SV484 = SV1785 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(4920,plain,
! [SV485: $i,SV1786: $i,SV1475: $i,SV1015: $i,SV1911: $i] :
( ( ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1015 = SV1786 )
| ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(4921,plain,
! [SV1912: $i,SV1017: $i,SV1477: $i,SV1787: $i,SV487: $i] :
( ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(4922,plain,
! [SV1479: $i,SV1019: $i,SV1788: $i,SV489: $i] :
( ( ( SV489 = SV1788 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1788 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1479 @ SV489 @ SV1788 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1479 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1788 = SV1019 )
= $true )
| ( ( c_in @ ( c_Pair @ SV489 @ SV1019 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1479 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(4923,plain,
! [SV1789: $i,SV1480: $i,SV1020: $i,SV1913: $i,SV490: $i] :
( ( ( SV490 = SV1913 )
= $true )
| ( ( ( SV490 = SV1020 )
| ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true )
| ( ( SV1020 = SV1913 )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(4924,plain,
! [SV1022: $i,SV492: $i,SV1791: $i,SV1482: $i] :
( ( ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1791 = SV492 )
| ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1791 = SV1022 )
= $true )
| ( ( SV1022 = SV1791 )
= $true )
| ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(4925,plain,
! [SV1023: $i,SV1792: $i,SV493: $i,SV1483: $i] :
( ( ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1023 = SV493 )
= $true )
| ( ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1483 = SV493 )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(4926,plain,
! [SV1914: $i,SV1793: $i,SV1484: $i,SV1024: $i,SV494: $i] :
( ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1793 = SV1914 ) )
= $true )
| ( ( SV1024 = SV1793 )
= $true )
| ( ( SV494 = SV1793 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(4927,plain,
! [SV1485: $i,SV495: $i,SV1794: $i,SV1025: $i] :
( ( ( SV1025 = SV1794 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV495 = SV1794 ) )
= $true )
| ( ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(4928,plain,
! [SV497: $i,SV1796: $i,SV1027: $i,SV1487: $i] :
( ( ( ~ ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV497 = SV1796 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(4929,plain,
! [SV1488: $i,SV1028: $i,SV1797: $i,SV498: $i] :
( ( ( SV498 = SV1797 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV498 = SV1028 )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4869]) ).
thf(4930,plain,
! [SV1915: $i,SV499: $i,SV1489: $i,SV1029: $i,SV1798: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( SV1029 = SV1915 )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(4931,plain,
! [SV1030: $i,SV1916: $i,SV1490: $i,SV1799: $i,SV500: $i] :
( ( ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV500 = SV1916 )
| ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4871]) ).
thf(4932,plain,
! [SV1800: $i,SV502: $i,SV1492: $i,SV1032: $i,SV1917: $i] :
( ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(4933,plain,
! [SV1494: $i,SV504: $i,SV1034: $i,SV1801: $i] :
( ( ( SV1801 = SV1034 )
= $true )
| ( ( c_in @ ( c_Pair @ SV504 @ SV1801 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1494 @ SV1801 @ SV1034 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1494 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV504 = SV1801 )
= $true )
| ( ( c_in @ ( c_Pair @ SV504 @ SV1034 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1494 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(4934,plain,
! [SV1918: $i,SV1495: $i,SV505: $i,SV1802: $i,SV1035: $i] :
( ( ( SV1035 = SV1802 )
= $true )
| ( ( ( SV505 = SV1035 )
| ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true )
| ( ( SV505 = SV1802 )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(4935,plain,
! [SV1919: $i,SV1053: $i,SV1803: $i,SV1502: $i,SV1956: $i,SV1968: $i,SV524: $i] :
( ( ( ( hAPP @ SV524 @ SV1968 )
= ( hAPP @ SV1956 @ SV1968 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1968 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(4936,plain,
! [SV1804: $i,SV1920: $i,SV529: $i,SV1506: $i,SV1058: $i,SV1957: $i] :
( ( ( c_in @ SV1957 @ SV1058 @ SV1506 )
= $false )
| ( ( SV529 = SV1920 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV529 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 )
= ( c_Product__Type_OSigma @ SV1920 @ ( c_COMBK @ SV1058 @ ( tc_fun @ SV1506 @ tc_bool ) @ SV1804 ) @ SV1804 @ SV1506 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(4937,plain,
! [SV745: $i,SV1839: $i,SV211: $i,SV1255: $i,SV1637: $i] :
( ( ( c_Relation_Otrans @ SV1637 @ SV1255 )
= $false )
