TSTP Solution File: SCT105+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SCT105+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 21:47:16 EDT 2022
% Result : Theorem 15.26s 15.50s
% Output : CNFRefutation 24.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 348
% Syntax : Number of formulae : 5286 (3059 unt; 163 typ; 0 def)
% Number of atoms : 32833 (10759 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 155941 (12814 ~;11167 |; 440 &;131003 @)
% ( 81 <=>; 436 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 471 ( 471 >; 0 *; 0 +; 0 <<)
% Number of symbols : 166 ( 163 usr; 23 con; 0-8 aty)
% Number of variables : 23040 ( 0 ^23022 !; 18 ?;23040 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Arrow__Order__Mirabelle_OLin,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_Omax__strict,type,
c_FunDef_Omax__strict: $i ).
thf(tp_c_FunDef_Omax__weak,type,
c_FunDef_Omax__weak: $i ).
thf(tp_c_FunDef_Omin__strict,type,
c_FunDef_Omin__strict: $i ).
thf(tp_c_FunDef_Omin__weak,type,
c_FunDef_Omin__weak: $i ).
thf(tp_c_FunDef_Opair__leq,type,
c_FunDef_Opair__leq: $i ).
thf(tp_c_FunDef_Opair__less,type,
c_FunDef_Opair__less: $i ).
thf(tp_c_FunDef_Oreduction__pair,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(tp_c_FunDef_Orp__inv__image,type,
c_FunDef_Orp__inv__image: $i > $i > $i > $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Owf__wfrec,type,
c_Nitpick_Owf__wfrec: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Owf__wfrec_H,type,
c_Nitpick_Owf__wfrec_H: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Order__Relation_Olinear__order__on,type,
c_Order__Relation_Olinear__order__on: $i > $i > $i > $o ).
thf(tp_c_Order__Relation_Opartial__order__on,type,
c_Order__Relation_Opartial__order__on: $i > $i > $i > $o ).
thf(tp_c_Order__Relation_Opreorder__on,type,
c_Order__Relation_Opreorder__on: $i > $i > $i > $o ).
thf(tp_c_Order__Relation_Ostrict__linear__order__on,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(tp_c_Order__Relation_Owell__order__on,type,
c_Order__Relation_Owell__order__on: $i > $i > $i > $o ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(tp_c_Product__Type_OPair,type,
c_Product__Type_OPair: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ocurry,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ointernal__split,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Ocut,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Osame__fst,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Owfrec,type,
c_Recdef_Owfrec: $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Owfrec__rel,type,
c_Recdef_Owfrec__rel: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(tp_c_Relation_OField,type,
c_Relation_OField: $i > $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i > $i ).
thf(tp_c_Relation_Oirrefl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_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_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_Set_Othe__elem,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Oless__than,type,
c_Wellfounded_Oless__than: $i ).
thf(tp_c_Wellfounded_Olex__prod,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__ext,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(tp_c_Wellfounded_Omin__ext,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Opred__nat,type,
c_Wellfounded_Opred__nat: $i ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_member,type,
c_member: $i > $i > $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__bot,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Osemilattice__sup,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $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_sK10_B_y,type,
sK10_B_y: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY706,type,
sK11_SY706: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_B_y,type,
sK12_B_y: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SY707,type,
sK13_SY707: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_B_a,type,
sK14_B_a: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK15_SY708,type,
sK15_SY708: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_SY711,type,
sK16_SY711: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_SY713,type,
sK17_SY713: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK18_B_a,type,
sK18_B_a: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY714,type,
sK19_SY714: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_B_x,type,
sK1_B_x: $i ).
thf(tp_sK20_SY717,type,
sK20_SY717: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK21_SY719,type,
sK21_SY719: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_B_x,type,
sK22_B_x: $i > $i > $i ).
thf(tp_sK23_B_x,type,
sK23_B_x: $i > $i > $i > $i > $i > $i ).
thf(tp_sK24_B_x,type,
sK24_B_x: $i > $i > $i > $i > $i > $i ).
thf(tp_sK25_B_x,type,
sK25_B_x: $i > $i > $i ).
thf(tp_sK26_B_x,type,
sK26_B_x: $i > $i > $i ).
thf(tp_sK27_SY720,type,
sK27_SY720: $i > $i > $i ).
thf(tp_sK28_B_x,type,
sK28_B_x: $i > $i > $i > $i ).
thf(tp_sK29_B_Q,type,
sK29_B_Q: $i > $i > $i ).
thf(tp_sK2_B_x,type,
sK2_B_x: $i ).
thf(tp_sK30_SY724,type,
sK30_SY724: $i > $i > $i > $i ).
thf(tp_sK31_SY722,type,
sK31_SY722: $i > $i > $i ).
thf(tp_sK32_B_x,type,
sK32_B_x: $i > $i > $i ).
thf(tp_sK33_B_x,type,
sK33_B_x: $i > $i > $i ).
thf(tp_sK34_SY725,type,
sK34_SY725: $i > $i > $i ).
thf(tp_sK35_B_x,type,
sK35_B_x: $i > $i > $i ).
thf(tp_sK36_B_x,type,
sK36_B_x: $i > $i > $i ).
thf(tp_sK37_B_c,type,
sK37_B_c: $i > $i > $i > $i > $i ).
thf(tp_sK38_B_y,type,
sK38_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK39_B_x,type,
sK39_B_x: $i > $i > $i > $i > $i ).
thf(tp_sK3_SY704,type,
sK3_SY704: $i ).
thf(tp_sK40_B_x,type,
sK40_B_x: $i > $i > $i ).
thf(tp_sK41_B_z,type,
sK41_B_z: $i > $i > $i > $i > $i ).
thf(tp_sK42_B_z,type,
sK42_B_z: $i > $i > $i > $i > $i ).
thf(tp_sK43_B_y,type,
sK43_B_y: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK44_B_y,type,
sK44_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK45_B_y,type,
sK45_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK46_B_a,type,
sK46_B_a: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK47_SY726,type,
sK47_SY726: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK48_B_x,type,
sK48_B_x: $i > $i > $i > $i ).
thf(tp_sK49_SY727,type,
sK49_SY727: $i > $i > $i > $i ).
thf(tp_sK4_REN,type,
sK4_REN: $o ).
thf(tp_sK50_SY729,type,
sK50_SY729: $i > $i > $i > $i ).
thf(tp_sK51_B_x,type,
sK51_B_x: $i > $i > $i > $i ).
thf(tp_sK52_SY730,type,
sK52_SY730: $i > $i > $i > $i ).
thf(tp_sK53_SY732,type,
sK53_SY732: $i > $i > $i > $i ).
thf(tp_sK54_B_g,type,
sK54_B_g: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK55_B_z,type,
sK55_B_z: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK56_B_z,type,
sK56_B_z: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK57_B_y,type,
sK57_B_y: $i > $i > $i > $i ).
thf(tp_sK58_B_z,type,
sK58_B_z: $i > $i > $i > $i ).
thf(tp_sK59_B_g,type,
sK59_B_g: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_B_x,type,
sK5_B_x: $i ).
thf(tp_sK60_B_z,type,
sK60_B_z: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK61_B_x,type,
sK61_B_x: $i > $i > $i > $i ).
thf(tp_sK62_B_y,type,
sK62_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK63_B_x,type,
sK63_B_x: $i > $i > $i > $i > $i ).
thf(tp_sK64_B_x,type,
sK64_B_x: $i > $i > $i > $i ).
thf(tp_sK65_B_y,type,
sK65_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK66_B_y,type,
sK66_B_y: $i > $i > $i > $i > $i ).
thf(tp_sK67_B_x,type,
sK67_B_x: $i > $i > $i > $i ).
thf(tp_sK68_SY735,type,
sK68_SY735: $i > $i > $i > $i ).
thf(tp_sK69_B_x,type,
sK69_B_x: $i > $i > $i ).
thf(tp_sK6_B_x,type,
sK6_B_x: $i ).
thf(tp_sK70_SY736,type,
sK70_SY736: $i > $i > $i ).
thf(tp_sK71_SY738,type,
sK71_SY738: $i > $i > $i ).
thf(tp_sK72_B_x,type,
sK72_B_x: $i > $i > $i ).
thf(tp_sK73_B_a,type,
sK73_B_a: $i > $i > $i > $i ).
thf(tp_sK74_SY739,type,
sK74_SY739: $i > $i > $i > $i ).
thf(tp_sK75_B_x1,type,
sK75_B_x1: $i > $i > $i > $i ).
thf(tp_sK76_B_x,type,
sK76_B_x: $i > $i > $i ).
thf(tp_sK77_B_x,type,
sK77_B_x: $i > $i > $i ).
thf(tp_sK78_SY740,type,
sK78_SY740: $i > $i > $i ).
thf(tp_sK79_SY742,type,
sK79_SY742: $i > $i > $i ).
thf(tp_sK7_SY705,type,
sK7_SY705: $i ).
thf(tp_sK8_REN,type,
sK8_REN: $o ).
thf(tp_sK9_B_x,type,
sK9_B_x: $i > $i > $i > $i > $i ).
thf(tp_tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_L,type,
v_L: $i ).
thf(1,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(2,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(11,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(12,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(13,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(14,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(15,axiom,
class_Lattices_Olattice @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(16,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(17,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(18,axiom,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(32,axiom,
! [V_s_2: $i,V_c_2: $i,T_c: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_b @ T_c ) @ ( c_Product__Type_OPair @ T_b @ T_c @ V_b_2 @ V_c_2 ) @ V_s_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_c ) @ ( c_Product__Type_OPair @ T_a @ T_c @ V_a_2 @ V_c_2 ) @ ( c_Relation_Orel__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(35,axiom,
! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
=> ~ ! [B_x: $i] :
( ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 )
=> ~ ( c_member @ T_b @ B_x @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
thf(48,axiom,
! [V_A_2: $i,T_a: $i] :
( ( c_Relation_OImage @ T_a @ T_a @ ( c_Relation_OId @ T_a ) @ V_A_2 )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(49,axiom,
! [V_r_2: $i,V_b_2: $i,T_b: $i,V_A_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_b @ V_b_2 @ ( c_Relation_OImage @ T_a @ T_b @ V_r_2 @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(50,axiom,
! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
<=> ? [B_x: $i] :
( ( c_member @ T_b @ B_x @ V_A_2 )
& ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(80,axiom,
( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__less__def) ).
thf(121,axiom,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(126,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(144,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(145,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(146,axiom,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(147,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(148,axiom,
! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(151,axiom,
! [V_P_2: $i,V_n_2: $i,V_m_2: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( V_m_2 = V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(152,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
=> ( V_s != V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(153,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m != V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(154,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(155,axiom,
! [V_y: $i,V_x: $i] :
( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(156,axiom,
! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 != V_n_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(157,axiom,
! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(161,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(162,axiom,
( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).
thf(192,axiom,
! [V_f_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_R_2 )
=> ( c_Wellfounded_Owf @ T_a @ ( c_Wellfounded_Omlex__prod @ T_a @ V_f_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(281,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).
thf(301,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
thf(302,axiom,
c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__than) ).
thf(305,axiom,
! [T_a: $i] :
( ( c_Wellfounded_Omeasure @ T_a )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ T_a @ c_Wellfounded_Oless__than ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
thf(325,axiom,
! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( c_Wellfounded_Owf @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfI) ).
thf(326,axiom,
! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ( B_x = B_y ) ) )
=> ( c_Relation_Oantisym @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymI) ).
thf(329,axiom,
! [T_a: $i,V_R_2: $i,T_b: $i,V_P_2: $i] :
( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ B_x ) )
=> ( c_Wellfounded_Owf @ T_b @ ( hAPP @ V_R_2 @ B_x ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(330,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
<=> ! [B_Q: $i] :
( ? [B_x: $i] : ( c_member @ T_a @ B_x @ B_Q )
=> ? [B_x: $i] :
( ( c_member @ T_a @ B_x @ B_Q )
& ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ~ ( c_member @ T_a @ B_y @ B_Q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(331,axiom,
! [T_b: $i,T_a: $i,B_M: $i,B_R: $i] :
( ( c_Wellfounded_Owf @ T_a @ B_R )
=> ! [B_x: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_x )
= ( hAPP @ ( hAPP @ B_M @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_R @ B_x ) ) @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
thf(332,axiom,
! [V_a_2: $i,V_H_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec) ).
thf(333,axiom,
! [V_a_2: $i,V_H_2: $i,V_r_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( V_f_2
= ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) )
=> ( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( hAPP @ V_f_2 @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__wfrec) ).
thf(335,axiom,
! [V_f_2: $i,T_a: $i] : ( c_Wellfounded_Owf @ T_a @ ( hAPP @ ( c_Wellfounded_Omeasure @ T_a ) @ V_f_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(352,axiom,
! [V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(353,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
<=> ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(354,axiom,
! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(355,axiom,
! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(356,axiom,
! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(357,axiom,
! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(358,axiom,
! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(359,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(360,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Owf @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(361,axiom,
! [V_rb_2: $i,T_b: $i,V_ra_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_ra_2 )
=> ( ( c_Wellfounded_Owf @ T_b @ V_rb_2 )
=> ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_ra_2 @ V_rb_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(362,axiom,
! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Owf @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(363,axiom,
! [V_r_2: $i,V_x_2: $i,V_y_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
<=> ( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(366,axiom,
! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
& ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__def) ).
thf(370,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Oantisym @ T_a @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ( B_x = B_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(374,axiom,
! [V_A_2: $i,T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(376,axiom,
! [T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(378,axiom,
! [V_A_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( ( c_Set_Oinsert @ T_a @ V_a_2 @ V_A_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(379,axiom,
! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_B_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(380,axiom,
! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
=> ( ~ ( c_member @ T_a @ V_x_2 @ V_B_2 )
=> ( ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(381,axiom,
! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
<=> ( ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(382,axiom,
! [V_B_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_a_2 @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(386,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ T_b @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(387,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_b @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(391,axiom,
! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(398,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_y_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(400,axiom,
! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(406,axiom,
! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
=> ( V_a_2 = V_b_2 ) )
=> ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(407,axiom,
! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
=> ( ( V_a_2 != V_b_2 )
=> ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(408,axiom,
! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Oantisym @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ V_r_2 )
=> ( V_a_2 = V_b_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).
thf(411,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
=> ( c_Relation_Oantisym @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(412,axiom,
! [V_r_2: $i,V_x_2: $i,V_y_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
<=> ( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(413,axiom,
! [V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Relation_OId @ T_a ) )
=> ~ ! [B_x: $i] :
( V_p_2
!= ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
thf(414,axiom,
! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(415,axiom,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) )
<=> ( V_a_2 = V_b_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(416,axiom,
! [T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(417,axiom,
! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(418,axiom,
! [V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
thf(420,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ~ ! [B_c: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_c ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_c @ V_b_2 ) @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclE) ).
thf(421,axiom,
! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ V_r_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_y ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__tranclE) ).
thf(422,axiom,
! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( V_x_2 != V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
thf(423,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
<=> ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(424,axiom,
! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
=> ? [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_z ) @ V_R_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
thf(425,axiom,
! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
=> ? [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_z ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_y_2 ) @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(426,axiom,
! [V_g_2: $i,V_x_2: $i,V_r_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) )
<=> ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
=> ( ( hAPP @ V_f_2 @ B_y )
= ( hAPP @ V_g_2 @ B_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(427,axiom,
! [T_b: $i,V_a_2: $i,V_x_2: $i,T_a: $i,B_f: $i,B_R: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ B_R )
=> ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ B_f @ B_R @ V_a_2 ) @ V_x_2 )
= ( hAPP @ B_f @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(428,axiom,
! [V_z_2: $i,V_r_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(429,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(430,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(431,axiom,
! [V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
=> ( ( V_a_2 = V_b_2 )
| ( ( V_a_2 != V_b_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(432,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(433,axiom,
! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
<=> ( ( V_x_2 = V_y_2 )
| ( ( V_x_2 != V_y_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(434,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(435,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(436,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(437,axiom,
! [V_c_2: $i,V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_R_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_R_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(438,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ORange @ T_a @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(439,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 )
= V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
thf(440,axiom,
! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__trancl) ).
thf(441,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ODomain @ T_a @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(442,axiom,
! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(443,axiom,
! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(444,axiom,
! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(445,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(446,axiom,
! [V_f_2: $i,T_b: $i,V_r_2: $i,V_a_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 )
=> ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(447,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(448,axiom,
! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
=> ( ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_y ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ B_y ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ B_z ) ) ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(449,axiom,
! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) )
=> ( ! [B_y: $i,B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ B_z ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ B_y ) ) ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(450,axiom,
! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( V_x_2 != V_z_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_y ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(451,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( V_a_2 != V_b_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_y ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_b_2 ) @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(452,axiom,
! [V_r_2: $i,V_zb_2: $i,V_za_2: $i,V_xb_2: $i,V_xa_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) )
=> ~ ! [B_a: $i,B_b: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(453,axiom,
! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) )
=> ( ! [B_a: $i,B_b: $i,B_aa: $i,B_ba: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_aa ) @ B_ba ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_a ) @ B_b ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(454,axiom,
! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) )
=> ( ! [B_a: $i,B_b: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ! [B_aa: $i,B_ba: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) ) @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_a ) @ B_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_aa ) @ B_ba ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(455,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(456,axiom,
! [V_r_2: $i,T_b: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
=> ( B_y = B_z ) ) )
=> ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(457,axiom,
! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(458,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(459,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(460,axiom,
! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(461,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_z_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(462,axiom,
! [V_y_2: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(463,axiom,
! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(464,axiom,
! [V_r_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(465,axiom,
! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ocurry @ T_b @ T_c @ T_a @ V_f_2 @ V_a_2 @ V_b_2 )
= ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(466,axiom,
! [V_A_2: $i,T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(467,axiom,
! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(468,axiom,
! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(469,axiom,
! [V_r_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
=> ( B_y = B_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(470,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_z_2 ) @ V_r_2 )
=> ( V_y_2 = V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(471,axiom,
! [V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(472,axiom,
! [V_b_2: $i,V_r_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(473,axiom,
! [V_r_2: $i,V_a_2: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(474,axiom,
! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 )
<=> ? [B_g: $i] :
( ( V_a2_2
= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) )
& ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_a1_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ B_g @ B_z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
thf(475,axiom,
! [V_g_2: $i,V_F_2: $i,T_b: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_x_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ V_g_2 @ B_z ) ) )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_x_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_g_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
thf(476,axiom,
! [V_r_2: $i,V_x_2: $i,T_a: $i] :
( ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
=> ( c_member @ T_a @ B_y @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
=> ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(477,axiom,
! [V_R_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) )
=> ~ ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_x_2 ) @ V_R_2 )
=> ( c_member @ T_a @ B_z @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(478,axiom,
! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
& ( c_Relation_Otrans @ T_a @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_preorder__on__def) ).
thf(479,axiom,
! [V_A_2: $i,T_a: $i] : ( c_Relation_Orefl__on @ T_a @ V_A_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(480,axiom,
! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) )
<=> ? [B_g: $i] :
( ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) )
& ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_a1_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ B_g @ B_z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
thf(481,axiom,
! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(482,axiom,
! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(483,axiom,
! [V_a_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(484,axiom,
! [V_a_2: $i,V_r_2: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(485,axiom,
! [V_r_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
<=> ! [B_x: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ V_a_2 ) @ V_r_2 )
=> ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(486,axiom,
! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
=> ~ ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
thf(487,axiom,
! [V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
=> ~ ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
thf(488,axiom,
! [V_A_2: $i,V_c_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_c_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
=> ~ ! [B_x: $i] :
( ( c_member @ T_a @ B_x @ V_A_2 )
=> ( V_c_2
!= ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(489,axiom,
! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Relation_Otrans @ T_a @ V_r_2 )
& ( c_Relation_Oirrefl @ T_a @ V_r_2 )
& ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__linear__order__on__def) ).
thf(490,axiom,
! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
<=> ? [B_y: $i] : ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_y @ V_a_2 ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(491,axiom,
! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
<=> ? [B_y: $i] : ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(492,axiom,
! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( c_Relation_Otrans @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__inv__image) ).
thf(493,axiom,
! [V_A_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(494,axiom,
! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(495,axiom,
! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(496,axiom,
! [V_R2_2: $i,T_b: $i,V_R1_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_R1_2 )
=> ( ( c_Relation_Otrans @ T_b @ V_R2_2 )
=> ( c_Relation_Otrans @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_R1_2 @ V_R2_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(497,axiom,
! [V_f_2: $i,V_r_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) )
<=> ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(498,axiom,
! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
<=> ! [B_x: $i] :
( ( c_member @ T_a @ B_x @ V_A_2 )
=> ! [B_xa: $i] :
( ( c_member @ T_a @ B_xa @ V_A_2 )
=> ( ( B_x != B_xa )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_xa ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_xa @ B_x ) @ V_r_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(499,axiom,
! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) )
=> ( c_Relation_Otrans @ T_a @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transI) ).
thf(500,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
thf(501,axiom,
! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(502,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
<=> ( ( V_x_2 = V_y_2 )
& ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(503,axiom,
! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_b @ V_b_2 @ ( c_Relation_ORange @ T_a @ T_b @ V_r_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
thf(504,axiom,
! [V_b_2: $i,V_a_2: $i,V_c_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ointernal__split @ T_b @ T_c @ T_a @ V_c_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_c_2 @ V_a_2 ) @ V_b_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(505,axiom,
! [V_s_2: $i,V_r_2: $i,V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
<=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 )
| ( ( V_a_2 = V_a_H_2 )
& ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(506,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ T_a @ V_r_2 )
<=> ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(507,axiom,
! [V_b_2: $i,V_a_2: $i,V_f1_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ T_b @ T_c @ T_a @ V_f1_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_f1_2 @ V_a_2 ) @ V_b_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(508,axiom,
! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( c_member @ T_a @ V_x_2 @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(509,axiom,
! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(510,axiom,
! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( c_member @ T_a @ V_b_2 @ V_A_2 )
=> ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(511,axiom,
! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(512,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(513,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(514,axiom,
! [T_b: $i,T_a: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(516,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ T_a @ V_r_2 )
<=> ! [B_x: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(517,axiom,
! [T_a: $i,V_R_2: $i,V_y_2: $i,V_y_H_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_y_H_2 @ V_y_2 ) @ ( hAPP @ V_R_2 @ V_x_2 ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_H_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(518,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) )
<=> ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(519,axiom,
! [V_c_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( c_member @ T_a @ V_c_2 @ V_A_2 )
=> ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) )
=> ~ ( ~ ( c_member @ T_a @ V_c_2 @ V_A_2 )
=> ( c_member @ T_a @ V_c_2 @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(520,axiom,
! [V_c_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transD) ).
thf(521,axiom,
! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).
thf(522,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(523,conjecture,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) )
<=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(524,negated_conjecture,
( ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) )
<=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[523]) ).
thf(525,plain,
( ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) )
<=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[524]) ).
thf(526,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(527,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(528,plain,
( ( class_Groups_Ominus @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(529,plain,
( ( class_Orderings_Obot @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(530,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(531,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(532,plain,
( ( class_Lattices_Olattice @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(533,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(534,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(535,plain,
( ( class_Lattices_Osemilattice__sup @ tc_Nat_Onat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(536,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_OImage @ T_a @ T_a @ ( c_Relation_OId @ T_a ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(537,plain,
( ( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(538,plain,
( ( c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(539,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(540,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(541,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(542,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(543,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(544,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(545,plain,
( ( ! [V_P_2: $i,V_n_2: $i,V_m_2: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( V_m_2 = V_n_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(546,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
=> ( V_s != V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(547,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
=> ( V_m != V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(548,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(549,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x != V_y )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(550,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 != V_n_2 )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(551,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(552,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(553,plain,
( ( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(554,plain,
( ( ! [V_f_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_R_2 )
=> ( c_Wellfounded_Owf @ T_a @ ( c_Wellfounded_Omlex__prod @ T_a @ V_f_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(555,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(556,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(557,plain,
( ( ! [T_a: $i] :
( ( c_Wellfounded_Omeasure @ T_a )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ T_a @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(558,plain,
( ( ! [T_a: $i,V_R_2: $i,T_b: $i,V_P_2: $i] :
( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ B_x ) )
=> ( c_Wellfounded_Owf @ T_b @ ( hAPP @ V_R_2 @ B_x ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(559,plain,
( ( ! [T_b: $i,T_a: $i,B_M: $i,B_R: $i] :
( ( c_Wellfounded_Owf @ T_a @ B_R )
=> ! [B_x: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_x )
= ( hAPP @ ( hAPP @ B_M @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_R @ B_x ) ) @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(560,plain,
( ( ! [V_a_2: $i,V_H_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(561,plain,
( ( ! [V_a_2: $i,V_H_2: $i,V_r_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( V_f_2
= ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) )
=> ( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( hAPP @ V_f_2 @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(562,plain,
( ( ! [V_f_2: $i,T_a: $i] : ( c_Wellfounded_Owf @ T_a @ ( hAPP @ ( c_Wellfounded_Omeasure @ T_a ) @ V_f_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(563,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(564,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Owf @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(565,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_Wellfounded_Owf @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(566,plain,
( ( ! [V_r_2: $i,V_x_2: $i,V_y_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
<=> ( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(567,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
& ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(568,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(569,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(570,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(571,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_y_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(572,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(573,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
=> ( c_Relation_Oantisym @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(574,plain,
( ( ! [V_r_2: $i,V_x_2: $i,V_y_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
<=> ( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(575,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(576,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ORange @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(577,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ODomain @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(578,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(579,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(580,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
=> ( ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_y ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ B_y ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ B_z ) ) ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(581,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) )
=> ( ! [B_y: $i,B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ B_z ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ B_y ) ) ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(582,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) )
=> ( ! [B_a: $i,B_b: $i,B_aa: $i,B_ba: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_aa ) @ B_ba ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_a ) @ B_b ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(583,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) )
=> ( ! [B_a: $i,B_b: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ! [B_aa: $i,B_ba: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_aa @ B_ba ) ) @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_a ) @ B_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_aa ) @ B_ba ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(584,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(585,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(586,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(587,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(588,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(589,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Orefl__on @ T_a @ V_A_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(590,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Relation_Otrans @ T_a @ V_r_2 )
& ( c_Relation_Oirrefl @ T_a @ V_r_2 )
& ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(591,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(592,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(593,plain,
( ( ! [T_a: $i,V_R_2: $i,V_y_2: $i,V_y_H_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_y_H_2 @ V_y_2 ) @ ( hAPP @ V_R_2 @ V_x_2 ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_H_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(594,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) )
<=> ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(595,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(596,plain,
( ( ! [V_s_2: $i,V_c_2: $i,T_c: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_b @ T_c ) @ ( c_Product__Type_OPair @ T_b @ T_c @ V_b_2 @ V_c_2 ) @ V_s_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_c ) @ ( c_Product__Type_OPair @ T_a @ T_c @ V_a_2 @ V_c_2 ) @ ( c_Relation_Orel__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(597,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
=> ~ ! [B_x: $i] :
( ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 )
=> ~ ( c_member @ T_b @ B_x @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(598,plain,
( ( ! [V_r_2: $i,V_b_2: $i,T_b: $i,V_A_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_b @ V_b_2 @ ( c_Relation_OImage @ T_a @ T_b @ V_r_2 @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(599,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
<=> ? [B_x: $i] :
( ( c_member @ T_b @ B_x @ V_A_2 )
& ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(600,plain,
( ( c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(601,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( c_Wellfounded_Owf @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(602,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ( B_x = B_y ) ) )
=> ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(603,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
<=> ! [B_Q: $i] :
( ? [B_x: $i] : ( c_member @ T_a @ B_x @ B_Q )
=> ? [B_x: $i] :
( ( c_member @ T_a @ B_x @ B_Q )
& ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ~ ( c_member @ T_a @ B_y @ B_Q ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(604,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(605,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
<=> ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(606,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(607,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(608,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(609,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(610,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(611,plain,
( ( ! [V_rb_2: $i,T_b: $i,V_ra_2: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ T_a @ V_ra_2 )
=> ( ( c_Wellfounded_Owf @ T_b @ V_rb_2 )
=> ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_ra_2 @ V_rb_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(612,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Oantisym @ T_a @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
=> ( B_x = B_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(613,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( ( c_Set_Oinsert @ T_a @ V_a_2 @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(614,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ V_B_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(615,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
=> ( ~ ( c_member @ T_a @ V_x_2 @ V_B_2 )
=> ( ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(616,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
<=> ( ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(617,plain,
( ( ! [V_B_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_a_2 @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(618,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ T_b @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(619,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_b @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(620,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
=> ( V_a_2 = V_b_2 ) )
=> ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(621,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
=> ( ( V_a_2 != V_b_2 )
=> ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(622,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Oantisym @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ V_r_2 )
=> ( V_a_2 = V_b_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(623,plain,
( ( ! [V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Relation_OId @ T_a ) )
=> ~ ! [B_x: $i] :
( V_p_2
!= ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(624,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(625,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) )
<=> ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(626,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(627,plain,
( ( ! [V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(628,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ~ ! [B_c: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_c ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_c @ V_b_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(629,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ V_r_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_y ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(630,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( V_x_2 != V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(631,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
<=> ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(632,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
=> ? [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_z ) @ V_R_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(633,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
=> ? [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_z ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(634,plain,
( ( ! [V_g_2: $i,V_x_2: $i,V_r_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) )
<=> ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
=> ( ( hAPP @ V_f_2 @ B_y )
= ( hAPP @ V_g_2 @ B_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(635,plain,
( ( ! [T_b: $i,V_a_2: $i,V_x_2: $i,T_a: $i,B_f: $i,B_R: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ B_R )
=> ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ B_f @ B_R @ V_a_2 ) @ V_x_2 )
= ( hAPP @ B_f @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(636,plain,
( ( ! [V_z_2: $i,V_r_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(637,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(638,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(639,plain,
( ( ! [V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
=> ( ( V_a_2 = V_b_2 )
| ( ( V_a_2 != V_b_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(640,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(641,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
<=> ( ( V_x_2 = V_y_2 )
| ( ( V_x_2 != V_y_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(642,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(643,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(644,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(645,plain,
( ( ! [V_c_2: $i,V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_R_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_R_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(646,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 )
= V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(647,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(648,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(649,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(650,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,V_a_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 )
=> ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(651,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(652,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( V_x_2 != V_z_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ B_y ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(653,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( V_a_2 != V_b_2 )
=> ~ ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ B_y ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_b_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(654,plain,
( ( ! [V_r_2: $i,V_zb_2: $i,V_za_2: $i,V_xb_2: $i,V_xa_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
=> ( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) )
=> ~ ! [B_a: $i,B_b: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) @ V_r_2 )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(655,plain,
( ( ! [V_r_2: $i,T_b: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
=> ( B_y = B_z ) ) )
=> ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(656,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(657,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(658,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(659,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(660,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_z_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(661,plain,
( ( ! [V_y_2: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(662,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(663,plain,
( ( ! [V_r_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(664,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ocurry @ T_b @ T_c @ T_a @ V_f_2 @ V_a_2 @ V_b_2 )
= ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(665,plain,
( ( ! [V_r_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
=> ( B_y = B_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(666,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_z_2 ) @ V_r_2 )
=> ( V_y_2 = V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(667,plain,
( ( ! [V_b_2: $i,V_r_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(668,plain,
( ( ! [V_r_2: $i,V_a_2: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
=> ( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(669,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 )
<=> ? [B_g: $i] :
( ( V_a2_2
= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) )
& ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_a1_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ B_g @ B_z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(670,plain,
( ( ! [V_g_2: $i,V_F_2: $i,T_b: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_x_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ V_g_2 @ B_z ) ) )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_x_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_g_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(671,plain,
( ( ! [V_r_2: $i,V_x_2: $i,T_a: $i] :
( ! [B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
=> ( c_member @ T_a @ B_y @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
=> ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(672,plain,
( ( ! [V_R_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) )
=> ~ ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_x_2 ) @ V_R_2 )
=> ( c_member @ T_a @ B_z @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(673,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
<=> ( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
& ( c_Relation_Otrans @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(674,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i,T_b: $i,T_a: $i] :
( ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) )
<=> ? [B_g: $i] :
( ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) )
& ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_z @ V_a1_2 ) @ V_R_2 )
=> ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ B_z @ ( hAPP @ B_g @ B_z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(675,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(676,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(677,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
=> ( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(678,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(679,plain,
( ( ! [V_r_2: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
<=> ! [B_x: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ V_a_2 ) @ V_r_2 )
=> ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(680,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
=> ~ ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(681,plain,
( ( ! [V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
=> ~ ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(682,plain,
( ( ! [V_A_2: $i,V_c_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_c_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
=> ~ ! [B_x: $i] :
( ( c_member @ T_a @ B_x @ V_A_2 )
=> ( V_c_2
!= ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(683,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
<=> ? [B_y: $i] : ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_y @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(684,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
<=> ? [B_y: $i] : ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(685,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( c_Relation_Otrans @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(686,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(687,plain,
( ( ! [V_R2_2: $i,T_b: $i,V_R1_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_R1_2 )
=> ( ( c_Relation_Otrans @ T_b @ V_R2_2 )
=> ( c_Relation_Otrans @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_R1_2 @ V_R2_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(688,plain,
( ( ! [V_f_2: $i,V_r_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) )
<=> ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(689,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
<=> ! [B_x: $i] :
( ( c_member @ T_a @ B_x @ V_A_2 )
=> ! [B_xa: $i] :
( ( c_member @ T_a @ B_xa @ V_A_2 )
=> ( ( B_x != B_xa )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_xa ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_xa @ B_x ) @ V_r_2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(690,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) )
=> ( c_Relation_Otrans @ T_a @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(691,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(692,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( c_member @ T_a @ V_a_2 @ V_A_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(693,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
<=> ( ( V_x_2 = V_y_2 )
& ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(694,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( c_member @ T_b @ V_b_2 @ ( c_Relation_ORange @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(695,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_c_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ointernal__split @ T_b @ T_c @ T_a @ V_c_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_c_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(696,plain,
( ( ! [V_s_2: $i,V_r_2: $i,V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
<=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 )
| ( ( V_a_2 = V_a_H_2 )
& ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(697,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ T_a @ V_r_2 )
<=> ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(698,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f1_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ T_b @ T_c @ T_a @ V_f1_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_f1_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(699,plain,
( ( ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( c_member @ T_a @ V_x_2 @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(700,plain,
( ( ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(701,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( c_member @ T_a @ V_b_2 @ V_A_2 )
=> ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(702,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(703,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(704,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(705,plain,
( ( ! [T_b: $i,T_a: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(706,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ T_a @ V_r_2 )
<=> ! [B_x: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(707,plain,
( ( ! [V_c_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( c_member @ T_a @ V_c_2 @ V_A_2 )
=> ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) )
=> ~ ( ~ ( c_member @ T_a @ V_c_2 @ V_A_2 )
=> ( c_member @ T_a @ V_c_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(708,plain,
( ( ! [V_c_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
=> ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(709,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_Otrans @ T_a @ V_r_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
=> ! [B_z: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
=> ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(710,plain,
( ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[525]) ).
thf(711,plain,
( ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[525]) ).
thf(712,plain,
( ( ~ ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[710]) ).
thf(713,plain,
( ( ~ ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ! [B_x: $i,B_y: $i] :
( ( B_x != B_y )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[711]) ).
thf(714,plain,
( ( ! [B_x: $i,B_y: $i] :
( ( B_x = B_y )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
& ( sK4_REN
=> ( ( sK2_B_x != sK3_SY704 )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[712]) ).
thf(715,plain,
( ( ! [B_x: $i,B_y: $i] :
( ( B_x = B_y )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
& ( sK8_REN
=> ( ( sK6_B_x != sK7_SY705 )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(716,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[526]) ).
thf(717,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m = V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[540]) ).
thf(718,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[541]) ).
thf(719,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m != V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[542]) ).
thf(720,plain,
( ( ! [V_P_2: $i] :
( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[545]) ).
thf(721,plain,
( ( ! [V_t: $i,V_s: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
| ( V_s != V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(722,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m != V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[547]) ).
thf(723,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(724,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 != V_n_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( V_m_2 != V_n_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[550]) ).
thf(725,plain,
( ( ! [V_f_2: $i,V_R_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_R_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Wellfounded_Omlex__prod @ T_a @ V_f_2 @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[554]) ).
thf(726,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[555]) ).
thf(727,plain,
( ( ! [T_a: $i,V_R_2: $i,T_b: $i,V_P_2: $i] :
( ( ( hBOOL @ ( hAPP @ V_P_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) )
& ~ ( c_Wellfounded_Owf @ T_b @ ( hAPP @ V_R_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[558]) ).
thf(728,plain,
( ( ! [T_b: $i,T_a: $i,B_M: $i,B_R: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ B_R )
| ! [B_x: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_x )
= ( hAPP @ ( hAPP @ B_M @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_R @ B_x ) ) @ B_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[559]) ).
thf(729,plain,
( ( ! [V_a_2: $i,V_H_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[560]) ).
thf(730,plain,
( ( ! [V_a_2: $i,V_H_2: $i,V_r_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( V_f_2
!= ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) )
| ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ V_f_2 @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[561]) ).
thf(731,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[563]) ).
thf(732,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[564]) ).
thf(733,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[565]) ).
thf(734,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[566]) ).
thf(735,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[567]) ).
thf(736,plain,
( ( ! [V_x_2: $i,V_A_2: $i] :
( ! [V_y_2: $i] :
( ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) )
| ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_y_2: $i] :
( ( V_y_2 != V_x_2 )
| ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) )
& ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [V_y_2: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[570]) ).
thf(737,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[573]) ).
thf(738,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[574]) ).
thf(739,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[580]) ).
thf(740,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[581]) ).
thf(741,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[582]) ).
thf(742,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[583]) ).
thf(743,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[586]) ).
thf(744,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[587]) ).
thf(745,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[588]) ).
thf(746,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[590]) ).
thf(747,plain,
( ( ! [T_a: $i,V_R_2: $i,V_y_2: $i,V_y_H_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_y_H_2 @ V_y_2 ) @ ( hAPP @ V_R_2 @ V_x_2 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_H_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[593]) ).
thf(748,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[594]) ).
thf(749,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) ) )
| ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[595]) ).
thf(750,plain,
( ( ! [V_s_2: $i,V_c_2: $i,T_c: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_c ) @ ( c_Product__Type_OPair @ T_b @ T_c @ V_b_2 @ V_c_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_c ) @ ( c_Product__Type_OPair @ T_a @ T_c @ V_a_2 @ V_c_2 ) @ ( c_Relation_Orel__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[596]) ).
thf(751,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 )
& ( c_member @ T_b @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[597]) ).
thf(752,plain,
( ( ! [V_r_2: $i,V_b_2: $i,T_b: $i,V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_OImage @ T_a @ T_b @ V_r_2 @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[598]) ).
thf(753,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i] :
( ! [V_b_2: $i,T_a: $i] :
( ! [B_x: $i] :
( ~ ( c_member @ T_b @ B_x @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) ) )
& ! [V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ T_b @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 )
& ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[599]) ).
thf(754,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK25_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[601]) ).
thf(755,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK26_B_x @ T_a @ V_r_2 ) @ ( sK27_SY720 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK27_SY720 @ T_a @ V_r_2 ) @ ( sK26_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK26_B_x @ T_a @ V_r_2 )
!= ( sK27_SY720 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[602]) ).
thf(756,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK31_SY722 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) )
& ! [SY723: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ SY723 ) @ V_r_2 )
& ( c_member @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) ) )
| ~ ( c_member @ T_a @ SY723 @ ( sK29_B_Q @ T_a @ V_r_2 ) ) ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_Q: $i] :
( ! [B_x: $i] :
~ ( c_member @ T_a @ B_x @ B_Q )
| ( ! [SY721: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY721 @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) ) @ V_r_2 )
| ~ ( c_member @ T_a @ SY721 @ B_Q ) )
& ( c_member @ T_a @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) @ B_Q ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[603]) ).
thf(757,plain,
( ( ! [V_y_2: $i] :
( ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[604]) ).
thf(758,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK32_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[605]) ).
thf(759,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[606]) ).
thf(760,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[607]) ).
thf(761,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[608]) ).
thf(762,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[609]) ).
thf(763,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[610]) ).
thf(764,plain,
( ( ! [V_rb_2: $i,T_b: $i,V_ra_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_ra_2 )
| ~ ( c_Wellfounded_Owf @ T_b @ V_rb_2 )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_ra_2 @ V_rb_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[611]) ).
thf(765,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK33_B_x @ T_a @ V_r_2 ) @ ( sK34_SY725 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK34_SY725 @ T_a @ V_r_2 ) @ ( sK33_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK33_B_x @ T_a @ V_r_2 )
!= ( sK34_SY725 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
| ( B_x = B_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[612]) ).
thf(766,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( ( c_Set_Oinsert @ T_a @ V_a_2 @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[613]) ).
thf(767,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[614]) ).
thf(768,plain,
( ( ! [V_B_2: $i,V_A_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
!= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( V_A_2 != V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[615]) ).
thf(769,plain,
( ( ! [V_A_2: $i,V_b_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[616]) ).
thf(770,plain,
( ( ! [V_b_2: $i,V_B_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[620]) ).
thf(771,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[621]) ).
thf(772,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ V_r_2 )
| ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[622]) ).
thf(773,plain,
( ( ! [V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Relation_OId @ T_a ) )
| ( V_p_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK35_B_x @ T_a @ V_p_2 ) @ ( sK35_B_x @ T_a @ V_p_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[623]) ).
thf(774,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK36_B_x @ T_a @ V_r_2 ) @ ( sK36_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[624]) ).
thf(775,plain,
( ( ! [V_b_2: $i] :
( ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) ) )
& ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[625]) ).
thf(776,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[628]) ).
thf(777,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[629]) ).
thf(778,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( V_x_2 != V_y_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[630]) ).
thf(779,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK40_B_x @ T_a @ V_r_2 ) @ ( sK40_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[631]) ).
thf(780,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ V_R_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[632]) ).
thf(781,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[633]) ).
thf(782,plain,
( ( ! [V_g_2: $i,V_x_2: $i,V_r_2: $i,V_f_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) @ V_x_2 ) @ V_r_2 )
& ( ( hAPP @ V_f_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) ) ) )
| ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
!= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) )
| ! [B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
| ( ( hAPP @ V_f_2 @ B_y )
= ( hAPP @ V_g_2 @ B_y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[634]) ).
thf(783,plain,
( ( ! [T_b: $i,V_a_2: $i,V_x_2: $i,T_a: $i,B_f: $i,B_R: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ B_R )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ B_f @ B_R @ V_a_2 ) @ V_x_2 )
= ( hAPP @ B_f @ V_x_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[635]) ).
thf(784,plain,
( ( ! [V_z_2: $i,V_r_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[636]) ).
thf(785,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[637]) ).
thf(786,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[638]) ).
thf(787,plain,
( ( ! [V_R_2: $i,V_b_2: $i] :
( ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_a_2 != V_b_2 )
| ( V_a_2 = V_b_2 ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[639]) ).
thf(788,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[640]) ).
thf(789,plain,
( ( ! [V_R_2: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 = V_y_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[641]) ).
thf(790,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[642]) ).
thf(791,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[643]) ).
thf(792,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[644]) ).
thf(793,plain,
( ( ! [V_c_2: $i,V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_R_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_R_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[645]) ).
thf(794,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 )
= V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[646]) ).
thf(795,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[648]) ).
thf(796,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[649]) ).
thf(797,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,V_a_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[650]) ).
thf(798,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[651]) ).
thf(799,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_x_2 = V_z_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[652]) ).
thf(800,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_a_2 = V_b_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[653]) ).
thf(801,plain,
( ( ! [V_r_2: $i,V_zb_2: $i,V_za_2: $i,V_xb_2: $i,V_xa_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ( ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[654]) ).
thf(802,plain,
( ( ! [V_r_2: $i,T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK49_SY727 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK49_SY727 @ T_a @ T_b @ V_r_2 )
!= ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[655]) ).
thf(803,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[657]) ).
thf(804,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[658]) ).
thf(805,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[659]) ).
thf(806,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_z_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[660]) ).
thf(807,plain,
( ( ! [V_y_2: $i,V_R_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[661]) ).
thf(808,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[662]) ).
thf(809,plain,
( ( ! [V_r_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK52_SY730 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK52_SY730 @ T_a @ T_b @ V_r_2 )
!= ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
| ( B_y = B_z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[665]) ).
thf(810,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( V_y_2 = V_z_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[666]) ).
thf(811,plain,
( ( ! [V_b_2: $i,V_r_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[667]) ).
thf(812,plain,
( ( ! [V_r_2: $i,V_a_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[668]) ).
thf(813,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( V_a2_2
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 )
| ( ! [SY733: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY733 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY733 @ ( hAPP @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY733 ) ) )
& ( V_a2_2
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[669]) ).
thf(814,plain,
( ( ! [V_g_2: $i,V_F_2: $i,T_b: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ ( hAPP @ V_g_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_x_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_g_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[670]) ).
thf(815,plain,
( ( ! [V_r_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ V_x_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[671]) ).
thf(816,plain,
( ( ! [V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_member @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[672]) ).
thf(817,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[673]) ).
thf(818,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) )
| ( ! [SY734: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY734 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY734 @ ( hAPP @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY734 ) ) )
& ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[674]) ).
thf(819,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[675]) ).
thf(820,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(821,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[677]) ).
thf(822,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[678]) ).
thf(823,plain,
( ( ! [V_r_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ V_a_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ! [B_x: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[679]) ).
thf(824,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK62_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[680]) ).
thf(825,plain,
( ( ! [V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK63_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[681]) ).
thf(826,plain,
( ( ! [V_A_2: $i,V_c_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_c_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( ( c_member @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ V_A_2 )
& ( V_c_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[682]) ).
thf(827,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_y @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK65_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[683]) ).
thf(828,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK66_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[684]) ).
thf(829,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Relation_Otrans @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[685]) ).
thf(830,plain,
( ( ! [V_R2_2: $i,T_b: $i,V_R1_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_R1_2 )
| ~ ( c_Relation_Otrans @ T_b @ V_R2_2 )
| ( c_Relation_Otrans @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_R1_2 @ V_R2_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[687]) ).
thf(831,plain,
( ( ! [V_f_2: $i,V_r_2: $i,T_b: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 ) )
& ! [V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[688]) ).
thf(832,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( c_member @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 )
!= ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ! [B_x: $i] :
( ~ ( c_member @ T_a @ B_x @ V_A_2 )
| ! [B_xa: $i] :
( ~ ( c_member @ T_a @ B_xa @ V_A_2 )
| ( B_x = B_xa )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_xa ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_xa @ B_x ) @ V_r_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[689]) ).
thf(833,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK70_SY736 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK70_SY736 @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[690]) ).
thf(834,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[691]) ).
thf(835,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[692]) ).
thf(836,plain,
( ( ! [V_A_2: $i,V_y_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[693]) ).
thf(837,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_ORange @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[694]) ).
thf(838,plain,
( ( ! [V_s_2: $i,V_r_2: $i,V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( V_a_2 = V_a_H_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i] :
( ( V_a_2 != V_a_H_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[696]) ).
thf(839,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK72_B_x @ T_a @ V_r_2 ) @ ( sK72_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[697]) ).
thf(840,plain,
( ( ! [V_x_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[699]) ).
thf(841,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_y_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[700]) ).
thf(842,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_b_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[701]) ).
thf(843,plain,
( ( ! [V_A_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[702]) ).
thf(844,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i] :
( ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_a = V_a_H ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_b = V_b_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[703]) ).
thf(845,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ( ( V_a_2 != V_a_H_2 )
| ( V_b_2 != V_b_H_2 )
| ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_a_2 = V_a_H_2 ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[704]) ).
thf(846,plain,
( ( ! [T_b: $i] :
( ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK75_B_x1 @ V_P_2 @ T_a @ T_b ) ) )
| ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) ) )
& ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK73_B_a @ V_P_2 @ T_a @ T_b ) @ ( sK74_SY739 @ V_P_2 @ T_a @ T_b ) ) ) )
| ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[705]) ).
thf(847,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK76_B_x @ T_a @ V_r_2 ) @ ( sK76_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Nitpick_Orefl_H @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Nitpick_Orefl_H @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(848,plain,
( ( ! [V_c_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i] :
( ! [V_A_2: $i] : ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[707]) ).
thf(849,plain,
( ( ! [V_c_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ V_r_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[708]) ).
thf(850,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK78_SY740 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK78_SY740 @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[709]) ).
thf(851,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK78_SY740 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK78_SY740 @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(852,plain,
( ( ! [V_c_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(853,plain,
( ( ! [V_c_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i] :
( ! [V_A_2: $i] : ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(854,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK76_B_x @ T_a @ V_r_2 ) @ ( sK76_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Nitpick_Orefl_H @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Nitpick_Orefl_H @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(855,plain,
( ( ! [T_b: $i] :
( ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK75_B_x1 @ V_P_2 @ T_a @ T_b ) ) )
| ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) ) )
& ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK73_B_a @ V_P_2 @ T_a @ T_b ) @ ( sK74_SY739 @ V_P_2 @ T_a @ T_b ) ) ) )
| ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(856,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ( ( V_a_2 != V_a_H_2 )
| ( V_b_2 != V_b_H_2 )
| ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_a_2 = V_a_H_2 ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(857,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i] :
( ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_a = V_a_H ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_b = V_b_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(858,plain,
( ( ! [V_A_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(859,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_b_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(860,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_y_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(861,plain,
( ( ! [V_x_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(862,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f1_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ T_b @ T_c @ T_a @ V_f1_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_f1_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(863,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK72_B_x @ T_a @ V_r_2 ) @ ( sK72_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(864,plain,
( ( ! [V_s_2: $i,V_r_2: $i,V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( V_a_2 = V_a_H_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i] :
( ( V_a_2 != V_a_H_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(865,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_c_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ointernal__split @ T_b @ T_c @ T_a @ V_c_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_c_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(866,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_ORange @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(867,plain,
( ( ! [V_A_2: $i,V_y_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(868,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(869,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(870,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK70_SY736 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK70_SY736 @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(871,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( c_member @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 )
!= ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ! [B_x: $i] :
( ~ ( c_member @ T_a @ B_x @ V_A_2 )
| ! [B_xa: $i] :
( ~ ( c_member @ T_a @ B_xa @ V_A_2 )
| ( B_x = B_xa )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_xa ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_xa @ B_x ) @ V_r_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(872,plain,
( ( ! [V_f_2: $i,V_r_2: $i,T_b: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 ) )
& ! [V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(873,plain,
( ( ! [V_R2_2: $i,T_b: $i,V_R1_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_R1_2 )
| ~ ( c_Relation_Otrans @ T_b @ V_R2_2 )
| ( c_Relation_Otrans @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_R1_2 @ V_R2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(874,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(875,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Relation_Otrans @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(876,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK66_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(877,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_y @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK65_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(878,plain,
( ( ! [V_A_2: $i,V_c_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_c_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( ( c_member @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ V_A_2 )
& ( V_c_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(879,plain,
( ( ! [V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK63_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(880,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK62_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(881,plain,
( ( ! [V_r_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ V_a_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ! [B_x: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(882,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(883,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(884,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(885,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(886,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) )
| ( ! [SY734: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY734 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY734 @ ( hAPP @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY734 ) ) )
& ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(887,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(888,plain,
( ( ! [V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_member @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(889,plain,
( ( ! [V_r_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ V_x_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(890,plain,
( ( ! [V_g_2: $i,V_F_2: $i,T_b: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ ( hAPP @ V_g_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_x_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_g_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(891,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( V_a2_2
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 )
| ( ! [SY733: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY733 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY733 @ ( hAPP @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY733 ) ) )
& ( V_a2_2
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(892,plain,
( ( ! [V_r_2: $i,V_a_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(893,plain,
( ( ! [V_b_2: $i,V_r_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(894,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( V_y_2 = V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(895,plain,
( ( ! [V_r_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK52_SY730 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK52_SY730 @ T_a @ T_b @ V_r_2 )
!= ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
| ( B_y = B_z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(896,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ocurry @ T_b @ T_c @ T_a @ V_f_2 @ V_a_2 @ V_b_2 )
= ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(897,plain,
( ( ! [V_r_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(898,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(899,plain,
( ( ! [V_y_2: $i,V_R_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(900,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_z_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(901,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(902,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(903,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(904,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(905,plain,
( ( ! [V_r_2: $i,T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK49_SY727 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK49_SY727 @ T_a @ T_b @ V_r_2 )
!= ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(906,plain,
( ( ! [V_r_2: $i,V_zb_2: $i,V_za_2: $i,V_xb_2: $i,V_xa_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ( ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(907,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_a_2 = V_b_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(908,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_x_2 = V_z_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(909,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(910,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,V_a_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(911,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(912,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(913,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(914,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 )
= V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(915,plain,
( ( ! [V_c_2: $i,V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_R_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_R_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(916,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(917,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(918,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(919,plain,
( ( ! [V_R_2: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 = V_y_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(920,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(921,plain,
( ( ! [V_R_2: $i,V_b_2: $i] :
( ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_a_2 != V_b_2 )
| ( V_a_2 = V_b_2 ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(922,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(923,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(924,plain,
( ( ! [V_z_2: $i,V_r_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(925,plain,
( ( ! [T_b: $i,V_a_2: $i,V_x_2: $i,T_a: $i,B_f: $i,B_R: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ B_R )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ B_f @ B_R @ V_a_2 ) @ V_x_2 )
= ( hAPP @ B_f @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(926,plain,
( ( ! [V_g_2: $i,V_x_2: $i,V_r_2: $i,V_f_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) @ V_x_2 ) @ V_r_2 )
& ( ( hAPP @ V_f_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) ) ) )
| ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
!= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) )
| ! [B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
| ( ( hAPP @ V_f_2 @ B_y )
= ( hAPP @ V_g_2 @ B_y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(927,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(928,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ V_R_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(929,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK40_B_x @ T_a @ V_r_2 ) @ ( sK40_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(930,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( V_x_2 != V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(931,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(932,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(933,plain,
( ( ! [V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(934,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(935,plain,
( ( ! [V_b_2: $i] :
( ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) ) )
& ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(936,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK36_B_x @ T_a @ V_r_2 ) @ ( sK36_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(937,plain,
( ( ! [V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Relation_OId @ T_a ) )
| ( V_p_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK35_B_x @ T_a @ V_p_2 ) @ ( sK35_B_x @ T_a @ V_p_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(938,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ V_r_2 )
| ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(939,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(940,plain,
( ( ! [V_b_2: $i,V_B_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(941,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_b @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(942,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ T_b @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(943,plain,
( ( ! [V_B_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_a_2 @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(944,plain,
( ( ! [V_A_2: $i,V_b_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(945,plain,
( ( ! [V_B_2: $i,V_A_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
!= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( V_A_2 != V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(946,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(947,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( ( c_Set_Oinsert @ T_a @ V_a_2 @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(948,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK33_B_x @ T_a @ V_r_2 ) @ ( sK34_SY725 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK34_SY725 @ T_a @ V_r_2 ) @ ( sK33_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK33_B_x @ T_a @ V_r_2 )
!= ( sK34_SY725 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
| ( B_x = B_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(949,plain,
( ( ! [V_rb_2: $i,T_b: $i,V_ra_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_ra_2 )
| ~ ( c_Wellfounded_Owf @ T_b @ V_rb_2 )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_ra_2 @ V_rb_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(950,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(951,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(952,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(953,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(954,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(955,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK32_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(956,plain,
( ( ! [V_y_2: $i] :
( ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(957,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK31_SY722 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) )
& ! [SY723: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ SY723 ) @ V_r_2 )
& ( c_member @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) ) )
| ~ ( c_member @ T_a @ SY723 @ ( sK29_B_Q @ T_a @ V_r_2 ) ) ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_Q: $i] :
( ! [B_x: $i] :
~ ( c_member @ T_a @ B_x @ B_Q )
| ( ! [SY721: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY721 @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) ) @ V_r_2 )
| ~ ( c_member @ T_a @ SY721 @ B_Q ) )
& ( c_member @ T_a @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) @ B_Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(958,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK26_B_x @ T_a @ V_r_2 ) @ ( sK27_SY720 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK27_SY720 @ T_a @ V_r_2 ) @ ( sK26_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK26_B_x @ T_a @ V_r_2 )
!= ( sK27_SY720 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(959,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK25_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(960,plain,
( ( c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(961,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i] :
( ! [V_b_2: $i,T_a: $i] :
( ! [B_x: $i] :
( ~ ( c_member @ T_b @ B_x @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) ) )
& ! [V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ T_b @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 )
& ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(962,plain,
( ( ! [V_r_2: $i,V_b_2: $i,T_b: $i,V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_OImage @ T_a @ T_b @ V_r_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(963,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 )
& ( c_member @ T_b @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(964,plain,
( ( ! [V_s_2: $i,V_c_2: $i,T_c: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_c ) @ ( c_Product__Type_OPair @ T_b @ T_c @ V_b_2 @ V_c_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_c ) @ ( c_Product__Type_OPair @ T_a @ T_c @ V_a_2 @ V_c_2 ) @ ( c_Relation_Orel__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(965,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) ) )
| ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(966,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(967,plain,
( ( ! [T_a: $i,V_R_2: $i,V_y_2: $i,V_y_H_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_y_H_2 @ V_y_2 ) @ ( hAPP @ V_R_2 @ V_x_2 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_H_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(968,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(969,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(970,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(971,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Orefl__on @ T_a @ V_A_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(972,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(973,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(974,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(975,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(976,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(977,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(978,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(979,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(980,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(981,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(982,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(983,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ODomain @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(984,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ORange @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(985,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(986,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(987,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(988,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(989,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_y_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(990,plain,
( ( ! [V_x_2: $i,V_A_2: $i] :
( ! [V_y_2: $i] :
( ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) )
| ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_y_2: $i] :
( ( V_y_2 != V_x_2 )
| ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) )
& ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [V_y_2: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(991,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(992,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(993,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(994,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(995,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(996,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(997,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(998,plain,
( ( ! [V_f_2: $i,T_a: $i] : ( c_Wellfounded_Owf @ T_a @ ( hAPP @ ( c_Wellfounded_Omeasure @ T_a ) @ V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(999,plain,
( ( ! [V_a_2: $i,V_H_2: $i,V_r_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( V_f_2
!= ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) )
| ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ V_f_2 @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1000,plain,
( ( ! [V_a_2: $i,V_H_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1001,plain,
( ( ! [T_b: $i,T_a: $i,B_M: $i,B_R: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ B_R )
| ! [B_x: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_x )
= ( hAPP @ ( hAPP @ B_M @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_R @ B_x ) ) @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_R_2: $i,T_b: $i,V_P_2: $i] :
( ( ( hBOOL @ ( hAPP @ V_P_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) )
& ~ ( c_Wellfounded_Owf @ T_b @ ( hAPP @ V_R_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1003,plain,
( ( ! [T_a: $i] :
( ( c_Wellfounded_Omeasure @ T_a )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ T_a @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1004,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1005,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1006,plain,
( ( ! [V_f_2: $i,V_R_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_R_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Wellfounded_Omlex__prod @ T_a @ V_f_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1007,plain,
( ( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1008,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1009,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(1010,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 != V_n_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( V_m_2 != V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1011,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1012,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1013,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m != V_n ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1014,plain,
( ( ! [V_t: $i,V_s: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
| ( V_s != V_t ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1015,plain,
( ( ! [V_P_2: $i] :
( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1016,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(1017,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1018,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m != V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1019,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1020,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1021,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1022,plain,
( ( c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1023,plain,
( ( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1024,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_OImage @ T_a @ T_a @ ( c_Relation_OId @ T_a ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1025,plain,
( ( class_Lattices_Osemilattice__sup @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1026,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1027,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1028,plain,
( ( class_Lattices_Olattice @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1029,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1030,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1031,plain,
( ( class_Orderings_Obot @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1032,plain,
( ( class_Groups_Ominus @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1033,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1034,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1035,plain,
( ( ! [B_x: $i,B_y: $i] :
( ( B_x = B_y )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L ) )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
& ( sK4_REN
=> ( ( sK2_B_x != sK3_SY704 )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1036,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(1037,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK51_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK52_SY730 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK51_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK53_SY732 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK52_SY730 @ SX2 @ SX1 @ SX0 )
!= ( sK53_SY732 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ! [SX5: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ SX3 @ SX5 ) @ SX0 )
| ( SX4 = SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1038,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( c_member @ SX2 @ SX5 @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 ) )
| ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_member @ SX2 @ ( sK24_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ ( sK24_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(1039,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK69_B_x @ SX1 @ SX0 ) @ ( sK70_SY736 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK70_SY736 @ SX1 @ SX0 ) @ ( sK71_SY738 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK69_B_x @ SX1 @ SX0 ) @ ( sK71_SY738 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(1040,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ~ ( ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) )
| ( SX5 = SX3 )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 ) )
| ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX6: $i] :
( ( SX5 != SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 )
| ! [SX7: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) ) )
| ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[864]) ).
thf(1041,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ! [SX6: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX6 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ SX2 @ SX6 ) @ SX1 ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ~ ( ~ ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX3 )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX6 @ ( hAPP @ ( sK59_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 ) ) )
| ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ SX2 @ ( sK59_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1042,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK61_B_x @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK61_B_x @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX1 ) @ SX0 )
| ( c_member @ SX2 @ SX3 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[881]) ).
thf(1043,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ ( sK9_B_x @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SX2 @ ( hAPP @ SX1 @ ( sK9_B_x @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SX0 @ SX2 ) @ ( c_Recdef_Osame__fst @ SX0 @ SX2 @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(1044,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ ( sK66_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(1045,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(1046,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX3 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[986]) ).
thf(1047,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) )
| ( ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 )
= ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ ( sK46_B_a @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK47_SY726 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ ( sK46_B_a @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK47_SY726 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1048,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ SX2 @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( c_member @ SX2 @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SX2 @ SX1 @ SX0 )
!= ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 )
| ! [SX3: $i] :
( ~ ( c_member @ SX2 @ SX3 @ SX1 )
| ! [SX4: $i] :
( ~ ( c_member @ SX2 @ SX4 @ SX1 )
| ( SX3 = SX4 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX4 @ SX3 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(1049,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(1050,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ ( sK23_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX1 )
| ~ ( c_member @ SX2 @ ( sK23_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1051,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ SX0 ) )
| ! [SX2: $i,SX3: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(1052,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 )
| ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX3 = SX1 ) )
| ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[856]) ).
thf(1053,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[956]) ).
thf(1054,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 != SX1 )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 = SX1 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ( SX2 != SX1 )
| ! [SX3: $i] : ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(1055,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1010]) ).
thf(1056,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Oirrefl @ SX2 @ SX0 )
| ~ ( c_Relation_Otrans @ SX2 @ SX0 )
| ~ ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Oirrefl @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Otrans @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[970]) ).
thf(1057,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ ( sK75_B_x1 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( c_Product__Type_OPair @ SX1 @ SX0 @ SX3 @ SX4 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ ( c_Product__Type_OPair @ SX1 @ SX0 @ ( sK73_B_a @ SX2 @ SX1 @ SX0 ) @ ( sK74_SY739 @ SX2 @ SX1 @ SX0 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[855]) ).
thf(1058,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
| ~ ~ ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1035]) ).
thf(1059,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[863]) ).
thf(1060,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1061,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX1 )
| ~ ( c_member @ SX3 @ SX2 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) )
| ( c_member @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1062,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK45_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK45_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1063,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
!= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 )
| ( SX1 != SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1064,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK37_B_c @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK37_B_c @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1065,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX3 @ SX1 ) )
| ( SX2 != SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX3 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX1 ) )
| ( SX2 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1066,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX3 = SX1 ) )
| ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[857]) ).
thf(1067,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX5 ) @ SX4 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK20_SY717 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK21_SY719 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK20_SY717 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK21_SY719 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[977]) ).
thf(1068,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ ( sK65_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1069,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ! [SX6: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX6 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0
!= ( hAPP @ ( hAPP @ SX2 @ SX6 ) @ SX1 ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX3 )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX6 @ ( hAPP @ ( sK54_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 ) ) )
| ( SX0
!= ( hAPP @ ( hAPP @ SX2 @ ( sK54_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(1070,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK42_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK42_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(1071,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i] :
( ! [SX5: $i] :
~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX4 @ SX3 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SX2 @ SX5 @ SX1 ) @ SX0 ) )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( hAPP @ SX0 @ SX4 ) @ ( hAPP @ SX0 @ SX3 ) ) @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( hAPP @ SX0 @ SX4 ) @ ( hAPP @ SX0 @ SX3 ) ) @ SX1 )
| ! [SX5: $i] : ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX4 @ SX3 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SX2 @ SX5 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1072,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ SX2 @ SX1 @ SX0 )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ! [SX2: $i] : ( c_member @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(1073,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX2 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK14_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY708 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK14_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK15_SY708 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX5 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[978]) ).
thf(1074,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX2 @ SX3 @ SX1 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX0 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX2 @ SX3 @ SX1 @ SX4 @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1075,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(1076,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[955]) ).
thf(1077,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[861]) ).
thf(1078,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(1079,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK48_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY727 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK48_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK50_SY729 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK49_SY727 @ SX2 @ SX1 @ SX0 )
!= ( sK50_SY729 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1080,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ( SX2 = SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ( SX2 = SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( SX2 = SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( SX2 = SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(1081,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK38_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK38_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(1082,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( c_Wellfounded_Owf @ SX3 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1083,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Orefl__on @ SX2 @ SX1 @ SX0 )
| ~ ( c_Relation_Otrans @ SX2 @ SX0 )
| ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Orefl__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Otrans @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[887]) ).
thf(1084,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Relation_OId__on @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ SX2 @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( SX1
!= ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[878]) ).
thf(1085,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] : ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(1086,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) )
| ( SX2 = SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX1 )
| ! [SX3: $i] : ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1087,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK12_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK12_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(1088,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK58_B_z @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK58_B_z @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1089,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX1 @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1090,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK44_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK44_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1091,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY706 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK11_SY706 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1092,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK41_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK41_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1093,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1005]) ).
thf(1094,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 != SX1 )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(1095,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ! [SX3: $i] : ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1096,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK26_B_x @ SX1 @ SX0 ) @ ( sK27_SY720 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK27_SY720 @ SX1 @ SX0 ) @ ( sK26_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK26_B_x @ SX1 @ SX0 )
!= ( sK27_SY720 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1097,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1098,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ~ ( c_Relation_Oantisym @ SX2 @ SX0 )
| ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Oantisym @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[993]) ).