| ( ( c_in @ ( c_Pair @ SV211 @ SV1839 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1839 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV211 @ SV745 @ SV1255 @ SV1255 ) @ SV1637 @ ( tc_prod @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(4938,plain,
! [SV746: $i,SV1840: $i,SV212: $i,SV1256: $i,SV1638: $i] :
( ( ( c_Relation_Otrans @ SV1638 @ SV1256 )
= $false )
| ( ( c_in @ ( c_Pair @ SV212 @ SV1840 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1840 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV212 @ SV746 @ SV1256 @ SV1256 ) @ SV1638 @ ( tc_prod @ SV1256 @ SV1256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(4939,plain,
! [SV1325: $i,SV1931: $i,SV298: $i,SV1676: $i,SV1853: $i,SV1961: $i,SV1969: $i,SV832: $i] :
( ( ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1969 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(4940,plain,
! [SV1856: $i,SV1962: $i,SV840: $i,SV1679: $i,SV1330: $i,SV1934: $i,SV306: $i] :
( ( ( c_lessequals @ SV306 @ SV1934 @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1679 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV840 @ SV1962 @ ( tc_fun @ ( tc_prod @ SV1679 @ SV1856 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV306 @ SV840 @ SV1330 @ SV1679 @ SV1856 ) @ ( c_Relation_Orel__comp @ SV1934 @ SV1962 @ SV1330 @ SV1679 @ SV1856 ) @ ( tc_fun @ ( tc_prod @ SV1330 @ SV1856 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4896]) ).
thf(4941,plain,
! [SV345: $i,SV1704: $i,SV1364: $i,SV879: $i,SV1870: $i] :
( ( ( c_in @ SV1870 @ SV879 @ SV1364 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1704 @ SV1364 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false )
| ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(4942,plain,
! [SV346: $i,SV1705: $i,SV1365: $i,SV880: $i,SV1871: $i] :
( ( ( c_in @ SV1871 @ SV880 @ SV1365 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1705 @ SV1365 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
= $false )
| ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(4943,plain,
! [SV1887: $i,SV1424: $i,SV424: $i,SV1945: $i,SV1742: $i,SV1966: $i,SV956: $i,SV1970: $i] :
( ( ( c_in @ ( c_Pair @ SV1970 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV424 @ SV1970 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(4944,plain,
! [SV1948: $i,SV1967: $i,SV431: $i,SV1429: $i,SV1892: $i,SV963: $i,SV1747: $i] :
( ( ( ~ ( c_in @ SV1747 @ SV963 @ SV1892 ) )
= $true )
| ( ( ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(4945,plain,
! [SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i,SV964: $i] :
( ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(4946,plain,
! [SV471: $i,SV1772: $i,SV1461: $i,SV1906: $i,SV1001: $i] :
( ( ( ~ ( c_in @ SV1001 @ SV1906 @ SV1461 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( c_in @ SV471 @ SV1906 @ SV1461 )
= $false )
| ( ( SV1001 = SV471 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(4947,plain,
! [SV1467: $i,SV477: $i,SV1778: $i,SV1007: $i] :
( ( ( SV1007 = SV1778 )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1778 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1467 @ SV1007 @ SV1778 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1467 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV477 = SV1778 )
= $true )
| ( ( SV477 = SV1778 )
= $true )
| ( ( c_in @ ( c_Pair @ SV477 @ SV1007 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1467 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(4948,plain,
! [SV1008: $i,SV1779: $i,SV1468: $i,SV478: $i] :
( ( ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1779 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV478 @ SV1468 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1779 @ SV478 @ SV1008 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV478 = SV1008 )
= $true )
| ( ( c_in @ SV1779 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV478 = SV1468 )
= $true )
| ( ( SV478 = SV1008 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4914]) ).
thf(4949,plain,
! [SV1009: $i,SV479: $i,SV1780: $i,SV1909: $i,SV1469: $i] :
( ( ( ~ ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1909 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV479 = SV1780 )
= $true )
| ( ( SV1009 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(4950,plain,
! [SV1010: $i,SV1470: $i,SV1781: $i,SV480: $i] :
( ( ( c_in @ ( c_Pair @ SV480 @ SV1781 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1470 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV480 = SV1781 )
= $true )
| ( ( SV1781 = SV1010 )
= $true )
| ( ( c_in @ SV1470 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV480 @ SV1010 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1470 @ SV1781 @ SV1010 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV480 = SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4916]) ).
thf(4951,plain,
! [SV1012: $i,SV482: $i,SV1783: $i,SV1472: $i] :
( ( ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1783 = SV482 )
| ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1783 = SV1012 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4917]) ).
thf(4952,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV1784 = SV1013 )
= $true )
| ( ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV483 = SV1013 )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(4953,plain,
! [SV1785: $i,SV1014: $i,SV1474: $i,SV1910: $i,SV484: $i] :
( ( ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV484 = SV1014 )
| ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( SV484 = SV1785 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4919]) ).
thf(4954,plain,
! [SV1911: $i,SV1475: $i,SV485: $i,SV1786: $i,SV1015: $i] :
( ( ( SV1015 = SV1786 )
= $true )
| ( ( ( SV485 = SV1015 )
| ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(4955,plain,
! [SV1912: $i,SV487: $i,SV1477: $i,SV1017: $i,SV1787: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(4956,plain,
! [SV1913: $i,SV1789: $i,SV1480: $i,SV1020: $i,SV490: $i] :
( ( ( SV490 = SV1020 )
= $true )
| ( ( ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1789 = SV1913 ) )
= $true )
| ( ( SV490 = SV1913 )
= $true )
| ( ( SV1020 = SV1913 )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(4957,plain,
! [SV1482: $i,SV1022: $i,SV492: $i,SV1791: $i] :
( ( ( SV1791 = SV492 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1791 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1482 @ SV1791 @ SV492 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1482 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1791 = SV1022 )
= $true )
| ( ( SV1022 = SV1791 )
= $true )
| ( ( c_in @ ( c_Pair @ SV492 @ SV1022 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1482 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4924]) ).
thf(4958,plain,
! [SV1023: $i,SV1792: $i,SV493: $i,SV1483: $i] :
( ( ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1792 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1483 @ SV493 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1792 @ SV1023 @ SV493 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV1023 = SV493 )
= $true )
| ( ( c_in @ SV1792 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1483 = SV493 )
= $true )
| ( ( SV493 = SV1023 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(4959,plain,
! [SV1024: $i,SV494: $i,SV1914: $i,SV1793: $i,SV1484: $i] :
( ( ( ~ ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1793 = SV1914 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1024 = SV1793 )
= $true )
| ( ( SV494 = SV1793 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(4960,plain,
! [SV1025: $i,SV1485: $i,SV495: $i,SV1794: $i] :
( ( ( c_in @ ( c_Pair @ SV1794 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1485 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV495 = SV1794 )
= $true )
| ( ( SV1025 = SV1794 )
= $true )
| ( ( c_in @ SV1485 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1025 @ SV495 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1485 @ SV1025 @ SV1794 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV495 = SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(4961,plain,
! [SV497: $i,SV1796: $i,SV1027: $i,SV1487: $i] :
( ( ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( ( SV1027 = SV1796 )
| ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV497 = SV1796 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(4962,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV498 = SV1797 )
= $true )
| ( ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV498 = SV1028 )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(4963,plain,
! [SV1915: $i,SV499: $i,SV1489: $i,SV1029: $i,SV1798: $i] :
( ( ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV499 = SV1029 )
| ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( SV1029 = SV1915 )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(4964,plain,
! [SV1799: $i,SV1490: $i,SV1030: $i,SV1916: $i,SV500: $i] :
( ( ( SV500 = SV1916 )
= $true )
| ( ( ( SV500 = SV1030 )
| ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(4965,plain,
! [SV1800: $i,SV1032: $i,SV1492: $i,SV1917: $i,SV502: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(4966,plain,
! [SV1918: $i,SV1802: $i,SV1495: $i,SV1035: $i,SV505: $i] :
( ( ( SV505 = SV1035 )
= $true )
| ( ( ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1802 = SV1918 ) )
= $true )
| ( ( SV1035 = SV1802 )
= $true )
| ( ( SV505 = SV1802 )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(4967,plain,
! [SV1919: $i,SV1956: $i,SV524: $i,SV1053: $i,SV1803: $i,SV1502: $i,SV1968: $i] :
( ( ( c_in @ ( c_Pair @ SV1968 @ SV1502 @ SV1803 @ SV1803 ) @ SV1053 @ ( tc_prod @ SV1803 @ SV1803 ) )
= $false )
| ( ( ( hAPP @ SV524 @ SV1968 )
= ( hAPP @ SV1956 @ SV1968 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV524 @ SV1053 @ SV1502 @ SV1803 @ SV1919 )
= ( c_Recdef_Ocut @ SV1956 @ SV1053 @ SV1502 @ SV1803 @ SV1919 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4935]) ).