thf(1099,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX2 )
| ~ ( ( ( hAPP @ SX3 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( hAPP @ SX0 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
= ( c_Recdef_Ocut @ SX5 @ SX4 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( c_Recdef_Ocut @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
!= ( c_Recdef_Ocut @ SX5 @ SX4 @ SX0 @ SX2 @ SX1 ) )
| ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX2 )
| ( ( hAPP @ SX3 @ SX6 )
= ( hAPP @ SX0 @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(1100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK57_B_y @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK57_B_y @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(1101,plain,
! [SV1: $i] :
( ( ! [SY743: $i,SY744: $i,SY745: $i,SY746: $i] :
( ~ ( c_Relation_Otrans @ SY746 @ SY745 )
| ~ ( c_member @ ( tc_prod @ SY746 @ SY746 ) @ ( c_Product__Type_OPair @ SY746 @ SY746 @ SY744 @ SY743 ) @ SY745 )
| ~ ( c_member @ ( tc_prod @ SY746 @ SY746 ) @ ( c_Product__Type_OPair @ SY746 @ SY746 @ SY743 @ SV1 ) @ SY745 )
| ( c_member @ ( tc_prod @ SY746 @ SY746 ) @ ( c_Product__Type_OPair @ SY746 @ SY746 @ SY744 @ SV1 ) @ SY745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1102,plain,
! [SV2: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i] :
( ( SY749 != SY748 )
| ~ ( c_member @ SY747 @ SY748 @ SV2 )
| ( c_member @ SY747 @ SY749 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1103,plain,
! [SV3: $i] :
( ( ! [SY750: $i,SY751: $i,SY752: $i,SY753: $i,SY754: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY754 @ SY753 @ SY752 @ SY751 @ ( c_Product__Type_OPair @ SY754 @ SY753 @ SY750 @ SV3 ) )
= ( hAPP @ ( hAPP @ SY751 @ SY750 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1104,plain,
! [SV4: $i] :
( ( ! [SY755: $i,SY756: $i,SY757: $i,SY758: $i,SY759: $i] :
( ( c_Product__Type_Ointernal__split @ SY759 @ SY758 @ SY757 @ SY756 @ ( c_Product__Type_OPair @ SY759 @ SY758 @ SY755 @ SV4 ) )
= ( hAPP @ ( hAPP @ SY756 @ SY755 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1105,plain,
! [SV5: $i] :
( ( ! [SY760: $i,SY761: $i,SY762: $i,SY763: $i] :
( ~ ( c_member @ ( tc_prod @ SY763 @ SY762 ) @ ( c_Product__Type_OPair @ SY763 @ SY762 @ SY761 @ SY760 ) @ SV5 )
| ( c_member @ SY762 @ SY760 @ ( c_Relation_ORange @ SY763 @ SY762 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1106,plain,
! [SV6: $i] :
( ( ! [SY764: $i,SY765: $i,SY766: $i] :
( ( SY766 != SY765 )
| ~ ( c_member @ SY764 @ SY766 @ SV6 )
| ( c_member @ ( tc_prod @ SY764 @ SY764 ) @ ( c_Product__Type_OPair @ SY764 @ SY764 @ SY766 @ SY765 ) @ ( c_Relation_OId__on @ SY764 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1107,plain,
! [SV7: $i] :
( ( ! [SY767: $i,SY768: $i,SY769: $i,SY770: $i] :
( ~ ( c_member @ ( tc_prod @ SY770 @ SY769 ) @ ( c_Product__Type_OPair @ SY770 @ SY769 @ SY768 @ SY767 ) @ SV7 )
| ( c_member @ SY770 @ SY768 @ ( c_Relation_ODomain @ SY770 @ SY769 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1108,plain,
! [SV8: $i] :
( ( ! [SY771: $i,SY772: $i,SY773: $i] :
( ~ ( c_Relation_Otrans @ SY773 @ SY772 )
| ~ ( c_Relation_Otrans @ SY771 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SY773 @ SY771 ) @ ( c_Wellfounded_Olex__prod @ SY773 @ SY771 @ SY772 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1109,plain,
! [SV9: $i] :
( ( ! [SY774: $i] : ( c_Relation_Otrans @ SY774 @ ( c_Relation_OId__on @ SY774 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1110,plain,
! [SV10: $i] :
( ( ! [SY775: $i,SY776: $i,SY777: $i] :
( ~ ( c_Relation_Otrans @ SY777 @ SY776 )
| ( c_Relation_Otrans @ SY775 @ ( hAPP @ ( c_Relation_Oinv__image @ SY777 @ SY775 @ SY776 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1111,plain,
! [SV11: $i] :
( ( ! [SY778: $i,SY779: $i,SY780: $i] :
( ~ ( c_member @ SY780 @ SY779 @ ( c_Relation_ORange @ SY778 @ SY780 @ SV11 ) )
| ( c_member @ ( tc_prod @ SY778 @ SY780 ) @ ( c_Product__Type_OPair @ SY778 @ SY780 @ ( sK63_B_x @ SY780 @ SY779 @ SY778 @ SV11 ) @ SY779 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1112,plain,
! [SV12: $i] :
( ( ! [SY781: $i,SY782: $i,SY783: $i] :
( ~ ( c_member @ SY783 @ SY782 @ ( c_Relation_ODomain @ SY783 @ SY781 @ SV12 ) )
| ( c_member @ ( tc_prod @ SY783 @ SY781 ) @ ( c_Product__Type_OPair @ SY783 @ SY781 @ SY782 @ ( sK62_B_y @ SY783 @ SY782 @ SY781 @ SV12 ) ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1113,plain,
! [SV13: $i] :
( ( ! [SY784: $i,SY785: $i,SY786: $i] :
( ~ ( c_member @ SY786 @ SY785 @ ( c_Wellfounded_Oacc @ SY786 @ SY784 ) )
| ~ ( c_member @ ( tc_prod @ SY786 @ SY786 ) @ ( c_Product__Type_OPair @ SY786 @ SY786 @ SV13 @ SY785 ) @ SY784 )
| ( c_member @ SY786 @ SV13 @ ( c_Wellfounded_Oacc @ SY786 @ SY784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1114,plain,
! [SV14: $i] :
( ( ! [SY787: $i,SY788: $i,SY789: $i] :
( ~ ( c_Relation_Orefl__on @ SY789 @ SY788 @ SY787 )
| ~ ( c_member @ SY789 @ SV14 @ SY788 )
| ( c_member @ ( tc_prod @ SY789 @ SY789 ) @ ( c_Product__Type_OPair @ SY789 @ SY789 @ SV14 @ SV14 ) @ SY787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1115,plain,
! [SV15: $i] :
( ( ! [SY790: $i,SY791: $i,SY792: $i,SY793: $i] :
( ~ ( c_Relation_Orefl__on @ SY793 @ SY792 @ SY791 )
| ~ ( c_member @ ( tc_prod @ SY793 @ SY793 ) @ ( c_Product__Type_OPair @ SY793 @ SY793 @ SY790 @ SV15 ) @ SY791 )
| ( c_member @ SY793 @ SY790 @ SY792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1116,plain,
! [SV16: $i] :
( ( ! [SY794: $i,SY795: $i,SY796: $i,SY797: $i] :
( ~ ( c_Relation_Orefl__on @ SY797 @ SY796 @ SY795 )
| ~ ( c_member @ ( tc_prod @ SY797 @ SY797 ) @ ( c_Product__Type_OPair @ SY797 @ SY797 @ SY794 @ SV16 ) @ SY795 )
| ( c_member @ SY797 @ SV16 @ SY796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1117,plain,
! [SV17: $i] :
( ( ! [SY798: $i,SY799: $i,SY800: $i] :
( ~ ( c_member @ ( tc_prod @ SY800 @ SY800 ) @ ( c_Product__Type_OPair @ SY800 @ SY800 @ SY799 @ SY798 ) @ ( c_Transitive__Closure_Ortrancl @ SY800 @ SV17 ) )
| ~ ( c_member @ SY800 @ SY798 @ ( c_Wellfounded_Oacc @ SY800 @ SV17 ) )
| ( c_member @ SY800 @ SY799 @ ( c_Wellfounded_Oacc @ SY800 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1118,plain,
! [SV18: $i] :
( ( ! [SY801: $i,SY802: $i,SY803: $i] :
( ~ ( c_member @ SY803 @ SY802 @ ( c_Wellfounded_Oacc @ SY803 @ SY801 ) )
| ~ ( c_member @ ( tc_prod @ SY803 @ SY803 ) @ ( c_Product__Type_OPair @ SY803 @ SY803 @ SV18 @ SY802 ) @ ( c_Transitive__Closure_Ortrancl @ SY803 @ SY801 ) )
| ( c_member @ SY803 @ SV18 @ ( c_Wellfounded_Oacc @ SY803 @ SY801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1119,plain,
! [SV19: $i] :
( ( ! [SY804: $i,SY805: $i,SY806: $i,SY807: $i,SY808: $i] :
( ~ ( c_Relation_Osingle__valued @ SY808 @ SY807 @ SY806 )
| ~ ( c_member @ ( tc_prod @ SY808 @ SY807 ) @ ( c_Product__Type_OPair @ SY808 @ SY807 @ SY805 @ SY804 ) @ SY806 )
| ~ ( c_member @ ( tc_prod @ SY808 @ SY807 ) @ ( c_Product__Type_OPair @ SY808 @ SY807 @ SY805 @ SV19 ) @ SY806 )
| ( SY804 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1120,plain,
! [SV20: $i] :
( ( ! [SY809: $i,SY810: $i,SY811: $i,SY812: $i,SY813: $i] :
( ( c_Product__Type_Ocurry @ SY813 @ SY812 @ SY811 @ SY810 @ SY809 @ SV20 )
= ( hAPP @ SY810 @ ( c_Product__Type_OPair @ SY813 @ SY812 @ SY809 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1121,plain,
! [SV21: $i] :
( ( ! [SY814: $i,SY815: $i] : ( c_member @ ( tc_prod @ SY815 @ SY815 ) @ ( c_Product__Type_OPair @ SY815 @ SY815 @ SY814 @ SY814 ) @ ( c_Transitive__Closure_Ortrancl @ SY815 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1122,plain,
! [SV22: $i] :
( ( ! [SY816: $i,SY817: $i] :
( ~ ( c_member @ ( tc_prod @ SY817 @ SY817 ) @ SY816 @ SV22 )
| ( c_member @ ( tc_prod @ SY817 @ SY817 ) @ SY816 @ ( c_Transitive__Closure_Ortrancl @ SY817 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1123,plain,
! [SV23: $i] :
( ( ! [SY818: $i,SY819: $i,SY820: $i,SY821: $i] :
( ~ ( c_Relation_Osingle__valued @ SY821 @ SY821 @ SY820 )
| ~ ( c_member @ ( tc_prod @ SY821 @ SY821 ) @ ( c_Product__Type_OPair @ SY821 @ SY821 @ SY819 @ SY818 ) @ ( c_Transitive__Closure_Ortrancl @ SY821 @ SY820 ) )
| ~ ( c_member @ ( tc_prod @ SY821 @ SY821 ) @ ( c_Product__Type_OPair @ SY821 @ SY821 @ SY819 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY821 @ SY820 ) )
| ( c_member @ ( tc_prod @ SY821 @ SY821 ) @ ( c_Product__Type_OPair @ SY821 @ SY821 @ SY818 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY821 @ SY820 ) )
| ( c_member @ ( tc_prod @ SY821 @ SY821 ) @ ( c_Product__Type_OPair @ SY821 @ SY821 @ SV23 @ SY818 ) @ ( c_Transitive__Closure_Ortrancl @ SY821 @ SY820 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1124,plain,
! [SV24: $i] :
( ( ! [SY822: $i,SY823: $i,SY824: $i,SY825: $i] :
( ~ ( c_member @ ( tc_prod @ SY825 @ SY825 ) @ ( c_Product__Type_OPair @ SY825 @ SY825 @ SY824 @ SY823 ) @ SY822 )
| ~ ( c_member @ ( tc_prod @ SY825 @ SY825 ) @ ( c_Product__Type_OPair @ SY825 @ SY825 @ SY823 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY825 @ SY822 ) )
| ( c_member @ ( tc_prod @ SY825 @ SY825 ) @ ( c_Product__Type_OPair @ SY825 @ SY825 @ SY824 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY825 @ SY822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1125,plain,
! [SV25: $i] :
( ( ! [SY826: $i,SY827: $i,SY828: $i,SY829: $i] :
( ~ ( c_member @ ( tc_prod @ SY829 @ SY829 ) @ ( c_Product__Type_OPair @ SY829 @ SY829 @ SY828 @ SY827 ) @ ( c_Transitive__Closure_Ortrancl @ SY829 @ SY826 ) )
| ~ ( c_member @ ( tc_prod @ SY829 @ SY829 ) @ ( c_Product__Type_OPair @ SY829 @ SY829 @ SY827 @ SV25 ) @ SY826 )
| ( c_member @ ( tc_prod @ SY829 @ SY829 ) @ ( c_Product__Type_OPair @ SY829 @ SY829 @ SY828 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SY829 @ SY826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1126,plain,
! [SV26: $i] :
( ( ! [SY830: $i,SY831: $i,SY832: $i,SY833: $i] :
( ~ ( c_member @ ( tc_prod @ SY833 @ SY833 ) @ ( c_Product__Type_OPair @ SY833 @ SY833 @ SY832 @ SY831 ) @ ( c_Transitive__Closure_Ortrancl @ SY833 @ SY830 ) )
| ~ ( c_member @ ( tc_prod @ SY833 @ SY833 ) @ ( c_Product__Type_OPair @ SY833 @ SY833 @ SY831 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY833 @ SY830 ) )
| ( c_member @ ( tc_prod @ SY833 @ SY833 ) @ ( c_Product__Type_OPair @ SY833 @ SY833 @ SY832 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY833 @ SY830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1127,plain,
! [SV27: $i] :
( ( ! [SY834: $i] : ( c_Relation_Otrans @ SY834 @ ( c_Transitive__Closure_Ortrancl @ SY834 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1128,plain,
! [SV28: $i] :
( ( ! [SY835: $i,SY836: $i,SY837: $i] :
( ~ ( c_member @ ( tc_prod @ SY837 @ SY837 ) @ ( c_Product__Type_OPair @ SY837 @ SY837 @ SY836 @ SY835 ) @ ( c_Transitive__Closure_Otrancl @ SY837 @ SV28 ) )
| ( c_member @ ( tc_prod @ SY837 @ SY837 ) @ ( c_Product__Type_OPair @ SY837 @ SY837 @ SY836 @ SY835 ) @ ( c_Transitive__Closure_Ortrancl @ SY837 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1129,plain,
! [SV29: $i] :
( ( ! [SY838: $i,SY839: $i,SY840: $i,SY841: $i,SY842: $i] :
( ~ ( c_member @ ( tc_prod @ SY842 @ SY842 ) @ ( c_Product__Type_OPair @ SY842 @ SY842 @ SY841 @ SY840 ) @ SY839 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY842 @ SY838 @ SV29 @ SY839 @ SY840 ) @ SY841 )
= ( hAPP @ SV29 @ SY841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1130,plain,
! [SV30: $i] :
( ( ! [SY843: $i,SY844: $i,SY845: $i] :
( ~ ( c_member @ ( tc_prod @ SY845 @ SY845 ) @ ( c_Product__Type_OPair @ SY845 @ SY845 @ SY844 @ SY843 ) @ SV30 )
| ( c_member @ ( tc_prod @ SY845 @ SY845 ) @ ( c_Product__Type_OPair @ SY845 @ SY845 @ SY844 @ SY843 ) @ ( c_Transitive__Closure_Otrancl @ SY845 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1131,plain,
! [SV31: $i] :
( ( ! [SY846: $i,SY847: $i] :
( ~ ( c_member @ ( tc_prod @ SY847 @ SY847 ) @ SY846 @ SV31 )
| ( c_member @ ( tc_prod @ SY847 @ SY847 ) @ SY846 @ ( c_Transitive__Closure_Otrancl @ SY847 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1132,plain,
! [SV32: $i] :
( ( ! [SY848: $i] : ( c_Relation_Otrans @ SY848 @ ( c_Transitive__Closure_Otrancl @ SY848 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1133,plain,
! [SV33: $i] :
( ( ! [SY849: $i] :
( ~ ( c_Relation_Otrans @ SY849 @ SV33 )
| ( ( c_Transitive__Closure_Otrancl @ SY849 @ SV33 )
= SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1134,plain,
! [SV34: $i] :
( ( ! [SY850: $i,SY851: $i,SY852: $i,SY853: $i] :
( ~ ( c_member @ ( tc_prod @ SY853 @ SY853 ) @ ( c_Product__Type_OPair @ SY853 @ SY853 @ SY852 @ SY851 ) @ SY850 )
| ~ ( c_member @ ( tc_prod @ SY853 @ SY853 ) @ ( c_Product__Type_OPair @ SY853 @ SY853 @ SY851 @ SV34 ) @ SY850 )
| ( c_member @ ( tc_prod @ SY853 @ SY853 ) @ ( c_Product__Type_OPair @ SY853 @ SY853 @ SY852 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SY853 @ SY850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1135,plain,
! [SV35: $i] :
( ( ! [SY854: $i,SY855: $i,SY856: $i,SY857: $i] :
( ~ ( c_member @ ( tc_prod @ SY857 @ SY857 ) @ ( c_Product__Type_OPair @ SY857 @ SY857 @ SY856 @ SY855 ) @ SY854 )
| ~ ( c_member @ ( tc_prod @ SY857 @ SY857 ) @ ( c_Product__Type_OPair @ SY857 @ SY857 @ SY855 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY857 @ SY854 ) )
| ( c_member @ ( tc_prod @ SY857 @ SY857 ) @ ( c_Product__Type_OPair @ SY857 @ SY857 @ SY856 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY857 @ SY854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1136,plain,
! [SV36: $i] :
( ( ! [SY858: $i,SY859: $i,SY860: $i,SY861: $i] :
( ~ ( c_member @ ( tc_prod @ SY861 @ SY861 ) @ ( c_Product__Type_OPair @ SY861 @ SY861 @ SY860 @ SY859 ) @ ( c_Transitive__Closure_Otrancl @ SY861 @ SY858 ) )
| ~ ( c_member @ ( tc_prod @ SY861 @ SY861 ) @ ( c_Product__Type_OPair @ SY861 @ SY861 @ SY859 @ SV36 ) @ SY858 )
| ( c_member @ ( tc_prod @ SY861 @ SY861 ) @ ( c_Product__Type_OPair @ SY861 @ SY861 @ SY860 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SY861 @ SY858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1137,plain,
! [SV37: $i] :
( ( ! [SY862: $i,SY863: $i,SY864: $i,SY865: $i] :
( ~ ( c_member @ ( tc_prod @ SY865 @ SY865 ) @ ( c_Product__Type_OPair @ SY865 @ SY865 @ SY864 @ SY863 ) @ ( c_Transitive__Closure_Otrancl @ SY865 @ SY862 ) )
| ~ ( c_member @ ( tc_prod @ SY865 @ SY865 ) @ ( c_Product__Type_OPair @ SY865 @ SY865 @ SY863 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY865 @ SY862 ) )
| ( c_member @ ( tc_prod @ SY865 @ SY865 ) @ ( c_Product__Type_OPair @ SY865 @ SY865 @ SY864 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY865 @ SY862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1138,plain,
! [SV38: $i] :
( ( ! [SY866: $i,SY867: $i,SY868: $i,SY869: $i] :
( ~ ( c_member @ ( tc_prod @ SY869 @ SY869 ) @ ( c_Product__Type_OPair @ SY869 @ SY869 @ SY868 @ SY867 ) @ SY866 )
| ~ ( c_member @ ( tc_prod @ SY869 @ SY869 ) @ ( c_Product__Type_OPair @ SY869 @ SY869 @ SY867 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SY869 @ SY866 ) )
| ( c_member @ ( tc_prod @ SY869 @ SY869 ) @ ( c_Product__Type_OPair @ SY869 @ SY869 @ SY868 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SY869 @ SY866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1139,plain,
! [SV39: $i] :
( ( ! [SY870: $i,SY871: $i,SY872: $i,SY873: $i] :
( ~ ( c_member @ ( tc_prod @ SY873 @ SY873 ) @ ( c_Product__Type_OPair @ SY873 @ SY873 @ SY872 @ SY871 ) @ ( c_Transitive__Closure_Ortrancl @ SY873 @ SY870 ) )
| ~ ( c_member @ ( tc_prod @ SY873 @ SY873 ) @ ( c_Product__Type_OPair @ SY873 @ SY873 @ SY871 @ SV39 ) @ SY870 )
| ( c_member @ ( tc_prod @ SY873 @ SY873 ) @ ( c_Product__Type_OPair @ SY873 @ SY873 @ SY872 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SY873 @ SY870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1140,plain,
! [SV40: $i] :
( ( ! [SY874: $i,SY875: $i,SY876: $i,SY877: $i] :
( ~ ( c_member @ ( tc_prod @ SY877 @ SY877 ) @ ( c_Product__Type_OPair @ SY877 @ SY877 @ SY876 @ SY875 ) @ ( c_Transitive__Closure_Otrancl @ SY877 @ SY874 ) )
| ~ ( c_member @ ( tc_prod @ SY877 @ SY877 ) @ ( c_Product__Type_OPair @ SY877 @ SY877 @ SY875 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SY877 @ SY874 ) )
| ( c_member @ ( tc_prod @ SY877 @ SY877 ) @ ( c_Product__Type_OPair @ SY877 @ SY877 @ SY876 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SY877 @ SY874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1141,plain,
! [SV41: $i] :
( ( ! [SY878: $i,SY879: $i,SY880: $i,SY881: $i] :
( ~ ( c_member @ ( tc_prod @ SY881 @ SY881 ) @ ( c_Product__Type_OPair @ SY881 @ SY881 @ SY880 @ SY879 ) @ ( c_Transitive__Closure_Ortrancl @ SY881 @ SY878 ) )
| ~ ( c_member @ ( tc_prod @ SY881 @ SY881 ) @ ( c_Product__Type_OPair @ SY881 @ SY881 @ SY879 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY881 @ SY878 ) )
| ( c_member @ ( tc_prod @ SY881 @ SY881 ) @ ( c_Product__Type_OPair @ SY881 @ SY881 @ SY880 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY881 @ SY878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1142,plain,
! [SV42: $i] :
( ( ! [SY882: $i,SY883: $i,SY884: $i,SY885: $i,SY886: $i] :
( ~ ( c_member @ ( tc_prod @ SY884 @ SY884 ) @ ( c_Product__Type_OPair @ SY884 @ SY884 @ SY883 @ SY882 ) @ SY886 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY884 @ SV42 @ SY885 @ SY886 @ SY882 ) @ SY883 )
= ( hAPP @ SY885 @ SY883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1143,plain,
! [SV43: $i] :
( ( ! [SY887: $i,SY888: $i,SY889: $i] :
( ( c_member @ ( tc_prod @ SY889 @ SY889 ) @ ( c_Product__Type_OPair @ SY889 @ SY889 @ ( sK39_B_x @ SY889 @ SY888 @ SY887 @ SV43 ) @ ( sK39_B_x @ SY889 @ SY888 @ SY887 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SY889 @ SY888 ) )
| ~ ( c_member @ ( tc_prod @ SY889 @ SY889 ) @ ( c_Product__Type_OPair @ SY889 @ SY889 @ SY887 @ SV43 ) @ SY888 )
| ( SY887 != SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1144,plain,
! [SV44: $i] :
( ( ! [SY890: $i] : ( c_member @ ( tc_prod @ SY890 @ SY890 ) @ ( c_Product__Type_OPair @ SY890 @ SY890 @ SV44 @ SV44 ) @ ( c_Relation_OId @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1145,plain,
! [SV45: $i] :
( ( c_Relation_Otrans @ SV45 @ ( c_Relation_OId @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1146,plain,
! [SV46: $i] :
( ( ! [SY891: $i] :
( ( c_member @ ( tc_prod @ SY891 @ SY891 ) @ ( c_Product__Type_OPair @ SY891 @ SY891 @ ( sK36_B_x @ SY891 @ SV46 ) @ ( sK36_B_x @ SY891 @ SV46 ) ) @ ( c_Transitive__Closure_Otrancl @ SY891 @ SV46 ) )
| ( c_Wellfounded_Oacyclic @ SY891 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1147,plain,
! [SV47: $i] :
( ( ! [SY892: $i] :
( ~ ( c_member @ ( tc_prod @ SY892 @ SY892 ) @ SV47 @ ( c_Relation_OId @ SY892 ) )
| ( SV47
= ( c_Product__Type_OPair @ SY892 @ SY892 @ ( sK35_B_x @ SY892 @ SV47 ) @ ( sK35_B_x @ SY892 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1148,plain,
! [SV48: $i] :
( ( ! [SY893: $i,SY894: $i,SY895: $i] :
( ~ ( c_Relation_Oantisym @ SY895 @ SY894 )
| ~ ( c_member @ ( tc_prod @ SY895 @ SY895 ) @ ( c_Product__Type_OPair @ SY895 @ SY895 @ SY893 @ SV48 ) @ SY894 )
| ~ ( c_member @ ( tc_prod @ SY895 @ SY895 ) @ ( c_Product__Type_OPair @ SY895 @ SY895 @ SV48 @ SY893 ) @ SY894 )
| ( SY893 = SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1149,plain,
! [SV49: $i] :
( ( ! [SY896: $i,SY897: $i,SY898: $i] :
( ~ ( c_member @ SY898 @ SY897 @ ( c_Set_Oinsert @ SY898 @ SY896 @ SV49 ) )
| ( SY897 = SY896 )
| ( c_member @ SY898 @ SY897 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1150,plain,
! [SV50: $i] :
( ( ! [SY899: $i,SY900: $i,SY901: $i,SY902: $i] :
( ( c_Relation_ODomain @ SY902 @ SY901 @ ( c_Set_Oinsert @ ( tc_prod @ SY902 @ SY901 ) @ ( c_Product__Type_OPair @ SY902 @ SY901 @ SY900 @ SY899 ) @ SV50 ) )
= ( c_Set_Oinsert @ SY902 @ SY900 @ ( c_Relation_ODomain @ SY902 @ SY901 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1151,plain,
! [SV51: $i] :
( ( ! [SY903: $i,SY904: $i,SY905: $i,SY906: $i] :
( ( c_Relation_ORange @ SY906 @ SY905 @ ( c_Set_Oinsert @ ( tc_prod @ SY906 @ SY905 ) @ ( c_Product__Type_OPair @ SY906 @ SY905 @ SY904 @ SY903 ) @ SV51 ) )
= ( c_Set_Oinsert @ SY905 @ SY903 @ ( c_Relation_ORange @ SY906 @ SY905 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1152,plain,
! [SV52: $i] :
( ( ! [SY907: $i,SY908: $i] : ( c_member @ SY908 @ SY907 @ ( c_Set_Oinsert @ SY908 @ SY907 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1153,plain,
! [SV53: $i] :
( ( ! [SY909: $i,SY910: $i,SY911: $i] :
( ~ ( c_member @ SY911 @ SY910 @ SY909 )
| ( c_member @ SY911 @ SY910 @ ( c_Set_Oinsert @ SY911 @ SV53 @ SY909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1154,plain,
! [SV54: $i] :
( ( ! [SY912: $i,SY913: $i] :
( ~ ( c_member @ SY913 @ SY912 @ SV54 )
| ( ( c_Set_Oinsert @ SY913 @ SY912 @ SV54 )
= SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1155,plain,
! [SV55: $i] :
( ( ! [SY914: $i,SY915: $i,SY916: $i] :
( ~ ( c_Wellfounded_Owf @ SY916 @ SY915 )
| ~ ( c_Wellfounded_Owf @ SY914 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY916 @ SY914 ) @ ( c_Wellfounded_Olex__prod @ SY916 @ SY914 @ SY915 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1156,plain,
! [SV56: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ~ ( c_Wellfounded_Owf @ SY918 @ SY917 )
| ~ ( c_member @ ( tc_prod @ SY918 @ SY918 ) @ ( c_Product__Type_OPair @ SY918 @ SY918 @ SV56 @ SV56 ) @ SY917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1157,plain,
! [SV57: $i] :
( ( ! [SY919: $i,SY920: $i,SY921: $i] :
( ~ ( c_Wellfounded_Owf @ SY921 @ SY920 )
| ~ ( c_member @ ( tc_prod @ SY921 @ SY921 ) @ ( c_Product__Type_OPair @ SY921 @ SY921 @ SY919 @ SV57 ) @ SY920 )
| ~ ( c_member @ ( tc_prod @ SY921 @ SY921 ) @ ( c_Product__Type_OPair @ SY921 @ SY921 @ SV57 @ SY919 ) @ SY920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1158,plain,
! [SV58: $i] :
( ( ! [SY922: $i,SY923: $i,SY924: $i] :
( ~ ( c_Wellfounded_Owf @ SY924 @ SY923 )
| ~ ( c_member @ ( tc_prod @ SY924 @ SY924 ) @ ( c_Product__Type_OPair @ SY924 @ SY924 @ SY922 @ SV58 ) @ SY923 )
| ~ ( c_member @ ( tc_prod @ SY924 @ SY924 ) @ ( c_Product__Type_OPair @ SY924 @ SY924 @ SV58 @ SY922 ) @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1159,plain,
! [SV59: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ~ ( c_Wellfounded_Owf @ SY926 @ SY925 )
| ~ ( c_member @ ( tc_prod @ SY926 @ SY926 ) @ ( c_Product__Type_OPair @ SY926 @ SY926 @ SV59 @ SV59 ) @ SY925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1160,plain,
! [SV60: $i] :
( ( ! [SY927: $i,SY928: $i] :
( ~ ( c_Wellfounded_Owf @ SY928 @ SY927 )
| ( c_member @ SY928 @ SV60 @ ( c_Wellfounded_Oacc @ SY928 @ SY927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1161,plain,
! [SV61: $i] :
( ( ! [SY929: $i] :
( ~ ( c_member @ SY929 @ ( sK25_B_x @ SY929 @ SV61 ) @ ( c_Wellfounded_Oacc @ SY929 @ SV61 ) )
| ( c_Wellfounded_Owf @ SY929 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1162,plain,
! [SV62: $i] :
( ( ! [SY930: $i,SY931: $i,SY932: $i,SY933: $i,SY934: $i] :
( ~ ( c_member @ SY934 @ SY933 @ SY932 )
| ~ ( c_member @ ( tc_prod @ SY934 @ SY931 ) @ ( c_Product__Type_OPair @ SY934 @ SY931 @ SY933 @ SY930 ) @ SV62 )
| ( c_member @ SY931 @ SY930 @ ( c_Relation_OImage @ SY934 @ SY931 @ SV62 @ SY932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1163,plain,
! [SV63: $i] :
( ( ! [SY935: $i,SY936: $i,SY937: $i,SY938: $i,SY939: $i,SY940: $i,SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SY941 @ SY940 ) @ ( c_Product__Type_OPair @ SY941 @ SY940 @ SY939 @ SY938 ) @ SY937 )
| ~ ( c_member @ ( tc_prod @ SY940 @ SY936 ) @ ( c_Product__Type_OPair @ SY940 @ SY936 @ SY938 @ SY935 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY941 @ SY936 ) @ ( c_Product__Type_OPair @ SY941 @ SY936 @ SY939 @ SY935 ) @ ( c_Relation_Orel__comp @ SY941 @ SY940 @ SY936 @ SY937 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1164,plain,
! [SV64: $i] :
( ( ! [SY942: $i] :
( ( ( hAPP @ SY942 @ ( sK22_B_x @ SY942 @ SV64 ) )
!= ( hAPP @ SV64 @ ( sK22_B_x @ SY942 @ SV64 ) ) )
| ( SY942 = SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1165,plain,
! [SV65: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i,SY946: $i,SY947: $i,SY948: $i] :
( ~ ( hBOOL @ ( hAPP @ SY948 @ SY947 ) )
| ~ ( c_member @ ( tc_prod @ SY946 @ SY946 ) @ ( c_Product__Type_OPair @ SY946 @ SY946 @ SY945 @ SY944 ) @ ( hAPP @ SY943 @ SY947 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SY946 ) @ ( tc_prod @ SV65 @ SY946 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SY946 ) @ ( tc_prod @ SV65 @ SY946 ) @ ( c_Product__Type_OPair @ SV65 @ SY946 @ SY947 @ SY945 ) @ ( c_Product__Type_OPair @ SV65 @ SY946 @ SY947 @ SY944 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SY946 @ SY948 @ SY943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1166,plain,
! [SV66: $i] :
( ( ! [SY949: $i] :
( ( c_Relation_ORange @ SY949 @ SY949 @ ( c_Relation_OId__on @ SY949 @ SV66 ) )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1167,plain,
! [SV67: $i] :
( ( ! [SY950: $i] :
( ( c_Relation_ODomain @ SY950 @ SY950 @ ( c_Relation_OId__on @ SY950 @ SV67 ) )
= SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1168,plain,
! [SV68: $i] :
( ( ! [SY951: $i] : ( c_Relation_Orefl__on @ SY951 @ SV68 @ ( c_Relation_OId__on @ SY951 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1169,plain,
! [SV69: $i] :
( ( ! [SY952: $i,SY953: $i,SY954: $i,SY955: $i] :
( ~ ( hBOOL @ ( hAPP @ SY955 @ ( c_Product__Type_OPair @ SY954 @ SY953 @ SY952 @ SV69 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY954 @ SY953 @ tc_HOL_Obool @ SY955 @ SY952 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1170,plain,
! [SV70: $i] :
( ( ! [SY956: $i,SY957: $i,SY958: $i,SY959: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY959 @ SY958 @ tc_HOL_Obool @ SY957 @ SY956 @ SV70 ) )
| ( hBOOL @ ( hAPP @ SY957 @ ( c_Product__Type_OPair @ SY959 @ SY958 @ SY956 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1171,plain,
! [SV71: $i] :
( ( ! [SY960: $i,SY961: $i,SY962: $i,SY963: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY963 @ SY962 @ tc_HOL_Obool @ SY961 @ SY960 @ SV71 ) )
| ( hBOOL @ ( hAPP @ SY961 @ ( c_Product__Type_OPair @ SY963 @ SY962 @ SY960 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1172,plain,
! [SV72: $i] :
( ( ! [SY964: $i] : ( c_Relation_Osingle__valued @ SY964 @ SY964 @ ( c_Relation_OId__on @ SY964 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1173,plain,
! [SV73: $i] :
( ( ! [SY965: $i] :
( ( c_Transitive__Closure_Ortrancl @ SY965 @ ( c_Transitive__Closure_Ortrancl @ SY965 @ SV73 ) )
= ( c_Transitive__Closure_Ortrancl @ SY965 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1174,plain,
! [SV74: $i] :
( ( ! [SY966: $i] :
( ( c_Transitive__Closure_Ortrancl @ SY966 @ ( c_Transitive__Closure_Otrancl @ SY966 @ SV74 ) )
= ( c_Transitive__Closure_Ortrancl @ SY966 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1175,plain,
! [SV75: $i] :
( ( ! [SY967: $i] :
( ( c_Transitive__Closure_Otrancl @ SY967 @ ( c_Transitive__Closure_Ortrancl @ SY967 @ SV75 ) )
= ( c_Transitive__Closure_Ortrancl @ SY967 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1176,plain,
! [SV76: $i] :
( ( ! [SY968: $i] :
( ( c_Relation_ODomain @ SY968 @ SY968 @ ( c_Transitive__Closure_Otrancl @ SY968 @ SV76 ) )
= ( c_Relation_ODomain @ SY968 @ SY968 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1177,plain,
! [SV77: $i] :
( ( ! [SY969: $i] :
( ( c_Relation_ORange @ SY969 @ SY969 @ ( c_Transitive__Closure_Otrancl @ SY969 @ SV77 ) )
= ( c_Relation_ORange @ SY969 @ SY969 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1178,plain,
! [SV78: $i] :
( ( c_Relation_Osingle__valued @ SV78 @ SV78 @ ( c_Relation_OId @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1179,plain,
! [SV79: $i] :
( ( ! [SY970: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY970 @ SV79 )
| ( c_Relation_Oantisym @ SY970 @ ( c_Transitive__Closure_Ortrancl @ SY970 @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1180,plain,
! [SV80: $i] :
( ( ! [SY971: $i,SY972: $i] :
( ( c_Set_Oinsert @ SY972 @ SY971 @ ( c_Set_Oinsert @ SY972 @ SY971 @ SV80 ) )
= ( c_Set_Oinsert @ SY972 @ SY971 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1181,plain,
! [SV81: $i] :
( ( ! [SY973: $i,SY974: $i,SY975: $i] :
( ( c_Set_Oinsert @ SY975 @ SY974 @ ( c_Set_Oinsert @ SY975 @ SY973 @ SV81 ) )
= ( c_Set_Oinsert @ SY975 @ SY973 @ ( c_Set_Oinsert @ SY975 @ SY974 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1182,plain,
! [SV82: $i] :
( ( c_Relation_Oantisym @ SV82 @ ( c_Relation_OId @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1183,plain,
! [SV83: $i] :
( ( ! [SY976: $i] : ( c_Relation_Oantisym @ SY976 @ ( c_Relation_OId__on @ SY976 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1184,plain,
! [SV84: $i] :
( ( ! [SY977: $i,SY978: $i,SY979: $i] :
( ~ ( c_Wellfounded_Owf @ SY979 @ SY978 )
| ( c_Wellfounded_Owf @ SY977 @ ( hAPP @ ( c_Relation_Oinv__image @ SY979 @ SY977 @ SY978 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1185,plain,
! [SV85: $i] :
( ( ! [SY980: $i] :
( ~ ( c_Wellfounded_Owf @ SY980 @ SV85 )
| ( c_Wellfounded_Owf @ SY980 @ ( c_Transitive__Closure_Otrancl @ SY980 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1186,plain,
! [SV86: $i] :
( ( ! [SY981: $i] :
( ~ ( c_Wellfounded_Owf @ SY981 @ SV86 )
| ( c_Wellfounded_Oacyclic @ SY981 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1187,plain,
! [SV87: $i] :
( ( ! [SY982: $i] : ( c_Wellfounded_Owf @ SY982 @ ( hAPP @ ( c_Wellfounded_Omeasure @ SY982 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1188,plain,
! [SV88: $i] :
( ( ! [SY983: $i,SY984: $i,SY985: $i,SY986: $i,SY987: $i] :
( ( SY987
!= ( c_Recdef_Owfrec @ SY986 @ SY985 @ SY984 @ SY983 ) )
| ~ ( c_Wellfounded_Owf @ SY986 @ SY984 )
| ( ( hAPP @ SY987 @ SV88 )
= ( hAPP @ ( hAPP @ SY983 @ ( c_Recdef_Ocut @ SY986 @ SY985 @ SY987 @ SY984 @ SV88 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1189,plain,
! [SV89: $i] :
( ( ! [SY988: $i,SY989: $i,SY990: $i,SY991: $i] :
( ~ ( c_Wellfounded_Owf @ SY991 @ SY990 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY991 @ SY989 @ SY990 @ SY988 ) @ SV89 )
= ( hAPP @ ( hAPP @ SY988 @ ( c_Recdef_Ocut @ SY991 @ SY989 @ ( c_Recdef_Owfrec @ SY991 @ SY989 @ SY990 @ SY988 ) @ SY990 @ SV89 ) ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1190,plain,
! [SV90: $i] :
( ( ! [SY992: $i,SY993: $i,SY994: $i] :
( ~ ( c_Wellfounded_Owf @ SY992 @ SY994 )
| ! [SY995: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SY992 @ SV90 @ SY994 @ SY993 ) @ SY995 )
= ( hAPP @ ( hAPP @ SY993 @ ( c_Recdef_Ocut @ SY992 @ SV90 @ ( c_Recdef_Owfrec @ SY992 @ SV90 @ SY994 @ SY993 ) @ SY994 @ SY995 ) ) @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1191,plain,
! [SV91: $i] :
( ( ( c_Wellfounded_Omeasure @ SV91 )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ SV91 @ c_Wellfounded_Oless__than ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1192,plain,
! [SV92: $i] :
( ( ! [SY996: $i,SY997: $i] :
( ~ ( c_Wellfounded_Owf @ SY997 @ SY996 )
| ( c_Wellfounded_Owf @ SY997 @ ( c_Wellfounded_Omlex__prod @ SY997 @ SV92 @ SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1193,plain,
! [SV93: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV93 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1194,plain,
! [SV94: $i] :
( ( ! [SY998: $i] :
( ( SY998 = SV94 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY998 @ SV94 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV94 @ SY998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1195,plain,
! [SV95: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV95 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1196,plain,
! [SV96: $i] :
( ( ! [SY999: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY999 @ SV96 )
| ( SV96 != SY999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1197,plain,
! [SV97: $i] :
( ( ! [SY1000: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1000 @ SV97 )
| ( SY1000 != SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1198,plain,
! [SV98: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV98 @ SV98 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1199,plain,
! [SV99: $i] :
( ( ! [SY1001: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1001 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV99 @ SY1001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1200,plain,
! [SV100: $i] :
( ( ! [SY1002: $i] :
( ( SY1002 != SV100 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1002 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1201,plain,
! [SV101: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1004 @ SY1003 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1003 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1004 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1202,plain,
! [SV102: $i] :
( ( ! [SY1005: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1005 @ SV102 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SY1005 )
| ( SY1005 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1203,plain,
! [SV103: $i] :
( ( ! [SY1006: $i,SY1007: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY1007 @ SY1006 ) @ SV103 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY1007 @ SV103 ) @ SY1006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1204,plain,
! [SV104: $i] :
( ( ! [SY1008: $i] :
( ( c_Relation_OImage @ SY1008 @ SY1008 @ ( c_Relation_OId @ SY1008 ) @ SV104 )
= SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1205,plain,
! [SV105: $i] :
( ( ! [SY1009: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SY1009 ) @ SV105 ) )
| ( SY1009 = SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1206,plain,
! [SV106: $i] :
( ( ! [SY1010: $i] :
( ( SY1010 != SV106 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ SY1010 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1207,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1208,plain,
! [SV107: $i] :
( ( ~ ( ~ ! [SY1011: $i,SY1012: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 )
!= ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1012 @ SY1011 @ SV107 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1014 @ SY1013 @ SV107 )
| ! [SY1015: $i,SY1016: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1016 ) @ SV107 )
| ! [SY1017: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1017 ) @ SV107 )
| ( SY1016 = SY1017 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1209,plain,
! [SV108: $i] :
( ( ! [SY1018: $i,SY1019: $i] :
~ ( ~ ! [SY1020: $i,SY1021: $i] :
( ! [SY1022: $i] :
( ~ ( c_member @ SY1019 @ SY1022 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SY1019 @ SY1021 ) @ ( c_Product__Type_OPair @ SY1019 @ SY1021 @ SY1022 @ SY1020 ) @ SY1018 ) )
| ( c_member @ SY1021 @ SY1020 @ ( c_Relation_OImage @ SY1019 @ SY1021 @ SY1018 @ SV108 ) ) )
| ~ ! [SY1023: $i,SY1024: $i] :
( ~ ( c_member @ SY1024 @ SY1023 @ ( c_Relation_OImage @ SY1019 @ SY1024 @ SY1018 @ SV108 ) )
| ~ ( ~ ( c_member @ SY1019 @ ( sK24_B_x @ SY1024 @ SY1023 @ SY1019 @ SY1018 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SY1019 @ SY1024 ) @ ( c_Product__Type_OPair @ SY1019 @ SY1024 @ ( sK24_B_x @ SY1024 @ SY1023 @ SY1019 @ SY1018 @ SV108 ) @ SY1023 ) @ SY1018 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1210,plain,
! [SV109: $i] :
( ( ! [SY1025: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1025 @ SY1025 ) @ ( c_Product__Type_OPair @ SY1025 @ SY1025 @ ( sK69_B_x @ SY1025 @ SV109 ) @ ( sK70_SY736 @ SY1025 @ SV109 ) ) @ SV109 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1025 @ SY1025 ) @ ( c_Product__Type_OPair @ SY1025 @ SY1025 @ ( sK70_SY736 @ SY1025 @ SV109 ) @ ( sK71_SY738 @ SY1025 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SY1025 @ SY1025 ) @ ( c_Product__Type_OPair @ SY1025 @ SY1025 @ ( sK69_B_x @ SY1025 @ SV109 ) @ ( sK71_SY738 @ SY1025 @ SV109 ) ) @ SV109 ) ) )
| ( c_Relation_Otrans @ SY1025 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1211,plain,
! [SV110: $i] :
( ( ! [SY1026: $i,SY1027: $i,SY1028: $i,SY1029: $i,SY1030: $i] :
~ ( ~ ~ ( ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1032 @ SY1031 ) @ ( tc_prod @ SY1032 @ SY1031 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1032 @ SY1031 ) @ ( tc_prod @ SY1032 @ SY1031 ) @ ( c_Product__Type_OPair @ SY1032 @ SY1031 @ SY1030 @ SY1029 ) @ ( c_Product__Type_OPair @ SY1032 @ SY1031 @ SY1028 @ SY1027 ) ) @ ( c_Wellfounded_Olex__prod @ SY1032 @ SY1031 @ SY1026 @ SV110 ) )
| ( SY1030 = SY1028 )
| ( c_member @ ( tc_prod @ SY1032 @ SY1032 ) @ ( c_Product__Type_OPair @ SY1032 @ SY1032 @ SY1030 @ SY1028 ) @ SY1026 ) )
| ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1034 @ SY1033 ) @ ( tc_prod @ SY1034 @ SY1033 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1034 @ SY1033 ) @ ( tc_prod @ SY1034 @ SY1033 ) @ ( c_Product__Type_OPair @ SY1034 @ SY1033 @ SY1030 @ SY1029 ) @ ( c_Product__Type_OPair @ SY1034 @ SY1033 @ SY1028 @ SY1027 ) ) @ ( c_Wellfounded_Olex__prod @ SY1034 @ SY1033 @ SY1026 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY1033 @ SY1033 ) @ ( c_Product__Type_OPair @ SY1033 @ SY1033 @ SY1029 @ SY1027 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY1034 @ SY1034 ) @ ( c_Product__Type_OPair @ SY1034 @ SY1034 @ SY1030 @ SY1028 ) @ SY1026 ) ) )
| ~ ~ ( ~ ! [SY1035: $i] :
( ( SY1030 != SY1028 )
| ~ ( c_member @ ( tc_prod @ SY1035 @ SY1035 ) @ ( c_Product__Type_OPair @ SY1035 @ SY1035 @ SY1029 @ SY1027 ) @ SV110 )
| ! [SY1036: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY1036 @ SY1035 ) @ ( tc_prod @ SY1036 @ SY1035 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1036 @ SY1035 ) @ ( tc_prod @ SY1036 @ SY1035 ) @ ( c_Product__Type_OPair @ SY1036 @ SY1035 @ SY1030 @ SY1029 ) @ ( c_Product__Type_OPair @ SY1036 @ SY1035 @ SY1028 @ SY1027 ) ) @ ( c_Wellfounded_Olex__prod @ SY1036 @ SY1035 @ SY1026 @ SV110 ) ) )
| ~ ! [SY1037: $i,SY1038: $i] :
( ~ ( c_member @ ( tc_prod @ SY1038 @ SY1038 ) @ ( c_Product__Type_OPair @ SY1038 @ SY1038 @ SY1030 @ SY1028 ) @ SY1026 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1038 @ SY1037 ) @ ( tc_prod @ SY1038 @ SY1037 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1038 @ SY1037 ) @ ( tc_prod @ SY1038 @ SY1037 ) @ ( c_Product__Type_OPair @ SY1038 @ SY1037 @ SY1030 @ SY1029 ) @ ( c_Product__Type_OPair @ SY1038 @ SY1037 @ SY1028 @ SY1027 ) ) @ ( c_Wellfounded_Olex__prod @ SY1038 @ SY1037 @ SY1026 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1212,plain,
! [SV111: $i] :
( ( ! [SY1039: $i,SY1040: $i,SY1041: $i] :
~ ( ~ ! [SY1042: $i,SY1043: $i] :
( ! [SY1044: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1043 @ SY1043 ) @ ( c_Product__Type_OPair @ SY1043 @ SY1043 @ ( sK60_B_z @ SY1044 @ SY1043 @ SY1042 @ SY1041 @ SY1040 @ SY1039 @ SV111 ) @ SY1039 ) @ SY1041 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1043 @ SY1042 @ SY1041 @ SY1040 @ ( sK60_B_z @ SY1044 @ SY1043 @ SY1042 @ SY1041 @ SY1040 @ SY1039 @ SV111 ) @ ( hAPP @ SY1044 @ ( sK60_B_z @ SY1044 @ SY1043 @ SY1042 @ SY1041 @ SY1040 @ SY1039 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SY1040 @ SV111 ) @ SY1039 )
!= ( hAPP @ ( hAPP @ SY1040 @ SY1044 ) @ SY1039 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1043 @ SY1042 @ SY1041 @ SY1040 @ SY1039 @ ( hAPP @ ( hAPP @ SY1040 @ SV111 ) @ SY1039 ) ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1046 @ SY1045 @ SY1041 @ SY1040 @ SY1039 @ ( hAPP @ ( hAPP @ SY1040 @ SV111 ) @ SY1039 ) )
| ~ ( ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SY1046 @ SY1046 ) @ ( c_Product__Type_OPair @ SY1046 @ SY1046 @ SY1047 @ SY1039 ) @ SY1041 )
| ( c_Recdef_Owfrec__rel @ SY1046 @ SY1045 @ SY1041 @ SY1040 @ SY1047 @ ( hAPP @ ( sK59_B_g @ SY1046 @ SY1045 @ SY1041 @ SY1040 @ SY1039 @ SV111 ) @ SY1047 ) ) )
| ( ( hAPP @ ( hAPP @ SY1040 @ SV111 ) @ SY1039 )
!= ( hAPP @ ( hAPP @ SY1040 @ ( sK59_B_g @ SY1046 @ SY1045 @ SY1041 @ SY1040 @ SY1039 @ SV111 ) ) @ SY1039 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1213,plain,
! [SV112: $i] :
( ( ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1049 @ SY1049 ) @ ( c_Product__Type_OPair @ SY1049 @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ SY1048 ) @ SV112 )
| ~ ~ ( c_member @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ( c_member @ SY1049 @ SY1048 @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ~ ! [SY1050: $i,SY1051: $i] :
( ~ ( c_member @ SY1051 @ SY1050 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) )
| ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SY1051 @ SY1051 ) @ ( c_Product__Type_OPair @ SY1051 @ SY1051 @ SY1052 @ SY1050 ) @ SV112 )
| ( c_member @ SY1051 @ SY1052 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1214,plain,
! [SV113: $i] :
( ( ! [SY1053: $i,SY1054: $i,SY1055: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY1055 @ ( sK9_B_x @ SY1055 @ SY1054 @ SY1053 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SY1054 @ ( hAPP @ SY1053 @ ( sK9_B_x @ SY1055 @ SY1054 @ SY1053 @ SV113 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SY1054 ) @ ( c_Recdef_Osame__fst @ SV113 @ SY1054 @ SY1055 @ SY1053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1215,plain,
! [SV114: $i] :
( ( ! [SY1056: $i] :
~ ( ~ ! [SY1057: $i,SY1058: $i] :
( ! [SY1059: $i] :
~ ( c_member @ ( tc_prod @ SY1058 @ SY1056 ) @ ( c_Product__Type_OPair @ SY1058 @ SY1056 @ SY1057 @ SY1059 ) @ SV114 )
| ( c_member @ SY1058 @ SY1057 @ ( c_Relation_ODomain @ SY1058 @ SY1056 @ SV114 ) ) )
| ~ ! [SY1060: $i,SY1061: $i] :
( ~ ( c_member @ SY1061 @ SY1060 @ ( c_Relation_ODomain @ SY1061 @ SY1056 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY1061 @ SY1056 ) @ ( c_Product__Type_OPair @ SY1061 @ SY1056 @ SY1060 @ ( sK66_B_y @ SY1061 @ SY1060 @ SY1056 @ SV114 ) ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1216,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1217,plain,
! [SV115: $i] :
( ( ! [SY1062: $i] :
~ ( ~ ! [SY1063: $i,SY1064: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1064 @ SV115 )
| ( c_member @ ( tc_prod @ SY1064 @ SY1064 ) @ ( c_Product__Type_OPair @ SY1064 @ SY1064 @ SY1062 @ SY1063 ) @ ( c_Transitive__Closure_Ortrancl @ SY1064 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1064 @ ( c_Set_Oinsert @ ( tc_prod @ SY1064 @ SY1064 ) @ ( c_Product__Type_OPair @ SY1064 @ SY1064 @ SY1063 @ SY1062 ) @ SV115 ) ) )
| ~ ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1066 @ ( c_Set_Oinsert @ ( tc_prod @ SY1066 @ SY1066 ) @ ( c_Product__Type_OPair @ SY1066 @ SY1066 @ SY1065 @ SY1062 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1066 @ SV115 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1068 @ ( c_Set_Oinsert @ ( tc_prod @ SY1068 @ SY1068 ) @ ( c_Product__Type_OPair @ SY1068 @ SY1068 @ SY1067 @ SY1062 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1068 @ SY1068 ) @ ( c_Product__Type_OPair @ SY1068 @ SY1068 @ SY1062 @ SY1067 ) @ ( c_Transitive__Closure_Ortrancl @ SY1068 @ SV115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1218,plain,
! [SV116: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i,SY1072: $i,SY1073: $i,SY1074: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1072 @ SY1071 ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1070 @ SY1069 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1074 @ SY1073 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1072 @ SY1071 )
= ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1070 @ SY1069 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1072 @ SY1071 ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ ( sK46_B_a @ SY1074 @ SY1073 @ SY1072 @ SY1071 @ SY1070 @ SY1069 @ SV116 ) @ ( sK47_SY726 @ SY1074 @ SY1073 @ SY1072 @ SY1071 @ SY1070 @ SY1069 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1074 @ SY1073 ) @ ( tc_prod @ SY1074 @ SY1073 ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ ( sK46_B_a @ SY1074 @ SY1073 @ SY1072 @ SY1071 @ SY1070 @ SY1069 @ SV116 ) @ ( sK47_SY726 @ SY1074 @ SY1073 @ SY1072 @ SY1071 @ SY1070 @ SY1069 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY1074 @ SY1073 @ SY1070 @ SY1069 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1074 @ SY1073 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1219,plain,
! [SV117: $i] :
( ( ~ ( ~ ! [SY1075: $i,SY1076: $i] :
( ~ ( ~ ( c_member @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( c_member @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY1076 @ SY1075 @ SV117 )
!= ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY1076 @ SY1075 @ SV117 ) )
| ~ ! [SY1077: $i,SY1078: $i] :
( ~ ( c_Relation_Ototal__on @ SY1078 @ SY1077 @ SV117 )
| ! [SY1079: $i] :
( ~ ( c_member @ SY1078 @ SY1079 @ SY1077 )
| ! [SY1080: $i] :
( ~ ( c_member @ SY1078 @ SY1080 @ SY1077 )
| ( SY1079 = SY1080 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1079 @ SY1080 ) @ SV117 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1080 @ SY1079 ) @ SV117 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1220,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1221,plain,
! [SV118: $i] :
( ( ! [SY1081: $i,SY1082: $i,SY1083: $i,SY1084: $i] :
( ~ ( c_member @ SY1084 @ SY1083 @ ( c_Relation_OImage @ SY1082 @ SY1084 @ SY1081 @ SV118 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1082 @ SY1084 ) @ ( c_Product__Type_OPair @ SY1082 @ SY1084 @ ( sK23_B_x @ SY1084 @ SY1083 @ SY1082 @ SY1081 @ SV118 ) @ SY1083 ) @ SY1081 )
| ~ ( c_member @ SY1082 @ ( sK23_B_x @ SY1084 @ SY1083 @ SY1082 @ SY1081 @ SV118 ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1222,plain,
! [SV119: $i] :
( ( ! [SY1085: $i] :
~ ( ~ ! [SY1086: $i] :
( ! [SY1087: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1087 @ SY1086 @ SY1085 ) @ SV119 ) )
| ( SY1086 = SV119 )
| ( hBOOL @ ( hAPP @ SY1085 @ SV119 ) ) )
| ~ ~ ( ~ ! [SY1088: $i] :
( ( SY1088 != SV119 )
| ! [SY1089: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1089 @ SY1088 @ SY1085 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1085 @ SV119 ) )
| ! [SY1090: $i,SY1091: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1091 @ SY1090 @ SY1085 ) @ SV119 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1223,plain,
! [SV120: $i] :
( ( ! [SY1092: $i,SY1093: $i,SY1094: $i] :
~ ( ~ ( ( SY1094 != SY1092 )
| ( SY1093 != SV120 )
| ! [SY1095: $i,SY1096: $i] :
( ( c_Product__Type_OPair @ SY1096 @ SY1095 @ SY1094 @ SY1093 )
= ( c_Product__Type_OPair @ SY1096 @ SY1095 @ SY1092 @ SV120 ) ) )
| ~ ~ ( ~ ( ! [SY1097: $i,SY1098: $i] :
( ( c_Product__Type_OPair @ SY1098 @ SY1097 @ SY1094 @ SY1093 )
!= ( c_Product__Type_OPair @ SY1098 @ SY1097 @ SY1092 @ SV120 ) )
| ( SY1094 = SY1092 ) )
| ~ ( ! [SY1099: $i,SY1100: $i] :
( ( c_Product__Type_OPair @ SY1100 @ SY1099 @ SY1094 @ SY1093 )
!= ( c_Product__Type_OPair @ SY1100 @ SY1099 @ SY1092 @ SV120 ) )
| ( SY1093 = SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1224,plain,
! [SV121: $i] :
( ( ~ ( ~ ! [SY1101: $i] :
( ( SY1101 != SV121 )
| ! [SY1102: $i] : ( c_member @ SY1102 @ SY1101 @ ( c_fequal @ SV121 ) ) )
| ~ ! [SY1103: $i] :
( ! [SY1104: $i] :
~ ( c_member @ SY1104 @ SY1103 @ ( c_fequal @ SV121 ) )
| ( SY1103 = SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1225,plain,
! [SV122: $i] :
( ( ! [SY1105: $i] :
~ ( ~ ~ ( ~ ! [SY1106: $i] :
( ! [SY1107: $i] :
~ ( c_member @ ( tc_prod @ SY1107 @ SY1107 ) @ ( c_Product__Type_OPair @ SY1107 @ SY1107 @ SY1106 @ SY1105 ) @ ( c_Transitive__Closure_Ortrancl @ SY1107 @ SV122 ) )
| ( SY1106 != SY1105 )
| ( SY1106 = SY1105 ) )
| ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( c_member @ ( tc_prod @ SY1109 @ SY1109 ) @ ( c_Product__Type_OPair @ SY1109 @ SY1109 @ SY1108 @ SY1105 ) @ ( c_Transitive__Closure_Ortrancl @ SY1109 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1109 @ SY1109 ) @ ( c_Product__Type_OPair @ SY1109 @ SY1109 @ SY1108 @ SY1105 ) @ ( c_Transitive__Closure_Otrancl @ SY1109 @ SV122 ) )
| ( SY1108 = SY1105 ) ) )
| ~ ~ ( ~ ! [SY1110: $i,SY1111: $i] :
( ( SY1110 = SY1105 )
| ~ ( c_member @ ( tc_prod @ SY1111 @ SY1111 ) @ ( c_Product__Type_OPair @ SY1111 @ SY1111 @ SY1110 @ SY1105 ) @ ( c_Transitive__Closure_Otrancl @ SY1111 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1111 @ SY1111 ) @ ( c_Product__Type_OPair @ SY1111 @ SY1111 @ SY1110 @ SY1105 ) @ ( c_Transitive__Closure_Ortrancl @ SY1111 @ SV122 ) ) )
| ~ ! [SY1112: $i] :
( ( SY1112 != SY1105 )
| ! [SY1113: $i] : ( c_member @ ( tc_prod @ SY1113 @ SY1113 ) @ ( c_Product__Type_OPair @ SY1113 @ SY1113 @ SY1112 @ SY1105 ) @ ( c_Transitive__Closure_Ortrancl @ SY1113 @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1227,plain,
! [SV123: $i] :
( ( ~ ( ~ ! [SY1114: $i,SY1115: $i] :
( ~ ( c_Relation_Oirrefl @ SY1115 @ SV123 )
| ~ ( c_Relation_Otrans @ SY1115 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SY1115 @ SY1114 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY1115 @ SY1114 @ SV123 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
| ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1228,plain,
! [SV124: $i] :
( ( ~ ( ~ ! [SY1122: $i,SY1123: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1123 @ ( sK75_B_x1 @ SY1123 @ SY1122 @ SV124 ) ) )
| ! [SY1124: $i,SY1125: $i] : ( hBOOL @ ( hAPP @ SY1123 @ ( c_Product__Type_OPair @ SY1122 @ SV124 @ SY1124 @ SY1125 ) ) ) )
| ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1127 @ ( c_Product__Type_OPair @ SY1126 @ SV124 @ ( sK73_B_a @ SY1127 @ SY1126 @ SV124 ) @ ( sK74_SY739 @ SY1127 @ SY1126 @ SV124 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1127 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1229,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
| ~ ~ ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1230,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1231,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1232,plain,
! [SV125: $i] :
( ( ! [SY1129: $i] :
~ ( ~ ! [SY1130: $i,SY1131: $i] :
( ( SY1130 != SY1129 )
| ~ ( c_member @ SY1131 @ SY1130 @ SV125 )
| ( c_member @ ( tc_prod @ SY1131 @ SY1131 ) @ ( c_Product__Type_OPair @ SY1131 @ SY1131 @ SY1130 @ SY1129 ) @ ( c_Relation_OId__on @ SY1131 @ SV125 ) ) )
| ~ ~ ( ~ ! [SY1132: $i] :
( ! [SY1133: $i] :
~ ( c_member @ ( tc_prod @ SY1133 @ SY1133 ) @ ( c_Product__Type_OPair @ SY1133 @ SY1133 @ SY1132 @ SY1129 ) @ ( c_Relation_OId__on @ SY1133 @ SV125 ) )
| ( SY1132 = SY1129 ) )
| ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( c_member @ ( tc_prod @ SY1135 @ SY1135 ) @ ( c_Product__Type_OPair @ SY1135 @ SY1135 @ SY1134 @ SY1129 ) @ ( c_Relation_OId__on @ SY1135 @ SV125 ) )
| ( c_member @ SY1135 @ SY1134 @ SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1233,plain,
! [SV126: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i] :
( ~ ( c_member @ ( tc_prod @ SY1138 @ SY1138 ) @ ( c_Product__Type_OPair @ SY1138 @ SY1138 @ SY1137 @ SY1136 ) @ ( c_Transitive__Closure_Ortrancl @ SY1138 @ SV126 ) )
| ( SY1137 = SY1136 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1138 @ SY1138 ) @ ( c_Product__Type_OPair @ SY1138 @ SY1138 @ SY1137 @ ( sK45_B_y @ SY1138 @ SY1137 @ SY1136 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1138 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SY1138 @ SY1138 ) @ ( c_Product__Type_OPair @ SY1138 @ SY1138 @ ( sK45_B_y @ SY1138 @ SY1137 @ SY1136 @ SV126 ) @ SY1136 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1234,plain,
! [SV127: $i] :
( ( ! [SY1139: $i] :
~ ( ~ ! [SY1140: $i,SY1141: $i] :
( ( c_member @ SY1141 @ SY1140 @ SY1139 )
| ( c_member @ SY1141 @ SY1140 @ SV127 )
| ( ( c_Set_Oinsert @ SY1141 @ SY1140 @ SY1139 )
!= ( c_Set_Oinsert @ SY1141 @ SY1140 @ SV127 ) )
| ( SY1139 = SV127 ) )
| ~ ! [SY1142: $i,SY1143: $i] :
( ( c_member @ SY1143 @ SY1142 @ SY1139 )
| ( c_member @ SY1143 @ SY1142 @ SV127 )
| ( SY1139 != SV127 )
| ( ( c_Set_Oinsert @ SY1143 @ SY1142 @ SY1139 )
= ( c_Set_Oinsert @ SY1143 @ SY1142 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1235,plain,
! [SV128: $i] :
( ( ! [SY1144: $i,SY1145: $i,SY1146: $i] :
( ~ ( c_member @ ( tc_prod @ SY1146 @ SY1146 ) @ ( c_Product__Type_OPair @ SY1146 @ SY1146 @ SY1145 @ SY1144 ) @ ( c_Transitive__Closure_Otrancl @ SY1146 @ SV128 ) )
| ( c_member @ ( tc_prod @ SY1146 @ SY1146 ) @ ( c_Product__Type_OPair @ SY1146 @ SY1146 @ SY1145 @ SY1144 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1146 @ SY1146 ) @ ( c_Product__Type_OPair @ SY1146 @ SY1146 @ SY1145 @ ( sK37_B_c @ SY1146 @ SY1145 @ SY1144 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1146 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SY1146 @ SY1146 ) @ ( c_Product__Type_OPair @ SY1146 @ SY1146 @ ( sK37_B_c @ SY1146 @ SY1145 @ SY1144 @ SV128 ) @ SY1144 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1236,plain,
! [SV129: $i] :
( ( ! [SY1147: $i] :
~ ( ~ ! [SY1148: $i,SY1149: $i] :
( ( c_member @ SY1149 @ SY1148 @ ( c_Relation_ODomain @ SY1149 @ SY1149 @ SY1147 ) )
| ( SY1148 != SV129 )
| ( c_member @ ( tc_prod @ SY1149 @ SY1149 ) @ ( c_Product__Type_OPair @ SY1149 @ SY1149 @ SY1148 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1149 @ SY1147 ) ) )
| ~ ! [SY1150: $i,SY1151: $i] :
( ( c_member @ SY1151 @ SY1150 @ ( c_Relation_ODomain @ SY1151 @ SY1151 @ SY1147 ) )
| ~ ( c_member @ ( tc_prod @ SY1151 @ SY1151 ) @ ( c_Product__Type_OPair @ SY1151 @ SY1151 @ SY1150 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1151 @ SY1147 ) )
| ( SY1150 = SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1237,plain,
! [SV130: $i] :
( ( ! [SY1152: $i,SY1153: $i,SY1154: $i] :
~ ( ~ ( ! [SY1155: $i,SY1156: $i] :
( ( c_Product__Type_OPair @ SY1156 @ SY1155 @ SY1154 @ SY1153 )
!= ( c_Product__Type_OPair @ SY1156 @ SY1155 @ SY1152 @ SV130 ) )
| ( SY1154 = SY1152 ) )
| ~ ( ! [SY1157: $i,SY1158: $i] :
( ( c_Product__Type_OPair @ SY1158 @ SY1157 @ SY1154 @ SY1153 )
!= ( c_Product__Type_OPair @ SY1158 @ SY1157 @ SY1152 @ SV130 ) )
| ( SY1153 = SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1238,plain,
! [SV131: $i] :
( ( ! [SY1159: $i,SY1160: $i,SY1161: $i,SY1162: $i,SY1163: $i,SY1164: $i,SY1165: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ SY1163 @ SY1162 ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ SY1161 @ SY1160 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1165 @ SY1164 ) @ SY1159 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1163 ) @ SY1162 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ SY1163 @ SY1162 ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ ( sK18_B_a @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) @ ( sK19_SY714 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1165 @ SY1164 ) @ SY1159 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1165 @ SY1164 ) @ ( tc_prod @ SY1165 @ SY1164 ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ ( sK18_B_a @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) @ ( sK19_SY714 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY1165 @ SY1164 @ ( sK20_SY717 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) @ ( sK21_SY719 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) ) @ SY1159 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) @ ( sK19_SY714 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) @ ( sK21_SY719 @ SY1165 @ SY1164 @ SY1163 @ SY1162 @ SY1161 @ SY1160 @ SY1159 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1161 ) @ SY1160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1239,plain,
! [SV132: $i] :
( ( ! [SY1166: $i] :
~ ( ~ ! [SY1167: $i,SY1168: $i] :
( ! [SY1169: $i] :
~ ( c_member @ ( tc_prod @ SY1166 @ SY1168 ) @ ( c_Product__Type_OPair @ SY1166 @ SY1168 @ SY1169 @ SY1167 ) @ SV132 )
| ( c_member @ SY1168 @ SY1167 @ ( c_Relation_ORange @ SY1166 @ SY1168 @ SV132 ) ) )
| ~ ! [SY1170: $i,SY1171: $i] :
( ~ ( c_member @ SY1171 @ SY1170 @ ( c_Relation_ORange @ SY1166 @ SY1171 @ SV132 ) )
| ( c_member @ ( tc_prod @ SY1166 @ SY1171 ) @ ( c_Product__Type_OPair @ SY1166 @ SY1171 @ ( sK65_B_y @ SY1171 @ SY1170 @ SY1166 @ SV132 ) @ SY1170 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1240,plain,
! [SV133: $i] :
( ( ! [SY1172: $i,SY1173: $i,SY1174: $i] :
~ ( ~ ! [SY1175: $i,SY1176: $i] :
( ! [SY1177: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1176 @ SY1176 ) @ ( c_Product__Type_OPair @ SY1176 @ SY1176 @ ( sK55_B_z @ SY1177 @ SY1176 @ SY1175 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) @ SY1172 ) @ SY1174 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1176 @ SY1175 @ SY1174 @ SY1173 @ ( sK55_B_z @ SY1177 @ SY1176 @ SY1175 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) @ ( hAPP @ SY1177 @ ( sK55_B_z @ SY1177 @ SY1176 @ SY1175 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SY1173 @ SY1177 ) @ SY1172 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1176 @ SY1175 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) )
| ~ ! [SY1178: $i,SY1179: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1179 @ SY1178 @ SY1174 @ SY1173 @ SY1172 @ SV133 )
| ~ ( ~ ! [SY1180: $i] :
( ~ ( c_member @ ( tc_prod @ SY1179 @ SY1179 ) @ ( c_Product__Type_OPair @ SY1179 @ SY1179 @ SY1180 @ SY1172 ) @ SY1174 )
| ( c_Recdef_Owfrec__rel @ SY1179 @ SY1178 @ SY1174 @ SY1173 @ SY1180 @ ( hAPP @ ( sK54_B_g @ SY1179 @ SY1178 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) @ SY1180 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SY1173 @ ( sK54_B_g @ SY1179 @ SY1178 @ SY1174 @ SY1173 @ SY1172 @ SV133 ) ) @ SY1172 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1241,plain,
! [SV134: $i] :
( ( ! [SY1181: $i,SY1182: $i,SY1183: $i] :
( ~ ( c_member @ ( tc_prod @ SY1183 @ SY1183 ) @ ( c_Product__Type_OPair @ SY1183 @ SY1183 @ SY1182 @ SY1181 ) @ ( c_Transitive__Closure_Otrancl @ SY1183 @ SV134 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1183 @ SY1183 ) @ ( c_Product__Type_OPair @ SY1183 @ SY1183 @ SY1182 @ ( sK42_B_z @ SY1183 @ SY1182 @ SY1181 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1183 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SY1183 @ SY1183 ) @ ( c_Product__Type_OPair @ SY1183 @ SY1183 @ ( sK42_B_z @ SY1183 @ SY1182 @ SY1181 @ SV134 ) @ SY1181 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1242,plain,
! [SV135: $i] :
( ( ! [SY1184: $i,SY1185: $i,SY1186: $i] :
~ ( ~ ! [SY1187: $i] :
( ! [SY1188: $i] :
~ ( c_member @ ( tc_prod @ SY1188 @ SY1188 ) @ ( c_Product__Type_OPair @ SY1188 @ SY1188 @ SY1187 @ SY1186 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY1185 @ SY1188 @ SY1184 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SY1185 @ SY1185 ) @ ( c_Product__Type_OPair @ SY1185 @ SY1185 @ ( hAPP @ SV135 @ SY1187 ) @ ( hAPP @ SV135 @ SY1186 ) ) @ SY1184 ) )
| ~ ! [SY1189: $i] :
( ~ ( c_member @ ( tc_prod @ SY1185 @ SY1185 ) @ ( c_Product__Type_OPair @ SY1185 @ SY1185 @ ( hAPP @ SV135 @ SY1189 ) @ ( hAPP @ SV135 @ SY1186 ) ) @ SY1184 )
| ! [SY1190: $i] : ( c_member @ ( tc_prod @ SY1190 @ SY1190 ) @ ( c_Product__Type_OPair @ SY1190 @ SY1190 @ SY1189 @ SY1186 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY1185 @ SY1190 @ SY1184 ) @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1243,plain,
! [SV136: $i] :
( ( ~ ( ~ ! [SY1191: $i] :
( ! [SY1192: $i] :
~ ( c_member @ SY1192 @ SY1191 @ SV136 )
| ( hBOOL @ ( hAPP @ SV136 @ SY1191 ) ) )
| ~ ! [SY1193: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ SY1193 ) )
| ! [SY1194: $i] : ( c_member @ SY1194 @ SY1193 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1244,plain,
! [SV137: $i] :
( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i,SY1199: $i,SY1200: $i,SY1201: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ SY1199 @ SY1198 ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ SY1197 @ SY1196 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1201 @ SY1200 ) @ SY1195 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1197 ) @ SY1196 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ ( sK14_B_a @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) @ ( sK15_SY708 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ ( sK16_SY711 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) @ ( sK17_SY713 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) ) @ SY1195 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1201 @ SY1200 ) @ ( tc_prod @ SY1201 @ SY1200 ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ ( sK16_SY711 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) @ ( sK17_SY713 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1201 @ SY1200 @ SY1197 @ SY1196 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1201 @ SY1200 ) @ SY1195 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) @ ( sK17_SY713 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) @ ( sK15_SY708 @ SY1201 @ SY1200 @ SY1199 @ SY1198 @ SY1197 @ SY1196 @ SY1195 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1199 ) @ SY1198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1245,plain,
! [SV138: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i,SY1205: $i,SY1206: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1206 @ SY1206 ) @ ( c_Product__Type_OPair @ SY1206 @ SY1206 @ ( sK56_B_z @ SY1206 @ SY1205 @ SY1204 @ SY1203 @ SY1202 @ SV138 ) @ SY1205 ) @ SY1204 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1206 @ SY1203 @ SY1204 @ SY1202 @ ( sK56_B_z @ SY1206 @ SY1205 @ SY1204 @ SY1203 @ SY1202 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SY1206 @ SY1205 @ SY1204 @ SY1203 @ SY1202 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY1206 @ SY1203 @ SY1204 @ SY1202 @ SY1205 @ ( hAPP @ ( hAPP @ SY1202 @ SV138 ) @ SY1205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1246,plain,
! [SV139: $i] :
( ( ~ ( ~ ! [SY1207: $i] :
( ( SY1207 != SV139 )
| ! [SY1208: $i] : ( c_member @ ( tc_prod @ SY1208 @ SY1208 ) @ ( c_Product__Type_OPair @ SY1208 @ SY1208 @ SY1207 @ SV139 ) @ ( c_Relation_OId @ SY1208 ) ) )
| ~ ! [SY1209: $i] :
( ! [SY1210: $i] :
~ ( c_member @ ( tc_prod @ SY1210 @ SY1210 ) @ ( c_Product__Type_OPair @ SY1210 @ SY1210 @ SY1209 @ SV139 ) @ ( c_Relation_OId @ SY1210 ) )
| ( SY1209 = SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1247,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1248,plain,
! [SV140: $i] :
( ( ! [SY1211: $i] :
~ ( ~ ! [SY1212: $i,SY1213: $i] :
( ( SY1213 != SY1212 )
| ~ ( c_member @ SY1211 @ SV140 @ SY1213 )
| ( c_member @ SY1211 @ SV140 @ SY1212 ) )
| ~ ! [SY1214: $i,SY1215: $i] :
( ( SY1215 != SY1214 )
| ~ ( c_member @ SY1211 @ SV140 @ SY1214 )
| ( c_member @ SY1211 @ SV140 @ SY1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1249,plain,
! [SV141: $i] :
( ( ! [SY1216: $i] :
~ ( ~ ! [SY1217: $i,SY1218: $i] :
( ( SY1218 != SY1217 )
| ~ ( c_member @ SY1216 @ SY1218 @ SV141 )
| ( c_member @ SY1216 @ SY1217 @ SV141 ) )
| ~ ! [SY1219: $i,SY1220: $i] :
( ( SY1220 != SY1219 )
| ~ ( c_member @ SY1216 @ SY1219 @ SV141 )
| ( c_member @ SY1216 @ SY1220 @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1250,plain,
! [SV142: $i] :
( ( ! [SY1221: $i,SY1222: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1222 @ SY1221 ) @ ( c_Product__Type_OPair @ SY1222 @ SY1221 @ ( sK48_B_x @ SY1222 @ SY1221 @ SV142 ) @ ( sK49_SY727 @ SY1222 @ SY1221 @ SV142 ) ) @ SV142 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1222 @ SY1221 ) @ ( c_Product__Type_OPair @ SY1222 @ SY1221 @ ( sK48_B_x @ SY1222 @ SY1221 @ SV142 ) @ ( sK50_SY729 @ SY1222 @ SY1221 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SY1222 @ SY1221 @ SV142 )
!= ( sK50_SY729 @ SY1222 @ SY1221 @ SV142 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1222 @ SY1221 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1251,plain,
! [SV143: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
| ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1252,plain,
! [SV144: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i] :
( ~ ( c_member @ ( tc_prod @ SY1241 @ SY1241 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1241 @ SY1240 @ SY1239 ) @ ( c_Transitive__Closure_Otrancl @ SY1241 @ SV144 ) )
| ( c_member @ ( tc_prod @ SY1241 @ SY1241 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1241 @ SY1240 @ SY1239 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1241 @ SY1241 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1241 @ SY1240 @ ( sK38_B_y @ SY1241 @ SY1240 @ SY1239 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SY1241 @ SY1241 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1241 @ ( sK38_B_y @ SY1241 @ SY1240 @ SY1239 @ SV144 ) @ SY1239 ) @ ( c_Transitive__Closure_Otrancl @ SY1241 @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1253,plain,
! [SV145: $i] :
( ( ! [SY1242: $i] :
~ ( ~ ! [SY1243: $i,SY1244: $i] :
( ~ ( c_Wellfounded_Owf @ SY1244 @ SV145 )
| ( c_member @ ( tc_prod @ SY1244 @ SY1244 ) @ ( c_Product__Type_OPair @ SY1244 @ SY1244 @ SY1242 @ SY1243 ) @ ( c_Transitive__Closure_Ortrancl @ SY1244 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1244 @ ( c_Set_Oinsert @ ( tc_prod @ SY1244 @ SY1244 ) @ ( c_Product__Type_OPair @ SY1244 @ SY1244 @ SY1243 @ SY1242 ) @ SV145 ) ) )
| ~ ~ ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( c_Wellfounded_Owf @ SY1246 @ ( c_Set_Oinsert @ ( tc_prod @ SY1246 @ SY1246 ) @ ( c_Product__Type_OPair @ SY1246 @ SY1246 @ SY1245 @ SY1242 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1246 @ SV145 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( c_Wellfounded_Owf @ SY1248 @ ( c_Set_Oinsert @ ( tc_prod @ SY1248 @ SY1248 ) @ ( c_Product__Type_OPair @ SY1248 @ SY1248 @ SY1247 @ SY1242 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1248 @ SY1248 ) @ ( c_Product__Type_OPair @ SY1248 @ SY1248 @ SY1242 @ SY1247 ) @ ( c_Transitive__Closure_Ortrancl @ SY1248 @ SV145 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1254,plain,
! [SV146: $i] :
( ( ~ ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( c_Relation_Orefl__on @ SY1250 @ SY1249 @ SV146 )
| ~ ( c_Relation_Otrans @ SY1250 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SY1250 @ SY1249 @ SV146 ) )