thf(4968,plain,
! [SV1853: $i,SV1961: $i,SV832: $i,SV1325: $i,SV1676: $i,SV1969: $i,SV1931: $i,SV298: $i] :
( ( ( c_lessequals @ SV298 @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1969 @ ( tc_fun @ SV1676 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1676 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1676 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV832 @ ( c_Product__Type_OSigma @ SV1969 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1676 ) @ SV1676 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1676 @ SV1853 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV298 @ SV832 @ SV1325 @ SV1676 @ SV1853 ) @ ( c_Product__Type_OSigma @ SV1931 @ ( c_COMBK @ SV1961 @ ( tc_fun @ SV1853 @ tc_bool ) @ SV1325 ) @ SV1325 @ SV1853 ) @ ( tc_fun @ ( tc_prod @ SV1325 @ SV1853 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4939]) ).
thf(4969,plain,
! [SV345: $i,SV879: $i,SV1870: $i,SV1364: $i,SV1704: $i] :
( ( ( c_Wellfounded_Owf @ SV1704 @ SV1364 )
= $false )
| ( ( c_in @ SV1870 @ SV879 @ SV1364 )
= $false )
| ( ( c_in @ ( c_Pair @ SV345 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV879 @ SV1704 @ SV1364 ) @ SV1364 @ SV1364 ) @ SV1704 @ ( tc_prod @ SV1364 @ SV1364 ) )
= $false )
| ( ( c_in @ SV345 @ SV879 @ SV1364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4941]) ).
thf(4970,plain,
! [SV346: $i,SV880: $i,SV1871: $i,SV1365: $i,SV1705: $i] :
( ( ( c_Wellfounded_Owf @ SV1705 @ SV1365 )
= $false )
| ( ( c_in @ SV1871 @ SV880 @ SV1365 )
= $false )
| ( ( c_in @ ( c_Pair @ SV346 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV880 @ SV1705 @ SV1365 ) @ SV1365 @ SV1365 ) @ SV1705 @ ( tc_prod @ SV1365 @ SV1365 ) )
= $false )
| ( ( c_in @ SV346 @ SV880 @ SV1365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(4971,plain,
! [SV1945: $i,SV1742: $i,SV956: $i,SV1887: $i,SV1966: $i,SV1424: $i,SV1970: $i,SV424: $i] :
( ( ( c_in @ ( c_Pair @ SV424 @ SV1970 @ SV1424 @ SV1966 ) @ SV1887 @ ( tc_prod @ SV1424 @ SV1966 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1970 @ SV956 @ SV1966 @ SV1742 ) @ SV1945 @ ( tc_prod @ SV1966 @ SV1742 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV424 @ SV956 @ SV1424 @ SV1742 ) @ ( c_Relation_Orel__comp @ SV1887 @ SV1945 @ SV1424 @ SV1966 @ SV1742 ) @ ( tc_prod @ SV1424 @ SV1742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(4972,plain,
! [SV1948: $i,SV1967: $i,SV431: $i,SV1429: $i,SV1892: $i,SV963: $i,SV1747: $i] :
( ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( ~ ( c_in @ SV1429 @ SV431 @ SV1892 )
| ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(4973,plain,
! [SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i,SV964: $i] :
( ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(4974,plain,
! [SV471: $i,SV1772: $i,SV1461: $i,SV1906: $i,SV1001: $i] :
( ( ( c_in @ SV1001 @ SV1906 @ SV1461 )
= $false )
| ( ( ~ ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 ) )
= $true )
| ( ( c_in @ SV471 @ SV1906 @ SV1461 )
= $false )
| ( ( SV1001 = SV471 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(4975,plain,
! [SV1009: $i,SV479: $i,SV1780: $i,SV1909: $i,SV1469: $i] :
( ( ( c_in @ SV1469 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1909 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1469 @ SV1909 @ SV1780 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV479 = SV1780 )
= $true )
| ( ( SV1009 = SV1780 )
= $true )
| ( ( c_in @ ( c_Pair @ SV479 @ SV1009 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1469 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(4976,plain,
! [SV1472: $i,SV1012: $i,SV482: $i,SV1783: $i] :
( ( ( SV1783 = SV482 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1783 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1472 @ SV1783 @ SV482 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1472 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1783 = SV1012 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1783 @ SV482 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV482 @ SV1012 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1472 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4951]) ).
thf(4977,plain,
! [SV1784: $i,SV1473: $i,SV1013: $i,SV483: $i] :
( ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1473 @ SV1784 @ SV1013 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV1784 = SV1013 )
= $true )
| ( ( c_in @ SV1473 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV483 = SV1013 )
= $true )
| ( ( c_in @ ( c_Pair @ SV483 @ SV1013 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1473 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(4978,plain,
! [SV1910: $i,SV1785: $i,SV1474: $i,SV1014: $i,SV484: $i] :
( ( ( SV484 = SV1014 )
= $true )
| ( ( ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1785 = SV1910 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV484 = SV1785 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(4979,plain,
! [SV1911: $i,SV1786: $i,SV1475: $i,SV1015: $i,SV485: $i] :
( ( ( SV485 = SV1015 )
= $true )
| ( ( ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1786 = SV1911 ) )
= $true )
| ( ( SV1015 = SV1786 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(4980,plain,
! [SV1912: $i,SV487: $i,SV1477: $i,SV1017: $i,SV1787: $i] :
( ( ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV487 = SV1017 )
| ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(4981,plain,
! [SV1020: $i,SV490: $i,SV1913: $i,SV1789: $i,SV1480: $i] :
( ( ( ~ ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1789 = SV1913 )
= $true )
| ( ( SV490 = SV1020 )
= $true )
| ( ( SV490 = SV1913 )
= $true )
| ( ( SV1020 = SV1913 )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(4982,plain,
! [SV1024: $i,SV494: $i,SV1914: $i,SV1793: $i,SV1484: $i] :
( ( ( c_in @ SV1484 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1793 = SV1914 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1484 @ SV1793 @ SV1914 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1024 = SV1793 )
= $true )
| ( ( SV494 = SV1793 )
= $true )
| ( ( c_in @ ( c_Pair @ SV494 @ SV1024 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1484 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4959]) ).
thf(4983,plain,
! [SV1487: $i,SV497: $i,SV1796: $i,SV1027: $i] :
( ( ( SV1027 = SV1796 )
= $true )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1487 @ SV1027 @ SV1796 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( c_in @ SV1487 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV497 = SV1796 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1027 @ SV1796 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV497 @ SV1027 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1487 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(4984,plain,
! [SV1797: $i,SV1488: $i,SV1028: $i,SV498: $i] :
( ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1488 @ SV498 @ SV1797 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV498 = SV1797 )
= $true )
| ( ( c_in @ SV1488 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV498 = SV1028 )
= $true )
| ( ( c_in @ ( c_Pair @ SV498 @ SV1028 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1488 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(4985,plain,
! [SV1915: $i,SV1798: $i,SV1489: $i,SV1029: $i,SV499: $i] :
( ( ( SV499 = SV1029 )
= $true )
| ( ( ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1798 = SV1915 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1029 = SV1915 )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4963]) ).
thf(4986,plain,
! [SV1916: $i,SV1799: $i,SV1490: $i,SV1030: $i,SV500: $i] :
( ( ( SV500 = SV1030 )
= $true )
| ( ( ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1799 = SV1916 ) )
= $true )
| ( ( SV500 = SV1916 )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(4987,plain,
! [SV1800: $i,SV1032: $i,SV1492: $i,SV1917: $i,SV502: $i] :
( ( ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV502 = SV1032 )
| ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(4988,plain,
! [SV1035: $i,SV505: $i,SV1918: $i,SV1802: $i,SV1495: $i] :
( ( ( ~ ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1802 = SV1918 )
= $true )
| ( ( SV505 = SV1035 )
= $true )
| ( ( SV1035 = SV1802 )
= $true )
| ( ( SV505 = SV1802 )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4966]) ).