| ~ ~ ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) )
| ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1255,plain,
! [SV147: $i] :
( ( ! [SY1255: $i,SY1256: $i] :
( ~ ( c_member @ ( tc_prod @ SY1256 @ SY1256 ) @ SY1255 @ ( c_Relation_OId__on @ SY1256 @ SV147 ) )
| ~ ( ~ ( c_member @ SY1256 @ ( sK64_B_x @ SY1256 @ SY1255 @ SV147 ) @ SV147 )
| ( SY1255
!= ( c_Product__Type_OPair @ SY1256 @ SY1256 @ ( sK64_B_x @ SY1256 @ SY1255 @ SV147 ) @ ( sK64_B_x @ SY1256 @ SY1255 @ SV147 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1256,plain,
! [SV148: $i] :
( ( ! [SY1257: $i] :
~ ( ~ ~ ( ~ ! [SY1258: $i,SY1259: $i] :
( ( SY1259 != SY1258 )
| ( c_member @ SY1257 @ SV148 @ SY1259 )
| ~ ( c_member @ SY1257 @ SV148 @ SY1259 ) )
| ~ ! [SY1260: $i,SY1261: $i] :
( ( SY1261 != SY1260 )
| ( c_member @ SY1257 @ SV148 @ SY1261 )
| ~ ( c_member @ SY1257 @ SV148 @ SY1260 ) ) )
| ~ ~ ( ~ ! [SY1262: $i,SY1263: $i] :
( ( SY1263 != SY1262 )
| ( c_member @ SY1257 @ SV148 @ SY1262 )
| ~ ( c_member @ SY1257 @ SV148 @ SY1263 ) )
| ~ ! [SY1264: $i] :
( ! [SX3: $i] : ( SX3 != SY1264 )
| ( c_member @ SY1257 @ SV148 @ SY1264 )
| ~ ( c_member @ SY1257 @ SV148 @ SY1264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1257,plain,
! [SV149: $i] :
( ( ! [SY1266: $i] :
~ ( ~ ! [SY1267: $i,SY1268: $i] :
( ~ ( c_member @ SY1268 @ SY1267 @ ( c_Set_Oinsert @ SY1268 @ SY1266 @ SV149 ) )
| ( SY1267 = SY1266 )
| ( c_member @ SY1268 @ SY1267 @ SV149 ) )
| ~ ~ ( ~ ! [SY1269: $i] :
( ( SY1269 != SY1266 )
| ! [SY1270: $i] : ( c_member @ SY1270 @ SY1269 @ ( c_Set_Oinsert @ SY1270 @ SY1266 @ SV149 ) ) )
| ~ ! [SY1271: $i,SY1272: $i] :
( ~ ( c_member @ SY1272 @ SY1271 @ SV149 )
| ( c_member @ SY1272 @ SY1271 @ ( c_Set_Oinsert @ SY1272 @ SY1266 @ SV149 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1258,plain,
! [SV150: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i,SY1276: $i] :
( ~ ( c_member @ ( tc_prod @ SY1276 @ SY1276 ) @ ( c_Product__Type_OPair @ SY1276 @ SY1276 @ SY1275 @ SY1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY1276 @ SY1273 ) )
| ~ ( hBOOL @ ( hAPP @ SV150 @ SY1274 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1276 @ SY1276 ) @ ( c_Product__Type_OPair @ SY1276 @ SY1276 @ ( sK12_B_y @ SY1276 @ SY1275 @ SY1274 @ SY1273 @ SV150 ) @ ( sK13_SY707 @ SY1276 @ SY1275 @ SY1274 @ SY1273 @ SV150 ) ) @ SY1273 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1276 @ SY1276 ) @ ( c_Product__Type_OPair @ SY1276 @ SY1276 @ ( sK13_SY707 @ SY1276 @ SY1275 @ SY1274 @ SY1273 @ SV150 ) @ SY1274 ) @ ( c_Transitive__Closure_Ortrancl @ SY1276 @ SY1273 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SY1276 @ SY1275 @ SY1274 @ SY1273 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SY1276 @ SY1275 @ SY1274 @ SY1273 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SY1275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1259,plain,
! [SV151: $i] :
( ( ! [SY1277: $i,SY1278: $i] :
( ( c_member @ SY1278 @ SY1277 @ ( c_Wellfounded_Oacc @ SY1278 @ SV151 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1278 @ SY1278 ) @ ( c_Product__Type_OPair @ SY1278 @ SY1278 @ ( sK58_B_z @ SY1278 @ SY1277 @ SV151 ) @ SY1277 ) @ SV151 )
| ~ ~ ( c_member @ SY1278 @ ( sK58_B_z @ SY1278 @ SY1277 @ SV151 ) @ ( c_Wellfounded_Oacc @ SY1278 @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1260,plain,
! [SV152: $i] :
( ( ! [SY1279: $i,SY1280: $i] :
~ ( ~ ! [SY1281: $i,SY1282: $i] :
( ~ ( c_member @ ( tc_prod @ SY1282 @ SY1281 ) @ ( c_Product__Type_OPair @ SY1282 @ SY1281 @ SY1279 @ SV152 ) @ SY1280 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1282 @ SY1281 @ SY1280 ) @ SY1279 ) @ SV152 ) ) )
| ~ ! [SY1283: $i,SY1284: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1284 @ SY1283 @ SY1280 ) @ SY1279 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1284 @ SY1283 ) @ ( c_Product__Type_OPair @ SY1284 @ SY1283 @ SY1279 @ SV152 ) @ SY1280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1261,plain,
! [SV153: $i] :
( ( ! [SY1285: $i,SY1286: $i,SY1287: $i] :
( ~ ( c_member @ ( tc_prod @ SY1287 @ SY1287 ) @ ( c_Product__Type_OPair @ SY1287 @ SY1287 @ SY1286 @ SY1285 ) @ ( c_Transitive__Closure_Ortrancl @ SY1287 @ SV153 ) )
| ( SY1286 = SY1285 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1287 @ SY1287 ) @ ( c_Product__Type_OPair @ SY1287 @ SY1287 @ SY1286 @ ( sK44_B_y @ SY1287 @ SY1286 @ SY1285 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SY1287 @ SY1287 ) @ ( c_Product__Type_OPair @ SY1287 @ SY1287 @ ( sK44_B_y @ SY1287 @ SY1286 @ SY1285 @ SV153 ) @ SY1285 ) @ ( c_Transitive__Closure_Ortrancl @ SY1287 @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1262,plain,
! [SV154: $i] :
( ( ! [SY1288: $i,SY1289: $i,SY1290: $i,SY1291: $i] :
( ~ ( c_member @ ( tc_prod @ SY1291 @ SY1291 ) @ ( c_Product__Type_OPair @ SY1291 @ SY1291 @ SY1290 @ SY1289 ) @ ( c_Transitive__Closure_Ortrancl @ SY1291 @ SY1288 ) )
| ~ ( hBOOL @ ( hAPP @ SV154 @ SY1290 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1291 @ SY1291 ) @ ( c_Product__Type_OPair @ SY1291 @ SY1291 @ SY1290 @ ( sK10_B_y @ SY1291 @ SY1290 @ SY1289 @ SY1288 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1291 @ SY1288 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1291 @ SY1291 ) @ ( c_Product__Type_OPair @ SY1291 @ SY1291 @ ( sK10_B_y @ SY1291 @ SY1290 @ SY1289 @ SY1288 @ SV154 ) @ ( sK11_SY706 @ SY1291 @ SY1290 @ SY1289 @ SY1288 @ SV154 ) ) @ SY1288 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SY1291 @ SY1290 @ SY1289 @ SY1288 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SY1291 @ SY1290 @ SY1289 @ SY1288 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SY1289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1263,plain,
! [SV155: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i] :
( ~ ( c_member @ ( tc_prod @ SY1294 @ SY1294 ) @ ( c_Product__Type_OPair @ SY1294 @ SY1294 @ SY1293 @ SY1292 ) @ ( c_Transitive__Closure_Otrancl @ SY1294 @ SV155 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1294 @ SY1294 ) @ ( c_Product__Type_OPair @ SY1294 @ SY1294 @ SY1293 @ ( sK41_B_z @ SY1294 @ SY1293 @ SY1292 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SY1294 @ SY1294 ) @ ( c_Product__Type_OPair @ SY1294 @ SY1294 @ ( sK41_B_z @ SY1294 @ SY1293 @ SY1292 @ SV155 ) @ SY1292 ) @ ( c_Transitive__Closure_Ortrancl @ SY1294 @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1264,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1265,plain,
! [SV156: $i] :
( ( ! [SY1295: $i] :
~ ( ~ ! [SY1296: $i] :
( ! [SY1297: $i] :
~ ( c_member @ ( tc_prod @ SY1297 @ SY1297 ) @ ( c_Product__Type_OPair @ SY1297 @ SY1297 @ SY1296 @ SY1295 ) @ ( c_Transitive__Closure_Ortrancl @ SY1297 @ SV156 ) )
| ( SY1296 != SY1295 )
| ( SY1296 = SY1295 ) )
| ~ ! [SY1298: $i,SY1299: $i] :
( ~ ( c_member @ ( tc_prod @ SY1299 @ SY1299 ) @ ( c_Product__Type_OPair @ SY1299 @ SY1299 @ SY1298 @ SY1295 ) @ ( c_Transitive__Closure_Ortrancl @ SY1299 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY1299 @ SY1299 ) @ ( c_Product__Type_OPair @ SY1299 @ SY1299 @ SY1298 @ SY1295 ) @ ( c_Transitive__Closure_Otrancl @ SY1299 @ SV156 ) )
| ( SY1298 = SY1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1266,plain,
! [SV157: $i] :
( ( ! [SY1300: $i] :
~ ( ~ ! [SY1301: $i,SY1302: $i] :
( ~ ( c_member @ SY1302 @ SY1301 @ SY1300 )
| ( c_member @ SY1302 @ SY1301 @ ( c_Set_Oinsert @ SY1302 @ SV157 @ SY1300 ) ) )
| ~ ! [SY1303: $i] :
( ( SY1303 != SV157 )
| ! [SY1304: $i] : ( c_member @ SY1304 @ SY1303 @ ( c_Set_Oinsert @ SY1304 @ SV157 @ SY1300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1267,plain,
! [SV158: $i] :
( ( ! [SY1305: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1305 @ SY1305 ) @ ( c_Product__Type_OPair @ SY1305 @ SY1305 @ ( sK26_B_x @ SY1305 @ SV158 ) @ ( sK27_SY720 @ SY1305 @ SV158 ) ) @ SV158 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1305 @ SY1305 ) @ ( c_Product__Type_OPair @ SY1305 @ SY1305 @ ( sK27_SY720 @ SY1305 @ SV158 ) @ ( sK26_B_x @ SY1305 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SY1305 @ SV158 )
!= ( sK27_SY720 @ SY1305 @ SV158 ) ) ) ) )
| ( c_Relation_Oantisym @ SY1305 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1268,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1269,plain,
! [SV159: $i] :
( ( ~ ( ~ ! [SY1306: $i,SY1307: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1307 @ SY1306 @ SV159 )
| ~ ( c_Relation_Oantisym @ SY1307 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SY1307 @ SY1306 @ SV159 ) )
| ~ ~ ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) )
| ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1270,plain,
! [SV160: $i] :
( ( ! [SY1312: $i,SY1313: $i,SY1314: $i] :
~ ( ~ ! [SY1315: $i,SY1316: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1316 @ SY1316 ) @ ( c_Product__Type_OPair @ SY1316 @ SY1316 @ ( sK43_B_y @ SY1316 @ SY1315 @ SY1314 @ SY1313 @ SY1312 @ SV160 ) @ SY1312 ) @ SY1313 )
| ~ ( ( ( hAPP @ SY1314 @ ( sK43_B_y @ SY1316 @ SY1315 @ SY1314 @ SY1313 @ SY1312 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY1316 @ SY1315 @ SY1314 @ SY1313 @ SY1312 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY1316 @ SY1315 @ SY1314 @ SY1313 @ SY1312 )
= ( c_Recdef_Ocut @ SY1316 @ SY1315 @ SV160 @ SY1313 @ SY1312 ) ) )
| ~ ! [SY1317: $i,SY1318: $i] :
( ( ( c_Recdef_Ocut @ SY1318 @ SY1317 @ SY1314 @ SY1313 @ SY1312 )
!= ( c_Recdef_Ocut @ SY1318 @ SY1317 @ SV160 @ SY1313 @ SY1312 ) )
| ! [SY1319: $i] :
( ~ ( c_member @ ( tc_prod @ SY1318 @ SY1318 ) @ ( c_Product__Type_OPair @ SY1318 @ SY1318 @ SY1319 @ SY1312 ) @ SY1313 )
| ( ( hAPP @ SY1314 @ SY1319 )
= ( hAPP @ SV160 @ SY1319 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1271,plain,
! [SV161: $i] :
( ( ! [SY1320: $i,SY1321: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1321 @ SY1321 ) @ ( c_Product__Type_OPair @ SY1321 @ SY1321 @ ( sK57_B_y @ SY1321 @ SY1320 @ SV161 ) @ SY1320 ) @ SV161 )
| ~ ~ ( c_member @ SY1321 @ ( sK57_B_y @ SY1321 @ SY1320 @ SV161 ) @ ( c_Wellfounded_Oacc @ SY1321 @ SV161 ) ) )
| ( c_member @ SY1321 @ SY1320 @ ( c_Wellfounded_Oacc @ SY1321 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1272,plain,
! [SV1: $i,SV162: $i] :
( ( ! [SY1322: $i,SY1323: $i,SY1324: $i] :
( ~ ( c_Relation_Otrans @ SY1324 @ SY1323 )
| ~ ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SY1322 @ SV162 ) @ SY1323 )
| ~ ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SV162 @ SV1 ) @ SY1323 )
| ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SY1322 @ SV1 ) @ SY1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1273,plain,
! [SV2: $i,SV163: $i] :
( ( ! [SY1325: $i,SY1326: $i] :
( ( SY1326 != SY1325 )
| ~ ( c_member @ SV163 @ SY1325 @ SV2 )
| ( c_member @ SV163 @ SY1326 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1274,plain,
! [SV3: $i,SV164: $i] :
( ( ! [SY1327: $i,SY1328: $i,SY1329: $i,SY1330: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY1330 @ SY1329 @ SY1328 @ SY1327 @ ( c_Product__Type_OPair @ SY1330 @ SY1329 @ SV164 @ SV3 ) )
= ( hAPP @ ( hAPP @ SY1327 @ SV164 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1275,plain,
! [SV4: $i,SV165: $i] :
( ( ! [SY1331: $i,SY1332: $i,SY1333: $i,SY1334: $i] :
( ( c_Product__Type_Ointernal__split @ SY1334 @ SY1333 @ SY1332 @ SY1331 @ ( c_Product__Type_OPair @ SY1334 @ SY1333 @ SV165 @ SV4 ) )
= ( hAPP @ ( hAPP @ SY1331 @ SV165 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1276,plain,
! [SV5: $i,SV166: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i] :
( ~ ( c_member @ ( tc_prod @ SY1337 @ SY1336 ) @ ( c_Product__Type_OPair @ SY1337 @ SY1336 @ SY1335 @ SV166 ) @ SV5 )
| ( c_member @ SY1336 @ SV166 @ ( c_Relation_ORange @ SY1337 @ SY1336 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1277,plain,
! [SV6: $i,SV167: $i] :
( ( ! [SY1338: $i,SY1339: $i] :
( ( SY1339 != SY1338 )
| ~ ( c_member @ SV167 @ SY1339 @ SV6 )
| ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SY1339 @ SY1338 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1278,plain,
! [SV7: $i,SV168: $i] :
( ( ! [SY1340: $i,SY1341: $i,SY1342: $i] :
( ~ ( c_member @ ( tc_prod @ SY1342 @ SY1341 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1340 @ SV168 ) @ SV7 )
| ( c_member @ SY1342 @ SY1340 @ ( c_Relation_ODomain @ SY1342 @ SY1341 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1279,plain,
! [SV8: $i,SV169: $i] :
( ( ! [SY1343: $i,SY1344: $i] :
( ~ ( c_Relation_Otrans @ SY1344 @ SY1343 )
| ~ ( c_Relation_Otrans @ SV169 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SY1344 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SY1344 @ SV169 @ SY1343 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1280,plain,
! [SV9: $i,SV170: $i] :
( ( c_Relation_Otrans @ SV170 @ ( c_Relation_OId__on @ SV170 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1281,plain,
! [SV10: $i,SV171: $i] :
( ( ! [SY1345: $i,SY1346: $i] :
( ~ ( c_Relation_Otrans @ SY1346 @ SY1345 )
| ( c_Relation_Otrans @ SV171 @ ( hAPP @ ( c_Relation_Oinv__image @ SY1346 @ SV171 @ SY1345 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1282,plain,
! [SV11: $i,SV172: $i] :
( ( ! [SY1347: $i,SY1348: $i] :
( ~ ( c_member @ SY1348 @ SY1347 @ ( c_Relation_ORange @ SV172 @ SY1348 @ SV11 ) )
| ( c_member @ ( tc_prod @ SV172 @ SY1348 ) @ ( c_Product__Type_OPair @ SV172 @ SY1348 @ ( sK63_B_x @ SY1348 @ SY1347 @ SV172 @ SV11 ) @ SY1347 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1283,plain,
! [SV12: $i,SV173: $i] :
( ( ! [SY1349: $i,SY1350: $i] :
( ~ ( c_member @ SY1350 @ SY1349 @ ( c_Relation_ODomain @ SY1350 @ SV173 @ SV12 ) )
| ( c_member @ ( tc_prod @ SY1350 @ SV173 ) @ ( c_Product__Type_OPair @ SY1350 @ SV173 @ SY1349 @ ( sK62_B_y @ SY1350 @ SY1349 @ SV173 @ SV12 ) ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1284,plain,
! [SV13: $i,SV174: $i] :
( ( ! [SY1351: $i,SY1352: $i] :
( ~ ( c_member @ SY1352 @ SY1351 @ ( c_Wellfounded_Oacc @ SY1352 @ SV174 ) )
| ~ ( c_member @ ( tc_prod @ SY1352 @ SY1352 ) @ ( c_Product__Type_OPair @ SY1352 @ SY1352 @ SV13 @ SY1351 ) @ SV174 )
| ( c_member @ SY1352 @ SV13 @ ( c_Wellfounded_Oacc @ SY1352 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1285,plain,
! [SV14: $i,SV175: $i] :
( ( ! [SY1353: $i,SY1354: $i] :
( ~ ( c_Relation_Orefl__on @ SY1354 @ SY1353 @ SV175 )
| ~ ( c_member @ SY1354 @ SV14 @ SY1353 )
| ( c_member @ ( tc_prod @ SY1354 @ SY1354 ) @ ( c_Product__Type_OPair @ SY1354 @ SY1354 @ SV14 @ SV14 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1286,plain,
! [SV15: $i,SV176: $i] :
( ( ! [SY1355: $i,SY1356: $i,SY1357: $i] :
( ~ ( c_Relation_Orefl__on @ SY1357 @ SY1356 @ SY1355 )
| ~ ( c_member @ ( tc_prod @ SY1357 @ SY1357 ) @ ( c_Product__Type_OPair @ SY1357 @ SY1357 @ SV176 @ SV15 ) @ SY1355 )
| ( c_member @ SY1357 @ SV176 @ SY1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1287,plain,
! [SV16: $i,SV177: $i] :
( ( ! [SY1358: $i,SY1359: $i,SY1360: $i] :
( ~ ( c_Relation_Orefl__on @ SY1360 @ SY1359 @ SY1358 )
| ~ ( c_member @ ( tc_prod @ SY1360 @ SY1360 ) @ ( c_Product__Type_OPair @ SY1360 @ SY1360 @ SV177 @ SV16 ) @ SY1358 )
| ( c_member @ SY1360 @ SV16 @ SY1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1288,plain,
! [SV17: $i,SV178: $i] :
( ( ! [SY1361: $i,SY1362: $i] :
( ~ ( c_member @ ( tc_prod @ SY1362 @ SY1362 ) @ ( c_Product__Type_OPair @ SY1362 @ SY1362 @ SY1361 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SY1362 @ SV17 ) )
| ~ ( c_member @ SY1362 @ SV178 @ ( c_Wellfounded_Oacc @ SY1362 @ SV17 ) )
| ( c_member @ SY1362 @ SY1361 @ ( c_Wellfounded_Oacc @ SY1362 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1289,plain,
! [SV18: $i,SV179: $i] :
( ( ! [SY1363: $i,SY1364: $i] :
( ~ ( c_member @ SY1364 @ SY1363 @ ( c_Wellfounded_Oacc @ SY1364 @ SV179 ) )
| ~ ( c_member @ ( tc_prod @ SY1364 @ SY1364 ) @ ( c_Product__Type_OPair @ SY1364 @ SY1364 @ SV18 @ SY1363 ) @ ( c_Transitive__Closure_Ortrancl @ SY1364 @ SV179 ) )
| ( c_member @ SY1364 @ SV18 @ ( c_Wellfounded_Oacc @ SY1364 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1290,plain,
! [SV19: $i,SV180: $i] :
( ( ! [SY1365: $i,SY1366: $i,SY1367: $i,SY1368: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1368 @ SY1367 @ SY1366 )
| ~ ( c_member @ ( tc_prod @ SY1368 @ SY1367 ) @ ( c_Product__Type_OPair @ SY1368 @ SY1367 @ SY1365 @ SV180 ) @ SY1366 )
| ~ ( c_member @ ( tc_prod @ SY1368 @ SY1367 ) @ ( c_Product__Type_OPair @ SY1368 @ SY1367 @ SY1365 @ SV19 ) @ SY1366 )
| ( SV180 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1291,plain,
! [SV20: $i,SV181: $i] :
( ( ! [SY1369: $i,SY1370: $i,SY1371: $i,SY1372: $i] :
( ( c_Product__Type_Ocurry @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SV181 @ SV20 )
= ( hAPP @ SY1369 @ ( c_Product__Type_OPair @ SY1372 @ SY1371 @ SV181 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1292,plain,
! [SV21: $i,SV182: $i] :
( ( ! [SY1373: $i] : ( c_member @ ( tc_prod @ SY1373 @ SY1373 ) @ ( c_Product__Type_OPair @ SY1373 @ SY1373 @ SV182 @ SV182 ) @ ( c_Transitive__Closure_Ortrancl @ SY1373 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1293,plain,
! [SV22: $i,SV183: $i] :
( ( ! [SY1374: $i] :
( ~ ( c_member @ ( tc_prod @ SY1374 @ SY1374 ) @ SV183 @ SV22 )
| ( c_member @ ( tc_prod @ SY1374 @ SY1374 ) @ SV183 @ ( c_Transitive__Closure_Ortrancl @ SY1374 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1294,plain,
! [SV23: $i,SV184: $i] :
( ( ! [SY1375: $i,SY1376: $i,SY1377: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1377 @ SY1377 @ SY1376 )
| ~ ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SY1375 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1377 @ SY1376 ) )
| ~ ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SY1375 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1377 @ SY1376 ) )
| ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1377 @ SY1376 ) )
| ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1377 @ SY1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1295,plain,
! [SV24: $i,SV185: $i] :
( ( ! [SY1378: $i,SY1379: $i,SY1380: $i] :
( ~ ( c_member @ ( tc_prod @ SY1380 @ SY1380 ) @ ( c_Product__Type_OPair @ SY1380 @ SY1380 @ SY1379 @ SY1378 ) @ SV185 )
| ~ ( c_member @ ( tc_prod @ SY1380 @ SY1380 ) @ ( c_Product__Type_OPair @ SY1380 @ SY1380 @ SY1378 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1380 @ SV185 ) )
| ( c_member @ ( tc_prod @ SY1380 @ SY1380 ) @ ( c_Product__Type_OPair @ SY1380 @ SY1380 @ SY1379 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1380 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1296,plain,
! [SV25: $i,SV186: $i] :
( ( ! [SY1381: $i,SY1382: $i,SY1383: $i] :
( ~ ( c_member @ ( tc_prod @ SY1383 @ SY1383 ) @ ( c_Product__Type_OPair @ SY1383 @ SY1383 @ SY1382 @ SY1381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1383 @ SV186 ) )
| ~ ( c_member @ ( tc_prod @ SY1383 @ SY1383 ) @ ( c_Product__Type_OPair @ SY1383 @ SY1383 @ SY1381 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SY1383 @ SY1383 ) @ ( c_Product__Type_OPair @ SY1383 @ SY1383 @ SY1382 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SY1383 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1297,plain,
! [SV26: $i,SV187: $i] :
( ( ! [SY1384: $i,SY1385: $i,SY1386: $i] :
( ~ ( c_member @ ( tc_prod @ SY1386 @ SY1386 ) @ ( c_Product__Type_OPair @ SY1386 @ SY1386 @ SY1385 @ SY1384 ) @ ( c_Transitive__Closure_Ortrancl @ SY1386 @ SV187 ) )
| ~ ( c_member @ ( tc_prod @ SY1386 @ SY1386 ) @ ( c_Product__Type_OPair @ SY1386 @ SY1386 @ SY1384 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1386 @ SV187 ) )
| ( c_member @ ( tc_prod @ SY1386 @ SY1386 ) @ ( c_Product__Type_OPair @ SY1386 @ SY1386 @ SY1385 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1386 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1298,plain,
! [SV27: $i,SV188: $i] :
( ( c_Relation_Otrans @ SV188 @ ( c_Transitive__Closure_Ortrancl @ SV188 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1299,plain,
! [SV28: $i,SV189: $i] :
( ( ! [SY1387: $i,SY1388: $i] :
( ~ ( c_member @ ( tc_prod @ SY1388 @ SY1388 ) @ ( c_Product__Type_OPair @ SY1388 @ SY1388 @ SY1387 @ SV189 ) @ ( c_Transitive__Closure_Otrancl @ SY1388 @ SV28 ) )
| ( c_member @ ( tc_prod @ SY1388 @ SY1388 ) @ ( c_Product__Type_OPair @ SY1388 @ SY1388 @ SY1387 @ SV189 ) @ ( c_Transitive__Closure_Ortrancl @ SY1388 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1300,plain,
! [SV29: $i,SV190: $i] :
( ( ! [SY1389: $i,SY1390: $i,SY1391: $i,SY1392: $i] :
( ~ ( c_member @ ( tc_prod @ SY1392 @ SY1392 ) @ ( c_Product__Type_OPair @ SY1392 @ SY1392 @ SY1391 @ SY1390 ) @ SY1389 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY1392 @ SV190 @ SV29 @ SY1389 @ SY1390 ) @ SY1391 )
= ( hAPP @ SV29 @ SY1391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1301,plain,
! [SV30: $i,SV191: $i] :
( ( ! [SY1393: $i,SY1394: $i] :
( ~ ( c_member @ ( tc_prod @ SY1394 @ SY1394 ) @ ( c_Product__Type_OPair @ SY1394 @ SY1394 @ SY1393 @ SV191 ) @ SV30 )
| ( c_member @ ( tc_prod @ SY1394 @ SY1394 ) @ ( c_Product__Type_OPair @ SY1394 @ SY1394 @ SY1393 @ SV191 ) @ ( c_Transitive__Closure_Otrancl @ SY1394 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1302,plain,
! [SV31: $i,SV192: $i] :
( ( ! [SY1395: $i] :
( ~ ( c_member @ ( tc_prod @ SY1395 @ SY1395 ) @ SV192 @ SV31 )
| ( c_member @ ( tc_prod @ SY1395 @ SY1395 ) @ SV192 @ ( c_Transitive__Closure_Otrancl @ SY1395 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1303,plain,
! [SV32: $i,SV193: $i] :
( ( c_Relation_Otrans @ SV193 @ ( c_Transitive__Closure_Otrancl @ SV193 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1304,plain,
! [SV33: $i,SV194: $i] :
( ( ~ ( c_Relation_Otrans @ SV194 @ SV33 )
| ( ( c_Transitive__Closure_Otrancl @ SV194 @ SV33 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1305,plain,
! [SV34: $i,SV195: $i] :
( ( ! [SY1396: $i,SY1397: $i,SY1398: $i] :
( ~ ( c_member @ ( tc_prod @ SY1398 @ SY1398 ) @ ( c_Product__Type_OPair @ SY1398 @ SY1398 @ SY1397 @ SY1396 ) @ SV195 )
| ~ ( c_member @ ( tc_prod @ SY1398 @ SY1398 ) @ ( c_Product__Type_OPair @ SY1398 @ SY1398 @ SY1396 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SY1398 @ SY1398 ) @ ( c_Product__Type_OPair @ SY1398 @ SY1398 @ SY1397 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SY1398 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1306,plain,
! [SV35: $i,SV196: $i] :
( ( ! [SY1399: $i,SY1400: $i,SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SY1401 @ SY1401 ) @ ( c_Product__Type_OPair @ SY1401 @ SY1401 @ SY1400 @ SY1399 ) @ SV196 )
| ~ ( c_member @ ( tc_prod @ SY1401 @ SY1401 ) @ ( c_Product__Type_OPair @ SY1401 @ SY1401 @ SY1399 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1401 @ SV196 ) )
| ( c_member @ ( tc_prod @ SY1401 @ SY1401 ) @ ( c_Product__Type_OPair @ SY1401 @ SY1401 @ SY1400 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1401 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1307,plain,
! [SV36: $i,SV197: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i] :
( ~ ( c_member @ ( tc_prod @ SY1404 @ SY1404 ) @ ( c_Product__Type_OPair @ SY1404 @ SY1404 @ SY1403 @ SY1402 ) @ ( c_Transitive__Closure_Otrancl @ SY1404 @ SV197 ) )
| ~ ( c_member @ ( tc_prod @ SY1404 @ SY1404 ) @ ( c_Product__Type_OPair @ SY1404 @ SY1404 @ SY1402 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SY1404 @ SY1404 ) @ ( c_Product__Type_OPair @ SY1404 @ SY1404 @ SY1403 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SY1404 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1308,plain,
! [SV37: $i,SV198: $i] :
( ( ! [SY1405: $i,SY1406: $i,SY1407: $i] :
( ~ ( c_member @ ( tc_prod @ SY1407 @ SY1407 ) @ ( c_Product__Type_OPair @ SY1407 @ SY1407 @ SY1406 @ SY1405 ) @ ( c_Transitive__Closure_Otrancl @ SY1407 @ SV198 ) )
| ~ ( c_member @ ( tc_prod @ SY1407 @ SY1407 ) @ ( c_Product__Type_OPair @ SY1407 @ SY1407 @ SY1405 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1407 @ SV198 ) )
| ( c_member @ ( tc_prod @ SY1407 @ SY1407 ) @ ( c_Product__Type_OPair @ SY1407 @ SY1407 @ SY1406 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1407 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1309,plain,
! [SV38: $i,SV199: $i] :
( ( ! [SY1408: $i,SY1409: $i,SY1410: $i] :
( ~ ( c_member @ ( tc_prod @ SY1410 @ SY1410 ) @ ( c_Product__Type_OPair @ SY1410 @ SY1410 @ SY1409 @ SY1408 ) @ SV199 )
| ~ ( c_member @ ( tc_prod @ SY1410 @ SY1410 ) @ ( c_Product__Type_OPair @ SY1410 @ SY1410 @ SY1408 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SY1410 @ SV199 ) )
| ( c_member @ ( tc_prod @ SY1410 @ SY1410 ) @ ( c_Product__Type_OPair @ SY1410 @ SY1410 @ SY1409 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SY1410 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1310,plain,
! [SV39: $i,SV200: $i] :
( ( ! [SY1411: $i,SY1412: $i,SY1413: $i] :
( ~ ( c_member @ ( tc_prod @ SY1413 @ SY1413 ) @ ( c_Product__Type_OPair @ SY1413 @ SY1413 @ SY1412 @ SY1411 ) @ ( c_Transitive__Closure_Ortrancl @ SY1413 @ SV200 ) )
| ~ ( c_member @ ( tc_prod @ SY1413 @ SY1413 ) @ ( c_Product__Type_OPair @ SY1413 @ SY1413 @ SY1411 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SY1413 @ SY1413 ) @ ( c_Product__Type_OPair @ SY1413 @ SY1413 @ SY1412 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SY1413 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1311,plain,
! [SV40: $i,SV201: $i] :
( ( ! [SY1414: $i,SY1415: $i,SY1416: $i] :
( ~ ( c_member @ ( tc_prod @ SY1416 @ SY1416 ) @ ( c_Product__Type_OPair @ SY1416 @ SY1416 @ SY1415 @ SY1414 ) @ ( c_Transitive__Closure_Otrancl @ SY1416 @ SV201 ) )
| ~ ( c_member @ ( tc_prod @ SY1416 @ SY1416 ) @ ( c_Product__Type_OPair @ SY1416 @ SY1416 @ SY1414 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SY1416 @ SV201 ) )
| ( c_member @ ( tc_prod @ SY1416 @ SY1416 ) @ ( c_Product__Type_OPair @ SY1416 @ SY1416 @ SY1415 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SY1416 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1312,plain,
! [SV41: $i,SV202: $i] :
( ( ! [SY1417: $i,SY1418: $i,SY1419: $i] :
( ~ ( c_member @ ( tc_prod @ SY1419 @ SY1419 ) @ ( c_Product__Type_OPair @ SY1419 @ SY1419 @ SY1418 @ SY1417 ) @ ( c_Transitive__Closure_Ortrancl @ SY1419 @ SV202 ) )
| ~ ( c_member @ ( tc_prod @ SY1419 @ SY1419 ) @ ( c_Product__Type_OPair @ SY1419 @ SY1419 @ SY1417 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1419 @ SV202 ) )
| ( c_member @ ( tc_prod @ SY1419 @ SY1419 ) @ ( c_Product__Type_OPair @ SY1419 @ SY1419 @ SY1418 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1419 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1313,plain,
! [SV42: $i,SV203: $i] :
( ( ! [SY1420: $i,SY1421: $i,SY1422: $i,SY1423: $i] :
( ~ ( c_member @ ( tc_prod @ SY1421 @ SY1421 ) @ ( c_Product__Type_OPair @ SY1421 @ SY1421 @ SY1420 @ SV203 ) @ SY1423 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY1421 @ SV42 @ SY1422 @ SY1423 @ SV203 ) @ SY1420 )
= ( hAPP @ SY1422 @ SY1420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1314,plain,
! [SV43: $i,SV204: $i] :
( ( ! [SY1424: $i,SY1425: $i] :
( ( c_member @ ( tc_prod @ SY1425 @ SY1425 ) @ ( c_Product__Type_OPair @ SY1425 @ SY1425 @ ( sK39_B_x @ SY1425 @ SY1424 @ SV204 @ SV43 ) @ ( sK39_B_x @ SY1425 @ SY1424 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1425 @ SY1424 ) )
| ~ ( c_member @ ( tc_prod @ SY1425 @ SY1425 ) @ ( c_Product__Type_OPair @ SY1425 @ SY1425 @ SV204 @ SV43 ) @ SY1424 )
| ( SV204 != SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1315,plain,
! [SV44: $i,SV205: $i] :
( ( c_member @ ( tc_prod @ SV205 @ SV205 ) @ ( c_Product__Type_OPair @ SV205 @ SV205 @ SV44 @ SV44 ) @ ( c_Relation_OId @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1316,plain,
! [SV46: $i,SV206: $i] :
( ( ( c_member @ ( tc_prod @ SV206 @ SV206 ) @ ( c_Product__Type_OPair @ SV206 @ SV206 @ ( sK36_B_x @ SV206 @ SV46 ) @ ( sK36_B_x @ SV206 @ SV46 ) ) @ ( c_Transitive__Closure_Otrancl @ SV206 @ SV46 ) )
| ( c_Wellfounded_Oacyclic @ SV206 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1317,plain,
! [SV47: $i,SV207: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV207 @ SV207 ) @ SV47 @ ( c_Relation_OId @ SV207 ) )
| ( SV47
= ( c_Product__Type_OPair @ SV207 @ SV207 @ ( sK35_B_x @ SV207 @ SV47 ) @ ( sK35_B_x @ SV207 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1318,plain,
! [SV48: $i,SV208: $i] :
( ( ! [SY1426: $i,SY1427: $i] :
( ~ ( c_Relation_Oantisym @ SY1427 @ SY1426 )
| ~ ( c_member @ ( tc_prod @ SY1427 @ SY1427 ) @ ( c_Product__Type_OPair @ SY1427 @ SY1427 @ SV208 @ SV48 ) @ SY1426 )
| ~ ( c_member @ ( tc_prod @ SY1427 @ SY1427 ) @ ( c_Product__Type_OPair @ SY1427 @ SY1427 @ SV48 @ SV208 ) @ SY1426 )
| ( SV208 = SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1319,plain,
! [SV49: $i,SV209: $i] :
( ( ! [SY1428: $i,SY1429: $i] :
( ~ ( c_member @ SY1429 @ SY1428 @ ( c_Set_Oinsert @ SY1429 @ SV209 @ SV49 ) )
| ( SY1428 = SV209 )
| ( c_member @ SY1429 @ SY1428 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1320,plain,
! [SV50: $i,SV210: $i] :
( ( ! [SY1430: $i,SY1431: $i,SY1432: $i] :
( ( c_Relation_ODomain @ SY1432 @ SY1431 @ ( c_Set_Oinsert @ ( tc_prod @ SY1432 @ SY1431 ) @ ( c_Product__Type_OPair @ SY1432 @ SY1431 @ SY1430 @ SV210 ) @ SV50 ) )
= ( c_Set_Oinsert @ SY1432 @ SY1430 @ ( c_Relation_ODomain @ SY1432 @ SY1431 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1321,plain,
! [SV51: $i,SV211: $i] :
( ( ! [SY1433: $i,SY1434: $i,SY1435: $i] :
( ( c_Relation_ORange @ SY1435 @ SY1434 @ ( c_Set_Oinsert @ ( tc_prod @ SY1435 @ SY1434 ) @ ( c_Product__Type_OPair @ SY1435 @ SY1434 @ SY1433 @ SV211 ) @ SV51 ) )
= ( c_Set_Oinsert @ SY1434 @ SV211 @ ( c_Relation_ORange @ SY1435 @ SY1434 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1322,plain,
! [SV52: $i,SV212: $i] :
( ( ! [SY1436: $i] : ( c_member @ SY1436 @ SV212 @ ( c_Set_Oinsert @ SY1436 @ SV212 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1323,plain,
! [SV53: $i,SV213: $i] :
( ( ! [SY1437: $i,SY1438: $i] :
( ~ ( c_member @ SY1438 @ SY1437 @ SV213 )
| ( c_member @ SY1438 @ SY1437 @ ( c_Set_Oinsert @ SY1438 @ SV53 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1324,plain,
! [SV54: $i,SV214: $i] :
( ( ! [SY1439: $i] :
( ~ ( c_member @ SY1439 @ SV214 @ SV54 )
| ( ( c_Set_Oinsert @ SY1439 @ SV214 @ SV54 )
= SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1325,plain,
! [SV55: $i,SV215: $i] :
( ( ! [SY1440: $i,SY1441: $i] :
( ~ ( c_Wellfounded_Owf @ SY1441 @ SY1440 )
| ~ ( c_Wellfounded_Owf @ SV215 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY1441 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SY1441 @ SV215 @ SY1440 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1326,plain,
! [SV56: $i,SV216: $i] :
( ( ! [SY1442: $i] :
( ~ ( c_Wellfounded_Owf @ SY1442 @ SV216 )
| ~ ( c_member @ ( tc_prod @ SY1442 @ SY1442 ) @ ( c_Product__Type_OPair @ SY1442 @ SY1442 @ SV56 @ SV56 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1327,plain,
! [SV57: $i,SV217: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ~ ( c_Wellfounded_Owf @ SY1444 @ SY1443 )
| ~ ( c_member @ ( tc_prod @ SY1444 @ SY1444 ) @ ( c_Product__Type_OPair @ SY1444 @ SY1444 @ SV217 @ SV57 ) @ SY1443 )
| ~ ( c_member @ ( tc_prod @ SY1444 @ SY1444 ) @ ( c_Product__Type_OPair @ SY1444 @ SY1444 @ SV57 @ SV217 ) @ SY1443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1328,plain,
! [SV58: $i,SV218: $i] :
( ( ! [SY1445: $i,SY1446: $i] :
( ~ ( c_Wellfounded_Owf @ SY1446 @ SY1445 )
| ~ ( c_member @ ( tc_prod @ SY1446 @ SY1446 ) @ ( c_Product__Type_OPair @ SY1446 @ SY1446 @ SV218 @ SV58 ) @ SY1445 )
| ~ ( c_member @ ( tc_prod @ SY1446 @ SY1446 ) @ ( c_Product__Type_OPair @ SY1446 @ SY1446 @ SV58 @ SV218 ) @ SY1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1329,plain,
! [SV59: $i,SV219: $i] :
( ( ! [SY1447: $i] :
( ~ ( c_Wellfounded_Owf @ SY1447 @ SV219 )
| ~ ( c_member @ ( tc_prod @ SY1447 @ SY1447 ) @ ( c_Product__Type_OPair @ SY1447 @ SY1447 @ SV59 @ SV59 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1330,plain,
! [SV60: $i,SV220: $i] :
( ( ! [SY1448: $i] :
( ~ ( c_Wellfounded_Owf @ SY1448 @ SV220 )
| ( c_member @ SY1448 @ SV60 @ ( c_Wellfounded_Oacc @ SY1448 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1331,plain,
! [SV61: $i,SV221: $i] :
( ( ~ ( c_member @ SV221 @ ( sK25_B_x @ SV221 @ SV61 ) @ ( c_Wellfounded_Oacc @ SV221 @ SV61 ) )
| ( c_Wellfounded_Owf @ SV221 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1332,plain,
! [SV62: $i,SV222: $i] :
( ( ! [SY1449: $i,SY1450: $i,SY1451: $i,SY1452: $i] :
( ~ ( c_member @ SY1452 @ SY1451 @ SY1450 )
| ~ ( c_member @ ( tc_prod @ SY1452 @ SY1449 ) @ ( c_Product__Type_OPair @ SY1452 @ SY1449 @ SY1451 @ SV222 ) @ SV62 )
| ( c_member @ SY1449 @ SV222 @ ( c_Relation_OImage @ SY1452 @ SY1449 @ SV62 @ SY1450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1333,plain,
! [SV63: $i,SV223: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i,SY1456: $i,SY1457: $i,SY1458: $i] :
( ~ ( c_member @ ( tc_prod @ SY1458 @ SY1457 ) @ ( c_Product__Type_OPair @ SY1458 @ SY1457 @ SY1456 @ SY1455 ) @ SY1454 )
| ~ ( c_member @ ( tc_prod @ SY1457 @ SY1453 ) @ ( c_Product__Type_OPair @ SY1457 @ SY1453 @ SY1455 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1458 @ SY1453 ) @ ( c_Product__Type_OPair @ SY1458 @ SY1453 @ SY1456 @ SV223 ) @ ( c_Relation_Orel__comp @ SY1458 @ SY1457 @ SY1453 @ SY1454 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1334,plain,
! [SV64: $i,SV224: $i] :
( ( ( ( hAPP @ SV224 @ ( sK22_B_x @ SV224 @ SV64 ) )
!= ( hAPP @ SV64 @ ( sK22_B_x @ SV224 @ SV64 ) ) )
| ( SV224 = SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1335,plain,
! [SV65: $i,SV225: $i] :
( ( ! [SY1459: $i,SY1460: $i,SY1461: $i,SY1462: $i,SY1463: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1463 @ SY1462 ) )
| ~ ( c_member @ ( tc_prod @ SY1461 @ SY1461 ) @ ( c_Product__Type_OPair @ SY1461 @ SY1461 @ SY1460 @ SY1459 ) @ ( hAPP @ SV225 @ SY1462 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SY1461 ) @ ( tc_prod @ SV65 @ SY1461 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SY1461 ) @ ( tc_prod @ SV65 @ SY1461 ) @ ( c_Product__Type_OPair @ SV65 @ SY1461 @ SY1462 @ SY1460 ) @ ( c_Product__Type_OPair @ SV65 @ SY1461 @ SY1462 @ SY1459 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SY1461 @ SY1463 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1336,plain,
! [SV66: $i,SV226: $i] :
( ( ( c_Relation_ORange @ SV226 @ SV226 @ ( c_Relation_OId__on @ SV226 @ SV66 ) )
= SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1337,plain,
! [SV67: $i,SV227: $i] :
( ( ( c_Relation_ODomain @ SV227 @ SV227 @ ( c_Relation_OId__on @ SV227 @ SV67 ) )
= SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1338,plain,
! [SV68: $i,SV228: $i] :
( ( c_Relation_Orefl__on @ SV228 @ SV68 @ ( c_Relation_OId__on @ SV228 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1339,plain,
! [SV69: $i,SV229: $i] :
( ( ! [SY1464: $i,SY1465: $i,SY1466: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1466 @ ( c_Product__Type_OPair @ SY1465 @ SY1464 @ SV229 @ SV69 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY1465 @ SY1464 @ tc_HOL_Obool @ SY1466 @ SV229 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1340,plain,
! [SV70: $i,SV230: $i] :
( ( ! [SY1467: $i,SY1468: $i,SY1469: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1469 @ SY1468 @ tc_HOL_Obool @ SY1467 @ SV230 @ SV70 ) )
| ( hBOOL @ ( hAPP @ SY1467 @ ( c_Product__Type_OPair @ SY1469 @ SY1468 @ SV230 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1341,plain,
! [SV71: $i,SV231: $i] :
( ( ! [SY1470: $i,SY1471: $i,SY1472: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1472 @ SY1471 @ tc_HOL_Obool @ SY1470 @ SV231 @ SV71 ) )
| ( hBOOL @ ( hAPP @ SY1470 @ ( c_Product__Type_OPair @ SY1472 @ SY1471 @ SV231 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1342,plain,
! [SV72: $i,SV232: $i] :
( ( c_Relation_Osingle__valued @ SV232 @ SV232 @ ( c_Relation_OId__on @ SV232 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1343,plain,
! [SV73: $i,SV233: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV233 @ ( c_Transitive__Closure_Ortrancl @ SV233 @ SV73 ) )
= ( c_Transitive__Closure_Ortrancl @ SV233 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1344,plain,
! [SV74: $i,SV234: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV234 @ ( c_Transitive__Closure_Otrancl @ SV234 @ SV74 ) )
= ( c_Transitive__Closure_Ortrancl @ SV234 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1345,plain,
! [SV75: $i,SV235: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV235 @ ( c_Transitive__Closure_Ortrancl @ SV235 @ SV75 ) )
= ( c_Transitive__Closure_Ortrancl @ SV235 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1346,plain,
! [SV76: $i,SV236: $i] :
( ( ( c_Relation_ODomain @ SV236 @ SV236 @ ( c_Transitive__Closure_Otrancl @ SV236 @ SV76 ) )
= ( c_Relation_ODomain @ SV236 @ SV236 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1347,plain,
! [SV77: $i,SV237: $i] :
( ( ( c_Relation_ORange @ SV237 @ SV237 @ ( c_Transitive__Closure_Otrancl @ SV237 @ SV77 ) )
= ( c_Relation_ORange @ SV237 @ SV237 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1348,plain,
! [SV79: $i,SV238: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV238 @ SV79 )
| ( c_Relation_Oantisym @ SV238 @ ( c_Transitive__Closure_Ortrancl @ SV238 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1349,plain,
! [SV80: $i,SV239: $i] :
( ( ! [SY1473: $i] :
( ( c_Set_Oinsert @ SY1473 @ SV239 @ ( c_Set_Oinsert @ SY1473 @ SV239 @ SV80 ) )
= ( c_Set_Oinsert @ SY1473 @ SV239 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1350,plain,
! [SV81: $i,SV240: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ( c_Set_Oinsert @ SY1475 @ SY1474 @ ( c_Set_Oinsert @ SY1475 @ SV240 @ SV81 ) )
= ( c_Set_Oinsert @ SY1475 @ SV240 @ ( c_Set_Oinsert @ SY1475 @ SY1474 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1351,plain,
! [SV83: $i,SV241: $i] :
( ( c_Relation_Oantisym @ SV241 @ ( c_Relation_OId__on @ SV241 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1352,plain,
! [SV84: $i,SV242: $i] :
( ( ! [SY1476: $i,SY1477: $i] :
( ~ ( c_Wellfounded_Owf @ SY1477 @ SY1476 )
| ( c_Wellfounded_Owf @ SV242 @ ( hAPP @ ( c_Relation_Oinv__image @ SY1477 @ SV242 @ SY1476 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1353,plain,
! [SV85: $i,SV243: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV243 @ SV85 )
| ( c_Wellfounded_Owf @ SV243 @ ( c_Transitive__Closure_Otrancl @ SV243 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1354,plain,
! [SV86: $i,SV244: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV244 @ SV86 )
| ( c_Wellfounded_Oacyclic @ SV244 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1355,plain,
! [SV87: $i,SV245: $i] :
( ( c_Wellfounded_Owf @ SV245 @ ( hAPP @ ( c_Wellfounded_Omeasure @ SV245 ) @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1356,plain,
! [SV88: $i,SV246: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i,SY1481: $i] :
( ( SY1481
!= ( c_Recdef_Owfrec @ SY1480 @ SY1479 @ SY1478 @ SV246 ) )
| ~ ( c_Wellfounded_Owf @ SY1480 @ SY1478 )
| ( ( hAPP @ SY1481 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SY1480 @ SY1479 @ SY1481 @ SY1478 @ SV88 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1357,plain,
! [SV89: $i,SV247: $i] :
( ( ! [SY1482: $i,SY1483: $i,SY1484: $i] :
( ~ ( c_Wellfounded_Owf @ SY1484 @ SY1483 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY1484 @ SY1482 @ SY1483 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SY1484 @ SY1482 @ ( c_Recdef_Owfrec @ SY1484 @ SY1482 @ SY1483 @ SV247 ) @ SY1483 @ SV89 ) ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1358,plain,
! [SV90: $i,SV248: $i] :
( ( ! [SY1485: $i,SY1486: $i] :
( ~ ( c_Wellfounded_Owf @ SV248 @ SY1486 )
| ! [SY1487: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SY1486 @ SY1485 ) @ SY1487 )
= ( hAPP @ ( hAPP @ SY1485 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SY1486 @ SY1485 ) @ SY1486 @ SY1487 ) ) @ SY1487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1359,plain,
! [SV92: $i,SV249: $i] :
( ( ! [SY1488: $i] :
( ~ ( c_Wellfounded_Owf @ SY1488 @ SV249 )
| ( c_Wellfounded_Owf @ SY1488 @ ( c_Wellfounded_Omlex__prod @ SY1488 @ SV92 @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1360,plain,
! [SV93: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV93 @ SV93 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1361,plain,
! [SV94: $i,SV250: $i] :
( ( ( SV250 = SV94 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV250 @ SV94 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV94 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1362,plain,
! [SV95: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV95 @ SV95 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1363,plain,
! [SV96: $i,SV251: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV251 @ SV96 )
| ( SV96 != SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1364,plain,
! [SV97: $i,SV252: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV252 @ SV97 )
| ( SV252 != SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1365,plain,
! [SV99: $i,SV253: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV253 @ SV99 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV99 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1366,plain,
! [SV100: $i,SV254: $i] :
( ( ( SV254 != SV100 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV254 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1367,plain,
! [SV101: $i,SV255: $i] :
( ( ! [SY1489: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1489 @ SV255 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY1489 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1368,plain,
! [SV102: $i,SV256: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV256 @ SV102 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SV256 )
| ( SV256 = SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1369,plain,
! [SV103: $i,SV257: $i] :
( ( ! [SY1490: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY1490 @ SV257 ) @ SV103 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY1490 @ SV103 ) @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1370,plain,
! [SV104: $i,SV258: $i] :
( ( ( c_Relation_OImage @ SV258 @ SV258 @ ( c_Relation_OId @ SV258 ) @ SV104 )
= SV104 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1371,plain,
! [SV105: $i,SV259: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SV259 ) @ SV105 ) )
| ( SV259 = SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1372,plain,
! [SV106: $i,SV260: $i] :
( ( ( SV260 != SV106 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ SV260 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1373,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1374,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1375,plain,
! [SV107: $i] :
( ( ~ ! [SY1011: $i,SY1012: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 )
!= ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1012 @ SY1011 @ SV107 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1014 @ SY1013 @ SV107 )
| ! [SY1015: $i,SY1016: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1016 ) @ SV107 )
| ! [SY1017: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1017 ) @ SV107 )
| ( SY1016 = SY1017 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1376,plain,
! [SV261: $i,SV108: $i] :
( ( ! [SY1491: $i] :
~ ( ~ ! [SY1492: $i,SY1493: $i] :
( ! [SY1494: $i] :
( ~ ( c_member @ SY1491 @ SY1494 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SY1491 @ SY1493 ) @ ( c_Product__Type_OPair @ SY1491 @ SY1493 @ SY1494 @ SY1492 ) @ SV261 ) )
| ( c_member @ SY1493 @ SY1492 @ ( c_Relation_OImage @ SY1491 @ SY1493 @ SV261 @ SV108 ) ) )
| ~ ! [SY1495: $i,SY1496: $i] :
( ~ ( c_member @ SY1496 @ SY1495 @ ( c_Relation_OImage @ SY1491 @ SY1496 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SY1491 @ ( sK24_B_x @ SY1496 @ SY1495 @ SY1491 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SY1491 @ SY1496 ) @ ( c_Product__Type_OPair @ SY1491 @ SY1496 @ ( sK24_B_x @ SY1496 @ SY1495 @ SY1491 @ SV261 @ SV108 ) @ SY1495 ) @ SV261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1377,plain,
! [SV109: $i,SV262: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK70_SY736 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) ) )
| ( c_Relation_Otrans @ SV262 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1378,plain,
! [SV110: $i,SV263: $i] :
( ( ! [SY1497: $i,SY1498: $i,SY1499: $i,SY1500: $i] :
~ ( ~ ~ ( ~ ! [SY1501: $i,SY1502: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1502 @ SY1501 ) @ ( tc_prod @ SY1502 @ SY1501 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1502 @ SY1501 ) @ ( tc_prod @ SY1502 @ SY1501 ) @ ( c_Product__Type_OPair @ SY1502 @ SY1501 @ SY1500 @ SY1499 ) @ ( c_Product__Type_OPair @ SY1502 @ SY1501 @ SY1498 @ SY1497 ) ) @ ( c_Wellfounded_Olex__prod @ SY1502 @ SY1501 @ SV263 @ SV110 ) )
| ( SY1500 = SY1498 )
| ( c_member @ ( tc_prod @ SY1502 @ SY1502 ) @ ( c_Product__Type_OPair @ SY1502 @ SY1502 @ SY1500 @ SY1498 ) @ SV263 ) )
| ~ ! [SY1503: $i,SY1504: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1504 @ SY1503 ) @ ( tc_prod @ SY1504 @ SY1503 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1504 @ SY1503 ) @ ( tc_prod @ SY1504 @ SY1503 ) @ ( c_Product__Type_OPair @ SY1504 @ SY1503 @ SY1500 @ SY1499 ) @ ( c_Product__Type_OPair @ SY1504 @ SY1503 @ SY1498 @ SY1497 ) ) @ ( c_Wellfounded_Olex__prod @ SY1504 @ SY1503 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY1503 @ SY1503 ) @ ( c_Product__Type_OPair @ SY1503 @ SY1503 @ SY1499 @ SY1497 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY1504 @ SY1504 ) @ ( c_Product__Type_OPair @ SY1504 @ SY1504 @ SY1500 @ SY1498 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY1505: $i] :
( ( SY1500 != SY1498 )
| ~ ( c_member @ ( tc_prod @ SY1505 @ SY1505 ) @ ( c_Product__Type_OPair @ SY1505 @ SY1505 @ SY1499 @ SY1497 ) @ SV110 )
| ! [SY1506: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY1506 @ SY1505 ) @ ( tc_prod @ SY1506 @ SY1505 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1506 @ SY1505 ) @ ( tc_prod @ SY1506 @ SY1505 ) @ ( c_Product__Type_OPair @ SY1506 @ SY1505 @ SY1500 @ SY1499 ) @ ( c_Product__Type_OPair @ SY1506 @ SY1505 @ SY1498 @ SY1497 ) ) @ ( c_Wellfounded_Olex__prod @ SY1506 @ SY1505 @ SV263 @ SV110 ) ) )
| ~ ! [SY1507: $i,SY1508: $i] :
( ~ ( c_member @ ( tc_prod @ SY1508 @ SY1508 ) @ ( c_Product__Type_OPair @ SY1508 @ SY1508 @ SY1500 @ SY1498 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1508 @ SY1507 ) @ ( tc_prod @ SY1508 @ SY1507 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1508 @ SY1507 ) @ ( tc_prod @ SY1508 @ SY1507 ) @ ( c_Product__Type_OPair @ SY1508 @ SY1507 @ SY1500 @ SY1499 ) @ ( c_Product__Type_OPair @ SY1508 @ SY1507 @ SY1498 @ SY1497 ) ) @ ( c_Wellfounded_Olex__prod @ SY1508 @ SY1507 @ SV263 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1379,plain,
! [SV111: $i,SV264: $i] :
( ( ! [SY1509: $i,SY1510: $i] :
~ ( ~ ! [SY1511: $i,SY1512: $i] :
( ! [SY1513: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1512 @ SY1512 ) @ ( c_Product__Type_OPair @ SY1512 @ SY1512 @ ( sK60_B_z @ SY1513 @ SY1512 @ SY1511 @ SY1510 @ SY1509 @ SV264 @ SV111 ) @ SV264 ) @ SY1510 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1512 @ SY1511 @ SY1510 @ SY1509 @ ( sK60_B_z @ SY1513 @ SY1512 @ SY1511 @ SY1510 @ SY1509 @ SV264 @ SV111 ) @ ( hAPP @ SY1513 @ ( sK60_B_z @ SY1513 @ SY1512 @ SY1511 @ SY1510 @ SY1509 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SY1509 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SY1509 @ SY1513 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1512 @ SY1511 @ SY1510 @ SY1509 @ SV264 @ ( hAPP @ ( hAPP @ SY1509 @ SV111 ) @ SV264 ) ) )
| ~ ! [SY1514: $i,SY1515: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1515 @ SY1514 @ SY1510 @ SY1509 @ SV264 @ ( hAPP @ ( hAPP @ SY1509 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1516: $i] :
( ~ ( c_member @ ( tc_prod @ SY1515 @ SY1515 ) @ ( c_Product__Type_OPair @ SY1515 @ SY1515 @ SY1516 @ SV264 ) @ SY1510 )
| ( c_Recdef_Owfrec__rel @ SY1515 @ SY1514 @ SY1510 @ SY1509 @ SY1516 @ ( hAPP @ ( sK59_B_g @ SY1515 @ SY1514 @ SY1510 @ SY1509 @ SV264 @ SV111 ) @ SY1516 ) ) )
| ( ( hAPP @ ( hAPP @ SY1509 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SY1509 @ ( sK59_B_g @ SY1515 @ SY1514 @ SY1510 @ SY1509 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1380,plain,
! [SV112: $i] :
( ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1049 @ SY1049 ) @ ( c_Product__Type_OPair @ SY1049 @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ SY1048 ) @ SV112 )
| ~ ~ ( c_member @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ( c_member @ SY1049 @ SY1048 @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ~ ! [SY1050: $i,SY1051: $i] :
( ~ ( c_member @ SY1051 @ SY1050 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) )
| ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SY1051 @ SY1051 ) @ ( c_Product__Type_OPair @ SY1051 @ SY1051 @ SY1052 @ SY1050 ) @ SV112 )
| ( c_member @ SY1051 @ SY1052 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1381,plain,
! [SV113: $i,SV265: $i] :
( ( ! [SY1517: $i,SY1518: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY1518 @ ( sK9_B_x @ SY1518 @ SY1517 @ SV265 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SY1517 @ ( hAPP @ SV265 @ ( sK9_B_x @ SY1518 @ SY1517 @ SV265 @ SV113 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SY1517 ) @ ( c_Recdef_Osame__fst @ SV113 @ SY1517 @ SY1518 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1382,plain,
! [SV114: $i,SV266: $i] :
( ( ~ ( ~ ! [SY1519: $i,SY1520: $i] :
( ! [SY1521: $i] :
~ ( c_member @ ( tc_prod @ SY1520 @ SV266 ) @ ( c_Product__Type_OPair @ SY1520 @ SV266 @ SY1519 @ SY1521 ) @ SV114 )
| ( c_member @ SY1520 @ SY1519 @ ( c_Relation_ODomain @ SY1520 @ SV266 @ SV114 ) ) )
| ~ ! [SY1522: $i,SY1523: $i] :
( ~ ( c_member @ SY1523 @ SY1522 @ ( c_Relation_ODomain @ SY1523 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY1523 @ SV266 ) @ ( c_Product__Type_OPair @ SY1523 @ SV266 @ SY1522 @ ( sK66_B_y @ SY1523 @ SY1522 @ SV266 @ SV114 ) ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1384,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1385,plain,
! [SV267: $i,SV115: $i] :
( ( ~ ( ~ ! [SY1524: $i,SY1525: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1525 @ SV115 )
| ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SV267 @ SY1524 ) @ ( c_Transitive__Closure_Ortrancl @ SY1525 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1525 @ ( c_Set_Oinsert @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV267 ) @ SV115 ) ) )
| ~ ~ ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) )
| ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1386,plain,
! [SV116: $i,SV268: $i] :
( ( ! [SY1530: $i,SY1531: $i,SY1532: $i,SY1533: $i,SY1534: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1532 @ SY1531 ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1530 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1534 @ SY1533 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1532 @ SY1531 )
= ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1530 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1532 @ SY1531 ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ ( sK46_B_a @ SY1534 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1534 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1534 @ SY1533 ) @ ( tc_prod @ SY1534 @ SY1533 ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ ( sK46_B_a @ SY1534 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1534 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY1534 @ SY1533 @ SY1530 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1534 @ SY1533 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1387,plain,
! [SV117: $i] :
( ( ~ ! [SY1075: $i,SY1076: $i] :
( ~ ( ~ ( c_member @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( c_member @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY1076 @ SY1075 @ SV117 )
!= ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY1076 @ SY1075 @ SV117 ) )
| ~ ! [SY1077: $i,SY1078: $i] :
( ~ ( c_Relation_Ototal__on @ SY1078 @ SY1077 @ SV117 )
| ! [SY1079: $i] :
( ~ ( c_member @ SY1078 @ SY1079 @ SY1077 )
| ! [SY1080: $i] :
( ~ ( c_member @ SY1078 @ SY1080 @ SY1077 )
| ( SY1079 = SY1080 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1079 @ SY1080 ) @ SV117 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1080 @ SY1079 ) @ SV117 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1388,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1389,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1390,plain,
! [SV118: $i,SV269: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i] :
( ~ ( c_member @ SY1537 @ SY1536 @ ( c_Relation_OImage @ SY1535 @ SY1537 @ SV269 @ SV118 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1535 @ SY1537 ) @ ( c_Product__Type_OPair @ SY1535 @ SY1537 @ ( sK23_B_x @ SY1537 @ SY1536 @ SY1535 @ SV269 @ SV118 ) @ SY1536 ) @ SV269 )
| ~ ( c_member @ SY1535 @ ( sK23_B_x @ SY1537 @ SY1536 @ SY1535 @ SV269 @ SV118 ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1391,plain,
! [SV119: $i,SV270: $i] :
( ( ~ ( ~ ! [SY1538: $i] :
( ! [SY1539: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1539 @ SY1538 @ SV270 ) @ SV119 ) )
| ( SY1538 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
| ~ ~ ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1392,plain,
! [SV120: $i,SV271: $i] :
( ( ! [SY1544: $i,SY1545: $i] :
~ ( ~ ( ( SY1545 != SV271 )
| ( SY1544 != SV120 )
| ! [SY1546: $i,SY1547: $i] :
( ( c_Product__Type_OPair @ SY1547 @ SY1546 @ SY1545 @ SY1544 )
= ( c_Product__Type_OPair @ SY1547 @ SY1546 @ SV271 @ SV120 ) ) )
| ~ ~ ( ~ ( ! [SY1548: $i,SY1549: $i] :
( ( c_Product__Type_OPair @ SY1549 @ SY1548 @ SY1545 @ SY1544 )
!= ( c_Product__Type_OPair @ SY1549 @ SY1548 @ SV271 @ SV120 ) )
| ( SY1545 = SV271 ) )
| ~ ( ! [SY1550: $i,SY1551: $i] :
( ( c_Product__Type_OPair @ SY1551 @ SY1550 @ SY1545 @ SY1544 )
!= ( c_Product__Type_OPair @ SY1551 @ SY1550 @ SV271 @ SV120 ) )
| ( SY1544 = SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1393,plain,
! [SV121: $i] :
( ( ~ ! [SY1101: $i] :
( ( SY1101 != SV121 )
| ! [SY1102: $i] : ( c_member @ SY1102 @ SY1101 @ ( c_fequal @ SV121 ) ) )
| ~ ! [SY1103: $i] :
( ! [SY1104: $i] :
~ ( c_member @ SY1104 @ SY1103 @ ( c_fequal @ SV121 ) )
| ( SY1103 = SV121 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1394,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) )
| ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) )
| ~ ~ ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) )
| ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1395,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1396,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1397,plain,
! [SV123: $i] :
( ( ~ ! [SY1114: $i,SY1115: $i] :
( ~ ( c_Relation_Oirrefl @ SY1115 @ SV123 )
| ~ ( c_Relation_Otrans @ SY1115 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SY1115 @ SY1114 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY1115 @ SY1114 @ SV123 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
| ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1398,plain,
! [SV124: $i] :
( ( ~ ! [SY1122: $i,SY1123: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1123 @ ( sK75_B_x1 @ SY1123 @ SY1122 @ SV124 ) ) )
| ! [SY1124: $i,SY1125: $i] : ( hBOOL @ ( hAPP @ SY1123 @ ( c_Product__Type_OPair @ SY1122 @ SV124 @ SY1124 @ SY1125 ) ) ) )
| ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1127 @ ( c_Product__Type_OPair @ SY1126 @ SV124 @ ( sK73_B_a @ SY1127 @ SY1126 @ SV124 ) @ ( sK74_SY739 @ SY1127 @ SY1126 @ SV124 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1127 @ SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1399,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1400,plain,
( ( ~ ~ ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1401,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1402,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1403,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1404,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1405,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ( ~ ! [SY1560: $i,SY1561: $i] :
( ( SY1560 != SV273 )
| ~ ( c_member @ SY1561 @ SY1560 @ SV125 )
| ( c_member @ ( tc_prod @ SY1561 @ SY1561 ) @ ( c_Product__Type_OPair @ SY1561 @ SY1561 @ SY1560 @ SV273 ) @ ( c_Relation_OId__on @ SY1561 @ SV125 ) ) )
| ~ ~ ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) )
| ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1406,plain,
! [SV126: $i,SV274: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SY1567 @ SY1567 ) @ ( c_Product__Type_OPair @ SY1567 @ SY1567 @ SY1566 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SY1567 @ SV126 ) )
| ( SY1566 = SV274 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1567 @ SY1567 ) @ ( c_Product__Type_OPair @ SY1567 @ SY1567 @ SY1566 @ ( sK45_B_y @ SY1567 @ SY1566 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1567 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SY1567 @ SY1567 ) @ ( c_Product__Type_OPair @ SY1567 @ SY1567 @ ( sK45_B_y @ SY1567 @ SY1566 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1407,plain,
! [SV127: $i,SV275: $i] :
( ( ~ ( ~ ! [SY1568: $i,SY1569: $i] :
( ( c_member @ SY1569 @ SY1568 @ SV275 )
| ( c_member @ SY1569 @ SY1568 @ SV127 )
| ( ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV275 )
!= ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV127 ) )
| ( SV275 = SV127 ) )
| ~ ! [SY1570: $i,SY1571: $i] :
( ( c_member @ SY1571 @ SY1570 @ SV275 )
| ( c_member @ SY1571 @ SY1570 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV275 )
= ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1408,plain,
! [SV128: $i,SV276: $i] :
( ( ! [SY1572: $i,SY1573: $i] :
( ~ ( c_member @ ( tc_prod @ SY1573 @ SY1573 ) @ ( c_Product__Type_OPair @ SY1573 @ SY1573 @ SY1572 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SY1573 @ SV128 ) )
| ( c_member @ ( tc_prod @ SY1573 @ SY1573 ) @ ( c_Product__Type_OPair @ SY1573 @ SY1573 @ SY1572 @ SV276 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1573 @ SY1573 ) @ ( c_Product__Type_OPair @ SY1573 @ SY1573 @ SY1572 @ ( sK37_B_c @ SY1573 @ SY1572 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1573 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SY1573 @ SY1573 ) @ ( c_Product__Type_OPair @ SY1573 @ SY1573 @ ( sK37_B_c @ SY1573 @ SY1572 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1409,plain,
! [SV129: $i,SV277: $i] :
( ( ~ ( ~ ! [SY1574: $i,SY1575: $i] :
( ( c_member @ SY1575 @ SY1574 @ ( c_Relation_ODomain @ SY1575 @ SY1575 @ SV277 ) )
| ( SY1574 != SV129 )
| ( c_member @ ( tc_prod @ SY1575 @ SY1575 ) @ ( c_Product__Type_OPair @ SY1575 @ SY1575 @ SY1574 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1575 @ SV277 ) ) )
| ~ ! [SY1576: $i,SY1577: $i] :
( ( c_member @ SY1577 @ SY1576 @ ( c_Relation_ODomain @ SY1577 @ SY1577 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SY1577 @ SY1577 ) @ ( c_Product__Type_OPair @ SY1577 @ SY1577 @ SY1576 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1577 @ SV277 ) )
| ( SY1576 = SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1410,plain,
! [SV130: $i,SV278: $i] :
( ( ! [SY1578: $i,SY1579: $i] :
~ ( ~ ( ! [SY1580: $i,SY1581: $i] :
( ( c_Product__Type_OPair @ SY1581 @ SY1580 @ SY1579 @ SY1578 )
!= ( c_Product__Type_OPair @ SY1581 @ SY1580 @ SV278 @ SV130 ) )
| ( SY1579 = SV278 ) )
| ~ ( ! [SY1582: $i,SY1583: $i] :
( ( c_Product__Type_OPair @ SY1583 @ SY1582 @ SY1579 @ SY1578 )
!= ( c_Product__Type_OPair @ SY1583 @ SY1582 @ SV278 @ SV130 ) )
| ( SY1578 = SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1411,plain,
! [SV131: $i,SV279: $i] :
( ( ! [SY1584: $i,SY1585: $i,SY1586: $i,SY1587: $i,SY1588: $i,SY1589: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ SY1587 @ SY1586 ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ SY1585 @ SY1584 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1589 @ SY1588 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1587 ) @ SY1586 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ SY1587 @ SY1586 ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ ( sK18_B_a @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1589 @ SY1588 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1589 @ SY1588 ) @ ( tc_prod @ SY1589 @ SY1588 ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ ( sK18_B_a @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY1589 @ SY1588 @ ( sK20_SY717 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY1589 @ SY1588 @ SY1587 @ SY1586 @ SY1585 @ SY1584 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1585 ) @ SY1584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1412,plain,
! [SV132: $i,SV280: $i] :
( ( ~ ( ~ ! [SY1590: $i,SY1591: $i] :
( ! [SY1592: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SY1591 ) @ ( c_Product__Type_OPair @ SV280 @ SY1591 @ SY1592 @ SY1590 ) @ SV132 )
| ( c_member @ SY1591 @ SY1590 @ ( c_Relation_ORange @ SV280 @ SY1591 @ SV132 ) ) )
| ~ ! [SY1593: $i,SY1594: $i] :
( ~ ( c_member @ SY1594 @ SY1593 @ ( c_Relation_ORange @ SV280 @ SY1594 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SY1594 ) @ ( c_Product__Type_OPair @ SV280 @ SY1594 @ ( sK65_B_y @ SY1594 @ SY1593 @ SV280 @ SV132 ) @ SY1593 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1413,plain,
! [SV133: $i,SV281: $i] :
( ( ! [SY1595: $i,SY1596: $i] :
~ ( ~ ! [SY1597: $i,SY1598: $i] :
( ! [SY1599: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1598 @ SY1598 ) @ ( c_Product__Type_OPair @ SY1598 @ SY1598 @ ( sK55_B_z @ SY1599 @ SY1598 @ SY1597 @ SY1596 @ SY1595 @ SV281 @ SV133 ) @ SV281 ) @ SY1596 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1598 @ SY1597 @ SY1596 @ SY1595 @ ( sK55_B_z @ SY1599 @ SY1598 @ SY1597 @ SY1596 @ SY1595 @ SV281 @ SV133 ) @ ( hAPP @ SY1599 @ ( sK55_B_z @ SY1599 @ SY1598 @ SY1597 @ SY1596 @ SY1595 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SY1595 @ SY1599 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1598 @ SY1597 @ SY1596 @ SY1595 @ SV281 @ SV133 ) )
| ~ ! [SY1600: $i,SY1601: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1601 @ SY1600 @ SY1596 @ SY1595 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1602: $i] :
( ~ ( c_member @ ( tc_prod @ SY1601 @ SY1601 ) @ ( c_Product__Type_OPair @ SY1601 @ SY1601 @ SY1602 @ SV281 ) @ SY1596 )
| ( c_Recdef_Owfrec__rel @ SY1601 @ SY1600 @ SY1596 @ SY1595 @ SY1602 @ ( hAPP @ ( sK54_B_g @ SY1601 @ SY1600 @ SY1596 @ SY1595 @ SV281 @ SV133 ) @ SY1602 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SY1595 @ ( sK54_B_g @ SY1601 @ SY1600 @ SY1596 @ SY1595 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1414,plain,
! [SV134: $i,SV282: $i] :
( ( ! [SY1603: $i,SY1604: $i] :
( ~ ( c_member @ ( tc_prod @ SY1604 @ SY1604 ) @ ( c_Product__Type_OPair @ SY1604 @ SY1604 @ SY1603 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SY1604 @ SV134 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1604 @ SY1604 ) @ ( c_Product__Type_OPair @ SY1604 @ SY1604 @ SY1603 @ ( sK42_B_z @ SY1604 @ SY1603 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1604 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SY1604 @ SY1604 ) @ ( c_Product__Type_OPair @ SY1604 @ SY1604 @ ( sK42_B_z @ SY1604 @ SY1603 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1415,plain,
! [SV135: $i,SV283: $i] :
( ( ! [SY1605: $i,SY1606: $i] :
~ ( ~ ! [SY1607: $i] :
( ! [SY1608: $i] :
~ ( c_member @ ( tc_prod @ SY1608 @ SY1608 ) @ ( c_Product__Type_OPair @ SY1608 @ SY1608 @ SY1607 @ SY1606 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY1605 @ SY1608 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SY1605 @ SY1605 ) @ ( c_Product__Type_OPair @ SY1605 @ SY1605 @ ( hAPP @ SV135 @ SY1607 ) @ ( hAPP @ SV135 @ SY1606 ) ) @ SV283 ) )
| ~ ! [SY1609: $i] :
( ~ ( c_member @ ( tc_prod @ SY1605 @ SY1605 ) @ ( c_Product__Type_OPair @ SY1605 @ SY1605 @ ( hAPP @ SV135 @ SY1609 ) @ ( hAPP @ SV135 @ SY1606 ) ) @ SV283 )
| ! [SY1610: $i] : ( c_member @ ( tc_prod @ SY1610 @ SY1610 ) @ ( c_Product__Type_OPair @ SY1610 @ SY1610 @ SY1609 @ SY1606 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY1605 @ SY1610 @ SV283 ) @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1416,plain,
! [SV136: $i] :
( ( ~ ! [SY1191: $i] :
( ! [SY1192: $i] :
~ ( c_member @ SY1192 @ SY1191 @ SV136 )
| ( hBOOL @ ( hAPP @ SV136 @ SY1191 ) ) )
| ~ ! [SY1193: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ SY1193 ) )
| ! [SY1194: $i] : ( c_member @ SY1194 @ SY1193 @ SV136 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1417,plain,
! [SV137: $i,SV284: $i] :
( ( ! [SY1611: $i,SY1612: $i,SY1613: $i,SY1614: $i,SY1615: $i,SY1616: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ SY1614 @ SY1613 ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ SY1612 @ SY1611 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1616 @ SY1615 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1612 ) @ SY1611 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ ( sK14_B_a @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ ( sK16_SY711 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1616 @ SY1615 ) @ ( tc_prod @ SY1616 @ SY1615 ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ ( sK16_SY711 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1616 @ SY1615 @ SY1612 @ SY1611 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1616 @ SY1615 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY1616 @ SY1615 @ SY1614 @ SY1613 @ SY1612 @ SY1611 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1614 ) @ SY1613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1418,plain,