thf(4989,plain,
! [SV1747: $i,SV1948: $i,SV1967: $i,SV963: $i,SV1892: $i,SV431: $i,SV1429: $i] :
( ( ( ~ ( c_in @ SV1429 @ SV431 @ SV1892 ) )
= $true )
| ( ( ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(4990,plain,
! [SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i,SV964: $i] :
( ( ( ~ ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(4991,plain,
! [SV471: $i,SV1001: $i,SV1461: $i,SV1772: $i,SV1906: $i] :
( ( ( c_Relation_Ototal__on @ SV1906 @ SV1772 @ SV1461 )
= $false )
| ( ( c_in @ SV1001 @ SV1906 @ SV1461 )
= $false )
| ( ( c_in @ SV471 @ SV1906 @ SV1461 )
= $false )
| ( ( SV1001 = SV471 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1001 @ SV471 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV471 @ SV1001 @ SV1461 @ SV1461 ) @ SV1772 @ ( tc_prod @ SV1461 @ SV1461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(4992,plain,
! [SV1014: $i,SV484: $i,SV1910: $i,SV1785: $i,SV1474: $i] :
( ( ( ~ ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1785 = SV1910 )
= $true )
| ( ( SV484 = SV1014 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV484 = SV1785 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(4993,plain,
! [SV1015: $i,SV485: $i,SV1911: $i,SV1786: $i,SV1475: $i] :
( ( ( ~ ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1786 = SV1911 )
= $true )
| ( ( SV485 = SV1015 )
= $true )
| ( ( SV1015 = SV1786 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(4994,plain,
! [SV1912: $i,SV1787: $i,SV1477: $i,SV1017: $i,SV487: $i] :
( ( ( SV487 = SV1017 )
= $true )
| ( ( ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1787 = SV1912 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(4995,plain,
! [SV1020: $i,SV490: $i,SV1913: $i,SV1789: $i,SV1480: $i] :
( ( ( c_in @ SV1480 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1789 = SV1913 )
= $true )
| ( ( SV490 = SV1020 )
= $true )
| ( ( SV490 = SV1913 )
= $true )
| ( ( SV1020 = SV1913 )
= $true )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1480 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV490 @ SV1020 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1480 @ SV1789 @ SV1913 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(4996,plain,
! [SV1029: $i,SV499: $i,SV1915: $i,SV1798: $i,SV1489: $i] :
( ( ( ~ ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1798 = SV1915 )
= $true )
| ( ( SV499 = SV1029 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1029 = SV1915 )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(4997,plain,
! [SV1030: $i,SV500: $i,SV1916: $i,SV1799: $i,SV1490: $i] :
( ( ( ~ ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1799 = SV1916 )
= $true )
| ( ( SV500 = SV1030 )
= $true )
| ( ( SV500 = SV1916 )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(4998,plain,
! [SV1917: $i,SV1800: $i,SV1492: $i,SV1032: $i,SV502: $i] :
( ( ( SV502 = SV1032 )
= $true )
| ( ( ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( SV1800 = SV1917 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4987]) ).
thf(4999,plain,
! [SV1035: $i,SV505: $i,SV1918: $i,SV1802: $i,SV1495: $i] :
( ( ( c_in @ SV1495 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1802 = SV1918 )
= $true )
| ( ( SV505 = SV1035 )
= $true )
| ( ( SV1035 = SV1802 )
= $true )
| ( ( SV505 = SV1802 )
= $true )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1495 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV505 @ SV1035 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1495 @ SV1802 @ SV1918 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5000,plain,
! [SV1747: $i,SV1948: $i,SV1967: $i,SV963: $i,SV1892: $i,SV431: $i,SV1429: $i] :
( ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5001,plain,
! [SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i,SV964: $i] :
( ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
| ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) ) )
= $true )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5002,plain,
! [SV1014: $i,SV484: $i,SV1910: $i,SV1785: $i,SV1474: $i] :
( ( ( c_in @ SV1474 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1785 = SV1910 )
= $true )
| ( ( SV484 = SV1014 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1910 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV484 = SV1785 )
= $true )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1474 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV484 @ SV1014 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1474 @ SV1785 @ SV1910 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4992]) ).
thf(5003,plain,
! [SV1015: $i,SV485: $i,SV1911: $i,SV1786: $i,SV1475: $i] :
( ( ( c_in @ SV1475 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1786 = SV1911 )
= $true )
| ( ( SV485 = SV1015 )
= $true )
| ( ( SV1015 = SV1786 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1911 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1475 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV485 @ SV1015 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1475 @ SV1786 @ SV1911 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5004,plain,
! [SV1017: $i,SV487: $i,SV1912: $i,SV1787: $i,SV1477: $i] :
( ( ( ~ ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1787 = SV1912 )
= $true )
| ( ( SV487 = SV1017 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(5005,plain,
! [SV1029: $i,SV499: $i,SV1915: $i,SV1798: $i,SV1489: $i] :
( ( ( c_in @ SV1489 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1798 = SV1915 )
= $true )
| ( ( SV499 = SV1029 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1798 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1029 = SV1915 )
= $true )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1489 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV499 @ SV1029 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1489 @ SV1798 @ SV1915 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4996]) ).
thf(5006,plain,
! [SV1030: $i,SV500: $i,SV1916: $i,SV1799: $i,SV1490: $i] :
( ( ( c_in @ SV1490 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1799 = SV1916 )
= $true )
| ( ( SV500 = SV1030 )
= $true )
| ( ( SV500 = SV1916 )
= $true )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1799 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1490 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV500 @ SV1030 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1490 @ SV1799 @ SV1916 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4997]) ).
thf(5007,plain,
! [SV1032: $i,SV502: $i,SV1917: $i,SV1800: $i,SV1492: $i] :
( ( ( ~ ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
= $true )
| ( ( SV1800 = SV1917 )
= $true )
| ( ( SV502 = SV1032 )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4998]) ).
thf(5008,plain,
! [SV1747: $i,SV1429: $i,SV431: $i,SV1892: $i,SV1948: $i,SV1967: $i,SV963: $i] :
( ( ( ~ ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(5009,plain,
! [SV964: $i,SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) )
= $true )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(5010,plain,
! [SV1017: $i,SV487: $i,SV1912: $i,SV1787: $i,SV1477: $i] :
( ( ( c_in @ SV1477 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1787 = SV1912 )
= $true )
| ( ( SV487 = SV1017 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1787 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1787 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1477 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV487 @ SV1017 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ SV1477 @ SV1787 @ SV1912 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5004]) ).
thf(5011,plain,
! [SV1032: $i,SV502: $i,SV1917: $i,SV1800: $i,SV1492: $i] :
( ( ( c_in @ SV1492 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
= $false )
| ( ( SV1800 = SV1917 )
= $true )
| ( ( SV502 = SV1032 )
= $true )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1917 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1917 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1492 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV502 @ SV1032 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ SV1492 @ SV1800 @ SV1917 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5012,plain,
! [SV1747: $i,SV1429: $i,SV431: $i,SV1892: $i,SV1948: $i,SV1967: $i,SV963: $i] :
( ( ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5013,plain,
! [SV964: $i,SV432: $i,SV1748: $i,SV1430: $i,SV1949: $i,SV1893: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1893 @ SV1949 @ SV1430 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1748 @ SV432 @ SV1430 @ SV1430 ) @ SV1949 @ ( tc_prod @ SV1430 @ SV1430 ) )
= $true )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV964 @ ( c_Equiv__Relations_Oquotient @ SV1893 @ SV1949 @ SV1430 ) @ ( tc_fun @ SV1430 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1748 @ SV964 @ SV1430 )
= $false )
| ( ( c_in @ SV432 @ SV964 @ SV1430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5014,plain,
! [SV1747: $i,SV1429: $i,SV963: $i,SV1892: $i,SV1948: $i,SV1967: $i,SV431: $i] :
( ( ( ~ ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5012]) ).
thf(5015,plain,
! [SV1747: $i,SV1429: $i,SV963: $i,SV1892: $i,SV1948: $i,SV1967: $i,SV431: $i] :
( ( ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 ) )
= $true )
| ( ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5014]) ).
thf(5016,plain,
! [SV1747: $i,SV1429: $i,SV963: $i,SV431: $i,SV1892: $i,SV1948: $i,SV1967: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1967 @ SV1948 @ SV1892 )
= $false )
| ( ( c_in @ SV431 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( c_in @ SV963 @ ( c_Equiv__Relations_Oquotient @ SV1967 @ SV1948 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( c_in @ SV1429 @ SV431 @ SV1892 )
= $false )
| ( ( c_in @ SV1747 @ SV963 @ SV1892 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1429 @ SV1747 @ SV1892 @ SV1892 ) @ SV1948 @ ( tc_prod @ SV1892 @ SV1892 ) )
= $false )
| ( ( SV431 = SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5015]) ).