! [SV138: $i,SV285: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i,SY1620: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1620 @ SY1620 ) @ ( c_Product__Type_OPair @ SY1620 @ SY1620 @ ( sK56_B_z @ SY1620 @ SY1619 @ SY1618 @ SY1617 @ SV285 @ SV138 ) @ SY1619 ) @ SY1618 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1620 @ SY1617 @ SY1618 @ SV285 @ ( sK56_B_z @ SY1620 @ SY1619 @ SY1618 @ SY1617 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SY1620 @ SY1619 @ SY1618 @ SY1617 @ SV285 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY1620 @ SY1617 @ SY1618 @ SV285 @ SY1619 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SY1619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1419,plain,
! [SV139: $i] :
( ( ~ ! [SY1207: $i] :
( ( SY1207 != SV139 )
| ! [SY1208: $i] : ( c_member @ ( tc_prod @ SY1208 @ SY1208 ) @ ( c_Product__Type_OPair @ SY1208 @ SY1208 @ SY1207 @ SV139 ) @ ( c_Relation_OId @ SY1208 ) ) )
| ~ ! [SY1209: $i] :
( ! [SY1210: $i] :
~ ( c_member @ ( tc_prod @ SY1210 @ SY1210 ) @ ( c_Product__Type_OPair @ SY1210 @ SY1210 @ SY1209 @ SV139 ) @ ( c_Relation_OId @ SY1210 ) )
| ( SY1209 = SV139 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1420,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1421,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1422,plain,
! [SV140: $i,SV286: $i] :
( ( ~ ( ~ ! [SY1621: $i,SY1622: $i] :
( ( SY1622 != SY1621 )
| ~ ( c_member @ SV286 @ SV140 @ SY1622 )
| ( c_member @ SV286 @ SV140 @ SY1621 ) )
| ~ ! [SY1623: $i,SY1624: $i] :
( ( SY1624 != SY1623 )
| ~ ( c_member @ SV286 @ SV140 @ SY1623 )
| ( c_member @ SV286 @ SV140 @ SY1624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1423,plain,
! [SV141: $i,SV287: $i] :
( ( ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ( SY1626 != SY1625 )
| ~ ( c_member @ SV287 @ SY1626 @ SV141 )
| ( c_member @ SV287 @ SY1625 @ SV141 ) )
| ~ ! [SY1627: $i,SY1628: $i] :
( ( SY1628 != SY1627 )
| ~ ( c_member @ SV287 @ SY1627 @ SV141 )
| ( c_member @ SV287 @ SY1628 @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1424,plain,
! [SV142: $i,SV288: $i] :
( ( ! [SY1629: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1629 @ SV288 ) @ ( c_Product__Type_OPair @ SY1629 @ SV288 @ ( sK48_B_x @ SY1629 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SY1629 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1629 @ SV288 ) @ ( c_Product__Type_OPair @ SY1629 @ SV288 @ ( sK48_B_x @ SY1629 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SY1629 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SY1629 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SY1629 @ SV288 @ SV142 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1629 @ SV288 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1425,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
| ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1426,plain,
! [SV144: $i,SV289: $i] :
( ( ! [SY1630: $i,SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SY1631 @ SY1631 ) @ ( c_Product__Type_OPair @ SY1631 @ SY1631 @ SY1630 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SY1631 @ SV144 ) )
| ( c_member @ ( tc_prod @ SY1631 @ SY1631 ) @ ( c_Product__Type_OPair @ SY1631 @ SY1631 @ SY1630 @ SV289 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1631 @ SY1631 ) @ ( c_Product__Type_OPair @ SY1631 @ SY1631 @ SY1630 @ ( sK38_B_y @ SY1631 @ SY1630 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SY1631 @ SY1631 ) @ ( c_Product__Type_OPair @ SY1631 @ SY1631 @ ( sK38_B_y @ SY1631 @ SY1630 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SY1631 @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1427,plain,
! [SV290: $i,SV145: $i] :
( ( ~ ( ~ ! [SY1632: $i,SY1633: $i] :
( ~ ( c_Wellfounded_Owf @ SY1633 @ SV145 )
| ( c_member @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SV290 @ SY1632 ) @ ( c_Transitive__Closure_Ortrancl @ SY1633 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1633 @ ( c_Set_Oinsert @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SY1632 @ SV290 ) @ SV145 ) ) )
| ~ ~ ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) )
| ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1428,plain,
! [SV146: $i] :
( ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( c_Relation_Orefl__on @ SY1250 @ SY1249 @ SV146 )
| ~ ( c_Relation_Otrans @ SY1250 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SY1250 @ SY1249 @ SV146 ) )
| ~ ~ ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) )
| ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1429,plain,
! [SV147: $i,SV291: $i] :
( ( ! [SY1638: $i] :
( ~ ( c_member @ ( tc_prod @ SY1638 @ SY1638 ) @ SV291 @ ( c_Relation_OId__on @ SY1638 @ SV147 ) )
| ~ ( ~ ( c_member @ SY1638 @ ( sK64_B_x @ SY1638 @ SV291 @ SV147 ) @ SV147 )
| ( SV291
!= ( c_Product__Type_OPair @ SY1638 @ SY1638 @ ( sK64_B_x @ SY1638 @ SV291 @ SV147 ) @ ( sK64_B_x @ SY1638 @ SV291 @ SV147 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1430,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) )
| ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) )
| ~ ~ ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) )
| ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1431,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ( ~ ! [SY1647: $i,SY1648: $i] :
( ~ ( c_member @ SY1648 @ SY1647 @ ( c_Set_Oinsert @ SY1648 @ SV293 @ SV149 ) )
| ( SY1647 = SV293 )
| ( c_member @ SY1648 @ SY1647 @ SV149 ) )
| ~ ~ ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1432,plain,
! [SV150: $i,SV294: $i] :
( ( ! [SY1653: $i,SY1654: $i,SY1655: $i] :
( ~ ( c_member @ ( tc_prod @ SY1655 @ SY1655 ) @ ( c_Product__Type_OPair @ SY1655 @ SY1655 @ SY1654 @ SY1653 ) @ ( c_Transitive__Closure_Ortrancl @ SY1655 @ SV294 ) )
| ~ ( hBOOL @ ( hAPP @ SV150 @ SY1653 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1655 @ SY1655 ) @ ( c_Product__Type_OPair @ SY1655 @ SY1655 @ ( sK12_B_y @ SY1655 @ SY1654 @ SY1653 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SY1655 @ SY1654 @ SY1653 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1655 @ SY1655 ) @ ( c_Product__Type_OPair @ SY1655 @ SY1655 @ ( sK13_SY707 @ SY1655 @ SY1654 @ SY1653 @ SV294 @ SV150 ) @ SY1653 ) @ ( c_Transitive__Closure_Ortrancl @ SY1655 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SY1655 @ SY1654 @ SY1653 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SY1655 @ SY1654 @ SY1653 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1433,plain,
! [SV151: $i,SV295: $i] :
( ( ! [SY1656: $i] :
( ( c_member @ SY1656 @ SV295 @ ( c_Wellfounded_Oacc @ SY1656 @ SV151 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1656 @ SY1656 ) @ ( c_Product__Type_OPair @ SY1656 @ SY1656 @ ( sK58_B_z @ SY1656 @ SV295 @ SV151 ) @ SV295 ) @ SV151 )
| ~ ~ ( c_member @ SY1656 @ ( sK58_B_z @ SY1656 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SY1656 @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1434,plain,
! [SV152: $i,SV296: $i] :
( ( ! [SY1657: $i] :
~ ( ~ ! [SY1658: $i,SY1659: $i] :
( ~ ( c_member @ ( tc_prod @ SY1659 @ SY1658 ) @ ( c_Product__Type_OPair @ SY1659 @ SY1658 @ SV296 @ SV152 ) @ SY1657 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1659 @ SY1658 @ SY1657 ) @ SV296 ) @ SV152 ) ) )
| ~ ! [SY1660: $i,SY1661: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1661 @ SY1660 @ SY1657 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1661 @ SY1660 ) @ ( c_Product__Type_OPair @ SY1661 @ SY1660 @ SV296 @ SV152 ) @ SY1657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1435,plain,
! [SV153: $i,SV297: $i] :
( ( ! [SY1662: $i,SY1663: $i] :
( ~ ( c_member @ ( tc_prod @ SY1663 @ SY1663 ) @ ( c_Product__Type_OPair @ SY1663 @ SY1663 @ SY1662 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SY1663 @ SV153 ) )
| ( SY1662 = SV297 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1663 @ SY1663 ) @ ( c_Product__Type_OPair @ SY1663 @ SY1663 @ SY1662 @ ( sK44_B_y @ SY1663 @ SY1662 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SY1663 @ SY1663 ) @ ( c_Product__Type_OPair @ SY1663 @ SY1663 @ ( sK44_B_y @ SY1663 @ SY1662 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SY1663 @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1436,plain,
! [SV154: $i,SV298: $i] :
( ( ! [SY1664: $i,SY1665: $i,SY1666: $i] :
( ~ ( c_member @ ( tc_prod @ SY1666 @ SY1666 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1666 @ SY1665 @ SY1664 ) @ ( c_Transitive__Closure_Ortrancl @ SY1666 @ SV298 ) )
| ~ ( hBOOL @ ( hAPP @ SV154 @ SY1665 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1666 @ SY1666 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1666 @ SY1665 @ ( sK10_B_y @ SY1666 @ SY1665 @ SY1664 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1666 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1666 @ SY1666 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1666 @ ( sK10_B_y @ SY1666 @ SY1665 @ SY1664 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SY1666 @ SY1665 @ SY1664 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SY1666 @ SY1665 @ SY1664 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SY1666 @ SY1665 @ SY1664 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SY1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1437,plain,
! [SV155: $i,SV299: $i] :
( ( ! [SY1667: $i,SY1668: $i] :
( ~ ( c_member @ ( tc_prod @ SY1668 @ SY1668 ) @ ( c_Product__Type_OPair @ SY1668 @ SY1668 @ SY1667 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SY1668 @ SV155 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1668 @ SY1668 ) @ ( c_Product__Type_OPair @ SY1668 @ SY1668 @ SY1667 @ ( sK41_B_z @ SY1668 @ SY1667 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SY1668 @ SY1668 ) @ ( c_Product__Type_OPair @ SY1668 @ SY1668 @ ( sK41_B_z @ SY1668 @ SY1667 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SY1668 @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1438,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1439,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1440,plain,
! [SV156: $i,SV300: $i] :
( ( ~ ( ~ ! [SY1669: $i] :
( ! [SY1670: $i] :
~ ( c_member @ ( tc_prod @ SY1670 @ SY1670 ) @ ( c_Product__Type_OPair @ SY1670 @ SY1670 @ SY1669 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1670 @ SV156 ) )
| ( SY1669 != SV300 )
| ( SY1669 = SV300 ) )
| ~ ! [SY1671: $i,SY1672: $i] :
( ~ ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1672 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SY1672 @ SV156 ) )
| ( SY1671 = SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1441,plain,
! [SV157: $i,SV301: $i] :
( ( ~ ( ~ ! [SY1673: $i,SY1674: $i] :
( ~ ( c_member @ SY1674 @ SY1673 @ SV301 )
| ( c_member @ SY1674 @ SY1673 @ ( c_Set_Oinsert @ SY1674 @ SV157 @ SV301 ) ) )
| ~ ! [SY1675: $i] :
( ( SY1675 != SV157 )
| ! [SY1676: $i] : ( c_member @ SY1676 @ SY1675 @ ( c_Set_Oinsert @ SY1676 @ SV157 @ SV301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1442,plain,
! [SV158: $i,SV302: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK26_B_x @ SV302 @ SV158 ) @ ( sK27_SY720 @ SV302 @ SV158 ) ) @ SV158 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) ) )
| ( c_Relation_Oantisym @ SV302 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1443,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1444,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1445,plain,
! [SV159: $i] :
( ( ~ ! [SY1306: $i,SY1307: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1307 @ SY1306 @ SV159 )
| ~ ( c_Relation_Oantisym @ SY1307 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SY1307 @ SY1306 @ SV159 ) )
| ~ ~ ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) )
| ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1446,plain,
! [SV160: $i,SV303: $i] :
( ( ! [SY1677: $i,SY1678: $i] :
~ ( ~ ! [SY1679: $i,SY1680: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1680 @ SY1680 ) @ ( c_Product__Type_OPair @ SY1680 @ SY1680 @ ( sK43_B_y @ SY1680 @ SY1679 @ SY1678 @ SY1677 @ SV303 @ SV160 ) @ SV303 ) @ SY1677 )
| ~ ( ( ( hAPP @ SY1678 @ ( sK43_B_y @ SY1680 @ SY1679 @ SY1678 @ SY1677 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY1680 @ SY1679 @ SY1678 @ SY1677 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY1680 @ SY1679 @ SY1678 @ SY1677 @ SV303 )
= ( c_Recdef_Ocut @ SY1680 @ SY1679 @ SV160 @ SY1677 @ SV303 ) ) )
| ~ ! [SY1681: $i,SY1682: $i] :
( ( ( c_Recdef_Ocut @ SY1682 @ SY1681 @ SY1678 @ SY1677 @ SV303 )
!= ( c_Recdef_Ocut @ SY1682 @ SY1681 @ SV160 @ SY1677 @ SV303 ) )
| ! [SY1683: $i] :
( ~ ( c_member @ ( tc_prod @ SY1682 @ SY1682 ) @ ( c_Product__Type_OPair @ SY1682 @ SY1682 @ SY1683 @ SV303 ) @ SY1677 )
| ( ( hAPP @ SY1678 @ SY1683 )
= ( hAPP @ SV160 @ SY1683 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1447,plain,
! [SV161: $i,SV304: $i] :
( ( ! [SY1684: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1684 @ SY1684 ) @ ( c_Product__Type_OPair @ SY1684 @ SY1684 @ ( sK57_B_y @ SY1684 @ SV304 @ SV161 ) @ SV304 ) @ SV161 )
| ~ ~ ( c_member @ SY1684 @ ( sK57_B_y @ SY1684 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SY1684 @ SV161 ) ) )
| ( c_member @ SY1684 @ SV304 @ ( c_Wellfounded_Oacc @ SY1684 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1448,plain,
! [SV1: $i,SV162: $i,SV305: $i] :
( ( ! [SY1685: $i,SY1686: $i] :
( ~ ( c_Relation_Otrans @ SY1686 @ SY1685 )
| ~ ( c_member @ ( tc_prod @ SY1686 @ SY1686 ) @ ( c_Product__Type_OPair @ SY1686 @ SY1686 @ SV305 @ SV162 ) @ SY1685 )
| ~ ( c_member @ ( tc_prod @ SY1686 @ SY1686 ) @ ( c_Product__Type_OPair @ SY1686 @ SY1686 @ SV162 @ SV1 ) @ SY1685 )
| ( c_member @ ( tc_prod @ SY1686 @ SY1686 ) @ ( c_Product__Type_OPair @ SY1686 @ SY1686 @ SV305 @ SV1 ) @ SY1685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1449,plain,
! [SV2: $i,SV163: $i,SV306: $i] :
( ( ! [SY1687: $i] :
( ( SY1687 != SV306 )
| ~ ( c_member @ SV163 @ SV306 @ SV2 )
| ( c_member @ SV163 @ SY1687 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1450,plain,
! [SV3: $i,SV164: $i,SV307: $i] :
( ( ! [SY1688: $i,SY1689: $i,SY1690: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY1690 @ SY1689 @ SY1688 @ SV307 @ ( c_Product__Type_OPair @ SY1690 @ SY1689 @ SV164 @ SV3 ) )
= ( hAPP @ ( hAPP @ SV307 @ SV164 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1451,plain,
! [SV4: $i,SV165: $i,SV308: $i] :
( ( ! [SY1691: $i,SY1692: $i,SY1693: $i] :
( ( c_Product__Type_Ointernal__split @ SY1693 @ SY1692 @ SY1691 @ SV308 @ ( c_Product__Type_OPair @ SY1693 @ SY1692 @ SV165 @ SV4 ) )
= ( hAPP @ ( hAPP @ SV308 @ SV165 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1452,plain,
! [SV5: $i,SV166: $i,SV309: $i] :
( ( ! [SY1694: $i,SY1695: $i] :
( ~ ( c_member @ ( tc_prod @ SY1695 @ SY1694 ) @ ( c_Product__Type_OPair @ SY1695 @ SY1694 @ SV309 @ SV166 ) @ SV5 )
| ( c_member @ SY1694 @ SV166 @ ( c_Relation_ORange @ SY1695 @ SY1694 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1453,plain,
! [SV6: $i,SV167: $i,SV310: $i] :
( ( ! [SY1696: $i] :
( ( SY1696 != SV310 )
| ~ ( c_member @ SV167 @ SY1696 @ SV6 )
| ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SY1696 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1454,plain,
! [SV7: $i,SV168: $i,SV311: $i] :
( ( ! [SY1697: $i,SY1698: $i] :
( ~ ( c_member @ ( tc_prod @ SY1698 @ SY1697 ) @ ( c_Product__Type_OPair @ SY1698 @ SY1697 @ SV311 @ SV168 ) @ SV7 )
| ( c_member @ SY1698 @ SV311 @ ( c_Relation_ODomain @ SY1698 @ SY1697 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1455,plain,
! [SV8: $i,SV169: $i,SV312: $i] :
( ( ! [SY1699: $i] :
( ~ ( c_Relation_Otrans @ SY1699 @ SV312 )
| ~ ( c_Relation_Otrans @ SV169 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SY1699 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SY1699 @ SV169 @ SV312 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1456,plain,
! [SV10: $i,SV171: $i,SV313: $i] :
( ( ! [SY1700: $i] :
( ~ ( c_Relation_Otrans @ SY1700 @ SV313 )
| ( c_Relation_Otrans @ SV171 @ ( hAPP @ ( c_Relation_Oinv__image @ SY1700 @ SV171 @ SV313 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1457,plain,
! [SV11: $i,SV172: $i,SV314: $i] :
( ( ! [SY1701: $i] :
( ~ ( c_member @ SY1701 @ SV314 @ ( c_Relation_ORange @ SV172 @ SY1701 @ SV11 ) )
| ( c_member @ ( tc_prod @ SV172 @ SY1701 ) @ ( c_Product__Type_OPair @ SV172 @ SY1701 @ ( sK63_B_x @ SY1701 @ SV314 @ SV172 @ SV11 ) @ SV314 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1458,plain,
! [SV12: $i,SV173: $i,SV315: $i] :
( ( ! [SY1702: $i] :
( ~ ( c_member @ SY1702 @ SV315 @ ( c_Relation_ODomain @ SY1702 @ SV173 @ SV12 ) )
| ( c_member @ ( tc_prod @ SY1702 @ SV173 ) @ ( c_Product__Type_OPair @ SY1702 @ SV173 @ SV315 @ ( sK62_B_y @ SY1702 @ SV315 @ SV173 @ SV12 ) ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1459,plain,
! [SV13: $i,SV174: $i,SV316: $i] :
( ( ! [SY1703: $i] :
( ~ ( c_member @ SY1703 @ SV316 @ ( c_Wellfounded_Oacc @ SY1703 @ SV174 ) )
| ~ ( c_member @ ( tc_prod @ SY1703 @ SY1703 ) @ ( c_Product__Type_OPair @ SY1703 @ SY1703 @ SV13 @ SV316 ) @ SV174 )
| ( c_member @ SY1703 @ SV13 @ ( c_Wellfounded_Oacc @ SY1703 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1460,plain,
! [SV14: $i,SV175: $i,SV317: $i] :
( ( ! [SY1704: $i] :
( ~ ( c_Relation_Orefl__on @ SY1704 @ SV317 @ SV175 )
| ~ ( c_member @ SY1704 @ SV14 @ SV317 )
| ( c_member @ ( tc_prod @ SY1704 @ SY1704 ) @ ( c_Product__Type_OPair @ SY1704 @ SY1704 @ SV14 @ SV14 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1461,plain,
! [SV15: $i,SV176: $i,SV318: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
( ~ ( c_Relation_Orefl__on @ SY1706 @ SY1705 @ SV318 )
| ~ ( c_member @ ( tc_prod @ SY1706 @ SY1706 ) @ ( c_Product__Type_OPair @ SY1706 @ SY1706 @ SV176 @ SV15 ) @ SV318 )
| ( c_member @ SY1706 @ SV176 @ SY1705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1462,plain,
! [SV16: $i,SV177: $i,SV319: $i] :
( ( ! [SY1707: $i,SY1708: $i] :
( ~ ( c_Relation_Orefl__on @ SY1708 @ SY1707 @ SV319 )
| ~ ( c_member @ ( tc_prod @ SY1708 @ SY1708 ) @ ( c_Product__Type_OPair @ SY1708 @ SY1708 @ SV177 @ SV16 ) @ SV319 )
| ( c_member @ SY1708 @ SV16 @ SY1707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1463,plain,
! [SV17: $i,SV178: $i,SV320: $i] :
( ( ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SY1709 @ SY1709 ) @ ( c_Product__Type_OPair @ SY1709 @ SY1709 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SY1709 @ SV17 ) )
| ~ ( c_member @ SY1709 @ SV178 @ ( c_Wellfounded_Oacc @ SY1709 @ SV17 ) )
| ( c_member @ SY1709 @ SV320 @ ( c_Wellfounded_Oacc @ SY1709 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1464,plain,
! [SV18: $i,SV179: $i,SV321: $i] :
( ( ! [SY1710: $i] :
( ~ ( c_member @ SY1710 @ SV321 @ ( c_Wellfounded_Oacc @ SY1710 @ SV179 ) )
| ~ ( c_member @ ( tc_prod @ SY1710 @ SY1710 ) @ ( c_Product__Type_OPair @ SY1710 @ SY1710 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SY1710 @ SV179 ) )
| ( c_member @ SY1710 @ SV18 @ ( c_Wellfounded_Oacc @ SY1710 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1465,plain,
! [SV19: $i,SV180: $i,SV322: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1713 @ SY1712 @ SY1711 )
| ~ ( c_member @ ( tc_prod @ SY1713 @ SY1712 ) @ ( c_Product__Type_OPair @ SY1713 @ SY1712 @ SV322 @ SV180 ) @ SY1711 )
| ~ ( c_member @ ( tc_prod @ SY1713 @ SY1712 ) @ ( c_Product__Type_OPair @ SY1713 @ SY1712 @ SV322 @ SV19 ) @ SY1711 )
| ( SV180 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1466,plain,
! [SV20: $i,SV181: $i,SV323: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i] :
( ( c_Product__Type_Ocurry @ SY1716 @ SY1715 @ SY1714 @ SV323 @ SV181 @ SV20 )
= ( hAPP @ SV323 @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SV181 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1467,plain,
! [SV21: $i,SV182: $i,SV324: $i] :
( ( c_member @ ( tc_prod @ SV324 @ SV324 ) @ ( c_Product__Type_OPair @ SV324 @ SV324 @ SV182 @ SV182 ) @ ( c_Transitive__Closure_Ortrancl @ SV324 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1468,plain,
! [SV22: $i,SV183: $i,SV325: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ SV22 )
| ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ ( c_Transitive__Closure_Ortrancl @ SV325 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1469,plain,
! [SV23: $i,SV184: $i,SV326: $i] :
( ( ! [SY1717: $i,SY1718: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1718 @ SY1718 @ SY1717 )
| ~ ( c_member @ ( tc_prod @ SY1718 @ SY1718 ) @ ( c_Product__Type_OPair @ SY1718 @ SY1718 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1718 @ SY1717 ) )
| ~ ( c_member @ ( tc_prod @ SY1718 @ SY1718 ) @ ( c_Product__Type_OPair @ SY1718 @ SY1718 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1718 @ SY1717 ) )
| ( c_member @ ( tc_prod @ SY1718 @ SY1718 ) @ ( c_Product__Type_OPair @ SY1718 @ SY1718 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1718 @ SY1717 ) )
| ( c_member @ ( tc_prod @ SY1718 @ SY1718 ) @ ( c_Product__Type_OPair @ SY1718 @ SY1718 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1718 @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1470,plain,
! [SV24: $i,SV185: $i,SV327: $i] :
( ( ! [SY1719: $i,SY1720: $i] :
( ~ ( c_member @ ( tc_prod @ SY1720 @ SY1720 ) @ ( c_Product__Type_OPair @ SY1720 @ SY1720 @ SY1719 @ SV327 ) @ SV185 )
| ~ ( c_member @ ( tc_prod @ SY1720 @ SY1720 ) @ ( c_Product__Type_OPair @ SY1720 @ SY1720 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1720 @ SV185 ) )
| ( c_member @ ( tc_prod @ SY1720 @ SY1720 ) @ ( c_Product__Type_OPair @ SY1720 @ SY1720 @ SY1719 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1720 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1471,plain,
! [SV25: $i,SV186: $i,SV328: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ~ ( c_member @ ( tc_prod @ SY1722 @ SY1722 ) @ ( c_Product__Type_OPair @ SY1722 @ SY1722 @ SY1721 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SY1722 @ SV186 ) )
| ~ ( c_member @ ( tc_prod @ SY1722 @ SY1722 ) @ ( c_Product__Type_OPair @ SY1722 @ SY1722 @ SV328 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SY1722 @ SY1722 ) @ ( c_Product__Type_OPair @ SY1722 @ SY1722 @ SY1721 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SY1722 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1472,plain,
! [SV26: $i,SV187: $i,SV329: $i] :
( ( ! [SY1723: $i,SY1724: $i] :
( ~ ( c_member @ ( tc_prod @ SY1724 @ SY1724 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1724 @ SY1723 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SY1724 @ SV187 ) )
| ~ ( c_member @ ( tc_prod @ SY1724 @ SY1724 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1724 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1724 @ SV187 ) )
| ( c_member @ ( tc_prod @ SY1724 @ SY1724 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1724 @ SY1723 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1724 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1473,plain,
! [SV28: $i,SV189: $i,SV330: $i] :
( ( ! [SY1725: $i] :
( ~ ( c_member @ ( tc_prod @ SY1725 @ SY1725 ) @ ( c_Product__Type_OPair @ SY1725 @ SY1725 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Otrancl @ SY1725 @ SV28 ) )
| ( c_member @ ( tc_prod @ SY1725 @ SY1725 ) @ ( c_Product__Type_OPair @ SY1725 @ SY1725 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Ortrancl @ SY1725 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1474,plain,
! [SV29: $i,SV190: $i,SV331: $i] :
( ( ! [SY1726: $i,SY1727: $i,SY1728: $i] :
( ~ ( c_member @ ( tc_prod @ SY1728 @ SY1728 ) @ ( c_Product__Type_OPair @ SY1728 @ SY1728 @ SY1727 @ SY1726 ) @ SV331 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY1728 @ SV190 @ SV29 @ SV331 @ SY1726 ) @ SY1727 )
= ( hAPP @ SV29 @ SY1727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1475,plain,
! [SV30: $i,SV191: $i,SV332: $i] :
( ( ! [SY1729: $i] :
( ~ ( c_member @ ( tc_prod @ SY1729 @ SY1729 ) @ ( c_Product__Type_OPair @ SY1729 @ SY1729 @ SV332 @ SV191 ) @ SV30 )
| ( c_member @ ( tc_prod @ SY1729 @ SY1729 ) @ ( c_Product__Type_OPair @ SY1729 @ SY1729 @ SV332 @ SV191 ) @ ( c_Transitive__Closure_Otrancl @ SY1729 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1476,plain,
! [SV31: $i,SV192: $i,SV333: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ SV31 )
| ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ ( c_Transitive__Closure_Otrancl @ SV333 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1477,plain,
! [SV33: $i,SV194: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV194 @ SV33 ) )
= $true )
| ( ( ( c_Transitive__Closure_Otrancl @ SV194 @ SV33 )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1478,plain,
! [SV34: $i,SV195: $i,SV334: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ~ ( c_member @ ( tc_prod @ SY1731 @ SY1731 ) @ ( c_Product__Type_OPair @ SY1731 @ SY1731 @ SY1730 @ SV334 ) @ SV195 )
| ~ ( c_member @ ( tc_prod @ SY1731 @ SY1731 ) @ ( c_Product__Type_OPair @ SY1731 @ SY1731 @ SV334 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SY1731 @ SY1731 ) @ ( c_Product__Type_OPair @ SY1731 @ SY1731 @ SY1730 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SY1731 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1479,plain,
! [SV35: $i,SV196: $i,SV335: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ~ ( c_member @ ( tc_prod @ SY1733 @ SY1733 ) @ ( c_Product__Type_OPair @ SY1733 @ SY1733 @ SY1732 @ SV335 ) @ SV196 )
| ~ ( c_member @ ( tc_prod @ SY1733 @ SY1733 ) @ ( c_Product__Type_OPair @ SY1733 @ SY1733 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1733 @ SV196 ) )
| ( c_member @ ( tc_prod @ SY1733 @ SY1733 ) @ ( c_Product__Type_OPair @ SY1733 @ SY1733 @ SY1732 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1733 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1480,plain,
! [SV36: $i,SV197: $i,SV336: $i] :
( ( ! [SY1734: $i,SY1735: $i] :
( ~ ( c_member @ ( tc_prod @ SY1735 @ SY1735 ) @ ( c_Product__Type_OPair @ SY1735 @ SY1735 @ SY1734 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SY1735 @ SV197 ) )
| ~ ( c_member @ ( tc_prod @ SY1735 @ SY1735 ) @ ( c_Product__Type_OPair @ SY1735 @ SY1735 @ SV336 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SY1735 @ SY1735 ) @ ( c_Product__Type_OPair @ SY1735 @ SY1735 @ SY1734 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SY1735 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1481,plain,
! [SV37: $i,SV198: $i,SV337: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ~ ( c_member @ ( tc_prod @ SY1737 @ SY1737 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1737 @ SY1736 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SY1737 @ SV198 ) )
| ~ ( c_member @ ( tc_prod @ SY1737 @ SY1737 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1737 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1737 @ SV198 ) )
| ( c_member @ ( tc_prod @ SY1737 @ SY1737 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1737 @ SY1736 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1737 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1482,plain,
! [SV38: $i,SV199: $i,SV338: $i] :
( ( ! [SY1738: $i,SY1739: $i] :
( ~ ( c_member @ ( tc_prod @ SY1739 @ SY1739 ) @ ( c_Product__Type_OPair @ SY1739 @ SY1739 @ SY1738 @ SV338 ) @ SV199 )
| ~ ( c_member @ ( tc_prod @ SY1739 @ SY1739 ) @ ( c_Product__Type_OPair @ SY1739 @ SY1739 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SY1739 @ SV199 ) )
| ( c_member @ ( tc_prod @ SY1739 @ SY1739 ) @ ( c_Product__Type_OPair @ SY1739 @ SY1739 @ SY1738 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SY1739 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1483,plain,
! [SV39: $i,SV200: $i,SV339: $i] :
( ( ! [SY1740: $i,SY1741: $i] :
( ~ ( c_member @ ( tc_prod @ SY1741 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1741 @ SY1741 @ SY1740 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SY1741 @ SV200 ) )
| ~ ( c_member @ ( tc_prod @ SY1741 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1741 @ SY1741 @ SV339 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SY1741 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1741 @ SY1741 @ SY1740 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SY1741 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1484,plain,
! [SV40: $i,SV201: $i,SV340: $i] :
( ( ! [SY1742: $i,SY1743: $i] :
( ~ ( c_member @ ( tc_prod @ SY1743 @ SY1743 ) @ ( c_Product__Type_OPair @ SY1743 @ SY1743 @ SY1742 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SY1743 @ SV201 ) )
| ~ ( c_member @ ( tc_prod @ SY1743 @ SY1743 ) @ ( c_Product__Type_OPair @ SY1743 @ SY1743 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SY1743 @ SV201 ) )
| ( c_member @ ( tc_prod @ SY1743 @ SY1743 ) @ ( c_Product__Type_OPair @ SY1743 @ SY1743 @ SY1742 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SY1743 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1485,plain,
! [SV41: $i,SV202: $i,SV341: $i] :
( ( ! [SY1744: $i,SY1745: $i] :
( ~ ( c_member @ ( tc_prod @ SY1745 @ SY1745 ) @ ( c_Product__Type_OPair @ SY1745 @ SY1745 @ SY1744 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SY1745 @ SV202 ) )
| ~ ( c_member @ ( tc_prod @ SY1745 @ SY1745 ) @ ( c_Product__Type_OPair @ SY1745 @ SY1745 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1745 @ SV202 ) )
| ( c_member @ ( tc_prod @ SY1745 @ SY1745 ) @ ( c_Product__Type_OPair @ SY1745 @ SY1745 @ SY1744 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1745 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1486,plain,
! [SV42: $i,SV203: $i,SV342: $i] :
( ( ! [SY1746: $i,SY1747: $i,SY1748: $i] :
( ~ ( c_member @ ( tc_prod @ SY1746 @ SY1746 ) @ ( c_Product__Type_OPair @ SY1746 @ SY1746 @ SV342 @ SV203 ) @ SY1748 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY1746 @ SV42 @ SY1747 @ SY1748 @ SV203 ) @ SV342 )
= ( hAPP @ SY1747 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1487,plain,
! [SV43: $i,SV204: $i,SV343: $i] :
( ( ! [SY1749: $i] :
( ( c_member @ ( tc_prod @ SY1749 @ SY1749 ) @ ( c_Product__Type_OPair @ SY1749 @ SY1749 @ ( sK39_B_x @ SY1749 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SY1749 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1749 @ SV343 ) )
| ~ ( c_member @ ( tc_prod @ SY1749 @ SY1749 ) @ ( c_Product__Type_OPair @ SY1749 @ SY1749 @ SV204 @ SV43 ) @ SV343 )
| ( SV204 != SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1488,plain,
! [SV46: $i,SV206: $i] :
( ( ( c_member @ ( tc_prod @ SV206 @ SV206 ) @ ( c_Product__Type_OPair @ SV206 @ SV206 @ ( sK36_B_x @ SV206 @ SV46 ) @ ( sK36_B_x @ SV206 @ SV46 ) ) @ ( c_Transitive__Closure_Otrancl @ SV206 @ SV46 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV206 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1489,plain,
! [SV47: $i,SV207: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV207 @ SV207 ) @ SV47 @ ( c_Relation_OId @ SV207 ) ) )
= $true )
| ( ( SV47
= ( c_Product__Type_OPair @ SV207 @ SV207 @ ( sK35_B_x @ SV207 @ SV47 ) @ ( sK35_B_x @ SV207 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1490,plain,
! [SV48: $i,SV208: $i,SV344: $i] :
( ( ! [SY1750: $i] :
( ~ ( c_Relation_Oantisym @ SY1750 @ SV344 )
| ~ ( c_member @ ( tc_prod @ SY1750 @ SY1750 ) @ ( c_Product__Type_OPair @ SY1750 @ SY1750 @ SV208 @ SV48 ) @ SV344 )
| ~ ( c_member @ ( tc_prod @ SY1750 @ SY1750 ) @ ( c_Product__Type_OPair @ SY1750 @ SY1750 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1491,plain,
! [SV49: $i,SV209: $i,SV345: $i] :
( ( ! [SY1751: $i] :
( ~ ( c_member @ SY1751 @ SV345 @ ( c_Set_Oinsert @ SY1751 @ SV209 @ SV49 ) )
| ( SV345 = SV209 )
| ( c_member @ SY1751 @ SV345 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1492,plain,
! [SV50: $i,SV210: $i,SV346: $i] :
( ( ! [SY1752: $i,SY1753: $i] :
( ( c_Relation_ODomain @ SY1753 @ SY1752 @ ( c_Set_Oinsert @ ( tc_prod @ SY1753 @ SY1752 ) @ ( c_Product__Type_OPair @ SY1753 @ SY1752 @ SV346 @ SV210 ) @ SV50 ) )
= ( c_Set_Oinsert @ SY1753 @ SV346 @ ( c_Relation_ODomain @ SY1753 @ SY1752 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1493,plain,
! [SV51: $i,SV211: $i,SV347: $i] :
( ( ! [SY1754: $i,SY1755: $i] :
( ( c_Relation_ORange @ SY1755 @ SY1754 @ ( c_Set_Oinsert @ ( tc_prod @ SY1755 @ SY1754 ) @ ( c_Product__Type_OPair @ SY1755 @ SY1754 @ SV347 @ SV211 ) @ SV51 ) )
= ( c_Set_Oinsert @ SY1754 @ SV211 @ ( c_Relation_ORange @ SY1755 @ SY1754 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1494,plain,
! [SV52: $i,SV212: $i,SV348: $i] :
( ( c_member @ SV348 @ SV212 @ ( c_Set_Oinsert @ SV348 @ SV212 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1495,plain,
! [SV53: $i,SV213: $i,SV349: $i] :
( ( ! [SY1756: $i] :
( ~ ( c_member @ SY1756 @ SV349 @ SV213 )
| ( c_member @ SY1756 @ SV349 @ ( c_Set_Oinsert @ SY1756 @ SV53 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1496,plain,
! [SV54: $i,SV214: $i,SV350: $i] :
( ( ~ ( c_member @ SV350 @ SV214 @ SV54 )
| ( ( c_Set_Oinsert @ SV350 @ SV214 @ SV54 )
= SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1497,plain,
! [SV55: $i,SV215: $i,SV351: $i] :
( ( ! [SY1757: $i] :
( ~ ( c_Wellfounded_Owf @ SY1757 @ SV351 )
| ~ ( c_Wellfounded_Owf @ SV215 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY1757 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SY1757 @ SV215 @ SV351 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1498,plain,
! [SV56: $i,SV216: $i,SV352: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV352 @ SV216 )
| ~ ( c_member @ ( tc_prod @ SV352 @ SV352 ) @ ( c_Product__Type_OPair @ SV352 @ SV352 @ SV56 @ SV56 ) @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1499,plain,
! [SV57: $i,SV217: $i,SV353: $i] :
( ( ! [SY1758: $i] :
( ~ ( c_Wellfounded_Owf @ SY1758 @ SV353 )
| ~ ( c_member @ ( tc_prod @ SY1758 @ SY1758 ) @ ( c_Product__Type_OPair @ SY1758 @ SY1758 @ SV217 @ SV57 ) @ SV353 )
| ~ ( c_member @ ( tc_prod @ SY1758 @ SY1758 ) @ ( c_Product__Type_OPair @ SY1758 @ SY1758 @ SV57 @ SV217 ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1500,plain,
! [SV58: $i,SV218: $i,SV354: $i] :
( ( ! [SY1759: $i] :
( ~ ( c_Wellfounded_Owf @ SY1759 @ SV354 )
| ~ ( c_member @ ( tc_prod @ SY1759 @ SY1759 ) @ ( c_Product__Type_OPair @ SY1759 @ SY1759 @ SV218 @ SV58 ) @ SV354 )
| ~ ( c_member @ ( tc_prod @ SY1759 @ SY1759 ) @ ( c_Product__Type_OPair @ SY1759 @ SY1759 @ SV58 @ SV218 ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1501,plain,
! [SV59: $i,SV219: $i,SV355: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV355 @ SV219 )
| ~ ( c_member @ ( tc_prod @ SV355 @ SV355 ) @ ( c_Product__Type_OPair @ SV355 @ SV355 @ SV59 @ SV59 ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1502,plain,
! [SV60: $i,SV220: $i,SV356: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV356 @ SV220 )
| ( c_member @ SV356 @ SV60 @ ( c_Wellfounded_Oacc @ SV356 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1503,plain,
! [SV61: $i,SV221: $i] :
( ( ( ~ ( c_member @ SV221 @ ( sK25_B_x @ SV221 @ SV61 ) @ ( c_Wellfounded_Oacc @ SV221 @ SV61 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV221 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1504,plain,
! [SV62: $i,SV222: $i,SV357: $i] :
( ( ! [SY1760: $i,SY1761: $i,SY1762: $i] :
( ~ ( c_member @ SY1762 @ SY1761 @ SY1760 )
| ~ ( c_member @ ( tc_prod @ SY1762 @ SV357 ) @ ( c_Product__Type_OPair @ SY1762 @ SV357 @ SY1761 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SY1762 @ SV357 @ SV62 @ SY1760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1505,plain,
! [SV63: $i,SV223: $i,SV358: $i] :
( ( ! [SY1763: $i,SY1764: $i,SY1765: $i,SY1766: $i,SY1767: $i] :
( ~ ( c_member @ ( tc_prod @ SY1767 @ SY1766 ) @ ( c_Product__Type_OPair @ SY1767 @ SY1766 @ SY1765 @ SY1764 ) @ SY1763 )
| ~ ( c_member @ ( tc_prod @ SY1766 @ SV358 ) @ ( c_Product__Type_OPair @ SY1766 @ SV358 @ SY1764 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1767 @ SV358 ) @ ( c_Product__Type_OPair @ SY1767 @ SV358 @ SY1765 @ SV223 ) @ ( c_Relation_Orel__comp @ SY1767 @ SY1766 @ SV358 @ SY1763 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1506,plain,
! [SV64: $i,SV224: $i] :
( ( ( ( ( hAPP @ SV224 @ ( sK22_B_x @ SV224 @ SV64 ) )
!= ( hAPP @ SV64 @ ( sK22_B_x @ SV224 @ SV64 ) ) ) )
= $true )
| ( ( SV224 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1507,plain,
! [SV65: $i,SV225: $i,SV359: $i] :
( ( ! [SY1768: $i,SY1769: $i,SY1770: $i,SY1771: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1771 @ SY1770 ) )
| ~ ( c_member @ ( tc_prod @ SY1769 @ SY1769 ) @ ( c_Product__Type_OPair @ SY1769 @ SY1769 @ SY1768 @ SV359 ) @ ( hAPP @ SV225 @ SY1770 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SY1769 ) @ ( tc_prod @ SV65 @ SY1769 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SY1769 ) @ ( tc_prod @ SV65 @ SY1769 ) @ ( c_Product__Type_OPair @ SV65 @ SY1769 @ SY1770 @ SY1768 ) @ ( c_Product__Type_OPair @ SV65 @ SY1769 @ SY1770 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SY1769 @ SY1771 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1508,plain,
! [SV69: $i,SV229: $i,SV360: $i] :
( ( ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1773 @ ( c_Product__Type_OPair @ SY1772 @ SV360 @ SV229 @ SV69 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY1772 @ SV360 @ tc_HOL_Obool @ SY1773 @ SV229 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1509,plain,
! [SV70: $i,SV230: $i,SV361: $i] :
( ( ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1775 @ SY1774 @ tc_HOL_Obool @ SV361 @ SV230 @ SV70 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Product__Type_OPair @ SY1775 @ SY1774 @ SV230 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1510,plain,
! [SV71: $i,SV231: $i,SV362: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1777 @ SY1776 @ tc_HOL_Obool @ SV362 @ SV231 @ SV71 ) )
| ( hBOOL @ ( hAPP @ SV362 @ ( c_Product__Type_OPair @ SY1777 @ SY1776 @ SV231 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1511,plain,
! [SV79: $i,SV238: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV238 @ SV79 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV238 @ ( c_Transitive__Closure_Ortrancl @ SV238 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1512,plain,
! [SV80: $i,SV239: $i,SV363: $i] :
( ( ( c_Set_Oinsert @ SV363 @ SV239 @ ( c_Set_Oinsert @ SV363 @ SV239 @ SV80 ) )
= ( c_Set_Oinsert @ SV363 @ SV239 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1513,plain,
! [SV81: $i,SV240: $i,SV364: $i] :
( ( ! [SY1778: $i] :
( ( c_Set_Oinsert @ SY1778 @ SV364 @ ( c_Set_Oinsert @ SY1778 @ SV240 @ SV81 ) )
= ( c_Set_Oinsert @ SY1778 @ SV240 @ ( c_Set_Oinsert @ SY1778 @ SV364 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1514,plain,
! [SV84: $i,SV242: $i,SV365: $i] :
( ( ! [SY1779: $i] :
( ~ ( c_Wellfounded_Owf @ SY1779 @ SV365 )
| ( c_Wellfounded_Owf @ SV242 @ ( hAPP @ ( c_Relation_Oinv__image @ SY1779 @ SV242 @ SV365 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1515,plain,
! [SV85: $i,SV243: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV243 @ SV85 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV243 @ ( c_Transitive__Closure_Otrancl @ SV243 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1516,plain,
! [SV86: $i,SV244: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV244 @ SV86 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV244 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1517,plain,
! [SV88: $i,SV246: $i,SV366: $i] :
( ( ! [SY1780: $i,SY1781: $i,SY1782: $i] :
( ( SY1782
!= ( c_Recdef_Owfrec @ SY1781 @ SY1780 @ SV366 @ SV246 ) )
| ~ ( c_Wellfounded_Owf @ SY1781 @ SV366 )
| ( ( hAPP @ SY1782 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SY1781 @ SY1780 @ SY1782 @ SV366 @ SV88 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1518,plain,
! [SV89: $i,SV247: $i,SV367: $i] :
( ( ! [SY1783: $i,SY1784: $i] :
( ~ ( c_Wellfounded_Owf @ SY1784 @ SY1783 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY1784 @ SV367 @ SY1783 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SY1784 @ SV367 @ ( c_Recdef_Owfrec @ SY1784 @ SV367 @ SY1783 @ SV247 ) @ SY1783 @ SV89 ) ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1519,plain,
! [SV368: $i,SV90: $i,SV248: $i] :
( ( ! [SY1785: $i] :
( ~ ( c_Wellfounded_Owf @ SV248 @ SY1785 )
| ! [SY1786: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SY1785 @ SV368 ) @ SY1786 )
= ( hAPP @ ( hAPP @ SV368 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SY1785 @ SV368 ) @ SY1785 @ SY1786 ) ) @ SY1786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1520,plain,
! [SV92: $i,SV249: $i,SV369: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV369 @ SV249 )
| ( c_Wellfounded_Owf @ SV369 @ ( c_Wellfounded_Omlex__prod @ SV369 @ SV92 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1521,plain,
! [SV94: $i,SV250: $i] :
( ( ( SV250 = SV94 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV250 @ SV94 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV94 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1522,plain,
! [SV96: $i,SV251: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV251 @ SV96 ) )
= $true )
| ( ( ( SV96 != SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1523,plain,
! [SV97: $i,SV252: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV252 @ SV97 ) )
= $true )
| ( ( ( SV252 != SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1524,plain,
! [SV99: $i,SV253: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV253 @ SV99 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV99 @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1525,plain,
! [SV100: $i,SV254: $i] :
( ( ( ( SV254 != SV100 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV254 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1526,plain,
! [SV101: $i,SV255: $i,SV370: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV255 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1527,plain,
! [SV102: $i,SV256: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV256 @ SV102 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SV256 )
| ( SV256 = SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1528,plain,
! [SV103: $i,SV257: $i,SV371: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV371 @ SV257 ) @ SV103 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV371 @ SV103 ) @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1529,plain,
! [SV105: $i,SV259: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SV259 ) @ SV105 ) ) )
= $true )
| ( ( SV259 = SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1530,plain,
! [SV106: $i,SV260: $i] :
( ( ( ( SV260 != SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV260 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1531,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1532,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1533,plain,
! [SV107: $i] :
( ( ~ ! [SY1011: $i,SY1012: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 )
!= ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1012 @ SY1011 @ SV107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1534,plain,
! [SV107: $i] :
( ( ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1014 @ SY1013 @ SV107 )
| ! [SY1015: $i,SY1016: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1016 ) @ SV107 )
| ! [SY1017: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1017 ) @ SV107 )
| ( SY1016 = SY1017 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1535,plain,
! [SV261: $i,SV108: $i,SV372: $i] :
( ( ~ ( ~ ! [SY1787: $i,SY1788: $i] :
( ! [SY1789: $i] :
( ~ ( c_member @ SV372 @ SY1789 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1788 ) @ ( c_Product__Type_OPair @ SV372 @ SY1788 @ SY1789 @ SY1787 ) @ SV261 ) )
| ( c_member @ SY1788 @ SY1787 @ ( c_Relation_OImage @ SV372 @ SY1788 @ SV261 @ SV108 ) ) )
| ~ ! [SY1790: $i,SY1791: $i] :
( ~ ( c_member @ SY1791 @ SY1790 @ ( c_Relation_OImage @ SV372 @ SY1791 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1791 ) @ ( c_Product__Type_OPair @ SV372 @ SY1791 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SY1790 ) @ SV261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1536,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK70_SY736 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1537,plain,
! [SV110: $i,SV263: $i,SV373: $i] :
( ( ! [SY1792: $i,SY1793: $i,SY1794: $i] :
~ ( ~ ~ ( ~ ! [SY1795: $i,SY1796: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1796 @ SY1795 ) @ ( tc_prod @ SY1796 @ SY1795 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1796 @ SY1795 ) @ ( tc_prod @ SY1796 @ SY1795 ) @ ( c_Product__Type_OPair @ SY1796 @ SY1795 @ SY1794 @ SY1793 ) @ ( c_Product__Type_OPair @ SY1796 @ SY1795 @ SY1792 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1796 @ SY1795 @ SV263 @ SV110 ) )
| ( SY1794 = SY1792 )
| ( c_member @ ( tc_prod @ SY1796 @ SY1796 ) @ ( c_Product__Type_OPair @ SY1796 @ SY1796 @ SY1794 @ SY1792 ) @ SV263 ) )
| ~ ! [SY1797: $i,SY1798: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1798 @ SY1797 ) @ ( tc_prod @ SY1798 @ SY1797 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1798 @ SY1797 ) @ ( tc_prod @ SY1798 @ SY1797 ) @ ( c_Product__Type_OPair @ SY1798 @ SY1797 @ SY1794 @ SY1793 ) @ ( c_Product__Type_OPair @ SY1798 @ SY1797 @ SY1792 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1798 @ SY1797 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY1797 @ SY1797 ) @ ( c_Product__Type_OPair @ SY1797 @ SY1797 @ SY1793 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY1798 @ SY1798 ) @ ( c_Product__Type_OPair @ SY1798 @ SY1798 @ SY1794 @ SY1792 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY1799: $i] :
( ( SY1794 != SY1792 )
| ~ ( c_member @ ( tc_prod @ SY1799 @ SY1799 ) @ ( c_Product__Type_OPair @ SY1799 @ SY1799 @ SY1793 @ SV373 ) @ SV110 )
| ! [SY1800: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY1800 @ SY1799 ) @ ( tc_prod @ SY1800 @ SY1799 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1800 @ SY1799 ) @ ( tc_prod @ SY1800 @ SY1799 ) @ ( c_Product__Type_OPair @ SY1800 @ SY1799 @ SY1794 @ SY1793 ) @ ( c_Product__Type_OPair @ SY1800 @ SY1799 @ SY1792 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1800 @ SY1799 @ SV263 @ SV110 ) ) )
| ~ ! [SY1801: $i,SY1802: $i] :
( ~ ( c_member @ ( tc_prod @ SY1802 @ SY1802 ) @ ( c_Product__Type_OPair @ SY1802 @ SY1802 @ SY1794 @ SY1792 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1802 @ SY1801 ) @ ( tc_prod @ SY1802 @ SY1801 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1802 @ SY1801 ) @ ( tc_prod @ SY1802 @ SY1801 ) @ ( c_Product__Type_OPair @ SY1802 @ SY1801 @ SY1794 @ SY1793 ) @ ( c_Product__Type_OPair @ SY1802 @ SY1801 @ SY1792 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1802 @ SY1801 @ SV263 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1538,plain,
! [SV111: $i,SV264: $i,SV374: $i] :
( ( ! [SY1803: $i] :
~ ( ~ ! [SY1804: $i,SY1805: $i] :
( ! [SY1806: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1805 @ SY1805 ) @ ( c_Product__Type_OPair @ SY1805 @ SY1805 @ ( sK60_B_z @ SY1806 @ SY1805 @ SY1804 @ SY1803 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SY1803 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1805 @ SY1804 @ SY1803 @ SV374 @ ( sK60_B_z @ SY1806 @ SY1805 @ SY1804 @ SY1803 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY1806 @ ( sK60_B_z @ SY1806 @ SY1805 @ SY1804 @ SY1803 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY1806 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1805 @ SY1804 @ SY1803 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) )
| ~ ! [SY1807: $i,SY1808: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1808 @ SY1807 @ SY1803 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1809: $i] :
( ~ ( c_member @ ( tc_prod @ SY1808 @ SY1808 ) @ ( c_Product__Type_OPair @ SY1808 @ SY1808 @ SY1809 @ SV264 ) @ SY1803 )
| ( c_Recdef_Owfrec__rel @ SY1808 @ SY1807 @ SY1803 @ SV374 @ SY1809 @ ( hAPP @ ( sK59_B_g @ SY1808 @ SY1807 @ SY1803 @ SV374 @ SV264 @ SV111 ) @ SY1809 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY1808 @ SY1807 @ SY1803 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1539,plain,
! [SV112: $i] :
( ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1049 @ SY1049 ) @ ( c_Product__Type_OPair @ SY1049 @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ SY1048 ) @ SV112 )
| ~ ~ ( c_member @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ( c_member @ SY1049 @ SY1048 @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1540,plain,
! [SV112: $i] :
( ( ~ ! [SY1050: $i,SY1051: $i] :
( ~ ( c_member @ SY1051 @ SY1050 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) )
| ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SY1051 @ SY1051 ) @ ( c_Product__Type_OPair @ SY1051 @ SY1051 @ SY1052 @ SY1050 ) @ SV112 )
| ( c_member @ SY1051 @ SY1052 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1541,plain,
! [SV113: $i,SV265: $i,SV375: $i] :
( ( ! [SY1810: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY1810 @ ( sK9_B_x @ SY1810 @ SV375 @ SV265 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SY1810 @ SV375 @ SV265 @ SV113 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SY1810 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1542,plain,
! [SV114: $i,SV266: $i] :
( ( ~ ! [SY1519: $i,SY1520: $i] :
( ! [SY1521: $i] :
~ ( c_member @ ( tc_prod @ SY1520 @ SV266 ) @ ( c_Product__Type_OPair @ SY1520 @ SV266 @ SY1519 @ SY1521 ) @ SV114 )
| ( c_member @ SY1520 @ SY1519 @ ( c_Relation_ODomain @ SY1520 @ SV266 @ SV114 ) ) )
| ~ ! [SY1522: $i,SY1523: $i] :
( ~ ( c_member @ SY1523 @ SY1522 @ ( c_Relation_ODomain @ SY1523 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY1523 @ SV266 ) @ ( c_Product__Type_OPair @ SY1523 @ SV266 @ SY1522 @ ( sK66_B_y @ SY1523 @ SY1522 @ SV266 @ SV114 ) ) @ SV114 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1543,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1545,plain,
! [SV267: $i,SV115: $i] :
( ( ~ ! [SY1524: $i,SY1525: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1525 @ SV115 )
| ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SV267 @ SY1524 ) @ ( c_Transitive__Closure_Ortrancl @ SY1525 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1525 @ ( c_Set_Oinsert @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV267 ) @ SV115 ) ) )
| ~ ~ ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) )
| ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1546,plain,
! [SV116: $i,SV268: $i,SV376: $i] :
( ( ! [SY1811: $i,SY1812: $i,SY1813: $i,SY1814: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SY1812 @ SY1811 ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1814 @ SY1813 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SY1812 @ SY1811 )
= ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SY1812 @ SY1811 ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ ( sK46_B_a @ SY1814 @ SY1813 @ SY1812 @ SY1811 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1814 @ SY1813 @ SY1812 @ SY1811 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1814 @ SY1813 ) @ ( tc_prod @ SY1814 @ SY1813 ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ ( sK46_B_a @ SY1814 @ SY1813 @ SY1812 @ SY1811 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1814 @ SY1813 @ SY1812 @ SY1811 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY1814 @ SY1813 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1814 @ SY1813 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1547,plain,
! [SV117: $i] :
( ( ~ ! [SY1075: $i,SY1076: $i] :
( ~ ( ~ ( c_member @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( c_member @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY1076 @ SY1075 @ SV117 )
!= ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY1076 @ SY1075 @ SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1548,plain,
! [SV117: $i] :
( ( ~ ! [SY1077: $i,SY1078: $i] :
( ~ ( c_Relation_Ototal__on @ SY1078 @ SY1077 @ SV117 )
| ! [SY1079: $i] :
( ~ ( c_member @ SY1078 @ SY1079 @ SY1077 )
| ! [SY1080: $i] :
( ~ ( c_member @ SY1078 @ SY1080 @ SY1077 )
| ( SY1079 = SY1080 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1079 @ SY1080 ) @ SV117 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1080 @ SY1079 ) @ SV117 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1549,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1550,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1551,plain,
! [SV118: $i,SV269: $i,SV377: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ~ ( c_member @ SY1816 @ SY1815 @ ( c_Relation_OImage @ SV377 @ SY1816 @ SV269 @ SV118 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV377 @ SY1816 ) @ ( c_Product__Type_OPair @ SV377 @ SY1816 @ ( sK23_B_x @ SY1816 @ SY1815 @ SV377 @ SV269 @ SV118 ) @ SY1815 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SY1816 @ SY1815 @ SV377 @ SV269 @ SV118 ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1552,plain,
! [SV119: $i,SV270: $i] :
( ( ~ ! [SY1538: $i] :
( ! [SY1539: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1539 @ SY1538 @ SV270 ) @ SV119 ) )
| ( SY1538 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
| ~ ~ ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1553,plain,
! [SV120: $i,SV378: $i,SV271: $i] :
( ( ! [SY1817: $i] :
~ ( ~ ( ( SY1817 != SV271 )
| ( SV378 != SV120 )
| ! [SY1818: $i,SY1819: $i] :
( ( c_Product__Type_OPair @ SY1819 @ SY1818 @ SY1817 @ SV378 )
= ( c_Product__Type_OPair @ SY1819 @ SY1818 @ SV271 @ SV120 ) ) )
| ~ ~ ( ~ ( ! [SY1820: $i,SY1821: $i] :
( ( c_Product__Type_OPair @ SY1821 @ SY1820 @ SY1817 @ SV378 )
!= ( c_Product__Type_OPair @ SY1821 @ SY1820 @ SV271 @ SV120 ) )
| ( SY1817 = SV271 ) )
| ~ ( ! [SY1822: $i,SY1823: $i] :
( ( c_Product__Type_OPair @ SY1823 @ SY1822 @ SY1817 @ SV378 )
!= ( c_Product__Type_OPair @ SY1823 @ SY1822 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1554,plain,
! [SV121: $i] :
( ( ~ ! [SY1101: $i] :
( ( SY1101 != SV121 )
| ! [SY1102: $i] : ( c_member @ SY1102 @ SY1101 @ ( c_fequal @ SV121 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1555,plain,
! [SV121: $i] :
( ( ~ ! [SY1103: $i] :
( ! [SY1104: $i] :
~ ( c_member @ SY1104 @ SY1103 @ ( c_fequal @ SV121 ) )
| ( SY1103 = SV121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1556,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ~ ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) )
| ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) )
| ~ ~ ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) )
| ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1558,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1559,plain,
! [SV123: $i] :
( ( ~ ! [SY1114: $i,SY1115: $i] :
( ~ ( c_Relation_Oirrefl @ SY1115 @ SV123 )
| ~ ( c_Relation_Otrans @ SY1115 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SY1115 @ SY1114 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY1115 @ SY1114 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1560,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
| ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1561,plain,
! [SV124: $i] :
( ( ~ ! [SY1122: $i,SY1123: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1123 @ ( sK75_B_x1 @ SY1123 @ SY1122 @ SV124 ) ) )
| ! [SY1124: $i,SY1125: $i] : ( hBOOL @ ( hAPP @ SY1123 @ ( c_Product__Type_OPair @ SY1122 @ SV124 @ SY1124 @ SY1125 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1562,plain,
! [SV124: $i] :
( ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1127 @ ( c_Product__Type_OPair @ SY1126 @ SV124 @ ( sK73_B_a @ SY1127 @ SY1126 @ SV124 ) @ ( sK74_SY739 @ SY1127 @ SY1126 @ SV124 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1127 @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1563,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1564,plain,
( ( ~ ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1565,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1567,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1568,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1569,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ! [SY1560: $i,SY1561: $i] :
( ( SY1560 != SV273 )
| ~ ( c_member @ SY1561 @ SY1560 @ SV125 )
| ( c_member @ ( tc_prod @ SY1561 @ SY1561 ) @ ( c_Product__Type_OPair @ SY1561 @ SY1561 @ SY1560 @ SV273 ) @ ( c_Relation_OId__on @ SY1561 @ SV125 ) ) )
| ~ ~ ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) )
| ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1570,plain,
! [SV126: $i,SV274: $i,SV379: $i] :
( ( ! [SY1824: $i] :
( ~ ( c_member @ ( tc_prod @ SY1824 @ SY1824 ) @ ( c_Product__Type_OPair @ SY1824 @ SY1824 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SY1824 @ SV126 ) )
| ( SV379 = SV274 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1824 @ SY1824 ) @ ( c_Product__Type_OPair @ SY1824 @ SY1824 @ SV379 @ ( sK45_B_y @ SY1824 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1824 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SY1824 @ SY1824 ) @ ( c_Product__Type_OPair @ SY1824 @ SY1824 @ ( sK45_B_y @ SY1824 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1571,plain,
! [SV127: $i,SV275: $i] :
( ( ~ ! [SY1568: $i,SY1569: $i] :
( ( c_member @ SY1569 @ SY1568 @ SV275 )
| ( c_member @ SY1569 @ SY1568 @ SV127 )
| ( ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV275 )
!= ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV127 ) )
| ( SV275 = SV127 ) )
| ~ ! [SY1570: $i,SY1571: $i] :
( ( c_member @ SY1571 @ SY1570 @ SV275 )
| ( c_member @ SY1571 @ SY1570 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV275 )
= ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1572,plain,
! [SV128: $i,SV276: $i,SV380: $i] :
( ( ! [SY1825: $i] :
( ~ ( c_member @ ( tc_prod @ SY1825 @ SY1825 ) @ ( c_Product__Type_OPair @ SY1825 @ SY1825 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SY1825 @ SV128 ) )
| ( c_member @ ( tc_prod @ SY1825 @ SY1825 ) @ ( c_Product__Type_OPair @ SY1825 @ SY1825 @ SV380 @ SV276 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1825 @ SY1825 ) @ ( c_Product__Type_OPair @ SY1825 @ SY1825 @ SV380 @ ( sK37_B_c @ SY1825 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1825 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SY1825 @ SY1825 ) @ ( c_Product__Type_OPair @ SY1825 @ SY1825 @ ( sK37_B_c @ SY1825 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1573,plain,
! [SV129: $i,SV277: $i] :
( ( ~ ! [SY1574: $i,SY1575: $i] :
( ( c_member @ SY1575 @ SY1574 @ ( c_Relation_ODomain @ SY1575 @ SY1575 @ SV277 ) )
| ( SY1574 != SV129 )
| ( c_member @ ( tc_prod @ SY1575 @ SY1575 ) @ ( c_Product__Type_OPair @ SY1575 @ SY1575 @ SY1574 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1575 @ SV277 ) ) )
| ~ ! [SY1576: $i,SY1577: $i] :
( ( c_member @ SY1577 @ SY1576 @ ( c_Relation_ODomain @ SY1577 @ SY1577 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SY1577 @ SY1577 ) @ ( c_Product__Type_OPair @ SY1577 @ SY1577 @ SY1576 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1577 @ SV277 ) )
| ( SY1576 = SV129 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1574,plain,
! [SV130: $i,SV278: $i,SV381: $i] :
( ( ! [SY1826: $i] :
~ ( ~ ( ! [SY1827: $i,SY1828: $i] :
( ( c_Product__Type_OPair @ SY1828 @ SY1827 @ SY1826 @ SV381 )
!= ( c_Product__Type_OPair @ SY1828 @ SY1827 @ SV278 @ SV130 ) )
| ( SY1826 = SV278 ) )
| ~ ( ! [SY1829: $i,SY1830: $i] :
( ( c_Product__Type_OPair @ SY1830 @ SY1829 @ SY1826 @ SV381 )
!= ( c_Product__Type_OPair @ SY1830 @ SY1829 @ SV278 @ SV130 ) )
| ( SV381 = SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1575,plain,
! [SV131: $i,SV279: $i,SV382: $i] :
( ( ! [SY1831: $i,SY1832: $i,SY1833: $i,SY1834: $i,SY1835: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ SY1833 @ SY1832 ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ SY1831 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1835 @ SY1834 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1833 ) @ SY1832 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ SY1833 @ SY1832 ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ ( sK18_B_a @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1835 @ SY1834 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1835 @ SY1834 ) @ ( tc_prod @ SY1835 @ SY1834 ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ ( sK18_B_a @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY1835 @ SY1834 @ ( sK20_SY717 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SY1831 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1831 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1576,plain,
! [SV132: $i,SV280: $i] :
( ( ~ ! [SY1590: $i,SY1591: $i] :
( ! [SY1592: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SY1591 ) @ ( c_Product__Type_OPair @ SV280 @ SY1591 @ SY1592 @ SY1590 ) @ SV132 )
| ( c_member @ SY1591 @ SY1590 @ ( c_Relation_ORange @ SV280 @ SY1591 @ SV132 ) ) )
| ~ ! [SY1593: $i,SY1594: $i] :
( ~ ( c_member @ SY1594 @ SY1593 @ ( c_Relation_ORange @ SV280 @ SY1594 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SY1594 ) @ ( c_Product__Type_OPair @ SV280 @ SY1594 @ ( sK65_B_y @ SY1594 @ SY1593 @ SV280 @ SV132 ) @ SY1593 ) @ SV132 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1577,plain,
! [SV133: $i,SV281: $i,SV383: $i] :
( ( ! [SY1836: $i] :
~ ( ~ ! [SY1837: $i,SY1838: $i] :
( ! [SY1839: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1838 @ SY1838 ) @ ( c_Product__Type_OPair @ SY1838 @ SY1838 @ ( sK55_B_z @ SY1839 @ SY1838 @ SY1837 @ SY1836 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SY1836 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1838 @ SY1837 @ SY1836 @ SV383 @ ( sK55_B_z @ SY1839 @ SY1838 @ SY1837 @ SY1836 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY1839 @ ( sK55_B_z @ SY1839 @ SY1838 @ SY1837 @ SY1836 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY1839 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1838 @ SY1837 @ SY1836 @ SV383 @ SV281 @ SV133 ) )
| ~ ! [SY1840: $i,SY1841: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1841 @ SY1840 @ SY1836 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1842: $i] :
( ~ ( c_member @ ( tc_prod @ SY1841 @ SY1841 ) @ ( c_Product__Type_OPair @ SY1841 @ SY1841 @ SY1842 @ SV281 ) @ SY1836 )
| ( c_Recdef_Owfrec__rel @ SY1841 @ SY1840 @ SY1836 @ SV383 @ SY1842 @ ( hAPP @ ( sK54_B_g @ SY1841 @ SY1840 @ SY1836 @ SV383 @ SV281 @ SV133 ) @ SY1842 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY1841 @ SY1840 @ SY1836 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1578,plain,
! [SV134: $i,SV282: $i,SV384: $i] :
( ( ! [SY1843: $i] :
( ~ ( c_member @ ( tc_prod @ SY1843 @ SY1843 ) @ ( c_Product__Type_OPair @ SY1843 @ SY1843 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SY1843 @ SV134 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1843 @ SY1843 ) @ ( c_Product__Type_OPair @ SY1843 @ SY1843 @ SV384 @ ( sK42_B_z @ SY1843 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1843 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SY1843 @ SY1843 ) @ ( c_Product__Type_OPair @ SY1843 @ SY1843 @ ( sK42_B_z @ SY1843 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1579,plain,
! [SV135: $i,SV283: $i,SV385: $i] :
( ( ! [SY1844: $i] :
~ ( ~ ! [SY1845: $i] :
( ! [SY1846: $i] :
~ ( c_member @ ( tc_prod @ SY1846 @ SY1846 ) @ ( c_Product__Type_OPair @ SY1846 @ SY1846 @ SY1845 @ SY1844 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1846 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1845 ) @ ( hAPP @ SV135 @ SY1844 ) ) @ SV283 ) )
| ~ ! [SY1847: $i] :
( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1847 ) @ ( hAPP @ SV135 @ SY1844 ) ) @ SV283 )
| ! [SY1848: $i] : ( c_member @ ( tc_prod @ SY1848 @ SY1848 ) @ ( c_Product__Type_OPair @ SY1848 @ SY1848 @ SY1847 @ SY1844 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1848 @ SV283 ) @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1580,plain,
! [SV136: $i] :
( ( ~ ! [SY1191: $i] :
( ! [SY1192: $i] :
~ ( c_member @ SY1192 @ SY1191 @ SV136 )
| ( hBOOL @ ( hAPP @ SV136 @ SY1191 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1581,plain,
! [SV136: $i] :
( ( ~ ! [SY1193: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ SY1193 ) )
| ! [SY1194: $i] : ( c_member @ SY1194 @ SY1193 @ SV136 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1582,plain,
! [SV137: $i,SV284: $i,SV386: $i] :
( ( ! [SY1849: $i,SY1850: $i,SY1851: $i,SY1852: $i,SY1853: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ SY1851 @ SY1850 ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ SY1849 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1853 @ SY1852 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1849 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ ( sK14_B_a @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ ( sK16_SY711 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1853 @ SY1852 ) @ ( tc_prod @ SY1853 @ SY1852 ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ ( sK16_SY711 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1853 @ SY1852 @ SY1849 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1853 @ SY1852 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY1853 @ SY1852 @ SY1851 @ SY1850 @ SY1849 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1851 ) @ SY1850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1583,plain,
! [SV138: $i,SV285: $i,SV387: $i] :
( ( ! [SY1854: $i,SY1855: $i,SY1856: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1856 @ SY1856 ) @ ( c_Product__Type_OPair @ SY1856 @ SY1856 @ ( sK56_B_z @ SY1856 @ SY1855 @ SY1854 @ SV387 @ SV285 @ SV138 ) @ SY1855 ) @ SY1854 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1856 @ SV387 @ SY1854 @ SV285 @ ( sK56_B_z @ SY1856 @ SY1855 @ SY1854 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SY1856 @ SY1855 @ SY1854 @ SV387 @ SV285 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY1856 @ SV387 @ SY1854 @ SV285 @ SY1855 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SY1855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1584,plain,
! [SV139: $i] :
( ( ~ ! [SY1207: $i] :
( ( SY1207 != SV139 )