thf(5017,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1187,5016,5013,5011,5010,5006,5005,5003,5002,4999,4995,4991,4984,4983,4982,4977,4976,4975,4971,4970,4969,4968,4967,4960,4958,4957,4950,4948,4947,4940,4938,4937,4936,4933,4922,4911,4910,4909,4908,4905,4904,4902,4901,4898,4897,4895,4894,4892,4891,4890,4889,4886,4885,4884,4883,4882,4881,4880,4879,4876,4873,4867,4860,4854,4849,4848,4846,4845,4836,4835,4833,4832,4831,4829,4828,4827,4826,4821,4820,4819,4818,4817,4811,4810,4809,4805,4804,4803,4802,4801,4799,4796,4792,4791,4790,4789,4784,4782,4781,4780,4779,4776,4770,4760,4755,4745,4744,4741,4739,4738,4733,4732,4729,4728,4727,4726,4725,4724,4716,4715,4714,4713,4712,4711,4705,4704,4692,4691,4690,4689,4686,4676,4675,4674,4669,4668,4667,4666,4665,4658,4656,4655,4654,4653,4652,4651,4650,4649,4648,4639,4638,4637,4636,4635,4634,4633,4632,4628,4627,4619,4618,4615,4576,4575,4574,4573,4564,4561,4545,4542,4541,4540,4528,4527,4526,4523,4522,4520,4517,4508,4502,4501,4493,4487,4484,4483,4481,4479,4478,4476,4475,4472,4471,4470,4469,4468,4467,4465,4464,4463,4462,4461,4459,4458,4457,4454,4453,4450,4449,4434,4433,4432,4430,4429,4428,4427,4424,4423,4422,4421,4420,4419,4416,4409,4408,4407,4406,4405,4399,4398,4397,4396,4389,4384,4383,4336,4329,4328,4308,4307,4305,4304,4303,4302,4294,4292,4291,4282,4281,4274,4273,4272,4266,4265,4263,4260,4236,4234,4233,4207,4206,4203,4200,4197,4193,4190,4183,4182,4174,4173,4166,4165,4164,4160,4158,4157,4156,4155,4154,4152,4151,4149,4146,4142,4137,4136,4133,4132,4131,4130,4126,4125,4118,4117,4116,4115,4109,4108,4107,4099,4098,4097,4096,4095,4094,4091,4090,4087,4086,4078,4075,4071,4070,4069,4023,4012,4009,3991,3990,3988,3987,3986,3985,3984,3983,3979,3978,3977,3976,3973,3946,3944,3943,3932,3931,3925,3919,3914,3911,3904,3903,3894,3887,3881,3876,3873,3871,3870,3846,3845,3841,3840,3824,3823,3822,3821,3820,3816,3813,3812,3808,3807,3805,3800,3799,3796,3795,3791,3790,3784,3779,3776,3774,3773,3764,3753,3752,3750,3747,3746,3745,3744,3733,3732,3725,3722,3721,3720,3719,3716,3715,3709,3708,3701,3700,3698,3696,3695,3690,3684,3678,3674,3673,3672,3671,3669,3668,3667,3666,3605,3604,3599,3596,3570,3568,3564,3563,3562,3559,3558,3557,3556,3540,3537,3530,3522,3517,3516,3515,3514,3487,3485,3466,3465,3391,3388,3383,3382,3369,3351,3350,3344,3339,3330,3308,3303,3302,3299,3284,3275,3254,3253,3250,3244,3242,3241,3240,3239,3232,3231,3228,3146,3145,3141,3140,3134,3130,3108,3107,3102,3101,3088,3087,2986,2985,2940,2911,2907,2899,2898,2851,2838,2837,2836,2820,2815,2811,2802,2784,2775,2774,2754,2746,2722,2628,2627,2606,2604,2603,2597,2596,2594,2592,2591,2583,2506,2503,2502,2499,2491,2488,2487,2478,2476,2450,2449,2432,2424,2423,2421,2420,2418,2395,2394,2326,2325,2276,2262,2241,2221,2216,2206,2204,2192,2190,2065,2048,1815,1666,1649,1648,1647,1646,1645,1644,1643,1642,1641,1567,1455]) ).
thf(5018,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT073-1 : 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
% 0.10/0.22 % Computer : n017.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 14:16:30 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 151.67/30.71 ....
% 151.67/30.71
% 151.67/30.71 No.of.Axioms: 549
% 151.67/30.71
% 151.67/30.71 Length.of.Defs: 0
% 151.67/30.71
% 151.67/30.71 Contains.Choice.Funs: false
% 151.67/30.71 ..................................................................................................................................................................................................
% 151.67/30.71
% 151.67/30.71 ********************************
% 151.67/30.71 * All subproblems solved! *
% 151.67/30.71 ********************************
% 151.67/30.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:549,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5017,loop_count:0,foatp_calls:1,translation:fof_full)
% 151.67/30.71
% 151.67/30.71 %**** Beginning of derivation protocol ****
% 151.67/30.71 % SZS output start CNFRefutation
% See solution above
% 151.67/30.78
% 151.67/30.78 %**** End of derivation protocol ****
% 151.67/30.78 %**** no. of clauses in derivation: 5018 ****
% 151.67/30.78 %**** clause counter: 5017 ****
% 151.67/30.78
% 151.67/30.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:549,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5017,loop_count:0,foatp_calls:1,translation:fof_full)
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