| ! [SY1208: $i] : ( c_member @ ( tc_prod @ SY1208 @ SY1208 ) @ ( c_Product__Type_OPair @ SY1208 @ SY1208 @ SY1207 @ SV139 ) @ ( c_Relation_OId @ SY1208 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1419]) ).
thf(1585,plain,
! [SV139: $i] :
( ( ~ ! [SY1209: $i] :
( ! [SY1210: $i] :
~ ( c_member @ ( tc_prod @ SY1210 @ SY1210 ) @ ( c_Product__Type_OPair @ SY1210 @ SY1210 @ SY1209 @ SV139 ) @ ( c_Relation_OId @ SY1210 ) )
| ( SY1209 = SV139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1419]) ).
thf(1586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1587,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1588,plain,
! [SV140: $i,SV286: $i] :
( ( ~ ! [SY1621: $i,SY1622: $i] :
( ( SY1622 != SY1621 )
| ~ ( c_member @ SV286 @ SV140 @ SY1622 )
| ( c_member @ SV286 @ SV140 @ SY1621 ) )
| ~ ! [SY1623: $i,SY1624: $i] :
( ( SY1624 != SY1623 )
| ~ ( c_member @ SV286 @ SV140 @ SY1623 )
| ( c_member @ SV286 @ SV140 @ SY1624 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1589,plain,
! [SV141: $i,SV287: $i] :
( ( ~ ! [SY1625: $i,SY1626: $i] :
( ( SY1626 != SY1625 )
| ~ ( c_member @ SV287 @ SY1626 @ SV141 )
| ( c_member @ SV287 @ SY1625 @ SV141 ) )
| ~ ! [SY1627: $i,SY1628: $i] :
( ( SY1628 != SY1627 )
| ~ ( c_member @ SV287 @ SY1627 @ SV141 )
| ( c_member @ SV287 @ SY1628 @ SV141 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1590,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1591,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
| ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1592,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1593,plain,
! [SV144: $i,SV289: $i,SV389: $i] :
( ( ! [SY1857: $i] :
( ~ ( c_member @ ( tc_prod @ SY1857 @ SY1857 ) @ ( c_Product__Type_OPair @ SY1857 @ SY1857 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SY1857 @ SV144 ) )
| ( c_member @ ( tc_prod @ SY1857 @ SY1857 ) @ ( c_Product__Type_OPair @ SY1857 @ SY1857 @ SV389 @ SV289 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1857 @ SY1857 ) @ ( c_Product__Type_OPair @ SY1857 @ SY1857 @ SV389 @ ( sK38_B_y @ SY1857 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SY1857 @ SY1857 ) @ ( c_Product__Type_OPair @ SY1857 @ SY1857 @ ( sK38_B_y @ SY1857 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SY1857 @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1594,plain,
! [SV290: $i,SV145: $i] :
( ( ~ ! [SY1632: $i,SY1633: $i] :
( ~ ( c_Wellfounded_Owf @ SY1633 @ SV145 )
| ( c_member @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SV290 @ SY1632 ) @ ( c_Transitive__Closure_Ortrancl @ SY1633 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1633 @ ( c_Set_Oinsert @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SY1632 @ SV290 ) @ SV145 ) ) )
| ~ ~ ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) )
| ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1595,plain,
! [SV146: $i] :
( ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( c_Relation_Orefl__on @ SY1250 @ SY1249 @ SV146 )
| ~ ( c_Relation_Otrans @ SY1250 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SY1250 @ SY1249 @ SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1596,plain,
! [SV146: $i] :
( ( ~ ~ ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) )
| ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1597,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
| ~ ( ~ ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 )
| ( SV291
!= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1598,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ~ ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) )
| ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) )
| ~ ~ ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) )
| ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1599,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ! [SY1647: $i,SY1648: $i] :
( ~ ( c_member @ SY1648 @ SY1647 @ ( c_Set_Oinsert @ SY1648 @ SV293 @ SV149 ) )
| ( SY1647 = SV293 )
| ( c_member @ SY1648 @ SY1647 @ SV149 ) )
| ~ ~ ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1600,plain,
! [SV150: $i,SV294: $i,SV391: $i] :
( ( ! [SY1858: $i,SY1859: $i] :
( ~ ( c_member @ ( tc_prod @ SY1859 @ SY1859 ) @ ( c_Product__Type_OPair @ SY1859 @ SY1859 @ SY1858 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SY1859 @ SV294 ) )
| ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1859 @ SY1859 ) @ ( c_Product__Type_OPair @ SY1859 @ SY1859 @ ( sK12_B_y @ SY1859 @ SY1858 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SY1859 @ SY1858 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1859 @ SY1859 ) @ ( c_Product__Type_OPair @ SY1859 @ SY1859 @ ( sK13_SY707 @ SY1859 @ SY1858 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SY1859 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SY1859 @ SY1858 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SY1859 @ SY1858 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SY1858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1601,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV392 @ SV392 ) @ ( c_Product__Type_OPair @ SV392 @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ SV295 ) @ SV151 )
| ~ ~ ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1602,plain,
! [SV393: $i,SV152: $i,SV296: $i] :
( ( ~ ( ~ ! [SY1860: $i,SY1861: $i] :
( ~ ( c_member @ ( tc_prod @ SY1861 @ SY1860 ) @ ( c_Product__Type_OPair @ SY1861 @ SY1860 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1861 @ SY1860 @ SV393 ) @ SV296 ) @ SV152 ) ) )
| ~ ! [SY1862: $i,SY1863: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1863 @ SY1862 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1863 @ SY1862 ) @ ( c_Product__Type_OPair @ SY1863 @ SY1862 @ SV296 @ SV152 ) @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1603,plain,
! [SV153: $i,SV297: $i,SV394: $i] :
( ( ! [SY1864: $i] :
( ~ ( c_member @ ( tc_prod @ SY1864 @ SY1864 ) @ ( c_Product__Type_OPair @ SY1864 @ SY1864 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SY1864 @ SV153 ) )
| ( SV394 = SV297 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1864 @ SY1864 ) @ ( c_Product__Type_OPair @ SY1864 @ SY1864 @ SV394 @ ( sK44_B_y @ SY1864 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SY1864 @ SY1864 ) @ ( c_Product__Type_OPair @ SY1864 @ SY1864 @ ( sK44_B_y @ SY1864 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SY1864 @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1604,plain,
! [SV154: $i,SV298: $i,SV395: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ~ ( c_member @ ( tc_prod @ SY1866 @ SY1866 ) @ ( c_Product__Type_OPair @ SY1866 @ SY1866 @ SY1865 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SY1866 @ SV298 ) )
| ~ ( hBOOL @ ( hAPP @ SV154 @ SY1865 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1866 @ SY1866 ) @ ( c_Product__Type_OPair @ SY1866 @ SY1866 @ SY1865 @ ( sK10_B_y @ SY1866 @ SY1865 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1866 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1866 @ SY1866 ) @ ( c_Product__Type_OPair @ SY1866 @ SY1866 @ ( sK10_B_y @ SY1866 @ SY1865 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SY1866 @ SY1865 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SY1866 @ SY1865 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SY1866 @ SY1865 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1605,plain,
! [SV155: $i,SV299: $i,SV396: $i] :
( ( ! [SY1867: $i] :
( ~ ( c_member @ ( tc_prod @ SY1867 @ SY1867 ) @ ( c_Product__Type_OPair @ SY1867 @ SY1867 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SY1867 @ SV155 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1867 @ SY1867 ) @ ( c_Product__Type_OPair @ SY1867 @ SY1867 @ SV396 @ ( sK41_B_z @ SY1867 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SY1867 @ SY1867 ) @ ( c_Product__Type_OPair @ SY1867 @ SY1867 @ ( sK41_B_z @ SY1867 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SY1867 @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1606,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1607,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1608,plain,
! [SV156: $i,SV300: $i] :
( ( ~ ! [SY1669: $i] :
( ! [SY1670: $i] :
~ ( c_member @ ( tc_prod @ SY1670 @ SY1670 ) @ ( c_Product__Type_OPair @ SY1670 @ SY1670 @ SY1669 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1670 @ SV156 ) )
| ( SY1669 != SV300 )
| ( SY1669 = SV300 ) )
| ~ ! [SY1671: $i,SY1672: $i] :
( ~ ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1672 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SY1672 @ SV156 ) )
| ( SY1671 = SV300 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1609,plain,
! [SV157: $i,SV301: $i] :
( ( ~ ! [SY1673: $i,SY1674: $i] :
( ~ ( c_member @ SY1674 @ SY1673 @ SV301 )
| ( c_member @ SY1674 @ SY1673 @ ( c_Set_Oinsert @ SY1674 @ SV157 @ SV301 ) ) )
| ~ ! [SY1675: $i] :
( ( SY1675 != SV157 )
| ! [SY1676: $i] : ( c_member @ SY1676 @ SY1675 @ ( c_Set_Oinsert @ SY1676 @ SV157 @ SV301 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1610,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK26_B_x @ SV302 @ SV158 ) @ ( sK27_SY720 @ SV302 @ SV158 ) ) @ SV158 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1613,plain,
! [SV159: $i] :
( ( ~ ! [SY1306: $i,SY1307: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1307 @ SY1306 @ SV159 )
| ~ ( c_Relation_Oantisym @ SY1307 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SY1307 @ SY1306 @ SV159 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1614,plain,
! [SV159: $i] :
( ( ~ ~ ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) )
| ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1615,plain,
! [SV160: $i,SV303: $i,SV397: $i] :
( ( ! [SY1868: $i] :
~ ( ~ ! [SY1869: $i,SY1870: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1870 @ SY1870 ) @ ( c_Product__Type_OPair @ SY1870 @ SY1870 @ ( sK43_B_y @ SY1870 @ SY1869 @ SY1868 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SY1868 @ ( sK43_B_y @ SY1870 @ SY1869 @ SY1868 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY1870 @ SY1869 @ SY1868 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY1870 @ SY1869 @ SY1868 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY1870 @ SY1869 @ SV160 @ SV397 @ SV303 ) ) )
| ~ ! [SY1871: $i,SY1872: $i] :
( ( ( c_Recdef_Ocut @ SY1872 @ SY1871 @ SY1868 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY1872 @ SY1871 @ SV160 @ SV397 @ SV303 ) )
| ! [SY1873: $i] :
( ~ ( c_member @ ( tc_prod @ SY1872 @ SY1872 ) @ ( c_Product__Type_OPair @ SY1872 @ SY1872 @ SY1873 @ SV303 ) @ SV397 )
| ( ( hAPP @ SY1868 @ SY1873 )
= ( hAPP @ SV160 @ SY1873 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1616,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV398 @ SV398 ) @ ( c_Product__Type_OPair @ SV398 @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ SV304 ) @ SV161 )
| ~ ~ ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) )
| ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1617,plain,
! [SV1: $i,SV162: $i,SV305: $i,SV399: $i] :
( ( ! [SY1874: $i] :
( ~ ( c_Relation_Otrans @ SY1874 @ SV399 )
| ~ ( c_member @ ( tc_prod @ SY1874 @ SY1874 ) @ ( c_Product__Type_OPair @ SY1874 @ SY1874 @ SV305 @ SV162 ) @ SV399 )
| ~ ( c_member @ ( tc_prod @ SY1874 @ SY1874 ) @ ( c_Product__Type_OPair @ SY1874 @ SY1874 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SY1874 @ SY1874 ) @ ( c_Product__Type_OPair @ SY1874 @ SY1874 @ SV305 @ SV1 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1618,plain,
! [SV2: $i,SV163: $i,SV306: $i,SV400: $i] :
( ( ( SV400 != SV306 )
| ~ ( c_member @ SV163 @ SV306 @ SV2 )
| ( c_member @ SV163 @ SV400 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1619,plain,
! [SV3: $i,SV164: $i,SV307: $i,SV401: $i] :
( ( ! [SY1875: $i,SY1876: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY1876 @ SY1875 @ SV401 @ SV307 @ ( c_Product__Type_OPair @ SY1876 @ SY1875 @ SV164 @ SV3 ) )
= ( hAPP @ ( hAPP @ SV307 @ SV164 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1620,plain,
! [SV4: $i,SV165: $i,SV308: $i,SV402: $i] :
( ( ! [SY1877: $i,SY1878: $i] :
( ( c_Product__Type_Ointernal__split @ SY1878 @ SY1877 @ SV402 @ SV308 @ ( c_Product__Type_OPair @ SY1878 @ SY1877 @ SV165 @ SV4 ) )
= ( hAPP @ ( hAPP @ SV308 @ SV165 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1621,plain,
! [SV5: $i,SV166: $i,SV309: $i,SV403: $i] :
( ( ! [SY1879: $i] :
( ~ ( c_member @ ( tc_prod @ SY1879 @ SV403 ) @ ( c_Product__Type_OPair @ SY1879 @ SV403 @ SV309 @ SV166 ) @ SV5 )
| ( c_member @ SV403 @ SV166 @ ( c_Relation_ORange @ SY1879 @ SV403 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1622,plain,
! [SV6: $i,SV167: $i,SV310: $i,SV404: $i] :
( ( ( SV404 != SV310 )
| ~ ( c_member @ SV167 @ SV404 @ SV6 )
| ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SV404 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1623,plain,
! [SV7: $i,SV168: $i,SV311: $i,SV405: $i] :
( ( ! [SY1880: $i] :
( ~ ( c_member @ ( tc_prod @ SY1880 @ SV405 ) @ ( c_Product__Type_OPair @ SY1880 @ SV405 @ SV311 @ SV168 ) @ SV7 )
| ( c_member @ SY1880 @ SV311 @ ( c_Relation_ODomain @ SY1880 @ SV405 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1624,plain,
! [SV8: $i,SV169: $i,SV312: $i,SV406: $i] :
( ( ~ ( c_Relation_Otrans @ SV406 @ SV312 )
| ~ ( c_Relation_Otrans @ SV169 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SV406 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SV406 @ SV169 @ SV312 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1625,plain,
! [SV10: $i,SV171: $i,SV313: $i,SV407: $i] :
( ( ~ ( c_Relation_Otrans @ SV407 @ SV313 )
| ( c_Relation_Otrans @ SV171 @ ( hAPP @ ( c_Relation_Oinv__image @ SV407 @ SV171 @ SV313 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1626,plain,
! [SV11: $i,SV172: $i,SV314: $i,SV408: $i] :
( ( ~ ( c_member @ SV408 @ SV314 @ ( c_Relation_ORange @ SV172 @ SV408 @ SV11 ) )
| ( c_member @ ( tc_prod @ SV172 @ SV408 ) @ ( c_Product__Type_OPair @ SV172 @ SV408 @ ( sK63_B_x @ SV408 @ SV314 @ SV172 @ SV11 ) @ SV314 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1627,plain,
! [SV12: $i,SV173: $i,SV315: $i,SV409: $i] :
( ( ~ ( c_member @ SV409 @ SV315 @ ( c_Relation_ODomain @ SV409 @ SV173 @ SV12 ) )
| ( c_member @ ( tc_prod @ SV409 @ SV173 ) @ ( c_Product__Type_OPair @ SV409 @ SV173 @ SV315 @ ( sK62_B_y @ SV409 @ SV315 @ SV173 @ SV12 ) ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1628,plain,
! [SV13: $i,SV174: $i,SV316: $i,SV410: $i] :
( ( ~ ( c_member @ SV410 @ SV316 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
| ~ ( c_member @ ( tc_prod @ SV410 @ SV410 ) @ ( c_Product__Type_OPair @ SV410 @ SV410 @ SV13 @ SV316 ) @ SV174 )
| ( c_member @ SV410 @ SV13 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1629,plain,
! [SV14: $i,SV175: $i,SV317: $i,SV411: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV411 @ SV317 @ SV175 )
| ~ ( c_member @ SV411 @ SV14 @ SV317 )
| ( c_member @ ( tc_prod @ SV411 @ SV411 ) @ ( c_Product__Type_OPair @ SV411 @ SV411 @ SV14 @ SV14 ) @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1630,plain,
! [SV15: $i,SV176: $i,SV318: $i,SV412: $i] :
( ( ! [SY1881: $i] :
( ~ ( c_Relation_Orefl__on @ SY1881 @ SV412 @ SV318 )
| ~ ( c_member @ ( tc_prod @ SY1881 @ SY1881 ) @ ( c_Product__Type_OPair @ SY1881 @ SY1881 @ SV176 @ SV15 ) @ SV318 )
| ( c_member @ SY1881 @ SV176 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1631,plain,
! [SV16: $i,SV177: $i,SV319: $i,SV413: $i] :
( ( ! [SY1882: $i] :
( ~ ( c_Relation_Orefl__on @ SY1882 @ SV413 @ SV319 )
| ~ ( c_member @ ( tc_prod @ SY1882 @ SY1882 ) @ ( c_Product__Type_OPair @ SY1882 @ SY1882 @ SV177 @ SV16 ) @ SV319 )
| ( c_member @ SY1882 @ SV16 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1632,plain,
! [SV17: $i,SV178: $i,SV320: $i,SV414: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV414 @ SV414 ) @ ( c_Product__Type_OPair @ SV414 @ SV414 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SV414 @ SV17 ) )
| ~ ( c_member @ SV414 @ SV178 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
| ( c_member @ SV414 @ SV320 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1633,plain,
! [SV18: $i,SV179: $i,SV321: $i,SV415: $i] :
( ( ~ ( c_member @ SV415 @ SV321 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
| ~ ( c_member @ ( tc_prod @ SV415 @ SV415 ) @ ( c_Product__Type_OPair @ SV415 @ SV415 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SV415 @ SV179 ) )
| ( c_member @ SV415 @ SV18 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1634,plain,
! [SV19: $i,SV180: $i,SV322: $i,SV416: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1884 @ SY1883 @ SV416 )
| ~ ( c_member @ ( tc_prod @ SY1884 @ SY1883 ) @ ( c_Product__Type_OPair @ SY1884 @ SY1883 @ SV322 @ SV180 ) @ SV416 )
| ~ ( c_member @ ( tc_prod @ SY1884 @ SY1883 ) @ ( c_Product__Type_OPair @ SY1884 @ SY1883 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1635,plain,
! [SV20: $i,SV181: $i,SV323: $i,SV417: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( c_Product__Type_Ocurry @ SY1886 @ SY1885 @ SV417 @ SV323 @ SV181 @ SV20 )
= ( hAPP @ SV323 @ ( c_Product__Type_OPair @ SY1886 @ SY1885 @ SV181 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1636,plain,
! [SV22: $i,SV183: $i,SV325: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ SV22 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ ( c_Transitive__Closure_Ortrancl @ SV325 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1637,plain,
! [SV23: $i,SV184: $i,SV326: $i,SV418: $i] :
( ( ! [SY1887: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1887 @ SY1887 @ SV418 )
| ~ ( c_member @ ( tc_prod @ SY1887 @ SY1887 ) @ ( c_Product__Type_OPair @ SY1887 @ SY1887 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1887 @ SV418 ) )
| ~ ( c_member @ ( tc_prod @ SY1887 @ SY1887 ) @ ( c_Product__Type_OPair @ SY1887 @ SY1887 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1887 @ SV418 ) )
| ( c_member @ ( tc_prod @ SY1887 @ SY1887 ) @ ( c_Product__Type_OPair @ SY1887 @ SY1887 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SY1887 @ SV418 ) )
| ( c_member @ ( tc_prod @ SY1887 @ SY1887 ) @ ( c_Product__Type_OPair @ SY1887 @ SY1887 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SY1887 @ SV418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1638,plain,
! [SV24: $i,SV185: $i,SV327: $i,SV419: $i] :
( ( ! [SY1888: $i] :
( ~ ( c_member @ ( tc_prod @ SY1888 @ SY1888 ) @ ( c_Product__Type_OPair @ SY1888 @ SY1888 @ SV419 @ SV327 ) @ SV185 )
| ~ ( c_member @ ( tc_prod @ SY1888 @ SY1888 ) @ ( c_Product__Type_OPair @ SY1888 @ SY1888 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1888 @ SV185 ) )
| ( c_member @ ( tc_prod @ SY1888 @ SY1888 ) @ ( c_Product__Type_OPair @ SY1888 @ SY1888 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SY1888 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1639,plain,
! [SV25: $i,SV186: $i,SV328: $i,SV420: $i] :
( ( ! [SY1889: $i] :
( ~ ( c_member @ ( tc_prod @ SY1889 @ SY1889 ) @ ( c_Product__Type_OPair @ SY1889 @ SY1889 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SY1889 @ SV186 ) )
| ~ ( c_member @ ( tc_prod @ SY1889 @ SY1889 ) @ ( c_Product__Type_OPair @ SY1889 @ SY1889 @ SV328 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SY1889 @ SY1889 ) @ ( c_Product__Type_OPair @ SY1889 @ SY1889 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SY1889 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1640,plain,
! [SV26: $i,SV187: $i,SV329: $i,SV421: $i] :
( ( ! [SY1890: $i] :
( ~ ( c_member @ ( tc_prod @ SY1890 @ SY1890 ) @ ( c_Product__Type_OPair @ SY1890 @ SY1890 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SY1890 @ SV187 ) )
| ~ ( c_member @ ( tc_prod @ SY1890 @ SY1890 ) @ ( c_Product__Type_OPair @ SY1890 @ SY1890 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1890 @ SV187 ) )
| ( c_member @ ( tc_prod @ SY1890 @ SY1890 ) @ ( c_Product__Type_OPair @ SY1890 @ SY1890 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SY1890 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1641,plain,
! [SV28: $i,SV189: $i,SV330: $i,SV422: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Otrancl @ SV422 @ SV28 ) )
| ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1642,plain,
! [SV29: $i,SV190: $i,SV331: $i,SV423: $i] :
( ( ! [SY1891: $i,SY1892: $i] :
( ~ ( c_member @ ( tc_prod @ SY1892 @ SY1892 ) @ ( c_Product__Type_OPair @ SY1892 @ SY1892 @ SY1891 @ SV423 ) @ SV331 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY1892 @ SV190 @ SV29 @ SV331 @ SV423 ) @ SY1891 )
= ( hAPP @ SV29 @ SY1891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1643,plain,
! [SV30: $i,SV191: $i,SV332: $i,SV424: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ SV30 )
| ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ ( c_Transitive__Closure_Otrancl @ SV424 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1644,plain,
! [SV31: $i,SV192: $i,SV333: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ SV31 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ ( c_Transitive__Closure_Otrancl @ SV333 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1645,plain,
! [SV33: $i,SV194: $i] :
( ( ( c_Relation_Otrans @ SV194 @ SV33 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV194 @ SV33 )
= SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1646,plain,
! [SV34: $i,SV195: $i,SV334: $i,SV425: $i] :
( ( ! [SY1893: $i] :
( ~ ( c_member @ ( tc_prod @ SY1893 @ SY1893 ) @ ( c_Product__Type_OPair @ SY1893 @ SY1893 @ SV425 @ SV334 ) @ SV195 )
| ~ ( c_member @ ( tc_prod @ SY1893 @ SY1893 ) @ ( c_Product__Type_OPair @ SY1893 @ SY1893 @ SV334 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SY1893 @ SY1893 ) @ ( c_Product__Type_OPair @ SY1893 @ SY1893 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SY1893 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1647,plain,
! [SV35: $i,SV196: $i,SV335: $i,SV426: $i] :
( ( ! [SY1894: $i] :
( ~ ( c_member @ ( tc_prod @ SY1894 @ SY1894 ) @ ( c_Product__Type_OPair @ SY1894 @ SY1894 @ SV426 @ SV335 ) @ SV196 )
| ~ ( c_member @ ( tc_prod @ SY1894 @ SY1894 ) @ ( c_Product__Type_OPair @ SY1894 @ SY1894 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1894 @ SV196 ) )
| ( c_member @ ( tc_prod @ SY1894 @ SY1894 ) @ ( c_Product__Type_OPair @ SY1894 @ SY1894 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SY1894 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1648,plain,
! [SV36: $i,SV197: $i,SV336: $i,SV427: $i] :
( ( ! [SY1895: $i] :
( ~ ( c_member @ ( tc_prod @ SY1895 @ SY1895 ) @ ( c_Product__Type_OPair @ SY1895 @ SY1895 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SY1895 @ SV197 ) )
| ~ ( c_member @ ( tc_prod @ SY1895 @ SY1895 ) @ ( c_Product__Type_OPair @ SY1895 @ SY1895 @ SV336 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SY1895 @ SY1895 ) @ ( c_Product__Type_OPair @ SY1895 @ SY1895 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SY1895 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1649,plain,
! [SV37: $i,SV198: $i,SV337: $i,SV428: $i] :
( ( ! [SY1896: $i] :
( ~ ( c_member @ ( tc_prod @ SY1896 @ SY1896 ) @ ( c_Product__Type_OPair @ SY1896 @ SY1896 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SY1896 @ SV198 ) )
| ~ ( c_member @ ( tc_prod @ SY1896 @ SY1896 ) @ ( c_Product__Type_OPair @ SY1896 @ SY1896 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1896 @ SV198 ) )
| ( c_member @ ( tc_prod @ SY1896 @ SY1896 ) @ ( c_Product__Type_OPair @ SY1896 @ SY1896 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SY1896 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1650,plain,
! [SV38: $i,SV199: $i,SV338: $i,SV429: $i] :
( ( ! [SY1897: $i] :
( ~ ( c_member @ ( tc_prod @ SY1897 @ SY1897 ) @ ( c_Product__Type_OPair @ SY1897 @ SY1897 @ SV429 @ SV338 ) @ SV199 )
| ~ ( c_member @ ( tc_prod @ SY1897 @ SY1897 ) @ ( c_Product__Type_OPair @ SY1897 @ SY1897 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SY1897 @ SV199 ) )
| ( c_member @ ( tc_prod @ SY1897 @ SY1897 ) @ ( c_Product__Type_OPair @ SY1897 @ SY1897 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SY1897 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1651,plain,
! [SV39: $i,SV200: $i,SV339: $i,SV430: $i] :
( ( ! [SY1898: $i] :
( ~ ( c_member @ ( tc_prod @ SY1898 @ SY1898 ) @ ( c_Product__Type_OPair @ SY1898 @ SY1898 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SY1898 @ SV200 ) )
| ~ ( c_member @ ( tc_prod @ SY1898 @ SY1898 ) @ ( c_Product__Type_OPair @ SY1898 @ SY1898 @ SV339 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SY1898 @ SY1898 ) @ ( c_Product__Type_OPair @ SY1898 @ SY1898 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SY1898 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1652,plain,
! [SV40: $i,SV201: $i,SV340: $i,SV431: $i] :
( ( ! [SY1899: $i] :
( ~ ( c_member @ ( tc_prod @ SY1899 @ SY1899 ) @ ( c_Product__Type_OPair @ SY1899 @ SY1899 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SY1899 @ SV201 ) )
| ~ ( c_member @ ( tc_prod @ SY1899 @ SY1899 ) @ ( c_Product__Type_OPair @ SY1899 @ SY1899 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SY1899 @ SV201 ) )
| ( c_member @ ( tc_prod @ SY1899 @ SY1899 ) @ ( c_Product__Type_OPair @ SY1899 @ SY1899 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SY1899 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1653,plain,
! [SV41: $i,SV202: $i,SV341: $i,SV432: $i] :
( ( ! [SY1900: $i] :
( ~ ( c_member @ ( tc_prod @ SY1900 @ SY1900 ) @ ( c_Product__Type_OPair @ SY1900 @ SY1900 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SY1900 @ SV202 ) )
| ~ ( c_member @ ( tc_prod @ SY1900 @ SY1900 ) @ ( c_Product__Type_OPair @ SY1900 @ SY1900 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1900 @ SV202 ) )
| ( c_member @ ( tc_prod @ SY1900 @ SY1900 ) @ ( c_Product__Type_OPair @ SY1900 @ SY1900 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SY1900 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1654,plain,
! [SV42: $i,SV203: $i,SV342: $i,SV433: $i] :
( ( ! [SY1901: $i,SY1902: $i] :
( ~ ( c_member @ ( tc_prod @ SV433 @ SV433 ) @ ( c_Product__Type_OPair @ SV433 @ SV433 @ SV342 @ SV203 ) @ SY1902 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV433 @ SV42 @ SY1901 @ SY1902 @ SV203 ) @ SV342 )
= ( hAPP @ SY1901 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1655,plain,
! [SV43: $i,SV204: $i,SV343: $i,SV434: $i] :
( ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SV434 @ SV343 ) )
| ~ ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ SV204 @ SV43 ) @ SV343 )
| ( SV204 != SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1656,plain,
! [SV47: $i,SV207: $i] :
( ( ( c_member @ ( tc_prod @ SV207 @ SV207 ) @ SV47 @ ( c_Relation_OId @ SV207 ) )
= $false )
| ( ( SV47
= ( c_Product__Type_OPair @ SV207 @ SV207 @ ( sK35_B_x @ SV207 @ SV47 ) @ ( sK35_B_x @ SV207 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1657,plain,
! [SV48: $i,SV208: $i,SV344: $i,SV435: $i] :
( ( ~ ( c_Relation_Oantisym @ SV435 @ SV344 )
| ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
| ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1658,plain,
! [SV49: $i,SV209: $i,SV345: $i,SV436: $i] :
( ( ~ ( c_member @ SV436 @ SV345 @ ( c_Set_Oinsert @ SV436 @ SV209 @ SV49 ) )
| ( SV345 = SV209 )
| ( c_member @ SV436 @ SV345 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1659,plain,
! [SV50: $i,SV210: $i,SV346: $i,SV437: $i] :
( ( ! [SY1903: $i] :
( ( c_Relation_ODomain @ SY1903 @ SV437 @ ( c_Set_Oinsert @ ( tc_prod @ SY1903 @ SV437 ) @ ( c_Product__Type_OPair @ SY1903 @ SV437 @ SV346 @ SV210 ) @ SV50 ) )
= ( c_Set_Oinsert @ SY1903 @ SV346 @ ( c_Relation_ODomain @ SY1903 @ SV437 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1660,plain,
! [SV51: $i,SV211: $i,SV347: $i,SV438: $i] :
( ( ! [SY1904: $i] :
( ( c_Relation_ORange @ SY1904 @ SV438 @ ( c_Set_Oinsert @ ( tc_prod @ SY1904 @ SV438 ) @ ( c_Product__Type_OPair @ SY1904 @ SV438 @ SV347 @ SV211 ) @ SV51 ) )
= ( c_Set_Oinsert @ SV438 @ SV211 @ ( c_Relation_ORange @ SY1904 @ SV438 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1661,plain,
! [SV53: $i,SV213: $i,SV349: $i,SV439: $i] :
( ( ~ ( c_member @ SV439 @ SV349 @ SV213 )
| ( c_member @ SV439 @ SV349 @ ( c_Set_Oinsert @ SV439 @ SV53 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1662,plain,
! [SV54: $i,SV214: $i,SV350: $i] :
( ( ( ~ ( c_member @ SV350 @ SV214 @ SV54 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV350 @ SV214 @ SV54 )
= SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1663,plain,
! [SV55: $i,SV215: $i,SV351: $i,SV440: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV440 @ SV351 )
| ~ ( c_Wellfounded_Owf @ SV215 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV440 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SV440 @ SV215 @ SV351 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1664,plain,
! [SV56: $i,SV216: $i,SV352: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV352 @ SV216 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV352 @ SV352 ) @ ( c_Product__Type_OPair @ SV352 @ SV352 @ SV56 @ SV56 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1665,plain,
! [SV57: $i,SV217: $i,SV353: $i,SV441: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV441 @ SV353 )
| ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 )
| ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1666,plain,
! [SV58: $i,SV218: $i,SV354: $i,SV442: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV442 @ SV354 )
| ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 )
| ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1667,plain,
! [SV59: $i,SV219: $i,SV355: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV355 @ SV219 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV355 @ SV355 ) @ ( c_Product__Type_OPair @ SV355 @ SV355 @ SV59 @ SV59 ) @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1668,plain,
! [SV60: $i,SV220: $i,SV356: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV356 @ SV220 ) )
= $true )
| ( ( c_member @ SV356 @ SV60 @ ( c_Wellfounded_Oacc @ SV356 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1669,plain,
! [SV61: $i,SV221: $i] :
( ( ( c_member @ SV221 @ ( sK25_B_x @ SV221 @ SV61 ) @ ( c_Wellfounded_Oacc @ SV221 @ SV61 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV221 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1670,plain,
! [SV62: $i,SV222: $i,SV357: $i,SV443: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ~ ( c_member @ SY1906 @ SY1905 @ SV443 )
| ~ ( c_member @ ( tc_prod @ SY1906 @ SV357 ) @ ( c_Product__Type_OPair @ SY1906 @ SV357 @ SY1905 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SY1906 @ SV357 @ SV62 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1671,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i,SY1910: $i] :
( ~ ( c_member @ ( tc_prod @ SY1910 @ SY1909 ) @ ( c_Product__Type_OPair @ SY1910 @ SY1909 @ SY1908 @ SY1907 ) @ SV444 )
| ~ ( c_member @ ( tc_prod @ SY1909 @ SV358 ) @ ( c_Product__Type_OPair @ SY1909 @ SV358 @ SY1907 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1910 @ SV358 ) @ ( c_Product__Type_OPair @ SY1910 @ SV358 @ SY1908 @ SV223 ) @ ( c_Relation_Orel__comp @ SY1910 @ SY1909 @ SV358 @ SV444 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1672,plain,
! [SV64: $i,SV224: $i] :
( ( ( ( hAPP @ SV224 @ ( sK22_B_x @ SV224 @ SV64 ) )
= ( hAPP @ SV64 @ ( sK22_B_x @ SV224 @ SV64 ) ) )
= $false )
| ( ( SV224 = SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1673,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i] :
( ( ! [SY1911: $i,SY1912: $i,SY1913: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1913 @ SY1912 ) )
| ~ ( c_member @ ( tc_prod @ SY1911 @ SY1911 ) @ ( c_Product__Type_OPair @ SY1911 @ SY1911 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SY1912 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SY1911 ) @ ( tc_prod @ SV65 @ SY1911 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SY1911 ) @ ( tc_prod @ SV65 @ SY1911 ) @ ( c_Product__Type_OPair @ SV65 @ SY1911 @ SY1912 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SY1911 @ SY1912 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SY1911 @ SY1913 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1674,plain,
! [SV69: $i,SV229: $i,SV360: $i,SV446: $i] :
( ( ! [SY1914: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1914 @ ( c_Product__Type_OPair @ SV446 @ SV360 @ SV229 @ SV69 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SV446 @ SV360 @ tc_HOL_Obool @ SY1914 @ SV229 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1675,plain,
! [SV70: $i,SV230: $i,SV361: $i,SV447: $i] :
( ( ! [SY1915: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1915 @ SV447 @ tc_HOL_Obool @ SV361 @ SV230 @ SV70 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Product__Type_OPair @ SY1915 @ SV447 @ SV230 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1676,plain,
! [SV71: $i,SV231: $i,SV362: $i,SV448: $i] :
( ( ! [SY1916: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY1916 @ SV448 @ tc_HOL_Obool @ SV362 @ SV231 @ SV71 ) )
| ( hBOOL @ ( hAPP @ SV362 @ ( c_Product__Type_OPair @ SY1916 @ SV448 @ SV231 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1677,plain,
! [SV79: $i,SV238: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV238 @ SV79 )
= $false )
| ( ( c_Relation_Oantisym @ SV238 @ ( c_Transitive__Closure_Ortrancl @ SV238 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1678,plain,
! [SV81: $i,SV240: $i,SV364: $i,SV449: $i] :
( ( ( c_Set_Oinsert @ SV449 @ SV364 @ ( c_Set_Oinsert @ SV449 @ SV240 @ SV81 ) )
= ( c_Set_Oinsert @ SV449 @ SV240 @ ( c_Set_Oinsert @ SV449 @ SV364 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1679,plain,
! [SV84: $i,SV242: $i,SV365: $i,SV450: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV450 @ SV365 )
| ( c_Wellfounded_Owf @ SV242 @ ( hAPP @ ( c_Relation_Oinv__image @ SV450 @ SV242 @ SV365 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1680,plain,
! [SV85: $i,SV243: $i] :
( ( ( c_Wellfounded_Owf @ SV243 @ SV85 )
= $false )
| ( ( c_Wellfounded_Owf @ SV243 @ ( c_Transitive__Closure_Otrancl @ SV243 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1681,plain,
! [SV86: $i,SV244: $i] :
( ( ( c_Wellfounded_Owf @ SV244 @ SV86 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV244 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1682,plain,
! [SV88: $i,SV246: $i,SV366: $i,SV451: $i] :
( ( ! [SY1917: $i,SY1918: $i] :
( ( SY1918
!= ( c_Recdef_Owfrec @ SY1917 @ SV451 @ SV366 @ SV246 ) )
| ~ ( c_Wellfounded_Owf @ SY1917 @ SV366 )
| ( ( hAPP @ SY1918 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SY1917 @ SV451 @ SY1918 @ SV366 @ SV88 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1683,plain,
! [SV89: $i,SV247: $i,SV367: $i,SV452: $i] :
( ( ! [SY1919: $i] :
( ~ ( c_Wellfounded_Owf @ SY1919 @ SV452 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY1919 @ SV367 @ SV452 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SY1919 @ SV367 @ ( c_Recdef_Owfrec @ SY1919 @ SV367 @ SV452 @ SV247 ) @ SV452 @ SV89 ) ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1684,plain,
! [SV368: $i,SV90: $i,SV453: $i,SV248: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV248 @ SV453 )
| ! [SY1920: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SY1920 )
= ( hAPP @ ( hAPP @ SV368 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SV453 @ SY1920 ) ) @ SY1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1685,plain,
! [SV92: $i,SV249: $i,SV369: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV369 @ SV249 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV369 @ ( c_Wellfounded_Omlex__prod @ SV369 @ SV92 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1686,plain,
! [SV94: $i,SV250: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV250 @ SV94 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV94 @ SV250 )
= $true )
| ( ( SV250 = SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1687,plain,
! [SV96: $i,SV251: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV251 @ SV96 )
= $false )
| ( ( ( SV96 != SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1688,plain,
! [SV97: $i,SV252: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV252 @ SV97 )
= $false )
| ( ( ( SV252 != SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1689,plain,
! [SV100: $i,SV254: $i] :
( ( ( SV254 = SV100 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV254 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1690,plain,
! [SV101: $i,SV255: $i,SV370: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV255 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1691,plain,
! [SV102: $i,SV256: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV256 @ SV102 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SV256 )
| ( SV256 = SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1692,plain,
! [SV105: $i,SV259: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV259 ) @ SV105 ) )
= $false )
| ( ( SV259 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1693,plain,
! [SV106: $i,SV260: $i] :
( ( ( SV260 = SV106 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV260 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1694,plain,
! [SV454: $i] :
( ( ! [SY1921: $i] :
( ~ ( ~ ( c_member @ SY1921 @ ( sK31_SY722 @ SY1921 @ SV454 ) @ ( sK29_B_Q @ SY1921 @ SV454 ) )
| ~ ! [SY1922: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1921 @ SY1921 ) @ ( c_Product__Type_OPair @ SY1921 @ SY1921 @ ( sK30_SY724 @ SY1922 @ SY1921 @ SV454 ) @ SY1922 ) @ SV454 )
| ~ ( c_member @ SY1921 @ ( sK30_SY724 @ SY1922 @ SY1921 @ SV454 ) @ ( sK29_B_Q @ SY1921 @ SV454 ) ) )
| ~ ( c_member @ SY1921 @ SY1922 @ ( sK29_B_Q @ SY1921 @ SV454 ) ) ) )
| ( c_Wellfounded_Owf @ SY1921 @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1695,plain,
! [SV455: $i] :
( ( ! [SY1923: $i] :
( ~ ( c_Wellfounded_Owf @ SY1923 @ SV455 )
| ! [SY1924: $i] :
( ! [SX3: $i] :
~ ( c_member @ SY1923 @ SX3 @ SY1924 )
| ~ ( ~ ! [SY1926: $i] :
( ~ ( c_member @ ( tc_prod @ SY1923 @ SY1923 ) @ ( c_Product__Type_OPair @ SY1923 @ SY1923 @ SY1926 @ ( sK28_B_x @ SY1924 @ SY1923 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SY1923 @ SY1926 @ SY1924 ) )
| ~ ( c_member @ SY1923 @ ( sK28_B_x @ SY1924 @ SY1923 @ SV455 ) @ SY1924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1696,plain,
! [SV107: $i] :
( ( ! [SY1011: $i,SY1012: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1012 @ SY1011 ) @ ( c_Product__Type_OPair @ SY1012 @ SY1011 @ ( sK51_B_x @ SY1012 @ SY1011 @ SV107 ) @ ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SY1012 @ SY1011 @ SV107 )
!= ( sK53_SY732 @ SY1012 @ SY1011 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY1012 @ SY1011 @ SV107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1697,plain,
! [SV107: $i] :
( ( ! [SY1013: $i,SY1014: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1014 @ SY1013 @ SV107 )
| ! [SY1015: $i,SY1016: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1016 ) @ SV107 )
| ! [SY1017: $i] :
( ~ ( c_member @ ( tc_prod @ SY1014 @ SY1013 ) @ ( c_Product__Type_OPair @ SY1014 @ SY1013 @ SY1015 @ SY1017 ) @ SV107 )
| ( SY1016 = SY1017 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1698,plain,
! [SV261: $i,SV108: $i,SV372: $i] :
( ( ~ ! [SY1787: $i,SY1788: $i] :
( ! [SY1789: $i] :
( ~ ( c_member @ SV372 @ SY1789 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1788 ) @ ( c_Product__Type_OPair @ SV372 @ SY1788 @ SY1789 @ SY1787 ) @ SV261 ) )
| ( c_member @ SY1788 @ SY1787 @ ( c_Relation_OImage @ SV372 @ SY1788 @ SV261 @ SV108 ) ) )
| ~ ! [SY1790: $i,SY1791: $i] :
( ~ ( c_member @ SY1791 @ SY1790 @ ( c_Relation_OImage @ SV372 @ SY1791 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1791 ) @ ( c_Product__Type_OPair @ SV372 @ SY1791 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SY1790 ) @ SV261 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1699,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK70_SY736 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1700,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i] :
( ( ! [SY1927: $i,SY1928: $i] :
~ ( ~ ~ ( ~ ! [SY1929: $i,SY1930: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1930 @ SY1929 ) @ ( tc_prod @ SY1930 @ SY1929 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1930 @ SY1929 ) @ ( tc_prod @ SY1930 @ SY1929 ) @ ( c_Product__Type_OPair @ SY1930 @ SY1929 @ SY1928 @ SY1927 ) @ ( c_Product__Type_OPair @ SY1930 @ SY1929 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1930 @ SY1929 @ SV263 @ SV110 ) )
| ( SY1928 = SV456 )
| ( c_member @ ( tc_prod @ SY1930 @ SY1930 ) @ ( c_Product__Type_OPair @ SY1930 @ SY1930 @ SY1928 @ SV456 ) @ SV263 ) )
| ~ ! [SY1931: $i,SY1932: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1932 @ SY1931 ) @ ( tc_prod @ SY1932 @ SY1931 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1932 @ SY1931 ) @ ( tc_prod @ SY1932 @ SY1931 ) @ ( c_Product__Type_OPair @ SY1932 @ SY1931 @ SY1928 @ SY1927 ) @ ( c_Product__Type_OPair @ SY1932 @ SY1931 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1932 @ SY1931 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY1931 @ SY1931 ) @ ( c_Product__Type_OPair @ SY1931 @ SY1931 @ SY1927 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY1932 @ SY1932 ) @ ( c_Product__Type_OPair @ SY1932 @ SY1932 @ SY1928 @ SV456 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY1933: $i] :
( ( SY1928 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY1933 @ SY1933 ) @ ( c_Product__Type_OPair @ SY1933 @ SY1933 @ SY1927 @ SV373 ) @ SV110 )
| ! [SY1934: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY1934 @ SY1933 ) @ ( tc_prod @ SY1934 @ SY1933 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1934 @ SY1933 ) @ ( tc_prod @ SY1934 @ SY1933 ) @ ( c_Product__Type_OPair @ SY1934 @ SY1933 @ SY1928 @ SY1927 ) @ ( c_Product__Type_OPair @ SY1934 @ SY1933 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1934 @ SY1933 @ SV263 @ SV110 ) ) )
| ~ ! [SY1935: $i,SY1936: $i] :
( ~ ( c_member @ ( tc_prod @ SY1936 @ SY1936 ) @ ( c_Product__Type_OPair @ SY1936 @ SY1936 @ SY1928 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1936 @ SY1935 ) @ ( tc_prod @ SY1936 @ SY1935 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1936 @ SY1935 ) @ ( tc_prod @ SY1936 @ SY1935 ) @ ( c_Product__Type_OPair @ SY1936 @ SY1935 @ SY1928 @ SY1927 ) @ ( c_Product__Type_OPair @ SY1936 @ SY1935 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY1936 @ SY1935 @ SV263 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1701,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ~ ( ~ ! [SY1937: $i,SY1938: $i] :
( ! [SY1939: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1938 @ SY1938 ) @ ( c_Product__Type_OPair @ SY1938 @ SY1938 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY1939 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY1939 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) )
| ~ ! [SY1940: $i,SY1941: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1942: $i] :
( ~ ( c_member @ ( tc_prod @ SY1941 @ SY1941 ) @ ( c_Product__Type_OPair @ SY1941 @ SY1941 @ SY1942 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SY1942 @ ( hAPP @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY1942 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1702,plain,
! [SV112: $i] :
( ( ! [SY1048: $i,SY1049: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1049 @ SY1049 ) @ ( c_Product__Type_OPair @ SY1049 @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ SY1048 ) @ SV112 )
| ~ ~ ( c_member @ SY1049 @ ( sK61_B_x @ SY1049 @ SY1048 @ SV112 ) @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) )
| ( c_member @ SY1049 @ SY1048 @ ( c_Wellfounded_Oacc @ SY1049 @ SV112 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1703,plain,
! [SV112: $i] :
( ( ! [SY1050: $i,SY1051: $i] :
( ~ ( c_member @ SY1051 @ SY1050 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) )
| ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SY1051 @ SY1051 ) @ ( c_Product__Type_OPair @ SY1051 @ SY1051 @ SY1052 @ SY1050 ) @ SV112 )
| ( c_member @ SY1051 @ SY1052 @ ( c_Wellfounded_Oacc @ SY1051 @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1704,plain,
! [SV113: $i,SV265: $i,SV375: $i,SV458: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV458 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1705,plain,
! [SV114: $i,SV266: $i] :
( ( ~ ! [SY1519: $i,SY1520: $i] :
( ! [SY1521: $i] :
~ ( c_member @ ( tc_prod @ SY1520 @ SV266 ) @ ( c_Product__Type_OPair @ SY1520 @ SV266 @ SY1519 @ SY1521 ) @ SV114 )
| ( c_member @ SY1520 @ SY1519 @ ( c_Relation_ODomain @ SY1520 @ SV266 @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1706,plain,
! [SV114: $i,SV266: $i] :
( ( ~ ! [SY1522: $i,SY1523: $i] :
( ~ ( c_member @ SY1523 @ SY1522 @ ( c_Relation_ODomain @ SY1523 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY1523 @ SV266 ) @ ( c_Product__Type_OPair @ SY1523 @ SV266 @ SY1522 @ ( sK66_B_y @ SY1523 @ SY1522 @ SV266 @ SV114 ) ) @ SV114 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1707,plain,
! [SV459: $i] :
( ( ! [SY1943: $i] :
( ( c_member @ ( tc_prod @ SY1943 @ SY1943 ) @ ( c_Product__Type_OPair @ SY1943 @ SY1943 @ ( sK40_B_x @ SY1943 @ SV459 ) @ ( sK40_B_x @ SY1943 @ SV459 ) ) @ ( c_Transitive__Closure_Otrancl @ SY1943 @ SV459 ) )
| ( c_Wellfounded_Oacyclic @ SY1943 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1708,plain,
! [SV460: $i] :
( ( ! [SY1944: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1944 @ SV460 )
| ! [SY1945: $i] :
~ ( c_member @ ( tc_prod @ SY1944 @ SY1944 ) @ ( c_Product__Type_OPair @ SY1944 @ SY1944 @ SY1945 @ SY1945 ) @ ( c_Transitive__Closure_Otrancl @ SY1944 @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1709,plain,
! [SV267: $i,SV115: $i] :
( ( ~ ! [SY1524: $i,SY1525: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1525 @ SV115 )
| ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SV267 @ SY1524 ) @ ( c_Transitive__Closure_Ortrancl @ SY1525 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1525 @ ( c_Set_Oinsert @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV267 ) @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1710,plain,
! [SV115: $i,SV267: $i] :
( ( ~ ~ ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) )
| ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1711,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i] :
( ( ! [SY1946: $i,SY1947: $i,SY1948: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SY1946 @ SV461 ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1948 @ SY1947 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SY1946 @ SV461 )
= ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SY1946 @ SV461 ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ ( sK46_B_a @ SY1948 @ SY1947 @ SY1946 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1948 @ SY1947 @ SY1946 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1948 @ SY1947 ) @ ( tc_prod @ SY1948 @ SY1947 ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ ( sK46_B_a @ SY1948 @ SY1947 @ SY1946 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY1948 @ SY1947 @ SY1946 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY1948 @ SY1947 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1948 @ SY1947 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1712,plain,
! [SV117: $i] :
( ( ! [SY1075: $i,SY1076: $i] :
( ~ ( ~ ( c_member @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( c_member @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ SY1075 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY1076 @ SY1075 @ SV117 )
!= ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SY1076 @ SY1076 ) @ ( c_Product__Type_OPair @ SY1076 @ SY1076 @ ( sK68_SY735 @ SY1076 @ SY1075 @ SV117 ) @ ( sK67_B_x @ SY1076 @ SY1075 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY1076 @ SY1075 @ SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1713,plain,
! [SV117: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
( ~ ( c_Relation_Ototal__on @ SY1078 @ SY1077 @ SV117 )
| ! [SY1079: $i] :
( ~ ( c_member @ SY1078 @ SY1079 @ SY1077 )
| ! [SY1080: $i] :
( ~ ( c_member @ SY1078 @ SY1080 @ SY1077 )
| ( SY1079 = SY1080 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1079 @ SY1080 ) @ SV117 )
| ( c_member @ ( tc_prod @ SY1078 @ SY1078 ) @ ( c_Product__Type_OPair @ SY1078 @ SY1078 @ SY1080 @ SY1079 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1714,plain,
! [SV462: $i] :
( ( ! [SY1949: $i] :
( ~ ( c_member @ ( tc_prod @ SY1949 @ SY1949 ) @ ( c_Product__Type_OPair @ SY1949 @ SY1949 @ ( sK76_B_x @ SY1949 @ SV462 ) @ ( sK76_B_x @ SY1949 @ SV462 ) ) @ SV462 )
| ( c_Nitpick_Orefl_H @ SY1949 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1715,plain,
! [SV463: $i] :
( ( ! [SY1950: $i] :
( ~ ( c_Nitpick_Orefl_H @ SY1950 @ SV463 )
| ! [SY1951: $i] : ( c_member @ ( tc_prod @ SY1950 @ SY1950 ) @ ( c_Product__Type_OPair @ SY1950 @ SY1950 @ SY1951 @ SY1951 ) @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1716,plain,
! [SV118: $i,SV269: $i,SV377: $i,SV464: $i] :
( ( ! [SY1952: $i] :
( ~ ( c_member @ SY1952 @ SV464 @ ( c_Relation_OImage @ SV377 @ SY1952 @ SV269 @ SV118 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV377 @ SY1952 ) @ ( c_Product__Type_OPair @ SV377 @ SY1952 @ ( sK23_B_x @ SY1952 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SY1952 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1717,plain,
! [SV119: $i,SV270: $i] :
( ( ~ ! [SY1538: $i] :
( ! [SY1539: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1539 @ SY1538 @ SV270 ) @ SV119 ) )
| ( SY1538 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1718,plain,
! [SV270: $i,SV119: $i] :
( ( ~ ~ ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1719,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ~ ( ~ ( ( SV465 != SV271 )
| ( SV378 != SV120 )
| ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
| ~ ~ ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
| ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1720,plain,
! [SV121: $i] :
( ( ! [SY1101: $i] :
( ( SY1101 != SV121 )
| ! [SY1102: $i] : ( c_member @ SY1102 @ SY1101 @ ( c_fequal @ SV121 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1721,plain,
! [SV121: $i] :
( ( ! [SY1103: $i] :
( ! [SY1104: $i] :
~ ( c_member @ SY1104 @ SY1103 @ ( c_fequal @ SV121 ) )
| ( SY1103 = SV121 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1722,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ~ ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) )
| ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1723,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ~ ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) )
| ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1724,plain,
! [SV466: $i] :
( ( ! [SY1959: $i] :
( ( SY1959 = SV466 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1959 @ SV466 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV466 @ SY1959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1725,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1726,plain,
! [SV123: $i] :
( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( c_Relation_Oirrefl @ SY1115 @ SV123 )
| ~ ( c_Relation_Otrans @ SY1115 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SY1115 @ SY1114 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY1115 @ SY1114 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1727,plain,
! [SV123: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
| ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1728,plain,
! [SV124: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1123 @ ( sK75_B_x1 @ SY1123 @ SY1122 @ SV124 ) ) )
| ! [SY1124: $i,SY1125: $i] : ( hBOOL @ ( hAPP @ SY1123 @ ( c_Product__Type_OPair @ SY1122 @ SV124 @ SY1124 @ SY1125 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1729,plain,
! [SV124: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1127 @ ( c_Product__Type_OPair @ SY1126 @ SV124 @ ( sK73_B_a @ SY1127 @ SY1126 @ SV124 ) @ ( sK74_SY739 @ SY1127 @ SY1126 @ SV124 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1127 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1730,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1731,plain,
( ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1732,plain,
! [SV467: $i] :
( ( ! [SY1960: $i] :
( ( c_member @ ( tc_prod @ SY1960 @ SY1960 ) @ ( c_Product__Type_OPair @ SY1960 @ SY1960 @ ( sK72_B_x @ SY1960 @ SV467 ) @ ( sK72_B_x @ SY1960 @ SV467 ) ) @ SV467 )
| ( c_Relation_Oirrefl @ SY1960 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1733,plain,
! [SV468: $i] :
( ( ! [SY1961: $i] :
( ~ ( c_Relation_Oirrefl @ SY1961 @ SV468 )
| ! [SY1962: $i] :
~ ( c_member @ ( tc_prod @ SY1961 @ SY1961 ) @ ( c_Product__Type_OPair @ SY1961 @ SY1961 @ SY1962 @ SY1962 ) @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1734,plain,
! [SV469: $i] :
( ( ! [SY1963: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1963 @ SY1963 ) @ ( c_Product__Type_OPair @ SY1963 @ SY1963 @ ( sK77_B_x @ SY1963 @ SV469 ) @ ( sK78_SY740 @ SY1963 @ SV469 ) ) @ SV469 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1963 @ SY1963 ) @ ( c_Product__Type_OPair @ SY1963 @ SY1963 @ ( sK78_SY740 @ SY1963 @ SV469 ) @ ( sK79_SY742 @ SY1963 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SY1963 @ SY1963 ) @ ( c_Product__Type_OPair @ SY1963 @ SY1963 @ ( sK77_B_x @ SY1963 @ SV469 ) @ ( sK79_SY742 @ SY1963 @ SV469 ) ) @ SV469 ) ) )
| ( c_Relation_Otrans @ SY1963 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1735,plain,
! [SV470: $i] :
( ( ! [SY1964: $i] :
( ~ ( c_Relation_Otrans @ SY1964 @ SV470 )
| ! [SY1965: $i,SY1966: $i] :
( ~ ( c_member @ ( tc_prod @ SY1964 @ SY1964 ) @ ( c_Product__Type_OPair @ SY1964 @ SY1964 @ SY1965 @ SY1966 ) @ SV470 )
| ! [SY1967: $i] :
( ~ ( c_member @ ( tc_prod @ SY1964 @ SY1964 ) @ ( c_Product__Type_OPair @ SY1964 @ SY1964 @ SY1966 @ SY1967 ) @ SV470 )
| ( c_member @ ( tc_prod @ SY1964 @ SY1964 ) @ ( c_Product__Type_OPair @ SY1964 @ SY1964 @ SY1965 @ SY1967 ) @ SV470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1736,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ! [SY1560: $i,SY1561: $i] :
( ( SY1560 != SV273 )
| ~ ( c_member @ SY1561 @ SY1560 @ SV125 )
| ( c_member @ ( tc_prod @ SY1561 @ SY1561 ) @ ( c_Product__Type_OPair @ SY1561 @ SY1561 @ SY1560 @ SV273 ) @ ( c_Relation_OId__on @ SY1561 @ SV125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1737,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ~ ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) )
| ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1738,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ( SV379 = SV274 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1739,plain,
! [SV127: $i,SV275: $i] :
( ( ~ ! [SY1568: $i,SY1569: $i] :
( ( c_member @ SY1569 @ SY1568 @ SV275 )
| ( c_member @ SY1569 @ SY1568 @ SV127 )
| ( ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV275 )
!= ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV127 ) )
| ( SV275 = SV127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1740,plain,
! [SV127: $i,SV275: $i] :
( ( ~ ! [SY1570: $i,SY1571: $i] :
( ( c_member @ SY1571 @ SY1570 @ SV275 )
| ( c_member @ SY1571 @ SY1570 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV275 )
= ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1741,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1742,plain,
! [SV129: $i,SV277: $i] :
( ( ~ ! [SY1574: $i,SY1575: $i] :
( ( c_member @ SY1575 @ SY1574 @ ( c_Relation_ODomain @ SY1575 @ SY1575 @ SV277 ) )
| ( SY1574 != SV129 )
| ( c_member @ ( tc_prod @ SY1575 @ SY1575 ) @ ( c_Product__Type_OPair @ SY1575 @ SY1575 @ SY1574 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1575 @ SV277 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1743,plain,
! [SV129: $i,SV277: $i] :
( ( ~ ! [SY1576: $i,SY1577: $i] :
( ( c_member @ SY1577 @ SY1576 @ ( c_Relation_ODomain @ SY1577 @ SY1577 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SY1577 @ SY1577 ) @ ( c_Product__Type_OPair @ SY1577 @ SY1577 @ SY1576 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1577 @ SV277 ) )
| ( SY1576 = SV129 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1744,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ~ ( ~ ( ! [SY1968: $i,SY1969: $i] :
( ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV278 @ SV130 ) )
| ( SV473 = SV278 ) )
| ~ ( ! [SY1970: $i,SY1971: $i] :
( ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV278 @ SV130 ) )
| ( SV381 = SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1745,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i] :
( ( ! [SY1972: $i,SY1973: $i,SY1974: $i,SY1975: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ SY1973 @ SY1972 ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1975 @ SY1974 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY1973 ) @ SY1972 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ SY1973 @ SY1972 ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ ( sK18_B_a @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1975 @ SY1974 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1975 @ SY1974 ) @ ( tc_prod @ SY1975 @ SY1974 ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ ( sK18_B_a @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY1975 @ SY1974 @ ( sK20_SY717 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY1975 @ SY1974 @ SY1973 @ SY1972 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1746,plain,
! [SV132: $i,SV280: $i] :
( ( ~ ! [SY1590: $i,SY1591: $i] :
( ! [SY1592: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SY1591 ) @ ( c_Product__Type_OPair @ SV280 @ SY1591 @ SY1592 @ SY1590 ) @ SV132 )
| ( c_member @ SY1591 @ SY1590 @ ( c_Relation_ORange @ SV280 @ SY1591 @ SV132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1747,plain,
! [SV132: $i,SV280: $i] :
( ( ~ ! [SY1593: $i,SY1594: $i] :
( ~ ( c_member @ SY1594 @ SY1593 @ ( c_Relation_ORange @ SV280 @ SY1594 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SY1594 ) @ ( c_Product__Type_OPair @ SV280 @ SY1594 @ ( sK65_B_y @ SY1594 @ SY1593 @ SV280 @ SV132 ) @ SY1593 ) @ SV132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1748,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ~ ( ~ ! [SY1976: $i,SY1977: $i] :
( ! [SY1978: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1977 @ SY1977 ) @ ( c_Product__Type_OPair @ SY1977 @ SY1977 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY1978 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY1978 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1981: $i] :
( ~ ( c_member @ ( tc_prod @ SY1980 @ SY1980 ) @ ( c_Product__Type_OPair @ SY1980 @ SY1980 @ SY1981 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SY1981 @ ( hAPP @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY1981 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1749,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1750,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i] :
( ( ~ ( ~ ! [SY1982: $i] :
( ! [SY1983: $i] :
~ ( c_member @ ( tc_prod @ SY1983 @ SY1983 ) @ ( c_Product__Type_OPair @ SY1983 @ SY1983 @ SY1982 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1983 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1982 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) )
| ~ ! [SY1984: $i] :
( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1984 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
| ! [SY1985: $i] : ( c_member @ ( tc_prod @ SY1985 @ SY1985 ) @ ( c_Product__Type_OPair @ SY1985 @ SY1985 @ SY1984 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1985 @ SV283 ) @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1751,plain,
! [SV136: $i] :
( ( ! [SY1191: $i] :
( ! [SY1192: $i] :
~ ( c_member @ SY1192 @ SY1191 @ SV136 )
| ( hBOOL @ ( hAPP @ SV136 @ SY1191 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1752,plain,
! [SV136: $i] :
( ( ! [SY1193: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ SY1193 ) )
| ! [SY1194: $i] : ( c_member @ SY1194 @ SY1193 @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1753,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i,SY1989: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ SY1987 @ SY1986 ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1989 @ SY1988 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ ( sK14_B_a @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ ( sK16_SY711 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1989 @ SY1988 ) @ ( tc_prod @ SY1989 @ SY1988 ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ ( sK16_SY711 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY1989 @ SY1988 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1989 @ SY1988 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY1989 @ SY1988 @ SY1987 @ SY1986 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1987 ) @ SY1986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1754,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i] :
( ( ! [SY1990: $i,SY1991: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1991 @ SY1991 ) @ ( c_Product__Type_OPair @ SY1991 @ SY1991 @ ( sK56_B_z @ SY1991 @ SY1990 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SY1990 ) @ SV479 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1991 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SY1991 @ SY1990 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SY1991 @ SY1990 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY1991 @ SV387 @ SV479 @ SV285 @ SY1990 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SY1990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1755,plain,
! [SV139: $i] :
( ( ! [SY1207: $i] :
( ( SY1207 != SV139 )
| ! [SY1208: $i] : ( c_member @ ( tc_prod @ SY1208 @ SY1208 ) @ ( c_Product__Type_OPair @ SY1208 @ SY1208 @ SY1207 @ SV139 ) @ ( c_Relation_OId @ SY1208 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1756,plain,
! [SV139: $i] :
( ( ! [SY1209: $i] :
( ! [SY1210: $i] :
~ ( c_member @ ( tc_prod @ SY1210 @ SY1210 ) @ ( c_Product__Type_OPair @ SY1210 @ SY1210 @ SY1209 @ SV139 ) @ ( c_Relation_OId @ SY1210 ) )
| ( SY1209 = SV139 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1757,plain,
! [SV480: $i] :
( ( ! [SY1992: $i] :
( ~ ( c_member @ SY1992 @ ( sK32_B_x @ SY1992 @ SV480 ) @ ( c_Wellfounded_Oacc @ SY1992 @ SV480 ) )
| ( c_Wellfounded_Owf @ SY1992 @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1758,plain,
! [SV481: $i] :
( ( ! [SY1993: $i] :
( ~ ( c_Wellfounded_Owf @ SY1993 @ SV481 )
| ! [SY1994: $i] : ( c_member @ SY1993 @ SY1994 @ ( c_Wellfounded_Oacc @ SY1993 @ SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1759,plain,
! [SV140: $i,SV286: $i] :
( ( ~ ! [SY1621: $i,SY1622: $i] :
( ( SY1622 != SY1621 )
| ~ ( c_member @ SV286 @ SV140 @ SY1622 )
| ( c_member @ SV286 @ SV140 @ SY1621 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1760,plain,
! [SV140: $i,SV286: $i] :
( ( ~ ! [SY1623: $i,SY1624: $i] :
( ( SY1624 != SY1623 )
| ~ ( c_member @ SV286 @ SV140 @ SY1623 )
| ( c_member @ SV286 @ SV140 @ SY1624 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1761,plain,
! [SV141: $i,SV287: $i] :
( ( ~ ! [SY1625: $i,SY1626: $i] :
( ( SY1626 != SY1625 )
| ~ ( c_member @ SV287 @ SY1626 @ SV141 )
| ( c_member @ SV287 @ SY1625 @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1762,plain,
! [SV141: $i,SV287: $i] :
( ( ~ ! [SY1627: $i,SY1628: $i] :
( ( SY1628 != SY1627 )
| ~ ( c_member @ SV287 @ SY1627 @ SV141 )
| ( c_member @ SV287 @ SY1628 @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1763,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1764,plain,
! [SV143: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
| ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1765,plain,
! [SV143: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1766,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
| ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1767,plain,
! [SV290: $i,SV145: $i] :
( ( ~ ! [SY1632: $i,SY1633: $i] :
( ~ ( c_Wellfounded_Owf @ SY1633 @ SV145 )
| ( c_member @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SV290 @ SY1632 ) @ ( c_Transitive__Closure_Ortrancl @ SY1633 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1633 @ ( c_Set_Oinsert @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SY1632 @ SV290 ) @ SV145 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1768,plain,
! [SV145: $i,SV290: $i] :
( ( ~ ~ ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) )
| ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1769,plain,
! [SV146: $i] :
( ( ! [SY1249: $i,SY1250: $i] :
( ~ ( c_Relation_Orefl__on @ SY1250 @ SY1249 @ SV146 )
| ~ ( c_Relation_Otrans @ SY1250 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SY1250 @ SY1249 @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1770,plain,
! [SV146: $i] :
( ( ~ ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) )
| ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1771,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 )
| ( SV291
!= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1772,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ~ ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) )
| ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1773,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ~ ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) )
| ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1774,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ! [SY1647: $i,SY1648: $i] :
( ~ ( c_member @ SY1648 @ SY1647 @ ( c_Set_Oinsert @ SY1648 @ SV293 @ SV149 ) )
| ( SY1647 = SV293 )
| ( c_member @ SY1648 @ SY1647 @ SV149 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1775,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ~ ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1776,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i] :
( ( ! [SY1995: $i] :
( ~ ( c_member @ ( tc_prod @ SY1995 @ SY1995 ) @ ( c_Product__Type_OPair @ SY1995 @ SY1995 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SY1995 @ SV294 ) )
| ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1995 @ SY1995 ) @ ( c_Product__Type_OPair @ SY1995 @ SY1995 @ ( sK12_B_y @ SY1995 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SY1995 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1995 @ SY1995 ) @ ( c_Product__Type_OPair @ SY1995 @ SY1995 @ ( sK13_SY707 @ SY1995 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SY1995 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SY1995 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SY1995 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1777,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV392 @ SV392 ) @ ( c_Product__Type_OPair @ SV392 @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ SV295 ) @ SV151 )
| ~ ~ ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1778,plain,
! [SV393: $i,SV152: $i,SV296: $i] :
( ( ~ ! [SY1860: $i,SY1861: $i] :
( ~ ( c_member @ ( tc_prod @ SY1861 @ SY1860 ) @ ( c_Product__Type_OPair @ SY1861 @ SY1860 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1861 @ SY1860 @ SV393 ) @ SV296 ) @ SV152 ) ) )
| ~ ! [SY1862: $i,SY1863: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1863 @ SY1862 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1863 @ SY1862 ) @ ( c_Product__Type_OPair @ SY1863 @ SY1862 @ SV296 @ SV152 ) @ SV393 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1779,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
| ( SV394 = SV297 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1780,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i] :
( ( ! [SY1996: $i] :
( ~ ( c_member @ ( tc_prod @ SY1996 @ SY1996 ) @ ( c_Product__Type_OPair @ SY1996 @ SY1996 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SY1996 @ SV298 ) )
| ~ ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY1996 @ SY1996 ) @ ( c_Product__Type_OPair @ SY1996 @ SY1996 @ SV485 @ ( sK10_B_y @ SY1996 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY1996 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1996 @ SY1996 ) @ ( c_Product__Type_OPair @ SY1996 @ SY1996 @ ( sK10_B_y @ SY1996 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SY1996 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SY1996 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SY1996 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1781,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1782,plain,
! [SV487: $i] :
( ( ! [SY1997: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1997 @ SV487 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SY1997 @ SV487 ) @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1783,plain,
! [SV488: $i] :
( ( ! [SY1998: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SY1998 @ SV488 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1998 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1784,plain,
! [SV156: $i,SV300: $i] :
( ( ~ ! [SY1669: $i] :
( ! [SY1670: $i] :
~ ( c_member @ ( tc_prod @ SY1670 @ SY1670 ) @ ( c_Product__Type_OPair @ SY1670 @ SY1670 @ SY1669 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1670 @ SV156 ) )
| ( SY1669 != SV300 )
| ( SY1669 = SV300 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1785,plain,
! [SV156: $i,SV300: $i] :
( ( ~ ! [SY1671: $i,SY1672: $i] :
( ~ ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1672 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SY1672 @ SV156 ) )
| ( SY1671 = SV300 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1786,plain,
! [SV157: $i,SV301: $i] :
( ( ~ ! [SY1673: $i,SY1674: $i] :
( ~ ( c_member @ SY1674 @ SY1673 @ SV301 )
| ( c_member @ SY1674 @ SY1673 @ ( c_Set_Oinsert @ SY1674 @ SV157 @ SV301 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1787,plain,
! [SV301: $i,SV157: $i] :
( ( ~ ! [SY1675: $i] :
( ( SY1675 != SV157 )
| ! [SY1676: $i] : ( c_member @ SY1676 @ SY1675 @ ( c_Set_Oinsert @ SY1676 @ SV157 @ SV301 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1788,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK26_B_x @ SV302 @ SV158 ) @ ( sK27_SY720 @ SV302 @ SV158 ) ) @ SV158 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1789,plain,
! [SV489: $i] :
( ( ! [SY1999: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1999 @ SY1999 ) @ ( c_Product__Type_OPair @ SY1999 @ SY1999 @ ( sK33_B_x @ SY1999 @ SV489 ) @ ( sK34_SY725 @ SY1999 @ SV489 ) ) @ SV489 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY1999 @ SY1999 ) @ ( c_Product__Type_OPair @ SY1999 @ SY1999 @ ( sK34_SY725 @ SY1999 @ SV489 ) @ ( sK33_B_x @ SY1999 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SY1999 @ SV489 )
!= ( sK34_SY725 @ SY1999 @ SV489 ) ) ) ) )
| ( c_Relation_Oantisym @ SY1999 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1790,plain,
! [SV490: $i] :
( ( ! [SY2000: $i] :
( ~ ( c_Relation_Oantisym @ SY2000 @ SV490 )
| ! [SY2001: $i,SY2002: $i] :
( ~ ( c_member @ ( tc_prod @ SY2000 @ SY2000 ) @ ( c_Product__Type_OPair @ SY2000 @ SY2000 @ SY2001 @ SY2002 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SY2000 @ SY2000 ) @ ( c_Product__Type_OPair @ SY2000 @ SY2000 @ SY2002 @ SY2001 ) @ SV490 )
| ( SY2001 = SY2002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1791,plain,
! [SV159: $i] :
( ( ! [SY1306: $i,SY1307: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1307 @ SY1306 @ SV159 )
| ~ ( c_Relation_Oantisym @ SY1307 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SY1307 @ SY1306 @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1792,plain,
! [SV159: $i] :
( ( ~ ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) )
| ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1793,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ~ ( ~ ! [SY2003: $i,SY2004: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2004 @ SY2004 ) @ ( c_Product__Type_OPair @ SY2004 @ SY2004 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV160 @ SV397 @ SV303 ) ) )
| ~ ! [SY2005: $i,SY2006: $i] :
( ( ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2007: $i] :
( ~ ( c_member @ ( tc_prod @ SY2006 @ SY2006 ) @ ( c_Product__Type_OPair @ SY2006 @ SY2006 @ SY2007 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2007 )
= ( hAPP @ SV160 @ SY2007 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1794,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV398 @ SV398 ) @ ( c_Product__Type_OPair @ SV398 @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ SV304 ) @ SV161 )
| ~ ~ ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) ) )
= $true )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1795,plain,
! [SV1: $i,SV162: $i,SV305: $i,SV399: $i,SV492: $i] :
( ( ~ ( c_Relation_Otrans @ SV492 @ SV399 )
| ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
| ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1796,plain,
! [SV2: $i,SV163: $i,SV306: $i,SV400: $i] :
( ( ( ( SV400 != SV306 ) )
= $true )
| ( ( ~ ( c_member @ SV163 @ SV306 @ SV2 )
| ( c_member @ SV163 @ SV400 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1797,plain,
! [SV3: $i,SV164: $i,SV307: $i,SV401: $i,SV493: $i] :
( ( ! [SY2008: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY2008 @ SV493 @ SV401 @ SV307 @ ( c_Product__Type_OPair @ SY2008 @ SV493 @ SV164 @ SV3 ) )
= ( hAPP @ ( hAPP @ SV307 @ SV164 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1798,plain,
! [SV4: $i,SV165: $i,SV308: $i,SV402: $i,SV494: $i] :
( ( ! [SY2009: $i] :
( ( c_Product__Type_Ointernal__split @ SY2009 @ SV494 @ SV402 @ SV308 @ ( c_Product__Type_OPair @ SY2009 @ SV494 @ SV165 @ SV4 ) )
= ( hAPP @ ( hAPP @ SV308 @ SV165 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1799,plain,
! [SV5: $i,SV166: $i,SV309: $i,SV403: $i,SV495: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV495 @ SV403 ) @ ( c_Product__Type_OPair @ SV495 @ SV403 @ SV309 @ SV166 ) @ SV5 )
| ( c_member @ SV403 @ SV166 @ ( c_Relation_ORange @ SV495 @ SV403 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1800,plain,
! [SV6: $i,SV167: $i,SV310: $i,SV404: $i] :
( ( ( ( SV404 != SV310 ) )
= $true )
| ( ( ~ ( c_member @ SV167 @ SV404 @ SV6 )
| ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SV404 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1801,plain,
! [SV7: $i,SV168: $i,SV311: $i,SV405: $i,SV496: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV496 @ SV405 ) @ ( c_Product__Type_OPair @ SV496 @ SV405 @ SV311 @ SV168 ) @ SV7 )
| ( c_member @ SV496 @ SV311 @ ( c_Relation_ODomain @ SV496 @ SV405 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1802,plain,
! [SV8: $i,SV169: $i,SV312: $i,SV406: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV406 @ SV312 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV169 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SV406 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SV406 @ SV169 @ SV312 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1803,plain,
! [SV10: $i,SV171: $i,SV313: $i,SV407: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV407 @ SV313 ) )
= $true )
| ( ( c_Relation_Otrans @ SV171 @ ( hAPP @ ( c_Relation_Oinv__image @ SV407 @ SV171 @ SV313 ) @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1804,plain,
! [SV11: $i,SV172: $i,SV314: $i,SV408: $i] :
( ( ( ~ ( c_member @ SV408 @ SV314 @ ( c_Relation_ORange @ SV172 @ SV408 @ SV11 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV172 @ SV408 ) @ ( c_Product__Type_OPair @ SV172 @ SV408 @ ( sK63_B_x @ SV408 @ SV314 @ SV172 @ SV11 ) @ SV314 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1805,plain,
! [SV12: $i,SV173: $i,SV315: $i,SV409: $i] :
( ( ( ~ ( c_member @ SV409 @ SV315 @ ( c_Relation_ODomain @ SV409 @ SV173 @ SV12 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV409 @ SV173 ) @ ( c_Product__Type_OPair @ SV409 @ SV173 @ SV315 @ ( sK62_B_y @ SV409 @ SV315 @ SV173 @ SV12 ) ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1806,plain,
! [SV13: $i,SV174: $i,SV316: $i,SV410: $i] :
( ( ( ~ ( c_member @ SV410 @ SV316 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV410 @ SV410 ) @ ( c_Product__Type_OPair @ SV410 @ SV410 @ SV13 @ SV316 ) @ SV174 )
| ( c_member @ SV410 @ SV13 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1807,plain,
! [SV14: $i,SV175: $i,SV317: $i,SV411: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV411 @ SV317 @ SV175 ) )
= $true )
| ( ( ~ ( c_member @ SV411 @ SV14 @ SV317 )
| ( c_member @ ( tc_prod @ SV411 @ SV411 ) @ ( c_Product__Type_OPair @ SV411 @ SV411 @ SV14 @ SV14 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1808,plain,
! [SV15: $i,SV176: $i,SV318: $i,SV412: $i,SV497: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV497 @ SV412 @ SV318 )
| ~ ( c_member @ ( tc_prod @ SV497 @ SV497 ) @ ( c_Product__Type_OPair @ SV497 @ SV497 @ SV176 @ SV15 ) @ SV318 )
| ( c_member @ SV497 @ SV176 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1809,plain,
! [SV16: $i,SV177: $i,SV319: $i,SV413: $i,SV498: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV498 @ SV413 @ SV319 )
| ~ ( c_member @ ( tc_prod @ SV498 @ SV498 ) @ ( c_Product__Type_OPair @ SV498 @ SV498 @ SV177 @ SV16 ) @ SV319 )
| ( c_member @ SV498 @ SV16 @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1810,plain,
! [SV17: $i,SV178: $i,SV320: $i,SV414: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV414 @ SV414 ) @ ( c_Product__Type_OPair @ SV414 @ SV414 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SV414 @ SV17 ) ) )
= $true )
| ( ( ~ ( c_member @ SV414 @ SV178 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
| ( c_member @ SV414 @ SV320 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1811,plain,
! [SV18: $i,SV179: $i,SV321: $i,SV415: $i] :
( ( ( ~ ( c_member @ SV415 @ SV321 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV415 @ SV415 ) @ ( c_Product__Type_OPair @ SV415 @ SV415 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SV415 @ SV179 ) )
| ( c_member @ SV415 @ SV18 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1812,plain,
! [SV19: $i,SV180: $i,SV322: $i,SV416: $i,SV499: $i] :
( ( ! [SY2010: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2010 @ SV499 @ SV416 )
| ~ ( c_member @ ( tc_prod @ SY2010 @ SV499 ) @ ( c_Product__Type_OPair @ SY2010 @ SV499 @ SV322 @ SV180 ) @ SV416 )
| ~ ( c_member @ ( tc_prod @ SY2010 @ SV499 ) @ ( c_Product__Type_OPair @ SY2010 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1813,plain,
! [SV20: $i,SV181: $i,SV323: $i,SV417: $i,SV500: $i] :
( ( ! [SY2011: $i] :
( ( c_Product__Type_Ocurry @ SY2011 @ SV500 @ SV417 @ SV323 @ SV181 @ SV20 )
= ( hAPP @ SV323 @ ( c_Product__Type_OPair @ SY2011 @ SV500 @ SV181 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1814,plain,
! [SV22: $i,SV183: $i,SV325: $i] :
( ( ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ SV22 )
= $false )
| ( ( c_member @ ( tc_prod @ SV325 @ SV325 ) @ SV183 @ ( c_Transitive__Closure_Ortrancl @ SV325 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1815,plain,
! [SV23: $i,SV184: $i,SV326: $i,SV418: $i,SV501: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
| ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1816,plain,
! [SV24: $i,SV185: $i,SV327: $i,SV419: $i,SV502: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV327 ) @ SV185 )
| ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
| ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1817,plain,
! [SV25: $i,SV186: $i,SV328: $i,SV420: $i,SV503: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
| ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV328 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1818,plain,
! [SV26: $i,SV187: $i,SV329: $i,SV421: $i,SV504: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
| ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1819,plain,
! [SV28: $i,SV189: $i,SV330: $i,SV422: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Otrancl @ SV422 @ SV28 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1820,plain,
! [SV29: $i,SV190: $i,SV331: $i,SV423: $i,SV505: $i] :
( ( ! [SY2012: $i] :
( ~ ( c_member @ ( tc_prod @ SY2012 @ SY2012 ) @ ( c_Product__Type_OPair @ SY2012 @ SY2012 @ SV505 @ SV423 ) @ SV331 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY2012 @ SV190 @ SV29 @ SV331 @ SV423 ) @ SV505 )
= ( hAPP @ SV29 @ SV505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1821,plain,
! [SV30: $i,SV191: $i,SV332: $i,SV424: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ SV30 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ ( c_Transitive__Closure_Otrancl @ SV424 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1822,plain,
! [SV31: $i,SV192: $i,SV333: $i] :
( ( ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ SV31 )
= $false )
| ( ( c_member @ ( tc_prod @ SV333 @ SV333 ) @ SV192 @ ( c_Transitive__Closure_Otrancl @ SV333 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1823,plain,
! [SV34: $i,SV195: $i,SV334: $i,SV425: $i,SV506: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV334 ) @ SV195 )
| ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV334 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SV506 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1824,plain,
! [SV35: $i,SV196: $i,SV335: $i,SV426: $i,SV507: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV335 ) @ SV196 )
| ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
| ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1825,plain,
! [SV36: $i,SV197: $i,SV336: $i,SV427: $i,SV508: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
| ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV336 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1826,plain,
! [SV37: $i,SV198: $i,SV337: $i,SV428: $i,SV509: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
| ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
| ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1827,plain,
! [SV38: $i,SV199: $i,SV338: $i,SV429: $i,SV510: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV338 ) @ SV199 )
| ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SV510 @ SV199 ) )
| ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SV510 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1828,plain,
! [SV39: $i,SV200: $i,SV339: $i,SV430: $i,SV511: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SV511 @ SV200 ) )
| ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV339 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SV511 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1829,plain,
! [SV40: $i,SV201: $i,SV340: $i,SV431: $i,SV512: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
| ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SV512 @ SV201 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1830,plain,
! [SV41: $i,SV202: $i,SV341: $i,SV432: $i,SV513: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SV513 @ SV202 ) )
| ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
| ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1831,plain,
! [SV514: $i,SV42: $i,SV203: $i,SV342: $i,SV433: $i] :
( ( ! [SY2013: $i] :
( ~ ( c_member @ ( tc_prod @ SV433 @ SV433 ) @ ( c_Product__Type_OPair @ SV433 @ SV433 @ SV342 @ SV203 ) @ SY2013 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV433 @ SV42 @ SV514 @ SY2013 @ SV203 ) @ SV342 )
= ( hAPP @ SV514 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1832,plain,
! [SV43: $i,SV204: $i,SV343: $i,SV434: $i] :
( ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SV434 @ SV343 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ SV204 @ SV43 ) @ SV343 )
| ( SV204 != SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1833,plain,
! [SV48: $i,SV208: $i,SV344: $i,SV435: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV435 @ SV344 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
| ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1834,plain,
! [SV49: $i,SV209: $i,SV345: $i,SV436: $i] :
( ( ( ~ ( c_member @ SV436 @ SV345 @ ( c_Set_Oinsert @ SV436 @ SV209 @ SV49 ) ) )
= $true )
| ( ( ( SV345 = SV209 )
| ( c_member @ SV436 @ SV345 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1835,plain,
! [SV50: $i,SV210: $i,SV346: $i,SV437: $i,SV515: $i] :
( ( ( c_Relation_ODomain @ SV515 @ SV437 @ ( c_Set_Oinsert @ ( tc_prod @ SV515 @ SV437 ) @ ( c_Product__Type_OPair @ SV515 @ SV437 @ SV346 @ SV210 ) @ SV50 ) )
= ( c_Set_Oinsert @ SV515 @ SV346 @ ( c_Relation_ODomain @ SV515 @ SV437 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1836,plain,
! [SV51: $i,SV211: $i,SV347: $i,SV438: $i,SV516: $i] :
( ( ( c_Relation_ORange @ SV516 @ SV438 @ ( c_Set_Oinsert @ ( tc_prod @ SV516 @ SV438 ) @ ( c_Product__Type_OPair @ SV516 @ SV438 @ SV347 @ SV211 ) @ SV51 ) )
= ( c_Set_Oinsert @ SV438 @ SV211 @ ( c_Relation_ORange @ SV516 @ SV438 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1837,plain,
! [SV53: $i,SV213: $i,SV349: $i,SV439: $i] :
( ( ( ~ ( c_member @ SV439 @ SV349 @ SV213 ) )
= $true )
| ( ( c_member @ SV439 @ SV349 @ ( c_Set_Oinsert @ SV439 @ SV53 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1838,plain,
! [SV54: $i,SV214: $i,SV350: $i] :
( ( ( c_member @ SV350 @ SV214 @ SV54 )
= $false )
| ( ( ( c_Set_Oinsert @ SV350 @ SV214 @ SV54 )
= SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1839,plain,
! [SV55: $i,SV215: $i,SV351: $i,SV440: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV440 @ SV351 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV215 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV440 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SV440 @ SV215 @ SV351 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1840,plain,
! [SV56: $i,SV216: $i,SV352: $i] :
( ( ( c_Wellfounded_Owf @ SV352 @ SV216 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV352 @ SV352 ) @ ( c_Product__Type_OPair @ SV352 @ SV352 @ SV56 @ SV56 ) @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1841,plain,
! [SV57: $i,SV217: $i,SV353: $i,SV441: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV441 @ SV353 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 )
| ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1842,plain,
! [SV58: $i,SV218: $i,SV354: $i,SV442: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV442 @ SV354 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 )
| ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1843,plain,
! [SV59: $i,SV219: $i,SV355: $i] :
( ( ( c_Wellfounded_Owf @ SV355 @ SV219 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV355 @ SV355 ) @ ( c_Product__Type_OPair @ SV355 @ SV355 @ SV59 @ SV59 ) @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1844,plain,
! [SV60: $i,SV220: $i,SV356: $i] :
( ( ( c_Wellfounded_Owf @ SV356 @ SV220 )
= $false )
| ( ( c_member @ SV356 @ SV60 @ ( c_Wellfounded_Oacc @ SV356 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1845,plain,
! [SV62: $i,SV222: $i,SV357: $i,SV443: $i,SV517: $i] :
( ( ! [SY2014: $i] :
( ~ ( c_member @ SY2014 @ SV517 @ SV443 )
| ~ ( c_member @ ( tc_prod @ SY2014 @ SV357 ) @ ( c_Product__Type_OPair @ SY2014 @ SV357 @ SV517 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SY2014 @ SV357 @ SV62 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1846,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i] :
( ( ! [SY2015: $i,SY2016: $i,SY2017: $i] :
( ~ ( c_member @ ( tc_prod @ SY2017 @ SY2016 ) @ ( c_Product__Type_OPair @ SY2017 @ SY2016 @ SY2015 @ SV518 ) @ SV444 )
| ~ ( c_member @ ( tc_prod @ SY2016 @ SV358 ) @ ( c_Product__Type_OPair @ SY2016 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY2017 @ SV358 ) @ ( c_Product__Type_OPair @ SY2017 @ SV358 @ SY2015 @ SV223 ) @ ( c_Relation_Orel__comp @ SY2017 @ SY2016 @ SV358 @ SV444 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1847,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i] :
( ( ! [SY2018: $i,SY2019: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2019 @ SY2018 ) )
| ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SY2018 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SY2018 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SY2018 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SY2019 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1848,plain,
! [SV69: $i,SV229: $i,SV360: $i,SV446: $i,SV520: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV520 @ ( c_Product__Type_OPair @ SV446 @ SV360 @ SV229 @ SV69 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SV446 @ SV360 @ tc_HOL_Obool @ SV520 @ SV229 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1849,plain,
! [SV70: $i,SV230: $i,SV361: $i,SV447: $i,SV521: $i] :
( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV521 @ SV447 @ tc_HOL_Obool @ SV361 @ SV230 @ SV70 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Product__Type_OPair @ SV521 @ SV447 @ SV230 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1850,plain,
! [SV71: $i,SV231: $i,SV362: $i,SV448: $i,SV522: $i] :
( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV522 @ SV448 @ tc_HOL_Obool @ SV362 @ SV231 @ SV71 ) )
| ( hBOOL @ ( hAPP @ SV362 @ ( c_Product__Type_OPair @ SV522 @ SV448 @ SV231 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1851,plain,
! [SV84: $i,SV242: $i,SV365: $i,SV450: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV450 @ SV365 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV242 @ ( hAPP @ ( c_Relation_Oinv__image @ SV450 @ SV242 @ SV365 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1852,plain,
! [SV88: $i,SV246: $i,SV366: $i,SV451: $i,SV523: $i] :
( ( ! [SY2020: $i] :
( ( SY2020
!= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) )
| ~ ( c_Wellfounded_Owf @ SV523 @ SV366 )
| ( ( hAPP @ SY2020 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SY2020 @ SV366 @ SV88 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1853,plain,
! [SV89: $i,SV247: $i,SV367: $i,SV452: $i,SV524: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV524 @ SV452 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SV524 @ SV367 @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV452 @ SV89 ) ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1854,plain,
! [SV368: $i,SV90: $i,SV453: $i,SV248: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV248 @ SV453 ) )
= $true )
| ( ( ! [SY1920: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SY1920 )
= ( hAPP @ ( hAPP @ SV368 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SV453 @ SY1920 ) ) @ SY1920 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1855,plain,
! [SV92: $i,SV249: $i,SV369: $i] :
( ( ( c_Wellfounded_Owf @ SV369 @ SV249 )
= $false )
| ( ( c_Wellfounded_Owf @ SV369 @ ( c_Wellfounded_Omlex__prod @ SV369 @ SV92 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1856,plain,
! [SV251: $i,SV96: $i] :
( ( ( SV96 = SV251 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV251 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1857,plain,
! [SV97: $i,SV252: $i] :
( ( ( SV252 = SV97 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV252 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1858,plain,
! [SV101: $i,SV255: $i,SV370: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV255 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1859,plain,
! [SV256: $i,SV102: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SV256 ) )
= $true )
| ( ( SV256 = SV102 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV256 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1860,plain,
! [SV454: $i,SV525: $i] :
( ( ~ ( ~ ( c_member @ SV525 @ ( sK31_SY722 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
| ~ ! [SY2021: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ SY2021 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SY2021 @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) )
| ( c_Wellfounded_Owf @ SV525 @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1861,plain,
! [SV455: $i,SV526: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV526 @ SV455 )
| ! [SY2022: $i] :
( ! [SY2023: $i] :
~ ( c_member @ SV526 @ SY2023 @ SY2022 )
| ~ ( ~ ! [SY2024: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2024 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2024 @ SY2022 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) @ SY2022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1862,plain,
! [SV107: $i,SV527: $i] :
( ( ! [SY2025: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2025 @ SV527 ) @ ( c_Product__Type_OPair @ SY2025 @ SV527 @ ( sK51_B_x @ SY2025 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SY2025 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2025 @ SV527 ) @ ( c_Product__Type_OPair @ SY2025 @ SV527 @ ( sK51_B_x @ SY2025 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SY2025 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SY2025 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SY2025 @ SV527 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2025 @ SV527 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1863,plain,
! [SV107: $i,SV528: $i] :
( ( ! [SY2026: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2026 @ SV528 @ SV107 )
| ! [SY2027: $i,SY2028: $i] :
( ~ ( c_member @ ( tc_prod @ SY2026 @ SV528 ) @ ( c_Product__Type_OPair @ SY2026 @ SV528 @ SY2027 @ SY2028 ) @ SV107 )
| ! [SY2029: $i] :
( ~ ( c_member @ ( tc_prod @ SY2026 @ SV528 ) @ ( c_Product__Type_OPair @ SY2026 @ SV528 @ SY2027 @ SY2029 ) @ SV107 )
| ( SY2028 = SY2029 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1864,plain,
! [SV261: $i,SV108: $i,SV372: $i] :
( ( ~ ! [SY1787: $i,SY1788: $i] :
( ! [SY1789: $i] :
( ~ ( c_member @ SV372 @ SY1789 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1788 ) @ ( c_Product__Type_OPair @ SV372 @ SY1788 @ SY1789 @ SY1787 ) @ SV261 ) )
| ( c_member @ SY1788 @ SY1787 @ ( c_Relation_OImage @ SV372 @ SY1788 @ SV261 @ SV108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1865,plain,
! [SV108: $i,SV261: $i,SV372: $i] :
( ( ~ ! [SY1790: $i,SY1791: $i] :
( ~ ( c_member @ SY1791 @ SY1790 @ ( c_Relation_OImage @ SV372 @ SY1791 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1791 ) @ ( c_Product__Type_OPair @ SV372 @ SY1791 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SY1790 ) @ SV261 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1866,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK70_SY736 @ SV262 @ SV109 ) ) @ SV109 ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1867,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1868,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i] :
( ( ! [SY2030: $i] :
~ ( ~ ~ ( ~ ! [SY2031: $i,SY2032: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2032 @ SY2031 ) @ ( tc_prod @ SY2032 @ SY2031 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2032 @ SY2031 ) @ ( tc_prod @ SY2032 @ SY2031 ) @ ( c_Product__Type_OPair @ SY2032 @ SY2031 @ SY2030 @ SV529 ) @ ( c_Product__Type_OPair @ SY2032 @ SY2031 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2032 @ SY2031 @ SV263 @ SV110 ) )
| ( SY2030 = SV456 )
| ( c_member @ ( tc_prod @ SY2032 @ SY2032 ) @ ( c_Product__Type_OPair @ SY2032 @ SY2032 @ SY2030 @ SV456 ) @ SV263 ) )
| ~ ! [SY2033: $i,SY2034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2034 @ SY2033 ) @ ( tc_prod @ SY2034 @ SY2033 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2034 @ SY2033 ) @ ( tc_prod @ SY2034 @ SY2033 ) @ ( c_Product__Type_OPair @ SY2034 @ SY2033 @ SY2030 @ SV529 ) @ ( c_Product__Type_OPair @ SY2034 @ SY2033 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2034 @ SY2033 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2033 @ SY2033 ) @ ( c_Product__Type_OPair @ SY2033 @ SY2033 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2034 @ SY2034 ) @ ( c_Product__Type_OPair @ SY2034 @ SY2034 @ SY2030 @ SV456 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY2035: $i] :
( ( SY2030 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2035 @ SY2035 ) @ ( c_Product__Type_OPair @ SY2035 @ SY2035 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2036: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2036 @ SY2035 ) @ ( tc_prod @ SY2036 @ SY2035 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2036 @ SY2035 ) @ ( tc_prod @ SY2036 @ SY2035 ) @ ( c_Product__Type_OPair @ SY2036 @ SY2035 @ SY2030 @ SV529 ) @ ( c_Product__Type_OPair @ SY2036 @ SY2035 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2036 @ SY2035 @ SV263 @ SV110 ) ) )
| ~ ! [SY2037: $i,SY2038: $i] :
( ~ ( c_member @ ( tc_prod @ SY2038 @ SY2038 ) @ ( c_Product__Type_OPair @ SY2038 @ SY2038 @ SY2030 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2038 @ SY2037 ) @ ( tc_prod @ SY2038 @ SY2037 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2038 @ SY2037 ) @ ( tc_prod @ SY2038 @ SY2037 ) @ ( c_Product__Type_OPair @ SY2038 @ SY2037 @ SY2030 @ SV529 ) @ ( c_Product__Type_OPair @ SY2038 @ SY2037 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2038 @ SY2037 @ SV263 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1869,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ~ ! [SY1937: $i,SY1938: $i] :
( ! [SY1939: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1938 @ SY1938 ) @ ( c_Product__Type_OPair @ SY1938 @ SY1938 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY1939 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY1939 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) )
| ~ ! [SY1940: $i,SY1941: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1942: $i] :
( ~ ( c_member @ ( tc_prod @ SY1941 @ SY1941 ) @ ( c_Product__Type_OPair @ SY1941 @ SY1941 @ SY1942 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SY1942 @ ( hAPP @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY1942 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1870,plain,
! [SV112: $i,SV530: $i] :
( ( ! [SY2039: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2039 @ SY2039 ) @ ( c_Product__Type_OPair @ SY2039 @ SY2039 @ ( sK61_B_x @ SY2039 @ SV530 @ SV112 ) @ SV530 ) @ SV112 )
| ~ ~ ( c_member @ SY2039 @ ( sK61_B_x @ SY2039 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SY2039 @ SV112 ) ) )
| ( c_member @ SY2039 @ SV530 @ ( c_Wellfounded_Oacc @ SY2039 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1871,plain,
! [SV112: $i,SV531: $i] :
( ( ! [SY2040: $i] :
( ~ ( c_member @ SY2040 @ SV531 @ ( c_Wellfounded_Oacc @ SY2040 @ SV112 ) )
| ! [SY2041: $i] :
( ~ ( c_member @ ( tc_prod @ SY2040 @ SY2040 ) @ ( c_Product__Type_OPair @ SY2040 @ SY2040 @ SY2041 @ SV531 ) @ SV112 )
| ( c_member @ SY2040 @ SY2041 @ ( c_Wellfounded_Oacc @ SY2040 @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1872,plain,
! [SV113: $i,SV265: $i,SV375: $i,SV458: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV458 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1873,plain,
! [SV114: $i,SV266: $i] :
( ( ! [SY1519: $i,SY1520: $i] :
( ! [SY1521: $i] :
~ ( c_member @ ( tc_prod @ SY1520 @ SV266 ) @ ( c_Product__Type_OPair @ SY1520 @ SV266 @ SY1519 @ SY1521 ) @ SV114 )
| ( c_member @ SY1520 @ SY1519 @ ( c_Relation_ODomain @ SY1520 @ SV266 @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1874,plain,
! [SV114: $i,SV266: $i] :
( ( ! [SY1522: $i,SY1523: $i] :
( ~ ( c_member @ SY1523 @ SY1522 @ ( c_Relation_ODomain @ SY1523 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY1523 @ SV266 ) @ ( c_Product__Type_OPair @ SY1523 @ SV266 @ SY1522 @ ( sK66_B_y @ SY1523 @ SY1522 @ SV266 @ SV114 ) ) @ SV114 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1875,plain,
! [SV459: $i,SV532: $i] :
( ( ( c_member @ ( tc_prod @ SV532 @ SV532 ) @ ( c_Product__Type_OPair @ SV532 @ SV532 @ ( sK40_B_x @ SV532 @ SV459 ) @ ( sK40_B_x @ SV532 @ SV459 ) ) @ ( c_Transitive__Closure_Otrancl @ SV532 @ SV459 ) )
| ( c_Wellfounded_Oacyclic @ SV532 @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1876,plain,
! [SV460: $i,SV533: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV533 @ SV460 )
| ! [SY2042: $i] :
~ ( c_member @ ( tc_prod @ SV533 @ SV533 ) @ ( c_Product__Type_OPair @ SV533 @ SV533 @ SY2042 @ SY2042 ) @ ( c_Transitive__Closure_Otrancl @ SV533 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1877,plain,
! [SV267: $i,SV115: $i] :
( ( ! [SY1524: $i,SY1525: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1525 @ SV115 )
| ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SV267 @ SY1524 ) @ ( c_Transitive__Closure_Ortrancl @ SY1525 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1525 @ ( c_Set_Oinsert @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV267 ) @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1878,plain,
! [SV115: $i,SV267: $i] :
( ( ~ ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) )
| ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1879,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i] :
( ( ! [SY2043: $i,SY2044: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2044 @ SY2043 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ ( sK46_B_a @ SY2044 @ SY2043 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY2044 @ SY2043 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2044 @ SY2043 ) @ ( tc_prod @ SY2044 @ SY2043 ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ ( sK46_B_a @ SY2044 @ SY2043 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY2044 @ SY2043 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY2044 @ SY2043 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2044 @ SY2043 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1880,plain,
! [SV117: $i,SV535: $i] :
( ( ! [SY2045: $i] :
( ~ ( ~ ( c_member @ SY2045 @ ( sK67_B_x @ SY2045 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( c_member @ SY2045 @ ( sK68_SY735 @ SY2045 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY2045 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SY2045 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY2045 @ SY2045 ) @ ( c_Product__Type_OPair @ SY2045 @ SY2045 @ ( sK67_B_x @ SY2045 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SY2045 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SY2045 @ SY2045 ) @ ( c_Product__Type_OPair @ SY2045 @ SY2045 @ ( sK68_SY735 @ SY2045 @ SV535 @ SV117 ) @ ( sK67_B_x @ SY2045 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY2045 @ SV535 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1881,plain,
! [SV117: $i,SV536: $i] :
( ( ! [SY2046: $i] :
( ~ ( c_Relation_Ototal__on @ SY2046 @ SV536 @ SV117 )
| ! [SY2047: $i] :
( ~ ( c_member @ SY2046 @ SY2047 @ SV536 )
| ! [SY2048: $i] :
( ~ ( c_member @ SY2046 @ SY2048 @ SV536 )
| ( SY2047 = SY2048 )
| ( c_member @ ( tc_prod @ SY2046 @ SY2046 ) @ ( c_Product__Type_OPair @ SY2046 @ SY2046 @ SY2047 @ SY2048 ) @ SV117 )
| ( c_member @ ( tc_prod @ SY2046 @ SY2046 ) @ ( c_Product__Type_OPair @ SY2046 @ SY2046 @ SY2048 @ SY2047 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1882,plain,
! [SV462: $i,SV537: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV537 @ SV537 ) @ ( c_Product__Type_OPair @ SV537 @ SV537 @ ( sK76_B_x @ SV537 @ SV462 ) @ ( sK76_B_x @ SV537 @ SV462 ) ) @ SV462 )
| ( c_Nitpick_Orefl_H @ SV537 @ SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1883,plain,
! [SV463: $i,SV538: $i] :
( ( ~ ( c_Nitpick_Orefl_H @ SV538 @ SV463 )
| ! [SY2049: $i] : ( c_member @ ( tc_prod @ SV538 @ SV538 ) @ ( c_Product__Type_OPair @ SV538 @ SV538 @ SY2049 @ SY2049 ) @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1884,plain,
! [SV118: $i,SV269: $i,SV377: $i,SV464: $i,SV539: $i] :
( ( ~ ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1885,plain,
! [SV119: $i,SV270: $i] :
( ( ! [SY1538: $i] :
( ! [SY1539: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1539 @ SY1538 @ SV270 ) @ SV119 ) )
| ( SY1538 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1886,plain,
! [SV270: $i,SV119: $i] :
( ( ~ ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1887,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ~ ( ( SV465 != SV271 )
| ( SV378 != SV120 )
| ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
| ~ ~ ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
| ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1888,plain,
! [SV121: $i,SV540: $i] :
( ( ( SV540 != SV121 )
| ! [SY2050: $i] : ( c_member @ SY2050 @ SV540 @ ( c_fequal @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1889,plain,
! [SV121: $i,SV541: $i] :
( ( ! [SY2051: $i] :
~ ( c_member @ SY2051 @ SV541 @ ( c_fequal @ SV121 ) )
| ( SV541 = SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1890,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) )
| ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1891,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) )
| ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1892,plain,
! [SV466: $i,SV542: $i] :
( ( ( SV542 = SV466 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV542 @ SV466 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV466 @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1893,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1894,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1895,plain,
! [SV543: $i,SV123: $i] :
( ( ! [SY2052: $i] :
( ~ ( c_Relation_Oirrefl @ SY2052 @ SV123 )
| ~ ( c_Relation_Otrans @ SY2052 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SY2052 @ SV543 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY2052 @ SV543 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1896,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
| ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1897,plain,
! [SV124: $i,SV544: $i] :
( ( ! [SY2053: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2053 @ ( sK75_B_x1 @ SY2053 @ SV544 @ SV124 ) ) )
| ! [SY2054: $i,SY2055: $i] : ( hBOOL @ ( hAPP @ SY2053 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SY2054 @ SY2055 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1898,plain,
! [SV124: $i,SV545: $i] :
( ( ! [SY2056: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2056 @ ( c_Product__Type_OPair @ SV545 @ SV124 @ ( sK73_B_a @ SY2056 @ SV545 @ SV124 ) @ ( sK74_SY739 @ SY2056 @ SV545 @ SV124 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2056 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1899,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1900,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1901,plain,
( ( ~ ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1902,plain,
( ( ~ ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1903,plain,
! [SV467: $i,SV546: $i] :
( ( ( c_member @ ( tc_prod @ SV546 @ SV546 ) @ ( c_Product__Type_OPair @ SV546 @ SV546 @ ( sK72_B_x @ SV546 @ SV467 ) @ ( sK72_B_x @ SV546 @ SV467 ) ) @ SV467 )
| ( c_Relation_Oirrefl @ SV546 @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1904,plain,
! [SV468: $i,SV547: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV547 @ SV468 )
| ! [SY2058: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV547 ) @ ( c_Product__Type_OPair @ SV547 @ SV547 @ SY2058 @ SY2058 ) @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1905,plain,
! [SV469: $i,SV548: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK78_SY740 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) ) )
| ( c_Relation_Otrans @ SV548 @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1906,plain,
! [SV470: $i,SV549: $i] :
( ( ~ ( c_Relation_Otrans @ SV549 @ SV470 )
| ! [SY2059: $i,SY2060: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2060 ) @ SV470 )
| ! [SY2061: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2060 @ SY2061 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2061 ) @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(1907,plain,
! [SV125: $i,SV273: $i] :
( ( ! [SY1560: $i,SY1561: $i] :
( ( SY1560 != SV273 )
| ~ ( c_member @ SY1561 @ SY1560 @ SV125 )
| ( c_member @ ( tc_prod @ SY1561 @ SY1561 ) @ ( c_Product__Type_OPair @ SY1561 @ SY1561 @ SY1560 @ SV273 ) @ ( c_Relation_OId__on @ SY1561 @ SV125 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1908,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) )
| ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1909,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) ) )
= $true )
| ( ( ( SV379 = SV274 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1910,plain,
! [SV127: $i,SV275: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ( c_member @ SY1569 @ SY1568 @ SV275 )
| ( c_member @ SY1569 @ SY1568 @ SV127 )
| ( ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV275 )
!= ( c_Set_Oinsert @ SY1569 @ SY1568 @ SV127 ) )
| ( SV275 = SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1911,plain,
! [SV127: $i,SV275: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ( c_member @ SY1571 @ SY1570 @ SV275 )
| ( c_member @ SY1571 @ SY1570 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV275 )
= ( c_Set_Oinsert @ SY1571 @ SY1570 @ SV127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1912,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1913,plain,
! [SV129: $i,SV277: $i] :
( ( ! [SY1574: $i,SY1575: $i] :
( ( c_member @ SY1575 @ SY1574 @ ( c_Relation_ODomain @ SY1575 @ SY1575 @ SV277 ) )
| ( SY1574 != SV129 )
| ( c_member @ ( tc_prod @ SY1575 @ SY1575 ) @ ( c_Product__Type_OPair @ SY1575 @ SY1575 @ SY1574 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1575 @ SV277 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1914,plain,
! [SV129: $i,SV277: $i] :
( ( ! [SY1576: $i,SY1577: $i] :
( ( c_member @ SY1577 @ SY1576 @ ( c_Relation_ODomain @ SY1577 @ SY1577 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SY1577 @ SY1577 ) @ ( c_Product__Type_OPair @ SY1577 @ SY1577 @ SY1576 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY1577 @ SV277 ) )
| ( SY1576 = SV129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1915,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ~ ( ! [SY1968: $i,SY1969: $i] :
( ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV278 @ SV130 ) )
| ( SV473 = SV278 ) )
| ~ ( ! [SY1970: $i,SY1971: $i] :
( ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV278 @ SV130 ) )
| ( SV381 = SV130 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1916,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i] :
( ( ! [SY2062: $i,SY2063: $i,SY2064: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ SY2062 @ SV550 ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2064 @ SY2063 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY2062 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ SY2062 @ SV550 ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ ( sK18_B_a @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2064 @ SY2063 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2064 @ SY2063 ) @ ( tc_prod @ SY2064 @ SY2063 ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ ( sK18_B_a @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY2064 @ SY2063 @ ( sK20_SY717 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY2064 @ SY2063 @ SY2062 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1917,plain,
! [SV132: $i,SV280: $i] :
( ( ! [SY1590: $i,SY1591: $i] :
( ! [SY1592: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SY1591 ) @ ( c_Product__Type_OPair @ SV280 @ SY1591 @ SY1592 @ SY1590 ) @ SV132 )
| ( c_member @ SY1591 @ SY1590 @ ( c_Relation_ORange @ SV280 @ SY1591 @ SV132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1918,plain,
! [SV132: $i,SV280: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
( ~ ( c_member @ SY1594 @ SY1593 @ ( c_Relation_ORange @ SV280 @ SY1594 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SY1594 ) @ ( c_Product__Type_OPair @ SV280 @ SY1594 @ ( sK65_B_y @ SY1594 @ SY1593 @ SV280 @ SV132 ) @ SY1593 ) @ SV132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1919,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ~ ! [SY1976: $i,SY1977: $i] :
( ! [SY1978: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1977 @ SY1977 ) @ ( c_Product__Type_OPair @ SY1977 @ SY1977 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY1978 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY1978 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1981: $i] :
( ~ ( c_member @ ( tc_prod @ SY1980 @ SY1980 ) @ ( c_Product__Type_OPair @ SY1980 @ SY1980 @ SY1981 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SY1981 @ ( hAPP @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY1981 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1920,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1921,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i] :
( ( ~ ! [SY1982: $i] :
( ! [SY1983: $i] :
~ ( c_member @ ( tc_prod @ SY1983 @ SY1983 ) @ ( c_Product__Type_OPair @ SY1983 @ SY1983 @ SY1982 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1983 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1982 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) )
| ~ ! [SY1984: $i] :
( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1984 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
| ! [SY1985: $i] : ( c_member @ ( tc_prod @ SY1985 @ SY1985 ) @ ( c_Product__Type_OPair @ SY1985 @ SY1985 @ SY1984 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1985 @ SV283 ) @ SV135 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1922,plain,
! [SV136: $i,SV551: $i] :
( ( ! [SY2065: $i] :
~ ( c_member @ SY2065 @ SV551 @ SV136 )
| ( hBOOL @ ( hAPP @ SV136 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1923,plain,
! [SV552: $i,SV136: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV136 @ SV552 ) )
| ! [SY2066: $i] : ( c_member @ SY2066 @ SV552 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1924,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i] :
( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ SY2067 @ SV553 ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2069 @ SY2068 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ ( sK14_B_a @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ ( sK16_SY711 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2069 @ SY2068 ) @ ( tc_prod @ SY2069 @ SY2068 ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ ( sK16_SY711 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2069 @ SY2068 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2069 @ SY2068 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY2069 @ SY2068 @ SY2067 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY2067 ) @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1925,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i] :
( ( ! [SY2070: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2070 @ SY2070 ) @ ( c_Product__Type_OPair @ SY2070 @ SY2070 @ ( sK56_B_z @ SY2070 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2070 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SY2070 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SY2070 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY2070 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1926,plain,
! [SV139: $i,SV555: $i] :
( ( ( SV555 != SV139 )
| ! [SY2071: $i] : ( c_member @ ( tc_prod @ SY2071 @ SY2071 ) @ ( c_Product__Type_OPair @ SY2071 @ SY2071 @ SV555 @ SV139 ) @ ( c_Relation_OId @ SY2071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1927,plain,
! [SV139: $i,SV556: $i] :
( ( ! [SY2072: $i] :
~ ( c_member @ ( tc_prod @ SY2072 @ SY2072 ) @ ( c_Product__Type_OPair @ SY2072 @ SY2072 @ SV556 @ SV139 ) @ ( c_Relation_OId @ SY2072 ) )
| ( SV556 = SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(1928,plain,
! [SV480: $i,SV557: $i] :
( ( ~ ( c_member @ SV557 @ ( sK32_B_x @ SV557 @ SV480 ) @ ( c_Wellfounded_Oacc @ SV557 @ SV480 ) )
| ( c_Wellfounded_Owf @ SV557 @ SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1929,plain,
! [SV481: $i,SV558: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV558 @ SV481 )
| ! [SY2073: $i] : ( c_member @ SV558 @ SY2073 @ ( c_Wellfounded_Oacc @ SV558 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1930,plain,
! [SV140: $i,SV286: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ( SY1622 != SY1621 )
| ~ ( c_member @ SV286 @ SV140 @ SY1622 )
| ( c_member @ SV286 @ SV140 @ SY1621 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1931,plain,
! [SV140: $i,SV286: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
( ( SY1624 != SY1623 )
| ~ ( c_member @ SV286 @ SV140 @ SY1623 )
| ( c_member @ SV286 @ SV140 @ SY1624 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1932,plain,
! [SV141: $i,SV287: $i] :
( ( ! [SY1625: $i,SY1626: $i] :
( ( SY1626 != SY1625 )
| ~ ( c_member @ SV287 @ SY1626 @ SV141 )
| ( c_member @ SV287 @ SY1625 @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1933,plain,
! [SV141: $i,SV287: $i] :
( ( ! [SY1627: $i,SY1628: $i] :
( ( SY1628 != SY1627 )
| ~ ( c_member @ SV287 @ SY1627 @ SV141 )
| ( c_member @ SV287 @ SY1628 @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1934,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1935,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
| ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1936,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1937,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1938,plain,
! [SV290: $i,SV145: $i] :
( ( ! [SY1632: $i,SY1633: $i] :
( ~ ( c_Wellfounded_Owf @ SY1633 @ SV145 )
| ( c_member @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SV290 @ SY1632 ) @ ( c_Transitive__Closure_Ortrancl @ SY1633 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1633 @ ( c_Set_Oinsert @ ( tc_prod @ SY1633 @ SY1633 ) @ ( c_Product__Type_OPair @ SY1633 @ SY1633 @ SY1632 @ SV290 ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1939,plain,
! [SV145: $i,SV290: $i] :
( ( ~ ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) )
| ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1940,plain,
! [SV146: $i,SV559: $i] :
( ( ! [SY2074: $i] :
( ~ ( c_Relation_Orefl__on @ SY2074 @ SV559 @ SV146 )
| ~ ( c_Relation_Otrans @ SY2074 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SY2074 @ SV559 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1941,plain,
! [SV146: $i] :
( ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) )
| ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1942,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 )
| ( SV291
!= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1943,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) )
| ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1944,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) )
| ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1945,plain,
! [SV149: $i,SV293: $i] :
( ( ! [SY1647: $i,SY1648: $i] :
( ~ ( c_member @ SY1648 @ SY1647 @ ( c_Set_Oinsert @ SY1648 @ SV293 @ SV149 ) )
| ( SY1647 = SV293 )
| ( c_member @ SY1648 @ SY1647 @ SV149 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1946,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1947,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1948,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV392 @ SV392 ) @ ( c_Product__Type_OPair @ SV392 @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ SV295 ) @ SV151 )
| ~ ~ ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) ) )
= $false )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1949,plain,
! [SV393: $i,SV152: $i,SV296: $i] :
( ( ~ ! [SY1860: $i,SY1861: $i] :
( ~ ( c_member @ ( tc_prod @ SY1861 @ SY1860 ) @ ( c_Product__Type_OPair @ SY1861 @ SY1860 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1861 @ SY1860 @ SV393 ) @ SV296 ) @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1950,plain,
! [SV152: $i,SV296: $i,SV393: $i] :
( ( ~ ! [SY1862: $i,SY1863: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1863 @ SY1862 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1863 @ SY1862 ) @ ( c_Product__Type_OPair @ SY1863 @ SY1862 @ SV296 @ SV152 ) @ SV393 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1951,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) )
= $true )
| ( ( ( SV394 = SV297 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1952,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1953,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1954,plain,
! [SV487: $i,SV562: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV562 @ SV487 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV562 @ SV487 ) @ c_Wellfounded_Oless__than ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1955,plain,
! [SV488: $i,SV563: $i] :
( ( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV563 @ SV488 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV563 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1956,plain,
! [SV156: $i,SV300: $i] :
( ( ! [SY1669: $i] :
( ! [SY1670: $i] :
~ ( c_member @ ( tc_prod @ SY1670 @ SY1670 ) @ ( c_Product__Type_OPair @ SY1670 @ SY1670 @ SY1669 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1670 @ SV156 ) )
| ( SY1669 != SV300 )
| ( SY1669 = SV300 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1957,plain,
! [SV156: $i,SV300: $i] :
( ( ! [SY1671: $i,SY1672: $i] :
( ~ ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY1672 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY1672 @ SY1672 ) @ ( c_Product__Type_OPair @ SY1672 @ SY1672 @ SY1671 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SY1672 @ SV156 ) )
| ( SY1671 = SV300 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1958,plain,
! [SV157: $i,SV301: $i] :
( ( ! [SY1673: $i,SY1674: $i] :
( ~ ( c_member @ SY1674 @ SY1673 @ SV301 )
| ( c_member @ SY1674 @ SY1673 @ ( c_Set_Oinsert @ SY1674 @ SV157 @ SV301 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1959,plain,
! [SV301: $i,SV157: $i] :
( ( ! [SY1675: $i] :
( ( SY1675 != SV157 )
| ! [SY1676: $i] : ( c_member @ SY1676 @ SY1675 @ ( c_Set_Oinsert @ SY1676 @ SV157 @ SV301 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1960,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK26_B_x @ SV302 @ SV158 ) @ ( sK27_SY720 @ SV302 @ SV158 ) ) @ SV158 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1961,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1962,plain,
! [SV489: $i,SV564: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK33_B_x @ SV564 @ SV489 ) @ ( sK34_SY725 @ SV564 @ SV489 ) ) @ SV489 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) ) )
| ( c_Relation_Oantisym @ SV564 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1963,plain,
! [SV490: $i,SV565: $i] :
( ( ~ ( c_Relation_Oantisym @ SV565 @ SV490 )
| ! [SY2075: $i,SY2076: $i] :
( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2075 @ SY2076 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2076 @ SY2075 ) @ SV490 )
| ( SY2075 = SY2076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(1964,plain,
! [SV159: $i,SV566: $i] :
( ( ! [SY2077: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2077 @ SV566 @ SV159 )
| ~ ( c_Relation_Oantisym @ SY2077 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SY2077 @ SV566 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(1965,plain,
! [SV159: $i] :
( ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) )
| ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1966,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ~ ! [SY2003: $i,SY2004: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2004 @ SY2004 ) @ ( c_Product__Type_OPair @ SY2004 @ SY2004 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV160 @ SV397 @ SV303 ) ) )
| ~ ! [SY2005: $i,SY2006: $i] :
( ( ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2007: $i] :
( ~ ( c_member @ ( tc_prod @ SY2006 @ SY2006 ) @ ( c_Product__Type_OPair @ SY2006 @ SY2006 @ SY2007 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2007 )
= ( hAPP @ SV160 @ SY2007 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1967,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV398 @ SV398 ) @ ( c_Product__Type_OPair @ SV398 @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ SV304 ) @ SV161 )
| ~ ~ ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) )
= $false )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1968,plain,
! [SV1: $i,SV162: $i,SV305: $i,SV399: $i,SV492: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV492 @ SV399 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
| ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1969,plain,
! [SV2: $i,SV163: $i,SV306: $i,SV400: $i] :
( ( ( SV400 = SV306 )
= $false )
| ( ( ~ ( c_member @ SV163 @ SV306 @ SV2 )
| ( c_member @ SV163 @ SV400 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1970,plain,
! [SV3: $i,SV164: $i,SV307: $i,SV401: $i,SV493: $i,SV567: $i] :
( ( ( c_Product__Type_Oprod_Oprod__rec @ SV567 @ SV493 @ SV401 @ SV307 @ ( c_Product__Type_OPair @ SV567 @ SV493 @ SV164 @ SV3 ) )
= ( hAPP @ ( hAPP @ SV307 @ SV164 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1971,plain,
! [SV4: $i,SV165: $i,SV308: $i,SV402: $i,SV494: $i,SV568: $i] :
( ( ( c_Product__Type_Ointernal__split @ SV568 @ SV494 @ SV402 @ SV308 @ ( c_Product__Type_OPair @ SV568 @ SV494 @ SV165 @ SV4 ) )
= ( hAPP @ ( hAPP @ SV308 @ SV165 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1972,plain,
! [SV5: $i,SV166: $i,SV309: $i,SV403: $i,SV495: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV495 @ SV403 ) @ ( c_Product__Type_OPair @ SV495 @ SV403 @ SV309 @ SV166 ) @ SV5 ) )
= $true )
| ( ( c_member @ SV403 @ SV166 @ ( c_Relation_ORange @ SV495 @ SV403 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1973,plain,
! [SV6: $i,SV167: $i,SV310: $i,SV404: $i] :
( ( ( SV404 = SV310 )
= $false )
| ( ( ~ ( c_member @ SV167 @ SV404 @ SV6 )
| ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SV404 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1974,plain,
! [SV7: $i,SV168: $i,SV311: $i,SV405: $i,SV496: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV496 @ SV405 ) @ ( c_Product__Type_OPair @ SV496 @ SV405 @ SV311 @ SV168 ) @ SV7 ) )
= $true )
| ( ( c_member @ SV496 @ SV311 @ ( c_Relation_ODomain @ SV496 @ SV405 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1975,plain,
! [SV8: $i,SV169: $i,SV312: $i,SV406: $i] :
( ( ( c_Relation_Otrans @ SV406 @ SV312 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV169 @ SV8 )
| ( c_Relation_Otrans @ ( tc_prod @ SV406 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SV406 @ SV169 @ SV312 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1976,plain,
! [SV10: $i,SV171: $i,SV313: $i,SV407: $i] :
( ( ( c_Relation_Otrans @ SV407 @ SV313 )
= $false )
| ( ( c_Relation_Otrans @ SV171 @ ( hAPP @ ( c_Relation_Oinv__image @ SV407 @ SV171 @ SV313 ) @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1977,plain,
! [SV11: $i,SV172: $i,SV314: $i,SV408: $i] :
( ( ( c_member @ SV408 @ SV314 @ ( c_Relation_ORange @ SV172 @ SV408 @ SV11 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV172 @ SV408 ) @ ( c_Product__Type_OPair @ SV172 @ SV408 @ ( sK63_B_x @ SV408 @ SV314 @ SV172 @ SV11 ) @ SV314 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1978,plain,
! [SV12: $i,SV173: $i,SV315: $i,SV409: $i] :
( ( ( c_member @ SV409 @ SV315 @ ( c_Relation_ODomain @ SV409 @ SV173 @ SV12 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV409 @ SV173 ) @ ( c_Product__Type_OPair @ SV409 @ SV173 @ SV315 @ ( sK62_B_y @ SV409 @ SV315 @ SV173 @ SV12 ) ) @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1979,plain,
! [SV13: $i,SV174: $i,SV316: $i,SV410: $i] :
( ( ( c_member @ SV410 @ SV316 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV410 @ SV410 ) @ ( c_Product__Type_OPair @ SV410 @ SV410 @ SV13 @ SV316 ) @ SV174 )
| ( c_member @ SV410 @ SV13 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1980,plain,
! [SV14: $i,SV175: $i,SV317: $i,SV411: $i] :
( ( ( c_Relation_Orefl__on @ SV411 @ SV317 @ SV175 )
= $false )
| ( ( ~ ( c_member @ SV411 @ SV14 @ SV317 )
| ( c_member @ ( tc_prod @ SV411 @ SV411 ) @ ( c_Product__Type_OPair @ SV411 @ SV411 @ SV14 @ SV14 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1981,plain,
! [SV15: $i,SV176: $i,SV318: $i,SV412: $i,SV497: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV497 @ SV412 @ SV318 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV497 @ SV497 ) @ ( c_Product__Type_OPair @ SV497 @ SV497 @ SV176 @ SV15 ) @ SV318 )
| ( c_member @ SV497 @ SV176 @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1982,plain,
! [SV16: $i,SV177: $i,SV319: $i,SV413: $i,SV498: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV498 @ SV413 @ SV319 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV498 @ SV498 ) @ ( c_Product__Type_OPair @ SV498 @ SV498 @ SV177 @ SV16 ) @ SV319 )
| ( c_member @ SV498 @ SV16 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1983,plain,
! [SV17: $i,SV178: $i,SV320: $i,SV414: $i] :
( ( ( c_member @ ( tc_prod @ SV414 @ SV414 ) @ ( c_Product__Type_OPair @ SV414 @ SV414 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SV414 @ SV17 ) )
= $false )
| ( ( ~ ( c_member @ SV414 @ SV178 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
| ( c_member @ SV414 @ SV320 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1984,plain,
! [SV18: $i,SV179: $i,SV321: $i,SV415: $i] :
( ( ( c_member @ SV415 @ SV321 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV415 @ SV415 ) @ ( c_Product__Type_OPair @ SV415 @ SV415 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SV415 @ SV179 ) )
| ( c_member @ SV415 @ SV18 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1985,plain,
! [SV19: $i,SV180: $i,SV322: $i,SV416: $i,SV499: $i,SV569: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
| ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
| ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(1986,plain,
! [SV20: $i,SV181: $i,SV323: $i,SV417: $i,SV500: $i,SV570: $i] :
( ( ( c_Product__Type_Ocurry @ SV570 @ SV500 @ SV417 @ SV323 @ SV181 @ SV20 )
= ( hAPP @ SV323 @ ( c_Product__Type_OPair @ SV570 @ SV500 @ SV181 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1987,plain,
! [SV23: $i,SV184: $i,SV326: $i,SV418: $i,SV501: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1988,plain,
! [SV24: $i,SV185: $i,SV327: $i,SV419: $i,SV502: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV327 ) @ SV185 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
| ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1989,plain,
! [SV25: $i,SV186: $i,SV328: $i,SV420: $i,SV503: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV328 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1990,plain,
! [SV26: $i,SV187: $i,SV329: $i,SV421: $i,SV504: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
| ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1991,plain,
! [SV28: $i,SV189: $i,SV330: $i,SV422: $i] :
( ( ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Otrancl @ SV422 @ SV28 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV422 @ SV422 ) @ ( c_Product__Type_OPair @ SV422 @ SV422 @ SV330 @ SV189 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1992,plain,
! [SV29: $i,SV190: $i,SV331: $i,SV423: $i,SV505: $i,SV571: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV571 @ SV571 ) @ ( c_Product__Type_OPair @ SV571 @ SV571 @ SV505 @ SV423 ) @ SV331 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV571 @ SV190 @ SV29 @ SV331 @ SV423 ) @ SV505 )
= ( hAPP @ SV29 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1993,plain,
! [SV30: $i,SV191: $i,SV332: $i,SV424: $i] :
( ( ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ SV30 )
= $false )
| ( ( c_member @ ( tc_prod @ SV424 @ SV424 ) @ ( c_Product__Type_OPair @ SV424 @ SV424 @ SV332 @ SV191 ) @ ( c_Transitive__Closure_Otrancl @ SV424 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1994,plain,
! [SV34: $i,SV195: $i,SV334: $i,SV425: $i,SV506: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV334 ) @ SV195 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV334 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SV506 @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1995,plain,
! [SV35: $i,SV196: $i,SV335: $i,SV426: $i,SV507: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV335 ) @ SV196 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
| ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1996,plain,
! [SV36: $i,SV197: $i,SV336: $i,SV427: $i,SV508: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV336 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1997,plain,
! [SV37: $i,SV198: $i,SV337: $i,SV428: $i,SV509: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
| ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1998,plain,
! [SV38: $i,SV199: $i,SV338: $i,SV429: $i,SV510: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV338 ) @ SV199 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SV510 @ SV199 ) )
| ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SV510 @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1999,plain,
! [SV39: $i,SV200: $i,SV339: $i,SV430: $i,SV511: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SV511 @ SV200 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV339 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SV511 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2000,plain,
! [SV40: $i,SV201: $i,SV340: $i,SV431: $i,SV512: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SV512 @ SV201 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2001,plain,
! [SV41: $i,SV202: $i,SV341: $i,SV432: $i,SV513: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SV513 @ SV202 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
| ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2002,plain,
! [SV514: $i,SV42: $i,SV572: $i,SV203: $i,SV342: $i,SV433: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV433 @ SV433 ) @ ( c_Product__Type_OPair @ SV433 @ SV433 @ SV342 @ SV203 ) @ SV572 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV433 @ SV42 @ SV514 @ SV572 @ SV203 ) @ SV342 )
= ( hAPP @ SV514 @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2003,plain,
! [SV343: $i,SV43: $i,SV204: $i,SV434: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ SV204 @ SV43 ) @ SV343 ) )
= $true )
| ( ( ( SV204 != SV43 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SV434 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2004,plain,
! [SV48: $i,SV208: $i,SV344: $i,SV435: $i] :
( ( ( c_Relation_Oantisym @ SV435 @ SV344 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
| ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2005,plain,
! [SV49: $i,SV209: $i,SV345: $i,SV436: $i] :
( ( ( c_member @ SV436 @ SV345 @ ( c_Set_Oinsert @ SV436 @ SV209 @ SV49 ) )
= $false )
| ( ( ( SV345 = SV209 )
| ( c_member @ SV436 @ SV345 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2006,plain,
! [SV53: $i,SV213: $i,SV349: $i,SV439: $i] :
( ( ( c_member @ SV439 @ SV349 @ SV213 )
= $false )
| ( ( c_member @ SV439 @ SV349 @ ( c_Set_Oinsert @ SV439 @ SV53 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2007,plain,
! [SV55: $i,SV215: $i,SV351: $i,SV440: $i] :
( ( ( c_Wellfounded_Owf @ SV440 @ SV351 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV215 @ SV55 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV440 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SV440 @ SV215 @ SV351 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2008,plain,
! [SV216: $i,SV56: $i,SV352: $i] :
( ( ( c_member @ ( tc_prod @ SV352 @ SV352 ) @ ( c_Product__Type_OPair @ SV352 @ SV352 @ SV56 @ SV56 ) @ SV216 )
= $false )
| ( ( c_Wellfounded_Owf @ SV352 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2009,plain,
! [SV57: $i,SV217: $i,SV353: $i,SV441: $i] :
( ( ( c_Wellfounded_Owf @ SV441 @ SV353 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 )
| ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(2010,plain,
! [SV58: $i,SV218: $i,SV354: $i,SV442: $i] :
( ( ( c_Wellfounded_Owf @ SV442 @ SV354 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 )
| ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(2011,plain,
! [SV219: $i,SV59: $i,SV355: $i] :
( ( ( c_member @ ( tc_prod @ SV355 @ SV355 ) @ ( c_Product__Type_OPair @ SV355 @ SV355 @ SV59 @ SV59 ) @ SV219 )
= $false )
| ( ( c_Wellfounded_Owf @ SV355 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2012,plain,
! [SV62: $i,SV222: $i,SV357: $i,SV443: $i,SV517: $i,SV573: $i] :
( ( ~ ( c_member @ SV573 @ SV517 @ SV443 )
| ~ ( c_member @ ( tc_prod @ SV573 @ SV357 ) @ ( c_Product__Type_OPair @ SV573 @ SV357 @ SV517 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SV573 @ SV357 @ SV62 @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2013,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i,SV574: $i] :
( ( ! [SY2078: $i,SY2079: $i] :
( ~ ( c_member @ ( tc_prod @ SY2079 @ SY2078 ) @ ( c_Product__Type_OPair @ SY2079 @ SY2078 @ SV574 @ SV518 ) @ SV444 )
| ~ ( c_member @ ( tc_prod @ SY2078 @ SV358 ) @ ( c_Product__Type_OPair @ SY2078 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY2079 @ SV358 ) @ ( c_Product__Type_OPair @ SY2079 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SY2079 @ SY2078 @ SV358 @ SV444 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2014,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i,SV575: $i] :
( ( ! [SY2080: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2080 @ SV575 ) )
| ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SY2080 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2015,plain,
! [SV69: $i,SV229: $i,SV360: $i,SV446: $i,SV520: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV520 @ ( c_Product__Type_OPair @ SV446 @ SV360 @ SV229 @ SV69 ) ) ) )
= $true )
| ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV446 @ SV360 @ tc_HOL_Obool @ SV520 @ SV229 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2016,plain,
! [SV70: $i,SV230: $i,SV361: $i,SV447: $i,SV521: $i] :
( ( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV521 @ SV447 @ tc_HOL_Obool @ SV361 @ SV230 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Product__Type_OPair @ SV521 @ SV447 @ SV230 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2017,plain,
! [SV71: $i,SV231: $i,SV362: $i,SV448: $i,SV522: $i] :
( ( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV522 @ SV448 @ tc_HOL_Obool @ SV362 @ SV231 @ SV71 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV362 @ ( c_Product__Type_OPair @ SV522 @ SV448 @ SV231 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2018,plain,
! [SV84: $i,SV242: $i,SV365: $i,SV450: $i] :
( ( ( c_Wellfounded_Owf @ SV450 @ SV365 )
= $false )
| ( ( c_Wellfounded_Owf @ SV242 @ ( hAPP @ ( c_Relation_Oinv__image @ SV450 @ SV242 @ SV365 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2019,plain,
! [SV88: $i,SV246: $i,SV366: $i,SV451: $i,SV523: $i,SV576: $i] :
( ( ( SV576
!= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) )
| ~ ( c_Wellfounded_Owf @ SV523 @ SV366 )
| ( ( hAPP @ SV576 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SV576 @ SV366 @ SV88 ) ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2020,plain,
! [SV89: $i,SV247: $i,SV367: $i,SV452: $i,SV524: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV524 @ SV452 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SV524 @ SV367 @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV452 @ SV89 ) ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2021,plain,
! [SV368: $i,SV90: $i,SV453: $i,SV248: $i] :
( ( ( c_Wellfounded_Owf @ SV248 @ SV453 )
= $false )
| ( ( ! [SY1920: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SY1920 )
= ( hAPP @ ( hAPP @ SV368 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SV453 @ SY1920 ) ) @ SY1920 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2022,plain,
! [SV370: $i,SV101: $i,SV255: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV101 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2023,plain,
! [SV256: $i,SV102: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV102 @ SV256 )
= $false )
| ( ( SV256 = SV102 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV256 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2024,plain,
! [SV454: $i,SV525: $i] :
( ( ( ~ ( ~ ( c_member @ SV525 @ ( sK31_SY722 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
| ~ ! [SY2021: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ SY2021 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SY2021 @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(2025,plain,
! [SV455: $i,SV526: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV526 @ SV455 ) )
= $true )
| ( ( ! [SY2022: $i] :
( ! [SY2023: $i] :
~ ( c_member @ SV526 @ SY2023 @ SY2022 )
| ~ ( ~ ! [SY2024: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2024 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2024 @ SY2022 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) @ SY2022 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2026,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2027,plain,
! [SV107: $i,SV528: $i,SV578: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
| ! [SY2081: $i,SY2082: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2082 ) @ SV107 )
| ! [SY2083: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2083 ) @ SV107 )
| ( SY2082 = SY2083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2028,plain,
! [SV261: $i,SV108: $i,SV372: $i] :
( ( ! [SY1787: $i,SY1788: $i] :
( ! [SY1789: $i] :
( ~ ( c_member @ SV372 @ SY1789 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1788 ) @ ( c_Product__Type_OPair @ SV372 @ SY1788 @ SY1789 @ SY1787 ) @ SV261 ) )
| ( c_member @ SY1788 @ SY1787 @ ( c_Relation_OImage @ SV372 @ SY1788 @ SV261 @ SV108 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(2029,plain,
! [SV108: $i,SV261: $i,SV372: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ~ ( c_member @ SY1791 @ SY1790 @ ( c_Relation_OImage @ SV372 @ SY1791 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY1791 ) @ ( c_Product__Type_OPair @ SV372 @ SY1791 @ ( sK24_B_x @ SY1791 @ SY1790 @ SV372 @ SV261 @ SV108 ) @ SY1790 ) @ SV261 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(2030,plain,
! [SV109: $i,SV262: $i] :
( ( ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK70_SY736 @ SV262 @ SV109 ) ) @ SV109 )
= $true )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(2031,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(2032,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) )
| ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) )
| ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2033,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ~ ! [SY1937: $i,SY1938: $i] :
( ! [SY1939: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1938 @ SY1938 ) @ ( c_Product__Type_OPair @ SY1938 @ SY1938 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY1939 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY1939 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(2034,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ~ ! [SY1940: $i,SY1941: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1942: $i] :
( ~ ( c_member @ ( tc_prod @ SY1941 @ SY1941 ) @ ( c_Product__Type_OPair @ SY1941 @ SY1941 @ SY1942 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SY1942 @ ( hAPP @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY1942 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(2035,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV580 @ SV580 ) @ ( c_Product__Type_OPair @ SV580 @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ SV530 ) @ SV112 )
| ~ ~ ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) )
| ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2036,plain,
! [SV112: $i,SV531: $i,SV581: $i] :
( ( ~ ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
| ! [SY2092: $i] :
( ~ ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SY2092 @ SV531 ) @ SV112 )
| ( c_member @ SV581 @ SY2092 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2037,plain,
! [SV113: $i,SV265: $i,SV375: $i,SV458: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV458 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2038,plain,
! [SV114: $i,SV582: $i,SV266: $i] :
( ( ! [SY2093: $i] :
( ! [SY2094: $i] :
~ ( c_member @ ( tc_prod @ SY2093 @ SV266 ) @ ( c_Product__Type_OPair @ SY2093 @ SV266 @ SV582 @ SY2094 ) @ SV114 )
| ( c_member @ SY2093 @ SV582 @ ( c_Relation_ODomain @ SY2093 @ SV266 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2039,plain,
! [SV114: $i,SV266: $i,SV583: $i] :
( ( ! [SY2095: $i] :
( ~ ( c_member @ SY2095 @ SV583 @ ( c_Relation_ODomain @ SY2095 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SY2095 @ SV266 ) @ ( c_Product__Type_OPair @ SY2095 @ SV266 @ SV583 @ ( sK66_B_y @ SY2095 @ SV583 @ SV266 @ SV114 ) ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2040,plain,
! [SV459: $i,SV532: $i] :
( ( ( c_member @ ( tc_prod @ SV532 @ SV532 ) @ ( c_Product__Type_OPair @ SV532 @ SV532 @ ( sK40_B_x @ SV532 @ SV459 ) @ ( sK40_B_x @ SV532 @ SV459 ) ) @ ( c_Transitive__Closure_Otrancl @ SV532 @ SV459 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV532 @ SV459 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2041,plain,
! [SV460: $i,SV533: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV533 @ SV460 ) )
= $true )
| ( ( ! [SY2042: $i] :
~ ( c_member @ ( tc_prod @ SV533 @ SV533 ) @ ( c_Product__Type_OPair @ SV533 @ SV533 @ SY2042 @ SY2042 ) @ ( c_Transitive__Closure_Otrancl @ SV533 @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2042,plain,
! [SV584: $i,SV267: $i,SV115: $i] :
( ( ! [SY2096: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2096 @ SV115 )
| ( c_member @ ( tc_prod @ SY2096 @ SY2096 ) @ ( c_Product__Type_OPair @ SY2096 @ SY2096 @ SV267 @ SV584 ) @ ( c_Transitive__Closure_Ortrancl @ SY2096 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY2096 @ ( c_Set_Oinsert @ ( tc_prod @ SY2096 @ SY2096 ) @ ( c_Product__Type_OPair @ SY2096 @ SY2096 @ SV584 @ SV267 ) @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2043,plain,
! [SV115: $i,SV267: $i] :
( ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) )
| ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2044,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i] :
( ( ! [SY2097: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2097 @ SV585 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ ( sK46_B_a @ SY2097 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY2097 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2097 @ SV585 ) @ ( tc_prod @ SY2097 @ SV585 ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ ( sK46_B_a @ SY2097 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SY2097 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SY2097 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2097 @ SV585 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2045,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ~ ( ~ ( c_member @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) )
| ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2046,plain,
! [SV117: $i,SV536: $i,SV587: $i] :
( ( ~ ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
| ! [SY2098: $i] :
( ~ ( c_member @ SV587 @ SY2098 @ SV536 )
| ! [SY2099: $i] :
( ~ ( c_member @ SV587 @ SY2099 @ SV536 )
| ( SY2098 = SY2099 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2098 @ SY2099 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2099 @ SY2098 ) @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2047,plain,
! [SV462: $i,SV537: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV537 @ SV537 ) @ ( c_Product__Type_OPair @ SV537 @ SV537 @ ( sK76_B_x @ SV537 @ SV462 ) @ ( sK76_B_x @ SV537 @ SV462 ) ) @ SV462 ) )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV537 @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2048,plain,
! [SV463: $i,SV538: $i] :
( ( ( ~ ( c_Nitpick_Orefl_H @ SV538 @ SV463 ) )
= $true )
| ( ( ! [SY2049: $i] : ( c_member @ ( tc_prod @ SV538 @ SV538 ) @ ( c_Product__Type_OPair @ SV538 @ SV538 @ SY2049 @ SY2049 ) @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2049,plain,
! [SV118: $i,SV269: $i,SV377: $i,SV464: $i,SV539: $i] :
( ( ( ~ ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2050,plain,
! [SV119: $i,SV270: $i,SV588: $i] :
( ( ! [SY2100: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2100 @ SV588 @ SV270 ) @ SV119 ) )
| ( SV588 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2051,plain,
! [SV270: $i,SV119: $i] :
( ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2052,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ~ ( ( SV465 != SV271 )
| ( SV378 != SV120 )
| ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(2053,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ~ ~ ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
| ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(2054,plain,
! [SV121: $i,SV540: $i] :
( ( ( ( SV540 != SV121 ) )
= $true )
| ( ( ! [SY2050: $i] : ( c_member @ SY2050 @ SV540 @ ( c_fequal @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2055,plain,
! [SV121: $i,SV541: $i] :
( ( ( ! [SY2051: $i] :
~ ( c_member @ SY2051 @ SV541 @ ( c_fequal @ SV121 ) ) )
= $true )
| ( ( SV541 = SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2056,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) )
| ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2057,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) )
| ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2058,plain,
! [SV466: $i,SV542: $i] :
( ( ( SV542 = SV466 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV542 @ SV466 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV466 @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2059,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(2060,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2061,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV589 @ SV123 )
| ~ ( c_Relation_Otrans @ SV589 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2062,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2063,plain,
! [SV123: $i] :
( ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2064,plain,
! [SV124: $i,SV544: $i,SV590: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV590 @ ( sK75_B_x1 @ SV590 @ SV544 @ SV124 ) ) )
| ! [SY2101: $i,SY2102: $i] : ( hBOOL @ ( hAPP @ SV590 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SY2101 @ SY2102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2065,plain,
! [SV124: $i,SV545: $i,SV591: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_Product__Type_OPair @ SV545 @ SV124 @ ( sK73_B_a @ SV591 @ SV545 @ SV124 ) @ ( sK74_SY739 @ SV591 @ SV545 @ SV124 ) ) ) )
| ! [SY2103: $i] : ( hBOOL @ ( hAPP @ SV591 @ SY2103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2066,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2067,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2068,plain,
( ( sK4_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2069,plain,
( ( ~ sK4_REN
| ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(2070,plain,
! [SV467: $i,SV546: $i] :
( ( ( c_member @ ( tc_prod @ SV546 @ SV546 ) @ ( c_Product__Type_OPair @ SV546 @ SV546 @ ( sK72_B_x @ SV546 @ SV467 ) @ ( sK72_B_x @ SV546 @ SV467 ) ) @ SV467 )
= $true )
| ( ( c_Relation_Oirrefl @ SV546 @ SV467 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2071,plain,
! [SV468: $i,SV547: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV547 @ SV468 ) )
= $true )
| ( ( ! [SY2058: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV547 ) @ ( c_Product__Type_OPair @ SV547 @ SV547 @ SY2058 @ SY2058 ) @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2072,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK78_SY740 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2073,plain,
! [SV470: $i,SV549: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV549 @ SV470 ) )
= $true )
| ( ( ! [SY2059: $i,SY2060: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2060 ) @ SV470 )
| ! [SY2061: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2060 @ SY2061 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2061 ) @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2074,plain,
! [SV125: $i,SV273: $i,SV592: $i] :
( ( ! [SY2104: $i] :
( ( SV592 != SV273 )
| ~ ( c_member @ SY2104 @ SV592 @ SV125 )
| ( c_member @ ( tc_prod @ SY2104 @ SY2104 ) @ ( c_Product__Type_OPair @ SY2104 @ SY2104 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SY2104 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2075,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) )
| ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2076,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false )
| ( ( ( SV379 = SV274 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2077,plain,
! [SV127: $i,SV275: $i,SV593: $i] :
( ( ! [SY2105: $i] :
( ( c_member @ SY2105 @ SV593 @ SV275 )
| ( c_member @ SY2105 @ SV593 @ SV127 )
| ( ( c_Set_Oinsert @ SY2105 @ SV593 @ SV275 )
!= ( c_Set_Oinsert @ SY2105 @ SV593 @ SV127 ) )
| ( SV275 = SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2078,plain,
! [SV127: $i,SV275: $i,SV594: $i] :
( ( ! [SY2106: $i] :
( ( c_member @ SY2106 @ SV594 @ SV275 )
| ( c_member @ SY2106 @ SV594 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SY2106 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SY2106 @ SV594 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2079,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2080,plain,
! [SV129: $i,SV277: $i,SV595: $i] :
( ( ! [SY2107: $i] :
( ( c_member @ SY2107 @ SV595 @ ( c_Relation_ODomain @ SY2107 @ SY2107 @ SV277 ) )
| ( SV595 != SV129 )
| ( c_member @ ( tc_prod @ SY2107 @ SY2107 ) @ ( c_Product__Type_OPair @ SY2107 @ SY2107 @ SV595 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY2107 @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2081,plain,
! [SV129: $i,SV277: $i,SV596: $i] :
( ( ! [SY2108: $i] :
( ( c_member @ SY2108 @ SV596 @ ( c_Relation_ODomain @ SY2108 @ SY2108 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SY2108 @ SY2108 ) @ ( c_Product__Type_OPair @ SY2108 @ SY2108 @ SV596 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SY2108 @ SV277 ) )
| ( SV596 = SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2082,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ~ ( ! [SY1968: $i,SY1969: $i] :
( ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV278 @ SV130 ) )
| ( SV473 = SV278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2083,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ~ ( ! [SY1970: $i,SY1971: $i] :
( ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV278 @ SV130 ) )
| ( SV381 = SV130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2084,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i] :
( ( ! [SY2109: $i,SY2110: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2110 @ SY2109 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ ( sK18_B_a @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2110 @ SY2109 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2110 @ SY2109 ) @ ( tc_prod @ SY2110 @ SY2109 ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ ( sK18_B_a @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY2110 @ SY2109 @ ( sK20_SY717 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY2110 @ SY2109 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2085,plain,
! [SV132: $i,SV598: $i,SV280: $i] :
( ( ! [SY2111: $i] :
( ! [SY2112: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SY2111 ) @ ( c_Product__Type_OPair @ SV280 @ SY2111 @ SY2112 @ SV598 ) @ SV132 )
| ( c_member @ SY2111 @ SV598 @ ( c_Relation_ORange @ SV280 @ SY2111 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2086,plain,
! [SV132: $i,SV280: $i,SV599: $i] :
( ( ! [SY2113: $i] :
( ~ ( c_member @ SY2113 @ SV599 @ ( c_Relation_ORange @ SV280 @ SY2113 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SY2113 ) @ ( c_Product__Type_OPair @ SV280 @ SY2113 @ ( sK65_B_y @ SY2113 @ SV599 @ SV280 @ SV132 ) @ SV599 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2087,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ~ ! [SY1976: $i,SY1977: $i] :
( ! [SY1978: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1977 @ SY1977 ) @ ( c_Product__Type_OPair @ SY1977 @ SY1977 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY1978 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY1978 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2088,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ~ ! [SY1979: $i,SY1980: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1981: $i] :
( ~ ( c_member @ ( tc_prod @ SY1980 @ SY1980 ) @ ( c_Product__Type_OPair @ SY1980 @ SY1980 @ SY1981 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SY1981 @ ( hAPP @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY1981 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2089,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2090,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i] :
( ( ~ ! [SY1982: $i] :
( ! [SY1983: $i] :
~ ( c_member @ ( tc_prod @ SY1983 @ SY1983 ) @ ( c_Product__Type_OPair @ SY1983 @ SY1983 @ SY1982 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1983 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1982 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2091,plain,
! [SV283: $i,SV477: $i,SV135: $i,SV385: $i] :
( ( ~ ! [SY1984: $i] :
( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1984 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
| ! [SY1985: $i] : ( c_member @ ( tc_prod @ SY1985 @ SY1985 ) @ ( c_Product__Type_OPair @ SY1985 @ SY1985 @ SY1984 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1985 @ SV283 ) @ SV135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2092,plain,
! [SV136: $i,SV551: $i] :
( ( ( ! [SY2065: $i] :
~ ( c_member @ SY2065 @ SV551 @ SV136 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2093,plain,
! [SV552: $i,SV136: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV136 @ SV552 ) ) )
= $true )
| ( ( ! [SY2066: $i] : ( c_member @ SY2066 @ SV552 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2094,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i] :
( ( ! [SY2114: $i,SY2115: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2115 @ SY2114 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ ( sK14_B_a @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ ( sK16_SY711 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2115 @ SY2114 ) @ ( tc_prod @ SY2115 @ SY2114 ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ ( sK16_SY711 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2115 @ SY2114 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2115 @ SY2114 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY2115 @ SY2114 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2095,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i,SV601: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV601 @ SV601 ) @ ( c_Product__Type_OPair @ SV601 @ SV601 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2096,plain,
! [SV139: $i,SV555: $i] :
( ( ( ( SV555 != SV139 ) )
= $true )
| ( ( ! [SY2071: $i] : ( c_member @ ( tc_prod @ SY2071 @ SY2071 ) @ ( c_Product__Type_OPair @ SY2071 @ SY2071 @ SV555 @ SV139 ) @ ( c_Relation_OId @ SY2071 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2097,plain,
! [SV139: $i,SV556: $i] :
( ( ( ! [SY2072: $i] :
~ ( c_member @ ( tc_prod @ SY2072 @ SY2072 ) @ ( c_Product__Type_OPair @ SY2072 @ SY2072 @ SV556 @ SV139 ) @ ( c_Relation_OId @ SY2072 ) ) )
= $true )
| ( ( SV556 = SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2098,plain,
! [SV480: $i,SV557: $i] :
( ( ( ~ ( c_member @ SV557 @ ( sK32_B_x @ SV557 @ SV480 ) @ ( c_Wellfounded_Oacc @ SV557 @ SV480 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV557 @ SV480 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2099,plain,
! [SV481: $i,SV558: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV558 @ SV481 ) )
= $true )
| ( ( ! [SY2073: $i] : ( c_member @ SV558 @ SY2073 @ ( c_Wellfounded_Oacc @ SV558 @ SV481 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2100,plain,
! [SV140: $i,SV286: $i,SV602: $i] :
( ( ! [SY2116: $i] :
( ( SY2116 != SV602 )
| ~ ( c_member @ SV286 @ SV140 @ SY2116 )
| ( c_member @ SV286 @ SV140 @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2101,plain,
! [SV140: $i,SV286: $i,SV603: $i] :
( ( ! [SY2117: $i] :
( ( SY2117 != SV603 )
| ~ ( c_member @ SV286 @ SV140 @ SV603 )
| ( c_member @ SV286 @ SV140 @ SY2117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2102,plain,
! [SV141: $i,SV287: $i,SV604: $i] :
( ( ! [SY2118: $i] :
( ( SY2118 != SV604 )
| ~ ( c_member @ SV287 @ SY2118 @ SV141 )
| ( c_member @ SV287 @ SV604 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2103,plain,
! [SV141: $i,SV287: $i,SV605: $i] :
( ( ! [SY2119: $i] :
( ( SY2119 != SV605 )
| ~ ( c_member @ SV287 @ SV605 @ SV141 )
| ( c_member @ SV287 @ SY2119 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2104,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SV388 @ SV288 @ SV142 ) ) @ SV142 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2105,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2106,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2107,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2108,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2109,plain,
! [SV143: $i] :
( ( ~ ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2110,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2111,plain,
! [SV606: $i,SV290: $i,SV145: $i] :
( ( ! [SY2120: $i] :
( ~ ( c_Wellfounded_Owf @ SY2120 @ SV145 )
| ( c_member @ ( tc_prod @ SY2120 @ SY2120 ) @ ( c_Product__Type_OPair @ SY2120 @ SY2120 @ SV290 @ SV606 ) @ ( c_Transitive__Closure_Ortrancl @ SY2120 @ SV145 ) )
| ( c_Wellfounded_Owf @ SY2120 @ ( c_Set_Oinsert @ ( tc_prod @ SY2120 @ SY2120 ) @ ( c_Product__Type_OPair @ SY2120 @ SY2120 @ SV606 @ SV290 ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2112,plain,
! [SV145: $i,SV290: $i] :
( ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) )
| ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2113,plain,
! [SV146: $i,SV559: $i,SV607: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV607 @ SV559 @ SV146 )
| ~ ( c_Relation_Otrans @ SV607 @ SV146 )
| ( c_Order__Relation_Opreorder__on @ SV607 @ SV559 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2114,plain,
! [SV146: $i] :
( ( ~ ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2115,plain,
! [SV146: $i] :
( ( ~ ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2116,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ( ~ ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 )
| ( SV291
!= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2117,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) )
| ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2118,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) )
| ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2119,plain,
! [SV149: $i,SV293: $i,SV608: $i] :
( ( ! [SY2121: $i] :
( ~ ( c_member @ SY2121 @ SV608 @ ( c_Set_Oinsert @ SY2121 @ SV293 @ SV149 ) )
| ( SV608 = SV293 )
| ( c_member @ SY2121 @ SV608 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2120,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2121,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2122,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV392 @ SV392 ) @ ( c_Product__Type_OPair @ SV392 @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ SV295 ) @ SV151 ) )
= $false )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2123,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( ~ ~ ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) ) )
= $false )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2124,plain,
! [SV393: $i,SV152: $i,SV296: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( c_member @ ( tc_prod @ SY1861 @ SY1860 ) @ ( c_Product__Type_OPair @ SY1861 @ SY1860 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1861 @ SY1860 @ SV393 ) @ SV296 ) @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2125,plain,
! [SV152: $i,SV296: $i,SV393: $i] :
( ( ! [SY1862: $i,SY1863: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY1863 @ SY1862 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY1863 @ SY1862 ) @ ( c_Product__Type_OPair @ SY1863 @ SY1862 @ SV296 @ SV152 ) @ SV393 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2126,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false )
| ( ( ( SV394 = SV297 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2127,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2128,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2129,plain,
! [SV487: $i,SV562: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV562 @ SV487 ) )
= $true )
| ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV562 @ SV487 ) @ c_Wellfounded_Oless__than )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2130,plain,
! [SV488: $i,SV563: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV563 @ SV488 ) @ c_Wellfounded_Oless__than ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV563 @ SV488 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2131,plain,
! [SV156: $i,SV300: $i,SV609: $i] :
( ( ! [SY2122: $i] :
~ ( c_member @ ( tc_prod @ SY2122 @ SY2122 ) @ ( c_Product__Type_OPair @ SY2122 @ SY2122 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY2122 @ SV156 ) )
| ( SV609 != SV300 )
| ( SV609 = SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2132,plain,
! [SV156: $i,SV300: $i,SV610: $i] :
( ( ! [SY2123: $i] :
( ~ ( c_member @ ( tc_prod @ SY2123 @ SY2123 ) @ ( c_Product__Type_OPair @ SY2123 @ SY2123 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY2123 @ SV156 ) )
| ( c_member @ ( tc_prod @ SY2123 @ SY2123 ) @ ( c_Product__Type_OPair @ SY2123 @ SY2123 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SY2123 @ SV156 ) )
| ( SV610 = SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2133,plain,
! [SV157: $i,SV301: $i,SV611: $i] :
( ( ! [SY2124: $i] :
( ~ ( c_member @ SY2124 @ SV611 @ SV301 )
| ( c_member @ SY2124 @ SV611 @ ( c_Set_Oinsert @ SY2124 @ SV157 @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2134,plain,
! [SV301: $i,SV157: $i,SV612: $i] :
( ( ( SV612 != SV157 )
| ! [SY2125: $i] : ( c_member @ SY2125 @ SV612 @ ( c_Set_Oinsert @ SY2125 @ SV157 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2135,plain,
! [SV158: $i,SV302: $i] :
( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK26_B_x @ SV302 @ SV158 ) @ ( sK27_SY720 @ SV302 @ SV158 ) ) @ SV158 )
= $true )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2136,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2137,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK33_B_x @ SV564 @ SV489 ) @ ( sK34_SY725 @ SV564 @ SV489 ) ) @ SV489 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2138,plain,
! [SV490: $i,SV565: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV565 @ SV490 ) )
= $true )
| ( ( ! [SY2075: $i,SY2076: $i] :
( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2075 @ SY2076 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2076 @ SY2075 ) @ SV490 )
| ( SY2075 = SY2076 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2139,plain,
! [SV159: $i,SV566: $i,SV613: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV613 @ SV566 @ SV159 )
| ~ ( c_Relation_Oantisym @ SV613 @ SV159 )
| ( c_Order__Relation_Opartial__order__on @ SV613 @ SV566 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2140,plain,
! [SV159: $i] :
( ( ~ ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2141,plain,
! [SV159: $i] :
( ( ~ ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2142,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ~ ! [SY2003: $i,SY2004: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2004 @ SY2004 ) @ ( c_Product__Type_OPair @ SY2004 @ SY2004 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV160 @ SV397 @ SV303 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2143,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2007: $i] :
( ~ ( c_member @ ( tc_prod @ SY2006 @ SY2006 ) @ ( c_Product__Type_OPair @ SY2006 @ SY2006 @ SY2007 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2007 )
= ( hAPP @ SV160 @ SY2007 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2144,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV398 @ SV398 ) @ ( c_Product__Type_OPair @ SV398 @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ SV304 ) @ SV161 ) )
= $false )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2145,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( ~ ~ ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) )
= $false )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2146,plain,
! [SV1: $i,SV162: $i,SV305: $i,SV399: $i,SV492: $i] :
( ( ( c_Relation_Otrans @ SV492 @ SV399 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
| ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2147,plain,
! [SV400: $i,SV2: $i,SV306: $i,SV163: $i] :
( ( ( ~ ( c_member @ SV163 @ SV306 @ SV2 ) )
= $true )
| ( ( c_member @ SV163 @ SV400 @ SV2 )
= $true )
| ( ( SV400 = SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2148,plain,
! [SV5: $i,SV166: $i,SV309: $i,SV403: $i,SV495: $i] :
( ( ( c_member @ ( tc_prod @ SV495 @ SV403 ) @ ( c_Product__Type_OPair @ SV495 @ SV403 @ SV309 @ SV166 ) @ SV5 )
= $false )
| ( ( c_member @ SV403 @ SV166 @ ( c_Relation_ORange @ SV495 @ SV403 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2149,plain,
! [SV310: $i,SV6: $i,SV404: $i,SV167: $i] :
( ( ( ~ ( c_member @ SV167 @ SV404 @ SV6 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SV404 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) )
= $true )
| ( ( SV404 = SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2150,plain,
! [SV7: $i,SV168: $i,SV311: $i,SV405: $i,SV496: $i] :
( ( ( c_member @ ( tc_prod @ SV496 @ SV405 ) @ ( c_Product__Type_OPair @ SV496 @ SV405 @ SV311 @ SV168 ) @ SV7 )
= $false )
| ( ( c_member @ SV496 @ SV311 @ ( c_Relation_ODomain @ SV496 @ SV405 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2151,plain,
! [SV312: $i,SV406: $i,SV8: $i,SV169: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV169 @ SV8 ) )
= $true )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV406 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SV406 @ SV169 @ SV312 @ SV8 ) )
= $true )
| ( ( c_Relation_Otrans @ SV406 @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2152,plain,
! [SV174: $i,SV316: $i,SV13: $i,SV410: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV410 @ SV410 ) @ ( c_Product__Type_OPair @ SV410 @ SV410 @ SV13 @ SV316 ) @ SV174 ) )
= $true )
| ( ( c_member @ SV410 @ SV13 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
= $true )
| ( ( c_member @ SV410 @ SV316 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2153,plain,
! [SV175: $i,SV317: $i,SV14: $i,SV411: $i] :
( ( ( ~ ( c_member @ SV411 @ SV14 @ SV317 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV411 @ SV411 ) @ ( c_Product__Type_OPair @ SV411 @ SV411 @ SV14 @ SV14 ) @ SV175 )
= $true )
| ( ( c_Relation_Orefl__on @ SV411 @ SV317 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2154,plain,
! [SV15: $i,SV176: $i,SV318: $i,SV412: $i,SV497: $i] :
( ( ( c_Relation_Orefl__on @ SV497 @ SV412 @ SV318 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV497 @ SV497 ) @ ( c_Product__Type_OPair @ SV497 @ SV497 @ SV176 @ SV15 ) @ SV318 )
| ( c_member @ SV497 @ SV176 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2155,plain,
! [SV16: $i,SV177: $i,SV319: $i,SV413: $i,SV498: $i] :
( ( ( c_Relation_Orefl__on @ SV498 @ SV413 @ SV319 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV498 @ SV498 ) @ ( c_Product__Type_OPair @ SV498 @ SV498 @ SV177 @ SV16 ) @ SV319 )
| ( c_member @ SV498 @ SV16 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2156,plain,
! [SV320: $i,SV17: $i,SV178: $i,SV414: $i] :
( ( ( ~ ( c_member @ SV414 @ SV178 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) ) )
= $true )
| ( ( c_member @ SV414 @ SV320 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV414 @ SV414 ) @ ( c_Product__Type_OPair @ SV414 @ SV414 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SV414 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2157,plain,
! [SV179: $i,SV321: $i,SV18: $i,SV415: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV415 @ SV415 ) @ ( c_Product__Type_OPair @ SV415 @ SV415 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SV415 @ SV179 ) ) )
= $true )
| ( ( c_member @ SV415 @ SV18 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
= $true )
| ( ( c_member @ SV415 @ SV321 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2158,plain,
! [SV19: $i,SV180: $i,SV322: $i,SV416: $i,SV499: $i,SV569: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
| ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2159,plain,
! [SV23: $i,SV184: $i,SV326: $i,SV418: $i,SV501: $i] :
( ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2160,plain,
! [SV24: $i,SV185: $i,SV327: $i,SV419: $i,SV502: $i] :
( ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV327 ) @ SV185 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
| ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2161,plain,
! [SV25: $i,SV186: $i,SV328: $i,SV420: $i,SV503: $i] :
( ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV328 @ SV25 ) @ SV186 )
| ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2162,plain,
! [SV26: $i,SV187: $i,SV329: $i,SV421: $i,SV504: $i] :
( ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
| ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2163,plain,
! [SV29: $i,SV190: $i,SV331: $i,SV423: $i,SV505: $i,SV571: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV571 @ SV571 ) @ ( c_Product__Type_OPair @ SV571 @ SV571 @ SV505 @ SV423 ) @ SV331 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV571 @ SV190 @ SV29 @ SV331 @ SV423 ) @ SV505 )
= ( hAPP @ SV29 @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2164,plain,
! [SV34: $i,SV195: $i,SV334: $i,SV425: $i,SV506: $i] :
( ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV334 ) @ SV195 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV334 @ SV34 ) @ SV195 )
| ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SV506 @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2165,plain,
! [SV35: $i,SV196: $i,SV335: $i,SV426: $i,SV507: $i] :
( ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV335 ) @ SV196 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
| ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2166,plain,
! [SV36: $i,SV197: $i,SV336: $i,SV427: $i,SV508: $i] :
( ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV336 @ SV36 ) @ SV197 )
| ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2167,plain,
! [SV37: $i,SV198: $i,SV337: $i,SV428: $i,SV509: $i] :
( ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
| ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2168,plain,
! [SV38: $i,SV199: $i,SV338: $i,SV429: $i,SV510: $i] :
( ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV338 ) @ SV199 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SV510 @ SV199 ) )
| ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SV510 @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2169,plain,
! [SV39: $i,SV200: $i,SV339: $i,SV430: $i,SV511: $i] :
( ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SV511 @ SV200 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV339 @ SV39 ) @ SV200 )
| ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SV511 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2170,plain,
! [SV40: $i,SV201: $i,SV340: $i,SV431: $i,SV512: $i] :
( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SV512 @ SV201 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2171,plain,
! [SV41: $i,SV202: $i,SV341: $i,SV432: $i,SV513: $i] :
( ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SV513 @ SV202 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
| ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2172,plain,
! [SV514: $i,SV42: $i,SV572: $i,SV203: $i,SV342: $i,SV433: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV433 @ SV433 ) @ ( c_Product__Type_OPair @ SV433 @ SV433 @ SV342 @ SV203 ) @ SV572 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV433 @ SV42 @ SV514 @ SV572 @ SV203 ) @ SV342 )
= ( hAPP @ SV514 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2173,plain,
! [SV343: $i,SV43: $i,SV204: $i,SV434: $i] :
( ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ SV204 @ SV43 ) @ SV343 )
= $false )
| ( ( ( SV204 != SV43 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SV434 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2174,plain,
! [SV344: $i,SV48: $i,SV208: $i,SV435: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV435 @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2175,plain,
! [SV49: $i,SV436: $i,SV209: $i,SV345: $i] :
( ( ( SV345 = SV209 )
= $true )
| ( ( c_member @ SV436 @ SV345 @ SV49 )
= $true )
| ( ( c_member @ SV436 @ SV345 @ ( c_Set_Oinsert @ SV436 @ SV209 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2176,plain,
! [SV351: $i,SV440: $i,SV55: $i,SV215: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV215 @ SV55 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV440 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SV440 @ SV215 @ SV351 @ SV55 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV440 @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2177,plain,
! [SV353: $i,SV57: $i,SV217: $i,SV441: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV441 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2178,plain,
! [SV354: $i,SV58: $i,SV218: $i,SV442: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV442 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2179,plain,
! [SV62: $i,SV222: $i,SV357: $i,SV443: $i,SV517: $i,SV573: $i] :
( ( ( ~ ( c_member @ SV573 @ SV517 @ SV443 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV573 @ SV357 ) @ ( c_Product__Type_OPair @ SV573 @ SV357 @ SV517 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SV573 @ SV357 @ SV62 @ SV443 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2180,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i,SV574: $i,SV614: $i] :
( ( ! [SY2126: $i] :
( ~ ( c_member @ ( tc_prod @ SY2126 @ SV614 ) @ ( c_Product__Type_OPair @ SY2126 @ SV614 @ SV574 @ SV518 ) @ SV444 )
| ~ ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY2126 @ SV358 ) @ ( c_Product__Type_OPair @ SY2126 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SY2126 @ SV614 @ SV358 @ SV444 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2181,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i,SV575: $i,SV615: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV615 @ SV575 ) )
| ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SV615 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2182,plain,
! [SV69: $i,SV229: $i,SV360: $i,SV446: $i,SV520: $i] :
( ( ( hBOOL @ ( hAPP @ SV520 @ ( c_Product__Type_OPair @ SV446 @ SV360 @ SV229 @ SV69 ) ) )
= $false )
| ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV446 @ SV360 @ tc_HOL_Obool @ SV520 @ SV229 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2183,plain,
! [SV70: $i,SV230: $i,SV361: $i,SV447: $i,SV521: $i] :
( ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV521 @ SV447 @ tc_HOL_Obool @ SV361 @ SV230 @ SV70 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Product__Type_OPair @ SV521 @ SV447 @ SV230 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2184,plain,
! [SV71: $i,SV231: $i,SV362: $i,SV448: $i,SV522: $i] :
( ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV522 @ SV448 @ tc_HOL_Obool @ SV362 @ SV231 @ SV71 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV362 @ ( c_Product__Type_OPair @ SV522 @ SV448 @ SV231 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2185,plain,
! [SV88: $i,SV246: $i,SV366: $i,SV451: $i,SV523: $i,SV576: $i] :
( ( ( ( SV576
!= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV523 @ SV366 )
| ( ( hAPP @ SV576 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SV576 @ SV366 @ SV88 ) ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2186,plain,
! [SV89: $i,SV247: $i,SV367: $i,SV452: $i,SV524: $i] :
( ( ( c_Wellfounded_Owf @ SV524 @ SV452 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV89 )
= ( hAPP @ ( hAPP @ SV247 @ ( c_Recdef_Ocut @ SV524 @ SV367 @ ( c_Recdef_Owfrec @ SV524 @ SV367 @ SV452 @ SV247 ) @ SV452 @ SV89 ) ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2187,plain,
! [SV616: $i,SV368: $i,SV453: $i,SV90: $i,SV248: $i] :
( ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SV616 )
= ( hAPP @ ( hAPP @ SV368 @ ( c_Recdef_Ocut @ SV248 @ SV90 @ ( c_Recdef_Owfrec @ SV248 @ SV90 @ SV453 @ SV368 ) @ SV453 @ SV616 ) ) @ SV616 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV248 @ SV453 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2188,plain,
! [SV370: $i,SV101: $i,SV255: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV255 @ SV101 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV101 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV370 @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2189,plain,
! [SV454: $i,SV525: $i] :
( ( ( ~ ( c_member @ SV525 @ ( sK31_SY722 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
| ~ ! [SY2021: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ SY2021 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SY2021 @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2190,plain,
! [SV455: $i,SV526: $i] :
( ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false )
| ( ( ! [SY2022: $i] :
( ! [SY2023: $i] :
~ ( c_member @ SV526 @ SY2023 @ SY2022 )
| ~ ( ~ ! [SY2024: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2024 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2024 @ SY2022 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SY2022 @ SV526 @ SV455 ) @ SY2022 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2191,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2192,plain,
! [SV107: $i,SV528: $i,SV578: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 ) )
= $true )
| ( ( ! [SY2081: $i,SY2082: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2082 ) @ SV107 )
| ! [SY2083: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2083 ) @ SV107 )
| ( SY2082 = SY2083 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2193,plain,
! [SV261: $i,SV617: $i,SV108: $i,SV372: $i] :
( ( ! [SY2127: $i] :
( ! [SY2128: $i] :
( ~ ( c_member @ SV372 @ SY2128 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY2127 ) @ ( c_Product__Type_OPair @ SV372 @ SY2127 @ SY2128 @ SV617 ) @ SV261 ) )
| ( c_member @ SY2127 @ SV617 @ ( c_Relation_OImage @ SV372 @ SY2127 @ SV261 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2194,plain,
! [SV108: $i,SV261: $i,SV372: $i,SV618: $i] :
( ( ! [SY2129: $i] :
( ~ ( c_member @ SY2129 @ SV618 @ ( c_Relation_OImage @ SV372 @ SY2129 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SY2129 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SY2129 ) @ ( c_Product__Type_OPair @ SV372 @ SY2129 @ ( sK24_B_x @ SY2129 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2195,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
| ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2196,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ~ ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) )
| ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) )
| ~ ~ ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) )
| ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2197,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ! [SY1937: $i,SY1938: $i] :
( ! [SY1939: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1938 @ SY1938 ) @ ( c_Product__Type_OPair @ SY1938 @ SY1938 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY1939 @ ( sK60_B_z @ SY1939 @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY1939 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1938 @ SY1937 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2198,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY1942: $i] :
( ~ ( c_member @ ( tc_prod @ SY1941 @ SY1941 ) @ ( c_Product__Type_OPair @ SY1941 @ SY1941 @ SY1942 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SY1941 @ SY1940 @ SV457 @ SV374 @ SY1942 @ ( hAPP @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY1942 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY1941 @ SY1940 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2199,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV580 @ SV580 ) @ ( c_Product__Type_OPair @ SV580 @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ SV530 ) @ SV112 )
| ~ ~ ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) ) )
= $true )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2200,plain,
! [SV112: $i,SV531: $i,SV581: $i] :
( ( ( ~ ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) ) )
= $true )
| ( ( ! [SY2092: $i] :
( ~ ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SY2092 @ SV531 ) @ SV112 )
| ( c_member @ SV581 @ SY2092 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2201,plain,
! [SV113: $i,SV265: $i,SV375: $i,SV458: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV458 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2202,plain,
! [SV113: $i,SV458: $i,SV265: $i,SV375: $i] :
( ( ( ~ ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2203,plain,
! [SV114: $i,SV582: $i,SV266: $i,SV619: $i] :
( ( ! [SY2130: $i] :
~ ( c_member @ ( tc_prod @ SV619 @ SV266 ) @ ( c_Product__Type_OPair @ SV619 @ SV266 @ SV582 @ SY2130 ) @ SV114 )
| ( c_member @ SV619 @ SV582 @ ( c_Relation_ODomain @ SV619 @ SV266 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2204,plain,
! [SV114: $i,SV266: $i,SV583: $i,SV620: $i] :
( ( ~ ( c_member @ SV620 @ SV583 @ ( c_Relation_ODomain @ SV620 @ SV266 @ SV114 ) )
| ( c_member @ ( tc_prod @ SV620 @ SV266 ) @ ( c_Product__Type_OPair @ SV620 @ SV266 @ SV583 @ ( sK66_B_y @ SV620 @ SV583 @ SV266 @ SV114 ) ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2205,plain,
! [SV460: $i,SV533: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV533 @ SV460 )
= $false )
| ( ( ! [SY2042: $i] :
~ ( c_member @ ( tc_prod @ SV533 @ SV533 ) @ ( c_Product__Type_OPair @ SV533 @ SV533 @ SY2042 @ SY2042 ) @ ( c_Transitive__Closure_Otrancl @ SV533 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2206,plain,
! [SV584: $i,SV267: $i,SV115: $i,SV621: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV621 @ SV115 )
| ( c_member @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV267 @ SV584 ) @ ( c_Transitive__Closure_Ortrancl @ SV621 @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SV621 @ ( c_Set_Oinsert @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV584 @ SV267 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2207,plain,
! [SV115: $i,SV267: $i] :
( ( ~ ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2208,plain,
! [SV115: $i,SV267: $i] :
( ( ~ ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2209,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
| ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2210,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ~ ( c_member @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2211,plain,
! [SV117: $i,SV536: $i,SV587: $i] :
( ( ( ~ ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 ) )
= $true )
| ( ( ! [SY2098: $i] :
( ~ ( c_member @ SV587 @ SY2098 @ SV536 )
| ! [SY2099: $i] :
( ~ ( c_member @ SV587 @ SY2099 @ SV536 )
| ( SY2098 = SY2099 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2098 @ SY2099 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2099 @ SY2098 ) @ SV117 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2212,plain,
! [SV462: $i,SV537: $i] :
( ( ( c_member @ ( tc_prod @ SV537 @ SV537 ) @ ( c_Product__Type_OPair @ SV537 @ SV537 @ ( sK76_B_x @ SV537 @ SV462 ) @ ( sK76_B_x @ SV537 @ SV462 ) ) @ SV462 )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV537 @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2213,plain,
! [SV463: $i,SV538: $i] :
( ( ( c_Nitpick_Orefl_H @ SV538 @ SV463 )
= $false )
| ( ( ! [SY2049: $i] : ( c_member @ ( tc_prod @ SV538 @ SV538 ) @ ( c_Product__Type_OPair @ SV538 @ SV538 @ SY2049 @ SY2049 ) @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2214,plain,
! [SV118: $i,SV269: $i,SV377: $i,SV464: $i,SV539: $i] :
( ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2215,plain,
! [SV119: $i,SV270: $i,SV588: $i] :
( ( ( ! [SY2100: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2100 @ SV588 @ SV270 ) @ SV119 ) ) )
= $true )
| ( ( ( SV588 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2216,plain,
! [SV270: $i,SV119: $i] :
( ( ~ ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2217,plain,
! [SV119: $i,SV270: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2218,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ( SV465 != SV271 )
| ( SV378 != SV120 )
| ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2219,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ~ ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
| ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2220,plain,
! [SV121: $i,SV540: $i] :
( ( ( SV540 = SV121 )
= $false )
| ( ( ! [SY2050: $i] : ( c_member @ SY2050 @ SV540 @ ( c_fequal @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2221,plain,
! [SV121: $i,SV541: $i,SV623: $i] :
( ( ( ~ ( c_member @ SV623 @ SV541 @ ( c_fequal @ SV121 ) ) )
= $true )
| ( ( SV541 = SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2222,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2223,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2224,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2225,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2226,plain,
! [SV466: $i,SV542: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV542 @ SV466 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV466 @ SV542 )
= $true )
| ( ( SV542 = SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2227,plain,
! [SV624: $i] :
( ( ! [SY2131: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2131 @ SV624 )
| ( SY2131 != SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2228,plain,
! [SV625: $i] :
( ( ! [SY2132: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV625 @ SY2132 )
| ( SY2132 != SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2229,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV589 @ SV123 )
| ~ ( c_Relation_Otrans @ SV589 @ SV123 )
| ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2230,plain,
! [SV123: $i] :
( ( ~ ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2231,plain,
! [SV123: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1121 @ SY1120 @ SV123 )
| ( c_Relation_Ototal__on @ SY1121 @ SY1120 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2232,plain,
! [SV124: $i,SV544: $i,SV590: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV590 @ ( sK75_B_x1 @ SV590 @ SV544 @ SV124 ) ) ) )
= $true )
| ( ( ! [SY2101: $i,SY2102: $i] : ( hBOOL @ ( hAPP @ SV590 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SY2101 @ SY2102 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2233,plain,
! [SV124: $i,SV545: $i,SV591: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_Product__Type_OPair @ SV545 @ SV124 @ ( sK73_B_a @ SV591 @ SV545 @ SV124 ) @ ( sK74_SY739 @ SV591 @ SV545 @ SV124 ) ) ) ) )
= $true )
| ( ( ! [SY2103: $i] : ( hBOOL @ ( hAPP @ SV591 @ SY2103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2234,plain,
! [SV626: $i] :
( ( ! [SY2133: $i] :
( ( SV626 = SY2133 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SY2133 @ SV626 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV626 @ SY2133 ) @ v_L ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2235,plain,
( ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2236,plain,
( ( sK4_REN = $true )
| ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2237,plain,
( ( ( ~ sK4_REN )
= $true )
| ( ( ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2069]) ).
thf(2238,plain,
! [SV468: $i,SV547: $i] :
( ( ( c_Relation_Oirrefl @ SV547 @ SV468 )
= $false )
| ( ( ! [SY2058: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV547 ) @ ( c_Product__Type_OPair @ SV547 @ SV547 @ SY2058 @ SY2058 ) @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2239,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK78_SY740 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2240,plain,
! [SV470: $i,SV549: $i] :
( ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false )
| ( ( ! [SY2059: $i,SY2060: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2060 ) @ SV470 )
| ! [SY2061: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2060 @ SY2061 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2059 @ SY2061 ) @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2241,plain,
! [SV125: $i,SV627: $i,SV273: $i,SV592: $i] :
( ( ( SV592 != SV273 )
| ~ ( c_member @ SV627 @ SV592 @ SV125 )
| ( c_member @ ( tc_prod @ SV627 @ SV627 ) @ ( c_Product__Type_OPair @ SV627 @ SV627 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SV627 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2242,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2243,plain,
! [SV125: $i,SV273: $i] :
( ( ~ ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2244,plain,
! [SV126: $i,SV471: $i,SV274: $i,SV379: $i] :
( ( ( SV379 = SV274 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2245,plain,
! [SV127: $i,SV275: $i,SV593: $i,SV628: $i] :
( ( ( c_member @ SV628 @ SV593 @ SV275 )
| ( c_member @ SV628 @ SV593 @ SV127 )
| ( ( c_Set_Oinsert @ SV628 @ SV593 @ SV275 )
!= ( c_Set_Oinsert @ SV628 @ SV593 @ SV127 ) )
| ( SV275 = SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2246,plain,
! [SV127: $i,SV275: $i,SV594: $i,SV629: $i] :
( ( ( c_member @ SV629 @ SV594 @ SV275 )
| ( c_member @ SV629 @ SV594 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SV629 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SV629 @ SV594 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2247,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2248,plain,
! [SV129: $i,SV277: $i,SV595: $i,SV630: $i] :
( ( ( c_member @ SV630 @ SV595 @ ( c_Relation_ODomain @ SV630 @ SV630 @ SV277 ) )
| ( SV595 != SV129 )
| ( c_member @ ( tc_prod @ SV630 @ SV630 ) @ ( c_Product__Type_OPair @ SV630 @ SV630 @ SV595 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV630 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2249,plain,
! [SV129: $i,SV277: $i,SV596: $i,SV631: $i] :
( ( ( c_member @ SV631 @ SV596 @ ( c_Relation_ODomain @ SV631 @ SV631 @ SV277 ) )
| ~ ( c_member @ ( tc_prod @ SV631 @ SV631 ) @ ( c_Product__Type_OPair @ SV631 @ SV631 @ SV596 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV631 @ SV277 ) )
| ( SV596 = SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2250,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ! [SY1968: $i,SY1969: $i] :
( ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV278 @ SV130 ) )
| ( SV473 = SV278 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2251,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ! [SY1970: $i,SY1971: $i] :
( ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV278 @ SV130 ) )
| ( SV381 = SV130 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2252,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i] :
( ( ! [SY2134: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2134 @ SV632 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ ( sK18_B_a @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2134 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2134 @ SV632 ) @ ( tc_prod @ SY2134 @ SV632 ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ ( sK18_B_a @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SY2134 @ SV632 @ ( sK20_SY717 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SY2134 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2253,plain,
! [SV132: $i,SV598: $i,SV633: $i,SV280: $i] :
( ( ! [SY2135: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SV633 ) @ ( c_Product__Type_OPair @ SV280 @ SV633 @ SY2135 @ SV598 ) @ SV132 )
| ( c_member @ SV633 @ SV598 @ ( c_Relation_ORange @ SV280 @ SV633 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2254,plain,
! [SV132: $i,SV280: $i,SV599: $i,SV634: $i] :
( ( ~ ( c_member @ SV634 @ SV599 @ ( c_Relation_ORange @ SV280 @ SV634 @ SV132 ) )
| ( c_member @ ( tc_prod @ SV280 @ SV634 ) @ ( c_Product__Type_OPair @ SV280 @ SV634 @ ( sK65_B_y @ SV634 @ SV599 @ SV280 @ SV132 ) @ SV599 ) @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2255,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ! [SY1976: $i,SY1977: $i] :
( ! [SY1978: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY1977 @ SY1977 ) @ ( c_Product__Type_OPair @ SY1977 @ SY1977 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY1978 @ ( sK55_B_z @ SY1978 @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY1978 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY1977 @ SY1976 @ SV475 @ SV383 @ SV281 @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2256,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i] :
( ( ! [SY1979: $i,SY1980: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY1981: $i] :
( ~ ( c_member @ ( tc_prod @ SY1980 @ SY1980 ) @ ( c_Product__Type_OPair @ SY1980 @ SY1980 @ SY1981 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SY1980 @ SY1979 @ SV475 @ SV383 @ SY1981 @ ( hAPP @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY1981 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY1980 @ SY1979 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2257,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) )
| ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2258,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i] :
( ( ! [SY1982: $i] :
( ! [SY1983: $i] :
~ ( c_member @ ( tc_prod @ SY1983 @ SY1983 ) @ ( c_Product__Type_OPair @ SY1983 @ SY1983 @ SY1982 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1983 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1982 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2090]) ).
thf(2259,plain,
! [SV283: $i,SV477: $i,SV135: $i,SV385: $i] :
( ( ! [SY1984: $i] :
( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SY1984 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
| ! [SY1985: $i] : ( c_member @ ( tc_prod @ SY1985 @ SY1985 ) @ ( c_Product__Type_OPair @ SY1985 @ SY1985 @ SY1984 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY1985 @ SV283 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2260,plain,
! [SV136: $i,SV551: $i,SV635: $i] :
( ( ( ~ ( c_member @ SV635 @ SV551 @ SV136 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV551 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2261,plain,
! [SV552: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ SV552 ) )
= $false )
| ( ( ! [SY2066: $i] : ( c_member @ SY2066 @ SV552 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2262,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i] :
( ( ! [SY2136: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2136 @ SV636 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ ( sK14_B_a @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ ( sK16_SY711 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2136 @ SV636 ) @ ( tc_prod @ SY2136 @ SV636 ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ ( sK16_SY711 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SY2136 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2136 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SY2136 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2263,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i,SV601: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV601 @ SV601 ) @ ( c_Product__Type_OPair @ SV601 @ SV601 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2264,plain,
! [SV139: $i,SV555: $i] :
( ( ( SV555 = SV139 )
= $false )
| ( ( ! [SY2071: $i] : ( c_member @ ( tc_prod @ SY2071 @ SY2071 ) @ ( c_Product__Type_OPair @ SY2071 @ SY2071 @ SV555 @ SV139 ) @ ( c_Relation_OId @ SY2071 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2265,plain,
! [SV139: $i,SV556: $i,SV637: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV637 @ SV637 ) @ ( c_Product__Type_OPair @ SV637 @ SV637 @ SV556 @ SV139 ) @ ( c_Relation_OId @ SV637 ) ) )
= $true )
| ( ( SV556 = SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2266,plain,
! [SV480: $i,SV557: $i] :
( ( ( c_member @ SV557 @ ( sK32_B_x @ SV557 @ SV480 ) @ ( c_Wellfounded_Oacc @ SV557 @ SV480 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV557 @ SV480 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2267,plain,
! [SV481: $i,SV558: $i] :
( ( ( c_Wellfounded_Owf @ SV558 @ SV481 )
= $false )
| ( ( ! [SY2073: $i] : ( c_member @ SV558 @ SY2073 @ ( c_Wellfounded_Oacc @ SV558 @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2268,plain,
! [SV140: $i,SV286: $i,SV602: $i,SV638: $i] :
( ( ( SV638 != SV602 )
| ~ ( c_member @ SV286 @ SV140 @ SV638 )
| ( c_member @ SV286 @ SV140 @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2269,plain,
! [SV140: $i,SV286: $i,SV603: $i,SV639: $i] :
( ( ( SV639 != SV603 )
| ~ ( c_member @ SV286 @ SV140 @ SV603 )
| ( c_member @ SV286 @ SV140 @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2270,plain,
! [SV141: $i,SV287: $i,SV604: $i,SV640: $i] :
( ( ( SV640 != SV604 )
| ~ ( c_member @ SV287 @ SV640 @ SV141 )
| ( c_member @ SV287 @ SV604 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2271,plain,
! [SV141: $i,SV287: $i,SV605: $i,SV641: $i] :
( ( ( SV641 != SV605 )
| ~ ( c_member @ SV287 @ SV605 @ SV141 )
| ( c_member @ SV287 @ SV641 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2272,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK49_SY727 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2273,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2274,plain,
! [SV143: $i] :
( ( ~ ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2106]) ).
thf(2275,plain,
! [SV143: $i] :
( ( ~ ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2276,plain,
! [SV143: $i] :
( ( ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2277,plain,
! [SV143: $i] :
( ( ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2278,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2279,plain,
! [SV606: $i,SV290: $i,SV145: $i,SV642: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV642 @ SV145 )
| ( c_member @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV290 @ SV606 ) @ ( c_Transitive__Closure_Ortrancl @ SV642 @ SV145 ) )
| ( c_Wellfounded_Owf @ SV642 @ ( c_Set_Oinsert @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV606 @ SV290 ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2280,plain,
! [SV145: $i,SV290: $i] :
( ( ~ ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2281,plain,
! [SV145: $i,SV290: $i] :
( ( ~ ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2282,plain,
! [SV146: $i,SV559: $i,SV607: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV607 @ SV559 @ SV146 )
| ~ ( c_Relation_Otrans @ SV607 @ SV146 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV607 @ SV559 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2283,plain,
! [SV146: $i] :
( ( ! [SY1251: $i,SY1252: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1252 @ SY1251 @ SV146 )
| ( c_Relation_Orefl__on @ SY1252 @ SY1251 @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2284,plain,
! [SV146: $i] :
( ( ! [SY1253: $i,SY1254: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY1254 @ SY1253 @ SV146 )
| ( c_Relation_Otrans @ SY1254 @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2285,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ( ~ ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2116]) ).
thf(2286,plain,
! [SV147: $i,SV390: $i,SV291: $i] :
( ( ( ( SV291
!= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2116]) ).
thf(2287,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2288,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2289,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2290,plain,
! [SV148: $i,SV292: $i] :
( ( ~ ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2291,plain,
! [SV149: $i,SV293: $i,SV608: $i,SV643: $i] :
( ( ~ ( c_member @ SV643 @ SV608 @ ( c_Set_Oinsert @ SV643 @ SV293 @ SV149 ) )
| ( SV608 = SV293 )
| ( c_member @ SV643 @ SV608 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2292,plain,
! [SV149: $i,SV293: $i] :
( ( ~ ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2293,plain,
! [SV293: $i,SV149: $i] :
( ( ~ ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2120]) ).
thf(2294,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2295,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( c_member @ ( tc_prod @ SV392 @ SV392 ) @ ( c_Product__Type_OPair @ SV392 @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ SV295 ) @ SV151 )
= $true )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2296,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( ~ ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) ) )
= $true )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2297,plain,
! [SV393: $i,SV152: $i,SV296: $i,SV644: $i] :
( ( ! [SY2137: $i] :
( ~ ( c_member @ ( tc_prod @ SY2137 @ SV644 ) @ ( c_Product__Type_OPair @ SY2137 @ SV644 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY2137 @ SV644 @ SV393 ) @ SV296 ) @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2298,plain,
! [SV152: $i,SV296: $i,SV393: $i,SV645: $i] :
( ( ! [SY2138: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY2138 @ SV645 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SY2138 @ SV645 ) @ ( c_Product__Type_OPair @ SY2138 @ SV645 @ SV296 @ SV152 ) @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2299,plain,
! [SV153: $i,SV484: $i,SV297: $i,SV394: $i] :
( ( ( SV394 = SV297 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2300,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2301,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
| ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2302,plain,
! [SV487: $i,SV562: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV562 @ SV487 )
= $false )
| ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV562 @ SV487 ) @ c_Wellfounded_Oless__than )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2303,plain,
! [SV488: $i,SV563: $i] :
( ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV563 @ SV488 ) @ c_Wellfounded_Oless__than )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV563 @ SV488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2304,plain,
! [SV156: $i,SV300: $i,SV609: $i] :
( ( ( ! [SY2122: $i] :
~ ( c_member @ ( tc_prod @ SY2122 @ SY2122 ) @ ( c_Product__Type_OPair @ SY2122 @ SY2122 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SY2122 @ SV156 ) ) )
= $true )
| ( ( ( SV609 != SV300 )
| ( SV609 = SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2305,plain,
! [SV156: $i,SV300: $i,SV610: $i,SV646: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV646 @ SV156 ) )
| ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SV646 @ SV156 ) )
| ( SV610 = SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2306,plain,
! [SV157: $i,SV301: $i,SV611: $i,SV647: $i] :
( ( ~ ( c_member @ SV647 @ SV611 @ SV301 )
| ( c_member @ SV647 @ SV611 @ ( c_Set_Oinsert @ SV647 @ SV157 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2307,plain,
! [SV301: $i,SV157: $i,SV612: $i] :
( ( ( ( SV612 != SV157 ) )
= $true )
| ( ( ! [SY2125: $i] : ( c_member @ SY2125 @ SV612 @ ( c_Set_Oinsert @ SY2125 @ SV157 @ SV301 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2308,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
| ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2309,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK33_B_x @ SV564 @ SV489 ) @ ( sK34_SY725 @ SV564 @ SV489 ) ) @ SV489 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2310,plain,
! [SV490: $i,SV565: $i] :
( ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false )
| ( ( ! [SY2075: $i,SY2076: $i] :
( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2075 @ SY2076 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2076 @ SY2075 ) @ SV490 )
| ( SY2075 = SY2076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2311,plain,
! [SV159: $i,SV566: $i,SV613: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV613 @ SV566 @ SV159 )
| ~ ( c_Relation_Oantisym @ SV613 @ SV159 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV613 @ SV566 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2312,plain,
! [SV159: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1309 @ SY1308 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY1309 @ SY1308 @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2313,plain,
! [SV159: $i] :
( ( ! [SY1310: $i,SY1311: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY1311 @ SY1310 @ SV159 )
| ( c_Relation_Oantisym @ SY1311 @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2314,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ! [SY2003: $i,SY2004: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2004 @ SY2004 ) @ ( c_Product__Type_OPair @ SY2004 @ SY2004 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY2004 @ SY2003 @ SV160 @ SV397 @ SV303 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2315,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i] :
( ( ! [SY2005: $i,SY2006: $i] :
( ( ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY2006 @ SY2005 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2007: $i] :
( ~ ( c_member @ ( tc_prod @ SY2006 @ SY2006 ) @ ( c_Product__Type_OPair @ SY2006 @ SY2006 @ SY2007 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2007 )
= ( hAPP @ SV160 @ SY2007 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2316,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( c_member @ ( tc_prod @ SV398 @ SV398 ) @ ( c_Product__Type_OPair @ SV398 @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ SV304 ) @ SV161 )
= $true )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2317,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( ~ ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) ) )
= $true )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2318,plain,
! [SV1: $i,SV399: $i,SV162: $i,SV305: $i,SV492: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 ) )
= $true )
| ( ( c_Relation_Otrans @ SV492 @ SV399 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2319,plain,
! [SV400: $i,SV2: $i,SV306: $i,SV163: $i] :
( ( ( c_member @ SV163 @ SV306 @ SV2 )
= $false )
| ( ( c_member @ SV163 @ SV400 @ SV2 )
= $true )
| ( ( SV400 = SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2320,plain,
! [SV310: $i,SV6: $i,SV404: $i,SV167: $i] :
( ( ( c_member @ SV167 @ SV404 @ SV6 )
= $false )
| ( ( c_member @ ( tc_prod @ SV167 @ SV167 ) @ ( c_Product__Type_OPair @ SV167 @ SV167 @ SV404 @ SV310 ) @ ( c_Relation_OId__on @ SV167 @ SV6 ) )
= $true )
| ( ( SV404 = SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2321,plain,
! [SV312: $i,SV406: $i,SV8: $i,SV169: $i] :
( ( ( c_Relation_Otrans @ SV169 @ SV8 )
= $false )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV406 @ SV169 ) @ ( c_Wellfounded_Olex__prod @ SV406 @ SV169 @ SV312 @ SV8 ) )
= $true )
| ( ( c_Relation_Otrans @ SV406 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2322,plain,
! [SV174: $i,SV316: $i,SV13: $i,SV410: $i] :
( ( ( c_member @ ( tc_prod @ SV410 @ SV410 ) @ ( c_Product__Type_OPair @ SV410 @ SV410 @ SV13 @ SV316 ) @ SV174 )
= $false )
| ( ( c_member @ SV410 @ SV13 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
= $true )
| ( ( c_member @ SV410 @ SV316 @ ( c_Wellfounded_Oacc @ SV410 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2323,plain,
! [SV175: $i,SV317: $i,SV14: $i,SV411: $i] :
( ( ( c_member @ SV411 @ SV14 @ SV317 )
= $false )
| ( ( c_member @ ( tc_prod @ SV411 @ SV411 ) @ ( c_Product__Type_OPair @ SV411 @ SV411 @ SV14 @ SV14 ) @ SV175 )
= $true )
| ( ( c_Relation_Orefl__on @ SV411 @ SV317 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2324,plain,
! [SV412: $i,SV318: $i,SV15: $i,SV176: $i,SV497: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV497 @ SV497 ) @ ( c_Product__Type_OPair @ SV497 @ SV497 @ SV176 @ SV15 ) @ SV318 ) )
= $true )
| ( ( c_member @ SV497 @ SV176 @ SV412 )
= $true )
| ( ( c_Relation_Orefl__on @ SV497 @ SV412 @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2325,plain,
! [SV413: $i,SV319: $i,SV16: $i,SV177: $i,SV498: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV498 @ SV498 ) @ ( c_Product__Type_OPair @ SV498 @ SV498 @ SV177 @ SV16 ) @ SV319 ) )
= $true )
| ( ( c_member @ SV498 @ SV16 @ SV413 )
= $true )
| ( ( c_Relation_Orefl__on @ SV498 @ SV413 @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2326,plain,
! [SV320: $i,SV17: $i,SV178: $i,SV414: $i] :
( ( ( c_member @ SV414 @ SV178 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
= $false )
| ( ( c_member @ SV414 @ SV320 @ ( c_Wellfounded_Oacc @ SV414 @ SV17 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV414 @ SV414 ) @ ( c_Product__Type_OPair @ SV414 @ SV414 @ SV320 @ SV178 ) @ ( c_Transitive__Closure_Ortrancl @ SV414 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2327,plain,
! [SV179: $i,SV321: $i,SV18: $i,SV415: $i] :
( ( ( c_member @ ( tc_prod @ SV415 @ SV415 ) @ ( c_Product__Type_OPair @ SV415 @ SV415 @ SV18 @ SV321 ) @ ( c_Transitive__Closure_Ortrancl @ SV415 @ SV179 ) )
= $false )
| ( ( c_member @ SV415 @ SV18 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
= $true )
| ( ( c_member @ SV415 @ SV321 @ ( c_Wellfounded_Oacc @ SV415 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2328,plain,
! [SV19: $i,SV180: $i,SV322: $i,SV416: $i,SV499: $i,SV569: $i] :
( ( ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
| ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2329,plain,
! [SV23: $i,SV418: $i,SV184: $i,SV326: $i,SV501: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2330,plain,
! [SV419: $i,SV185: $i,SV24: $i,SV327: $i,SV502: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV327 ) @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2331,plain,
! [SV420: $i,SV186: $i,SV25: $i,SV328: $i,SV503: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV328 @ SV25 ) @ SV186 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2332,plain,
! [SV421: $i,SV187: $i,SV26: $i,SV329: $i,SV504: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2333,plain,
! [SV29: $i,SV190: $i,SV331: $i,SV423: $i,SV505: $i,SV571: $i] :
( ( ( c_member @ ( tc_prod @ SV571 @ SV571 ) @ ( c_Product__Type_OPair @ SV571 @ SV571 @ SV505 @ SV423 ) @ SV331 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV571 @ SV190 @ SV29 @ SV331 @ SV423 ) @ SV505 )
= ( hAPP @ SV29 @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2334,plain,
! [SV425: $i,SV195: $i,SV34: $i,SV334: $i,SV506: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV334 @ SV34 ) @ SV195 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SV506 @ SV195 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV334 ) @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2335,plain,
! [SV426: $i,SV196: $i,SV35: $i,SV335: $i,SV507: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV335 ) @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2336,plain,
! [SV427: $i,SV197: $i,SV36: $i,SV336: $i,SV508: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV336 @ SV36 ) @ SV197 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2337,plain,
! [SV428: $i,SV198: $i,SV37: $i,SV337: $i,SV509: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2338,plain,
! [SV429: $i,SV199: $i,SV38: $i,SV338: $i,SV510: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SV510 @ SV199 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SV510 @ SV199 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV338 ) @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2339,plain,
! [SV430: $i,SV200: $i,SV39: $i,SV339: $i,SV511: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV339 @ SV39 ) @ SV200 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SV511 @ SV200 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SV511 @ SV200 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2340,plain,
! [SV431: $i,SV201: $i,SV40: $i,SV340: $i,SV512: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SV512 @ SV201 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2341,plain,
! [SV432: $i,SV202: $i,SV41: $i,SV341: $i,SV513: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SV513 @ SV202 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2342,plain,
! [SV514: $i,SV42: $i,SV572: $i,SV203: $i,SV342: $i,SV433: $i] :
( ( ( c_member @ ( tc_prod @ SV433 @ SV433 ) @ ( c_Product__Type_OPair @ SV433 @ SV433 @ SV342 @ SV203 ) @ SV572 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV433 @ SV42 @ SV514 @ SV572 @ SV203 ) @ SV342 )
= ( hAPP @ SV514 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2343,plain,
! [SV343: $i,SV434: $i,SV43: $i,SV204: $i] :
( ( ( SV204 = SV43 )
= $false )
| ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ SV204 @ SV43 ) @ SV343 )
= $false )
| ( ( c_member @ ( tc_prod @ SV434 @ SV434 ) @ ( c_Product__Type_OPair @ SV434 @ SV434 @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) @ ( sK39_B_x @ SV434 @ SV343 @ SV204 @ SV43 ) ) @ ( c_Transitive__Closure_Otrancl @ SV434 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2344,plain,
! [SV344: $i,SV48: $i,SV208: $i,SV435: $i] :
( ( ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
| ( SV208 = SV48 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV435 @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2345,plain,
! [SV351: $i,SV440: $i,SV55: $i,SV215: $i] :
( ( ( c_Wellfounded_Owf @ SV215 @ SV55 )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV440 @ SV215 ) @ ( c_Wellfounded_Olex__prod @ SV440 @ SV215 @ SV351 @ SV55 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV440 @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2346,plain,
! [SV353: $i,SV57: $i,SV217: $i,SV441: $i] :
( ( ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV441 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2347,plain,
! [SV354: $i,SV58: $i,SV218: $i,SV442: $i] :
( ( ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV442 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2348,plain,
! [SV62: $i,SV222: $i,SV357: $i,SV443: $i,SV517: $i,SV573: $i] :
( ( ( c_member @ SV573 @ SV517 @ SV443 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV573 @ SV357 ) @ ( c_Product__Type_OPair @ SV573 @ SV357 @ SV517 @ SV222 ) @ SV62 )
| ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SV573 @ SV357 @ SV62 @ SV443 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2349,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i,SV574: $i,SV614: $i,SV648: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV648 @ SV614 ) @ ( c_Product__Type_OPair @ SV648 @ SV614 @ SV574 @ SV518 ) @ SV444 )
| ~ ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV648 @ SV358 ) @ ( c_Product__Type_OPair @ SV648 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SV648 @ SV614 @ SV358 @ SV444 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2350,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i,SV575: $i,SV615: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV615 @ SV575 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SV615 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2351,plain,
! [SV88: $i,SV246: $i,SV366: $i,SV451: $i,SV523: $i,SV576: $i] :
( ( ( SV576
= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV523 @ SV366 )
| ( ( hAPP @ SV576 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SV576 @ SV366 @ SV88 ) ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2352,plain,
! [SV454: $i,SV525: $i] :
( ( ( ~ ( c_member @ SV525 @ ( sK31_SY722 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2353,plain,
! [SV454: $i,SV525: $i] :
( ( ( ~ ! [SY2021: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ SY2021 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SY2021 @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2354,plain,
! [SV455: $i,SV649: $i,SV526: $i] :
( ( ( ! [SY2139: $i] :
~ ( c_member @ SV526 @ SY2139 @ SV649 )
| ~ ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2355,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2356,plain,
! [SV107: $i,SV528: $i,SV578: $i] :
( ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false )
| ( ( ! [SY2081: $i,SY2082: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2082 ) @ SV107 )
| ! [SY2083: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SY2081 @ SY2083 ) @ SV107 )
| ( SY2082 = SY2083 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2357,plain,
! [SV261: $i,SV617: $i,SV650: $i,SV108: $i,SV372: $i] :
( ( ! [SY2141: $i] :
( ~ ( c_member @ SV372 @ SY2141 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SY2141 @ SV617 ) @ SV261 ) )
| ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2358,plain,
! [SV108: $i,SV261: $i,SV372: $i,SV618: $i,SV651: $i] :
( ( ~ ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
| ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2359,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2360,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2361,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ~ ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) )
| ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2362,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV456: $i,SV579: $i] :
( ( ~ ~ ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) )
| ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2363,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i] :
( ( ! [SY2142: $i] :
( ! [SY2143: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2142 @ SY2142 ) @ ( c_Product__Type_OPair @ SY2142 @ SY2142 @ ( sK60_B_z @ SY2143 @ SY2142 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2142 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SY2143 @ SY2142 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY2143 @ ( sK60_B_z @ SY2143 @ SY2142 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY2143 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SY2142 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2364,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV653: $i] :
( ( ! [SY2144: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY2144 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY2145: $i] :
( ~ ( c_member @ ( tc_prod @ SY2144 @ SY2144 ) @ ( c_Product__Type_OPair @ SY2144 @ SY2144 @ SY2145 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SY2144 @ SV653 @ SV457 @ SV374 @ SY2145 @ ( hAPP @ ( sK59_B_g @ SY2144 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2145 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SY2144 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2365,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV580 @ SV580 ) @ ( c_Product__Type_OPair @ SV580 @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ SV530 ) @ SV112 )
| ~ ~ ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) )
= $false )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2366,plain,
! [SV112: $i,SV531: $i,SV581: $i] :
( ( ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $false )
| ( ( ! [SY2092: $i] :
( ~ ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SY2092 @ SV531 ) @ SV112 )
| ( c_member @ SV581 @ SY2092 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2367,plain,
! [SV113: $i,SV265: $i,SV375: $i,SV458: $i] :
( ( ( hBOOL @ ( hAPP @ SV458 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2368,plain,
! [SV113: $i,SV458: $i,SV265: $i,SV375: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2369,plain,
! [SV114: $i,SV582: $i,SV266: $i,SV619: $i] :
( ( ( ! [SY2130: $i] :
~ ( c_member @ ( tc_prod @ SV619 @ SV266 ) @ ( c_Product__Type_OPair @ SV619 @ SV266 @ SV582 @ SY2130 ) @ SV114 ) )
= $true )
| ( ( c_member @ SV619 @ SV582 @ ( c_Relation_ODomain @ SV619 @ SV266 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2370,plain,
! [SV114: $i,SV266: $i,SV583: $i,SV620: $i] :
( ( ( ~ ( c_member @ SV620 @ SV583 @ ( c_Relation_ODomain @ SV620 @ SV266 @ SV114 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV620 @ SV266 ) @ ( c_Product__Type_OPair @ SV620 @ SV266 @ SV583 @ ( sK66_B_y @ SV620 @ SV583 @ SV266 @ SV114 ) ) @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2371,plain,
! [SV460: $i,SV654: $i,SV533: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV533 @ SV533 ) @ ( c_Product__Type_OPair @ SV533 @ SV533 @ SV654 @ SV654 ) @ ( c_Transitive__Closure_Otrancl @ SV533 @ SV460 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV533 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2372,plain,
! [SV584: $i,SV267: $i,SV115: $i,SV621: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV621 @ SV115 )
| ( c_member @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV267 @ SV584 ) @ ( c_Transitive__Closure_Ortrancl @ SV621 @ SV115 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV621 @ ( c_Set_Oinsert @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV584 @ SV267 ) @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2373,plain,
! [SV115: $i,SV267: $i] :
( ( ! [SY1526: $i,SY1527: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1527 @ ( c_Set_Oinsert @ ( tc_prod @ SY1527 @ SY1527 ) @ ( c_Product__Type_OPair @ SY1527 @ SY1527 @ SY1526 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY1527 @ SV115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2374,plain,
! [SV115: $i,SV267: $i] :
( ( ! [SY1528: $i,SY1529: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY1529 @ ( c_Set_Oinsert @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SY1528 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY1529 @ SY1529 ) @ ( c_Product__Type_OPair @ SY1529 @ SY1529 @ SV267 @ SY1528 ) @ ( c_Transitive__Closure_Ortrancl @ SY1529 @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2375,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) )
= $true )
| ( ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2376,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2377,plain,
! [SV117: $i,SV536: $i,SV587: $i] :
( ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false )
| ( ( ! [SY2098: $i] :
( ~ ( c_member @ SV587 @ SY2098 @ SV536 )
| ! [SY2099: $i] :
( ~ ( c_member @ SV587 @ SY2099 @ SV536 )
| ( SY2098 = SY2099 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2098 @ SY2099 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2099 @ SY2098 ) @ SV117 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2378,plain,
! [SV463: $i,SV655: $i,SV538: $i] :
( ( ( c_member @ ( tc_prod @ SV538 @ SV538 ) @ ( c_Product__Type_OPair @ SV538 @ SV538 @ SV655 @ SV655 ) @ SV463 )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV538 @ SV463 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2379,plain,
! [SV118: $i,SV269: $i,SV464: $i,SV539: $i,SV377: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
| ~ ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) )
= $false )
| ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2380,plain,
! [SV119: $i,SV270: $i,SV588: $i,SV656: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV656 @ SV588 @ SV270 ) @ SV119 ) ) )
= $true )
| ( ( ( SV588 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2381,plain,
! [SV270: $i,SV119: $i] :
( ( ! [SY1540: $i] :
( ( SY1540 != SV119 )
| ! [SY1541: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1541 @ SY1540 @ SV270 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2382,plain,
! [SV119: $i,SV270: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
| ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2383,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ( ( SV465 != SV271 )
| ( SV378 != SV120 ) )
= $true )
| ( ( ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2384,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
| ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2385,plain,
! [SV121: $i,SV540: $i,SV657: $i] :
( ( ( c_member @ SV657 @ SV540 @ ( c_fequal @ SV121 ) )
= $true )
| ( ( SV540 = SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2386,plain,
! [SV121: $i,SV541: $i,SV623: $i] :
( ( ( c_member @ SV623 @ SV541 @ ( c_fequal @ SV121 ) )
= $false )
| ( ( SV541 = SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2387,plain,
! [SV122: $i,SV272: $i] :
( ( ! [SY1552: $i] :
( ! [SY1553: $i] :
~ ( c_member @ ( tc_prod @ SY1553 @ SY1553 ) @ ( c_Product__Type_OPair @ SY1553 @ SY1553 @ SY1552 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1553 @ SV122 ) )
| ( SY1552 != SV272 )
| ( SY1552 = SV272 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2388,plain,
! [SV122: $i,SV272: $i] :
( ( ! [SY1554: $i,SY1555: $i] :
( ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1555 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SY1554 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1555 @ SV122 ) )
| ( SY1554 = SV272 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2389,plain,
! [SV122: $i,SV272: $i] :
( ( ! [SY1556: $i,SY1557: $i] :
( ( SY1556 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY1557 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY1557 @ SY1557 ) @ ( c_Product__Type_OPair @ SY1557 @ SY1557 @ SY1556 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1557 @ SV122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2390,plain,
! [SV122: $i,SV272: $i] :
( ( ! [SY1558: $i] :
( ( SY1558 != SV272 )
| ! [SY1559: $i] : ( c_member @ ( tc_prod @ SY1559 @ SY1559 ) @ ( c_Product__Type_OPair @ SY1559 @ SY1559 @ SY1558 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY1559 @ SV122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2391,plain,
! [SV624: $i,SV658: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV658 @ SV624 )
| ( SV658 != SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2392,plain,
! [SV659: $i,SV625: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV625 @ SV659 )
| ( SV659 != SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2393,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV589 @ SV123 )
| ~ ( c_Relation_Otrans @ SV589 @ SV123 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2394,plain,
! [SV123: $i] :
( ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2395,plain,
! [SV123: $i,SV660: $i] :
( ( ! [SY2146: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2146 @ SV660 @ SV123 )
| ( c_Relation_Ototal__on @ SY2146 @ SV660 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2396,plain,
! [SV124: $i,SV544: $i,SV590: $i] :
( ( ( hBOOL @ ( hAPP @ SV590 @ ( sK75_B_x1 @ SV590 @ SV544 @ SV124 ) ) )
= $false )
| ( ( ! [SY2101: $i,SY2102: $i] : ( hBOOL @ ( hAPP @ SV590 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SY2101 @ SY2102 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2397,plain,
! [SV124: $i,SV545: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ ( c_Product__Type_OPair @ SV545 @ SV124 @ ( sK73_B_a @ SV591 @ SV545 @ SV124 ) @ ( sK74_SY739 @ SV591 @ SV545 @ SV124 ) ) ) )
= $false )
| ( ( ! [SY2103: $i] : ( hBOOL @ ( hAPP @ SV591 @ SY2103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2398,plain,
! [SV661: $i,SV626: $i] :
( ( ( SV626 = SV661 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV661 @ SV626 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV626 @ SV661 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2399,plain,
( ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2400,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2401,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
= $true )
| ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2402,plain,
( ( sK4_REN = $false )
| ( ( ~ ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2403,plain,
! [SV468: $i,SV662: $i,SV547: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV547 @ SV547 ) @ ( c_Product__Type_OPair @ SV547 @ SV547 @ SV662 @ SV662 ) @ SV468 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV547 @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2404,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK78_SY740 @ SV548 @ SV469 ) ) @ SV469 ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2405,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2406,plain,
! [SV470: $i,SV663: $i,SV549: $i] :
( ( ( ! [SY2147: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SY2147 ) @ SV470 )
| ! [SY2148: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SY2147 @ SY2148 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SY2148 ) @ SV470 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2407,plain,
! [SV125: $i,SV627: $i,SV273: $i,SV592: $i] :
( ( ( ( SV592 != SV273 )
| ~ ( c_member @ SV627 @ SV592 @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV627 @ SV627 ) @ ( c_Product__Type_OPair @ SV627 @ SV627 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SV627 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2408,plain,
! [SV125: $i,SV273: $i] :
( ( ! [SY1562: $i] :
( ! [SY1563: $i] :
~ ( c_member @ ( tc_prod @ SY1563 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1563 @ SY1563 @ SY1562 @ SV273 ) @ ( c_Relation_OId__on @ SY1563 @ SV125 ) )
| ( SY1562 = SV273 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2409,plain,
! [SV125: $i,SV273: $i] :
( ( ! [SY1564: $i,SY1565: $i] :
( ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1564 @ SV273 ) @ ( c_Relation_OId__on @ SY1565 @ SV125 ) )
| ( c_member @ SY1565 @ SY1564 @ SV125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2410,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
| ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) )
= $false )
| ( ( SV379 = SV274 )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2411,plain,
! [SV127: $i,SV275: $i,SV593: $i,SV628: $i] :
( ( ( c_member @ SV628 @ SV593 @ SV275 )
= $true )
| ( ( ( c_member @ SV628 @ SV593 @ SV127 )
| ( ( c_Set_Oinsert @ SV628 @ SV593 @ SV275 )
!= ( c_Set_Oinsert @ SV628 @ SV593 @ SV127 ) )
| ( SV275 = SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2412,plain,
! [SV127: $i,SV275: $i,SV594: $i,SV629: $i] :
( ( ( c_member @ SV629 @ SV594 @ SV275 )
= $true )
| ( ( ( c_member @ SV629 @ SV594 @ SV127 )
| ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SV629 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SV629 @ SV594 @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2413,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
| ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2414,plain,
! [SV129: $i,SV277: $i,SV595: $i,SV630: $i] :
( ( ( c_member @ SV630 @ SV595 @ ( c_Relation_ODomain @ SV630 @ SV630 @ SV277 ) )
= $true )
| ( ( ( SV595 != SV129 )
| ( c_member @ ( tc_prod @ SV630 @ SV630 ) @ ( c_Product__Type_OPair @ SV630 @ SV630 @ SV595 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV630 @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2415,plain,
! [SV129: $i,SV277: $i,SV596: $i,SV631: $i] :
( ( ( c_member @ SV631 @ SV596 @ ( c_Relation_ODomain @ SV631 @ SV631 @ SV277 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV631 @ SV631 ) @ ( c_Product__Type_OPair @ SV631 @ SV631 @ SV596 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV631 @ SV277 ) )
| ( SV596 = SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2416,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ( ! [SY1968: $i,SY1969: $i] :
( ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1969 @ SY1968 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV473 = SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2417,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i] :
( ( ( ! [SY1970: $i,SY1971: $i] :
( ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY1971 @ SY1970 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV381 = SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2418,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2419,plain,
! [SV132: $i,SV598: $i,SV633: $i,SV280: $i] :
( ( ( ! [SY2135: $i] :
~ ( c_member @ ( tc_prod @ SV280 @ SV633 ) @ ( c_Product__Type_OPair @ SV280 @ SV633 @ SY2135 @ SV598 ) @ SV132 ) )
= $true )
| ( ( c_member @ SV633 @ SV598 @ ( c_Relation_ORange @ SV280 @ SV633 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2420,plain,
! [SV132: $i,SV280: $i,SV599: $i,SV634: $i] :
( ( ( ~ ( c_member @ SV634 @ SV599 @ ( c_Relation_ORange @ SV280 @ SV634 @ SV132 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV280 @ SV634 ) @ ( c_Product__Type_OPair @ SV280 @ SV634 @ ( sK65_B_y @ SV634 @ SV599 @ SV280 @ SV132 ) @ SV599 ) @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2421,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i] :
( ( ! [SY2149: $i] :
( ! [SY2150: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2149 @ SY2149 ) @ ( c_Product__Type_OPair @ SY2149 @ SY2149 @ ( sK55_B_z @ SY2150 @ SY2149 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2149 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SY2150 @ SY2149 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY2150 @ ( sK55_B_z @ SY2150 @ SY2149 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY2150 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SY2149 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2422,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV666: $i] :
( ( ! [SY2151: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY2151 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY2152: $i] :
( ~ ( c_member @ ( tc_prod @ SY2151 @ SY2151 ) @ ( c_Product__Type_OPair @ SY2151 @ SY2151 @ SY2152 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SY2151 @ SV666 @ SV475 @ SV383 @ SY2152 @ ( hAPP @ ( sK54_B_g @ SY2151 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2152 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SY2151 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2423,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2424,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2425,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i,SV667: $i] :
( ( ! [SY2153: $i] :
~ ( c_member @ ( tc_prod @ SY2153 @ SY2153 ) @ ( c_Product__Type_OPair @ SY2153 @ SY2153 @ SV667 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY2153 @ SV283 ) @ SV135 ) )
| ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV667 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2426,plain,
! [SV283: $i,SV477: $i,SV668: $i,SV135: $i,SV385: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV668 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
| ! [SY2154: $i] : ( c_member @ ( tc_prod @ SY2154 @ SY2154 ) @ ( c_Product__Type_OPair @ SY2154 @ SY2154 @ SV668 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY2154 @ SV283 ) @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2427,plain,
! [SV136: $i,SV551: $i,SV635: $i] :
( ( ( c_member @ SV635 @ SV551 @ SV136 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2428,plain,
! [SV136: $i,SV552: $i,SV669: $i] :
( ( ( c_member @ SV669 @ SV552 @ SV136 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2429,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2430,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i,SV601: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV601 @ SV601 ) @ ( c_Product__Type_OPair @ SV601 @ SV601 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2431,plain,
! [SV139: $i,SV555: $i,SV671: $i] :
( ( ( c_member @ ( tc_prod @ SV671 @ SV671 ) @ ( c_Product__Type_OPair @ SV671 @ SV671 @ SV555 @ SV139 ) @ ( c_Relation_OId @ SV671 ) )
= $true )
| ( ( SV555 = SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2432,plain,
! [SV139: $i,SV556: $i,SV637: $i] :
( ( ( c_member @ ( tc_prod @ SV637 @ SV637 ) @ ( c_Product__Type_OPair @ SV637 @ SV637 @ SV556 @ SV139 ) @ ( c_Relation_OId @ SV637 ) )
= $false )
| ( ( SV556 = SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2433,plain,
! [SV481: $i,SV672: $i,SV558: $i] :
( ( ( c_member @ SV558 @ SV672 @ ( c_Wellfounded_Oacc @ SV558 @ SV481 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV558 @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2434,plain,
! [SV140: $i,SV286: $i,SV602: $i,SV638: $i] :
( ( ( ( SV638 != SV602 ) )
= $true )
| ( ( ~ ( c_member @ SV286 @ SV140 @ SV638 )
| ( c_member @ SV286 @ SV140 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2435,plain,
! [SV140: $i,SV286: $i,SV603: $i,SV639: $i] :
( ( ( ( SV639 != SV603 ) )
= $true )
| ( ( ~ ( c_member @ SV286 @ SV140 @ SV603 )
| ( c_member @ SV286 @ SV140 @ SV639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2436,plain,
! [SV141: $i,SV287: $i,SV604: $i,SV640: $i] :
( ( ( ( SV640 != SV604 ) )
= $true )
| ( ( ~ ( c_member @ SV287 @ SV640 @ SV141 )
| ( c_member @ SV287 @ SV604 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2437,plain,
! [SV141: $i,SV287: $i,SV605: $i,SV641: $i] :
( ( ( ( SV641 != SV605 ) )
= $true )
| ( ( ~ ( c_member @ SV287 @ SV605 @ SV141 )
| ( c_member @ SV287 @ SV641 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2438,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
| ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2439,plain,
! [SV143: $i] :
( ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) )
| ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2440,plain,
! [SV143: $i] :
( ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2441,plain,
! [SV143: $i] :
( ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) )
| ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2442,plain,
! [SV143: $i] :
( ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) )
| ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2443,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
| ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2444,plain,
! [SV606: $i,SV290: $i,SV145: $i,SV642: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV642 @ SV145 )
| ( c_member @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV290 @ SV606 ) @ ( c_Transitive__Closure_Ortrancl @ SV642 @ SV145 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV642 @ ( c_Set_Oinsert @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV606 @ SV290 ) @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2445,plain,
! [SV145: $i,SV290: $i] :
( ( ! [SY1634: $i,SY1635: $i] :
( ~ ( c_Wellfounded_Owf @ SY1635 @ ( c_Set_Oinsert @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SY1634 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY1635 @ SV145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2446,plain,
! [SV145: $i,SV290: $i] :
( ( ! [SY1636: $i,SY1637: $i] :
( ~ ( c_Wellfounded_Owf @ SY1637 @ ( c_Set_Oinsert @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SY1636 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY1637 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1637 @ SY1637 @ SV290 @ SY1636 ) @ ( c_Transitive__Closure_Ortrancl @ SY1637 @ SV145 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2447,plain,
! [SV146: $i,SV559: $i,SV607: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV607 @ SV559 @ SV146 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV607 @ SV146 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV607 @ SV559 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2448,plain,
! [SV146: $i,SV673: $i] :
( ( ! [SY2155: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2155 @ SV673 @ SV146 )
| ( c_Relation_Orefl__on @ SY2155 @ SV673 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2449,plain,
! [SV146: $i,SV674: $i] :
( ( ! [SY2156: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2156 @ SV674 @ SV146 )
| ( c_Relation_Otrans @ SY2156 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2450,plain,
! [SV147: $i,SV291: $i,SV390: $i] :
( ( ( c_member @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ SV147 )
= $true )
| ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2285]) ).
thf(2451,plain,
! [SV147: $i,SV390: $i,SV291: $i] :
( ( ( SV291
= ( c_Product__Type_OPair @ SV390 @ SV390 @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) @ ( sK64_B_x @ SV390 @ SV291 @ SV147 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV390 @ SV390 ) @ SV291 @ ( c_Relation_OId__on @ SV390 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2286]) ).
thf(2452,plain,
! [SV148: $i,SV292: $i] :
( ( ! [SY1639: $i,SY1640: $i] :
( ( SY1640 != SY1639 )
| ( c_member @ SV292 @ SV148 @ SY1640 )
| ~ ( c_member @ SV292 @ SV148 @ SY1640 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2453,plain,
! [SV148: $i,SV292: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ( SY1642 != SY1641 )
| ( c_member @ SV292 @ SV148 @ SY1642 )
| ~ ( c_member @ SV292 @ SV148 @ SY1641 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2454,plain,
! [SV148: $i,SV292: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ( SY1644 != SY1643 )
| ( c_member @ SV292 @ SV148 @ SY1643 )
| ~ ( c_member @ SV292 @ SV148 @ SY1644 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2455,plain,
! [SV148: $i,SV292: $i] :
( ( ! [SY1645: $i] :
( ! [SX3: $i] : ( SX3 != SY1645 )
| ( c_member @ SV292 @ SV148 @ SY1645 )
| ~ ( c_member @ SV292 @ SV148 @ SY1645 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2456,plain,
! [SV149: $i,SV293: $i,SV608: $i,SV643: $i] :
( ( ( ~ ( c_member @ SV643 @ SV608 @ ( c_Set_Oinsert @ SV643 @ SV293 @ SV149 ) ) )
= $true )
| ( ( ( SV608 = SV293 )
| ( c_member @ SV643 @ SV608 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2457,plain,
! [SV149: $i,SV293: $i] :
( ( ! [SY1649: $i] :
( ( SY1649 != SV293 )
| ! [SY1650: $i] : ( c_member @ SY1650 @ SY1649 @ ( c_Set_Oinsert @ SY1650 @ SV293 @ SV149 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2458,plain,
! [SV293: $i,SV149: $i] :
( ( ! [SY1651: $i,SY1652: $i] :
( ~ ( c_member @ SY1652 @ SY1651 @ SV149 )
| ( c_member @ SY1652 @ SY1651 @ ( c_Set_Oinsert @ SY1652 @ SV293 @ SV149 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2459,plain,
! [SV294: $i,SV483: $i,SV560: $i,SV391: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ SV391 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2460,plain,
! [SV151: $i,SV295: $i,SV392: $i] :
( ( ( c_member @ SV392 @ ( sK58_B_z @ SV392 @ SV295 @ SV151 ) @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $false )
| ( ( c_member @ SV392 @ SV295 @ ( c_Wellfounded_Oacc @ SV392 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2461,plain,
! [SV393: $i,SV152: $i,SV296: $i,SV644: $i,SV675: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV675 @ SV644 ) @ ( c_Product__Type_OPair @ SV675 @ SV644 @ SV296 @ SV152 ) @ SV393 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV675 @ SV644 @ SV393 ) @ SV296 ) @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2462,plain,
! [SV152: $i,SV296: $i,SV393: $i,SV645: $i,SV676: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV676 @ SV645 @ SV393 ) @ SV296 ) @ SV152 ) )
| ( c_member @ ( tc_prod @ SV676 @ SV645 ) @ ( c_Product__Type_OPair @ SV676 @ SV645 @ SV296 @ SV152 ) @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2463,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
| ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) )
= $false )
| ( ( SV394 = SV297 )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2464,plain,
! [SV298: $i,SV395: $i,SV561: $i,SV485: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ SV485 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2465,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2466,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2467,plain,
! [SV156: $i,SV300: $i,SV609: $i,SV677: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV677 @ SV677 ) @ ( c_Product__Type_OPair @ SV677 @ SV677 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV677 @ SV156 ) ) )
= $true )
| ( ( ( SV609 != SV300 )
| ( SV609 = SV300 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2468,plain,
! [SV156: $i,SV300: $i,SV610: $i,SV646: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV646 @ SV156 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SV646 @ SV156 ) )
| ( SV610 = SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2469,plain,
! [SV157: $i,SV301: $i,SV611: $i,SV647: $i] :
( ( ( ~ ( c_member @ SV647 @ SV611 @ SV301 ) )
= $true )
| ( ( c_member @ SV647 @ SV611 @ ( c_Set_Oinsert @ SV647 @ SV157 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2470,plain,
! [SV301: $i,SV157: $i,SV612: $i] :
( ( ( SV612 = SV157 )
= $false )
| ( ( ! [SY2125: $i] : ( c_member @ SY2125 @ SV612 @ ( c_Set_Oinsert @ SY2125 @ SV157 @ SV301 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2471,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2472,plain,
! [SV158: $i,SV302: $i] :
( ( ( ~ ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2473,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK33_B_x @ SV564 @ SV489 ) @ ( sK34_SY725 @ SV564 @ SV489 ) ) @ SV489 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2309]) ).
thf(2474,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2309]) ).
thf(2475,plain,
! [SV490: $i,SV678: $i,SV565: $i] :
( ( ( ! [SY2157: $i] :
( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SY2157 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SY2157 @ SV678 ) @ SV490 )
| ( SV678 = SY2157 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2476,plain,
! [SV159: $i,SV566: $i,SV613: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV613 @ SV566 @ SV159 ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV613 @ SV159 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV613 @ SV566 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2477,plain,
! [SV159: $i,SV679: $i] :
( ( ! [SY2158: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2158 @ SV679 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SY2158 @ SV679 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2478,plain,
! [SV159: $i,SV680: $i] :
( ( ! [SY2159: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2159 @ SV680 @ SV159 )
| ( c_Relation_Oantisym @ SY2159 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2479,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i] :
( ( ! [SY2160: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2160 @ SY2160 ) @ ( c_Product__Type_OPair @ SY2160 @ SY2160 @ ( sK43_B_y @ SY2160 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SY2160 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SY2160 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2160 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SY2160 @ SV681 @ SV160 @ SV397 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2480,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV682: $i] :
( ( ! [SY2161: $i] :
( ( ( c_Recdef_Ocut @ SY2161 @ SV682 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SY2161 @ SV682 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2007: $i] :
( ~ ( c_member @ ( tc_prod @ SY2161 @ SY2161 ) @ ( c_Product__Type_OPair @ SY2161 @ SY2161 @ SY2007 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2007 )
= ( hAPP @ SV160 @ SY2007 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2481,plain,
! [SV161: $i,SV304: $i,SV398: $i] :
( ( ( c_member @ SV398 @ ( sK57_B_y @ SV398 @ SV304 @ SV161 ) @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $false )
| ( ( c_member @ SV398 @ SV304 @ ( c_Wellfounded_Oacc @ SV398 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2482,plain,
! [SV1: $i,SV399: $i,SV162: $i,SV305: $i,SV492: $i] :
( ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
| ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 ) )
= $true )
| ( ( c_Relation_Otrans @ SV492 @ SV399 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2483,plain,
! [SV412: $i,SV318: $i,SV15: $i,SV176: $i,SV497: $i] :
( ( ( c_member @ ( tc_prod @ SV497 @ SV497 ) @ ( c_Product__Type_OPair @ SV497 @ SV497 @ SV176 @ SV15 ) @ SV318 )
= $false )
| ( ( c_member @ SV497 @ SV176 @ SV412 )
= $true )
| ( ( c_Relation_Orefl__on @ SV497 @ SV412 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2484,plain,
! [SV413: $i,SV319: $i,SV16: $i,SV177: $i,SV498: $i] :
( ( ( c_member @ ( tc_prod @ SV498 @ SV498 ) @ ( c_Product__Type_OPair @ SV498 @ SV498 @ SV177 @ SV16 ) @ SV319 )
= $false )
| ( ( c_member @ SV498 @ SV16 @ SV413 )
= $true )
| ( ( c_Relation_Orefl__on @ SV498 @ SV413 @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2485,plain,
! [SV19: $i,SV416: $i,SV180: $i,SV322: $i,SV499: $i,SV569: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2486,plain,
! [SV23: $i,SV418: $i,SV184: $i,SV326: $i,SV501: $i] :
( ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2487,plain,
! [SV419: $i,SV185: $i,SV24: $i,SV327: $i,SV502: $i] :
( ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV327 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV24 ) @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV185 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV502 @ SV502 ) @ ( c_Product__Type_OPair @ SV502 @ SV502 @ SV419 @ SV327 ) @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2488,plain,
! [SV420: $i,SV186: $i,SV25: $i,SV328: $i,SV503: $i] :
( ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV328 @ SV25 ) @ SV186 )
= $false )
| ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV25 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV503 @ SV503 ) @ ( c_Product__Type_OPair @ SV503 @ SV503 @ SV420 @ SV328 ) @ ( c_Transitive__Closure_Ortrancl @ SV503 @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2489,plain,
! [SV421: $i,SV187: $i,SV26: $i,SV329: $i,SV504: $i] :
( ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV329 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV26 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV504 @ SV504 ) @ ( c_Product__Type_OPair @ SV504 @ SV504 @ SV421 @ SV329 ) @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2490,plain,
! [SV425: $i,SV195: $i,SV34: $i,SV334: $i,SV506: $i] :
( ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV334 @ SV34 ) @ SV195 )
= $false )
| ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV34 ) @ ( c_Transitive__Closure_Otrancl @ SV506 @ SV195 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV506 @ SV506 ) @ ( c_Product__Type_OPair @ SV506 @ SV506 @ SV425 @ SV334 ) @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2491,plain,
! [SV426: $i,SV196: $i,SV35: $i,SV335: $i,SV507: $i] :
( ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV335 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV35 ) @ ( c_Transitive__Closure_Otrancl @ SV507 @ SV196 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV426 @ SV335 ) @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2492,plain,
! [SV427: $i,SV197: $i,SV36: $i,SV336: $i,SV508: $i] :
( ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV336 @ SV36 ) @ SV197 )
= $false )
| ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV36 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV508 @ SV508 ) @ ( c_Product__Type_OPair @ SV508 @ SV508 @ SV427 @ SV336 ) @ ( c_Transitive__Closure_Otrancl @ SV508 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2493,plain,
! [SV428: $i,SV198: $i,SV37: $i,SV337: $i,SV509: $i] :
( ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV337 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV37 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV509 @ SV509 ) @ ( c_Product__Type_OPair @ SV509 @ SV509 @ SV428 @ SV337 ) @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2494,plain,
! [SV429: $i,SV199: $i,SV38: $i,SV338: $i,SV510: $i] :
( ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV338 @ SV38 ) @ ( c_Transitive__Closure_Ortrancl @ SV510 @ SV199 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV38 ) @ ( c_Transitive__Closure_Otrancl @ SV510 @ SV199 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV510 @ SV510 ) @ ( c_Product__Type_OPair @ SV510 @ SV510 @ SV429 @ SV338 ) @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2495,plain,
! [SV430: $i,SV200: $i,SV39: $i,SV339: $i,SV511: $i] :
( ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV339 @ SV39 ) @ SV200 )
= $false )
| ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV39 ) @ ( c_Transitive__Closure_Otrancl @ SV511 @ SV200 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV511 @ SV511 ) @ ( c_Product__Type_OPair @ SV511 @ SV511 @ SV430 @ SV339 ) @ ( c_Transitive__Closure_Ortrancl @ SV511 @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2496,plain,
! [SV431: $i,SV201: $i,SV40: $i,SV340: $i,SV512: $i] :
( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV340 @ SV40 ) @ ( c_Transitive__Closure_Ortrancl @ SV512 @ SV201 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV40 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV431 @ SV340 ) @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV201 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2497,plain,
! [SV432: $i,SV202: $i,SV41: $i,SV341: $i,SV513: $i] :
( ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV341 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV41 ) @ ( c_Transitive__Closure_Otrancl @ SV513 @ SV202 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV513 @ SV513 ) @ ( c_Product__Type_OPair @ SV513 @ SV513 @ SV432 @ SV341 ) @ ( c_Transitive__Closure_Ortrancl @ SV513 @ SV202 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2498,plain,
! [SV344: $i,SV208: $i,SV48: $i,SV435: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 ) )
= $true )
| ( ( SV208 = SV48 )
= $true )
| ( ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
= $false )
| ( ( c_Relation_Oantisym @ SV435 @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2499,plain,
! [SV353: $i,SV217: $i,SV57: $i,SV441: $i] :
( ( ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV57 @ SV217 ) @ SV353 )
= $false )
| ( ( c_member @ ( tc_prod @ SV441 @ SV441 ) @ ( c_Product__Type_OPair @ SV441 @ SV441 @ SV217 @ SV57 ) @ SV353 )
= $false )
| ( ( c_Wellfounded_Owf @ SV441 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2500,plain,
! [SV354: $i,SV218: $i,SV58: $i,SV442: $i] :
( ( ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV58 @ SV218 ) @ SV354 )
= $false )
| ( ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV218 @ SV58 ) @ SV354 )
= $false )
| ( ( c_Wellfounded_Owf @ SV442 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2501,plain,
! [SV443: $i,SV62: $i,SV222: $i,SV517: $i,SV357: $i,SV573: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV573 @ SV357 ) @ ( c_Product__Type_OPair @ SV573 @ SV357 @ SV517 @ SV222 ) @ SV62 ) )
= $true )
| ( ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SV573 @ SV357 @ SV62 @ SV443 ) )
= $true )
| ( ( c_member @ SV573 @ SV517 @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2502,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i,SV574: $i,SV614: $i,SV648: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV648 @ SV614 ) @ ( c_Product__Type_OPair @ SV648 @ SV614 @ SV574 @ SV518 ) @ SV444 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV648 @ SV358 ) @ ( c_Product__Type_OPair @ SV648 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SV648 @ SV614 @ SV358 @ SV444 @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2503,plain,
! [SV65: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i,SV575: $i,SV615: $i] :
( ( ( hBOOL @ ( hAPP @ SV615 @ SV575 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SV615 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2504,plain,
! [SV451: $i,SV246: $i,SV88: $i,SV576: $i,SV366: $i,SV523: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV523 @ SV366 ) )
= $true )
| ( ( ( hAPP @ SV576 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SV576 @ SV366 @ SV88 ) ) @ SV88 ) )
= $true )
| ( ( SV576
= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2505,plain,
! [SV454: $i,SV525: $i] :
( ( ( c_member @ SV525 @ ( sK31_SY722 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2506,plain,
! [SV454: $i,SV525: $i] :
( ( ( ! [SY2021: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ SY2021 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SY2021 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SY2021 @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2507,plain,
! [SV455: $i,SV649: $i,SV526: $i] :
( ( ( ! [SY2139: $i] :
~ ( c_member @ SV526 @ SY2139 @ SV649 ) )
= $true )
| ( ( ~ ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2508,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SV577 @ SV527 @ SV107 ) ) @ SV107 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2355]) ).
thf(2509,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2355]) ).
thf(2510,plain,
! [SV107: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( ! [SY2163: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SY2163 ) @ SV107 )
| ! [SY2164: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SY2164 ) @ SV107 )
| ( SY2163 = SY2164 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2511,plain,
! [SV261: $i,SV617: $i,SV650: $i,SV108: $i,SV372: $i] :
( ( ( ! [SY2141: $i] :
( ~ ( c_member @ SV372 @ SY2141 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SY2141 @ SV617 ) @ SV261 ) ) )
= $true )
| ( ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2512,plain,
! [SV108: $i,SV261: $i,SV372: $i,SV618: $i,SV651: $i] :
( ( ( ~ ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2513,plain,
! [SV109: $i,SV262: $i] :
( ( ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK70_SY736 @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
= $true )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2514,plain,
! [SV109: $i,SV262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 ) )
= $true )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2515,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) )
| ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2516,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV456: $i,SV579: $i] :
( ( ~ ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) )
| ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2517,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV684: $i] :
( ( ! [SY2165: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY2165 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY2165 ) @ SV264 ) ) )
| ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2518,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV653: $i,SV685: $i] :
( ( ~ ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
| ~ ( ~ ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2519,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV580 @ SV580 ) @ ( c_Product__Type_OPair @ SV580 @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ SV530 ) @ SV112 ) )
= $false )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2520,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( ~ ~ ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) )
= $false )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2521,plain,
! [SV112: $i,SV531: $i,SV686: $i,SV581: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SV686 @ SV531 ) @ SV112 )
| ( c_member @ SV581 @ SV686 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) ) )
= $true )
| ( ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2522,plain,
! [SV113: $i,SV458: $i,SV265: $i,SV375: $i] :
( ( ( c_Wellfounded_Owf @ SV375 @ ( hAPP @ SV265 @ ( sK9_B_x @ SV458 @ SV375 @ SV265 @ SV113 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV113 @ SV375 ) @ ( c_Recdef_Osame__fst @ SV113 @ SV375 @ SV458 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2523,plain,
! [SV114: $i,SV687: $i,SV582: $i,SV266: $i,SV619: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV619 @ SV266 ) @ ( c_Product__Type_OPair @ SV619 @ SV266 @ SV582 @ SV687 ) @ SV114 ) )
= $true )
| ( ( c_member @ SV619 @ SV582 @ ( c_Relation_ODomain @ SV619 @ SV266 @ SV114 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2524,plain,
! [SV114: $i,SV266: $i,SV583: $i,SV620: $i] :
( ( ( c_member @ SV620 @ SV583 @ ( c_Relation_ODomain @ SV620 @ SV266 @ SV114 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV620 @ SV266 ) @ ( c_Product__Type_OPair @ SV620 @ SV266 @ SV583 @ ( sK66_B_y @ SV620 @ SV583 @ SV266 @ SV114 ) ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2525,plain,
! [SV460: $i,SV654: $i,SV533: $i] :
( ( ( c_member @ ( tc_prod @ SV533 @ SV533 ) @ ( c_Product__Type_OPair @ SV533 @ SV533 @ SV654 @ SV654 ) @ ( c_Transitive__Closure_Otrancl @ SV533 @ SV460 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV533 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2526,plain,
! [SV584: $i,SV267: $i,SV115: $i,SV621: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV621 @ SV115 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV267 @ SV584 ) @ ( c_Transitive__Closure_Ortrancl @ SV621 @ SV115 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV621 @ ( c_Set_Oinsert @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV584 @ SV267 ) @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2527,plain,
! [SV115: $i,SV267: $i,SV688: $i] :
( ( ! [SY2167: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2167 @ ( c_Set_Oinsert @ ( tc_prod @ SY2167 @ SY2167 ) @ ( c_Product__Type_OPair @ SY2167 @ SY2167 @ SV688 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SY2167 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2528,plain,
! [SV115: $i,SV267: $i,SV689: $i] :
( ( ! [SY2168: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2168 @ ( c_Set_Oinsert @ ( tc_prod @ SY2168 @ SY2168 ) @ ( c_Product__Type_OPair @ SY2168 @ SY2168 @ SV689 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SY2168 @ SY2168 ) @ ( c_Product__Type_OPair @ SY2168 @ SY2168 @ SV267 @ SV689 ) @ ( c_Transitive__Closure_Ortrancl @ SY2168 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2529,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false )
| ( ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2530,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ SV535 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2531,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2532,plain,
! [SV117: $i,SV536: $i,SV690: $i,SV587: $i] :
( ( ( ~ ( c_member @ SV587 @ SV690 @ SV536 )
| ! [SY2169: $i] :
( ~ ( c_member @ SV587 @ SY2169 @ SV536 )
| ( SV690 = SY2169 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SY2169 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2169 @ SV690 ) @ SV117 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2533,plain,
! [SV118: $i,SV269: $i,SV464: $i,SV539: $i,SV377: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 ) )
= $false )
| ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2534,plain,
! [SV118: $i,SV269: $i,SV464: $i,SV539: $i,SV377: $i] :
( ( ( ~ ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 ) )
= $false )
| ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2535,plain,
! [SV119: $i,SV270: $i,SV588: $i,SV656: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV656 @ SV588 @ SV270 ) @ SV119 ) )
= $false )
| ( ( ( SV588 = SV119 )
| ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2536,plain,
! [SV270: $i,SV119: $i,SV691: $i] :
( ( ( SV691 != SV119 )
| ! [SY2170: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2170 @ SV691 @ SV270 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2537,plain,
! [SV119: $i,SV270: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV270 @ SV119 ) ) )
= $true )
| ( ( ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2538,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ( ( SV465 != SV271 ) )
= $true )
| ( ( ( SV378 != SV120 ) )
= $true )
| ( ( ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2539,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ~ ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2540,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ~ ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2541,plain,
! [SV122: $i,SV272: $i,SV692: $i] :
( ( ! [SY2171: $i] :
~ ( c_member @ ( tc_prod @ SY2171 @ SY2171 ) @ ( c_Product__Type_OPair @ SY2171 @ SY2171 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2171 @ SV122 ) )
| ( SV692 != SV272 )
| ( SV692 = SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2542,plain,
! [SV122: $i,SV272: $i,SV693: $i] :
( ( ! [SY2172: $i] :
( ~ ( c_member @ ( tc_prod @ SY2172 @ SY2172 ) @ ( c_Product__Type_OPair @ SY2172 @ SY2172 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2172 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY2172 @ SY2172 ) @ ( c_Product__Type_OPair @ SY2172 @ SY2172 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY2172 @ SV122 ) )
| ( SV693 = SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2543,plain,
! [SV122: $i,SV272: $i,SV694: $i] :
( ( ! [SY2173: $i] :
( ( SV694 = SV272 )
| ~ ( c_member @ ( tc_prod @ SY2173 @ SY2173 ) @ ( c_Product__Type_OPair @ SY2173 @ SY2173 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SY2173 @ SV122 ) )
| ( c_member @ ( tc_prod @ SY2173 @ SY2173 ) @ ( c_Product__Type_OPair @ SY2173 @ SY2173 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2173 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2544,plain,
! [SV122: $i,SV272: $i,SV695: $i] :
( ( ( SV695 != SV272 )
| ! [SY2174: $i] : ( c_member @ ( tc_prod @ SY2174 @ SY2174 ) @ ( c_Product__Type_OPair @ SY2174 @ SY2174 @ SV695 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2174 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2545,plain,
! [SV624: $i,SV658: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV658 @ SV624 ) )
= $true )
| ( ( ( SV658 != SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2546,plain,
! [SV659: $i,SV625: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV625 @ SV659 ) )
= $true )
| ( ( ( SV659 != SV625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2547,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV589 @ SV123 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV589 @ SV123 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2548,plain,
! [SV123: $i] :
( ( ~ ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2549,plain,
! [SV123: $i] :
( ( ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2550,plain,
! [SV123: $i,SV660: $i,SV696: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV696 @ SV660 @ SV123 )
| ( c_Relation_Ototal__on @ SV696 @ SV660 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2551,plain,
! [SV697: $i,SV124: $i,SV544: $i,SV590: $i] :
( ( ( ! [SY2175: $i] : ( hBOOL @ ( hAPP @ SV590 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SV697 @ SY2175 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV590 @ ( sK75_B_x1 @ SV590 @ SV544 @ SV124 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2552,plain,
! [SV124: $i,SV545: $i,SV698: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ SV698 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV591 @ ( c_Product__Type_OPair @ SV545 @ SV124 @ ( sK73_B_a @ SV591 @ SV545 @ SV124 ) @ ( sK74_SY739 @ SV591 @ SV545 @ SV124 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2553,plain,
! [SV661: $i,SV626: $i] :
( ( ( SV626 = SV661 )
= $true )
| ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV661 @ SV626 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV626 @ SV661 ) @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2554,plain,
( ( ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2555,plain,
( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2556,plain,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK1_B_x @ sK1_B_x ) @ v_L )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2557,plain,
( ( ( ~ ( ( sK2_B_x != sK3_SY704 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2558,plain,
! [SV468: $i,SV662: $i,SV547: $i] :
( ( ( c_member @ ( tc_prod @ SV547 @ SV547 ) @ ( c_Product__Type_OPair @ SV547 @ SV547 @ SV662 @ SV662 ) @ SV468 )
= $false )
| ( ( c_Relation_Oirrefl @ SV547 @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2559,plain,
! [SV469: $i,SV548: $i] :
( ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK78_SY740 @ SV548 @ SV469 ) ) @ SV469 )
= $true )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2560,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2561,plain,
! [SV470: $i,SV699: $i,SV663: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 )
| ! [SY2176: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SY2176 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SY2176 ) @ SV470 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2562,plain,
! [SV125: $i,SV627: $i,SV273: $i,SV592: $i] :
( ( ( ( SV592 != SV273 ) )
= $true )
| ( ( ~ ( c_member @ SV627 @ SV592 @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV627 @ SV627 ) @ ( c_Product__Type_OPair @ SV627 @ SV627 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SV627 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2563,plain,
! [SV125: $i,SV273: $i,SV700: $i] :
( ( ! [SY2177: $i] :
~ ( c_member @ ( tc_prod @ SY2177 @ SY2177 ) @ ( c_Product__Type_OPair @ SY2177 @ SY2177 @ SV700 @ SV273 ) @ ( c_Relation_OId__on @ SY2177 @ SV125 ) )
| ( SV700 = SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2564,plain,
! [SV125: $i,SV273: $i,SV701: $i] :
( ( ! [SY2178: $i] :
( ~ ( c_member @ ( tc_prod @ SY2178 @ SY2178 ) @ ( c_Product__Type_OPair @ SY2178 @ SY2178 @ SV701 @ SV273 ) @ ( c_Relation_OId__on @ SY2178 @ SV125 ) )
| ( c_member @ SY2178 @ SV701 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2565,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) ) )
= $false )
| ( ( SV379 = SV274 )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2410]) ).
thf(2566,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 ) )
= $false )
| ( ( SV379 = SV274 )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2410]) ).
thf(2567,plain,
! [SV275: $i,SV127: $i,SV593: $i,SV628: $i] :
( ( ( c_member @ SV628 @ SV593 @ SV127 )
= $true )
| ( ( ( ( c_Set_Oinsert @ SV628 @ SV593 @ SV275 )
!= ( c_Set_Oinsert @ SV628 @ SV593 @ SV127 ) )
| ( SV275 = SV127 ) )
= $true )
| ( ( c_member @ SV628 @ SV593 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2568,plain,
! [SV275: $i,SV127: $i,SV594: $i,SV629: $i] :
( ( ( c_member @ SV629 @ SV594 @ SV127 )
= $true )
| ( ( ( SV275 != SV127 )
| ( ( c_Set_Oinsert @ SV629 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SV629 @ SV594 @ SV127 ) ) )
= $true )
| ( ( c_member @ SV629 @ SV594 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2569,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2570,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2413]) ).
thf(2571,plain,
! [SV277: $i,SV630: $i,SV129: $i,SV595: $i] :
( ( ( ( SV595 != SV129 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV630 @ SV630 ) @ ( c_Product__Type_OPair @ SV630 @ SV630 @ SV595 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV630 @ SV277 ) )
= $true )
| ( ( c_member @ SV630 @ SV595 @ ( c_Relation_ODomain @ SV630 @ SV630 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2572,plain,
! [SV277: $i,SV129: $i,SV596: $i,SV631: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV631 @ SV631 ) @ ( c_Product__Type_OPair @ SV631 @ SV631 @ SV596 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV631 @ SV277 ) ) )
= $true )
| ( ( SV596 = SV129 )
= $true )
| ( ( c_member @ SV631 @ SV596 @ ( c_Relation_ODomain @ SV631 @ SV631 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2573,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV702: $i] :
( ( ( ! [SY2179: $i] :
( ( c_Product__Type_OPair @ SY2179 @ SV702 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY2179 @ SV702 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV473 = SV278 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2574,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV703: $i] :
( ( ( ! [SY2180: $i] :
( ( c_Product__Type_OPair @ SY2180 @ SV703 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SY2180 @ SV703 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV381 = SV130 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2575,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2576,plain,
! [SV132: $i,SV598: $i,SV704: $i,SV633: $i,SV280: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV633 ) @ ( c_Product__Type_OPair @ SV280 @ SV633 @ SV704 @ SV598 ) @ SV132 ) )
= $true )
| ( ( c_member @ SV633 @ SV598 @ ( c_Relation_ORange @ SV280 @ SV633 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2577,plain,
! [SV132: $i,SV280: $i,SV599: $i,SV634: $i] :
( ( ( c_member @ SV634 @ SV599 @ ( c_Relation_ORange @ SV280 @ SV634 @ SV132 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV280 @ SV634 ) @ ( c_Product__Type_OPair @ SV280 @ SV634 @ ( sK65_B_y @ SV634 @ SV599 @ SV280 @ SV132 ) @ SV599 ) @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2578,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV705: $i] :
( ( ! [SY2181: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY2181 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY2181 ) @ SV281 ) ) )
| ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2579,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV666: $i,SV706: $i] :
( ( ~ ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
| ~ ( ~ ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2580,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV476 @ SV134 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2581,plain,
! [SV134: $i,SV282: $i,SV384: $i,SV476: $i] :
( ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ ( sK42_B_z @ SV476 @ SV384 @ SV282 @ SV134 ) @ SV282 ) @ SV134 )
= $true )
| ( ( c_member @ ( tc_prod @ SV476 @ SV476 ) @ ( c_Product__Type_OPair @ SV476 @ SV476 @ SV384 @ SV282 ) @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2582,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i,SV667: $i] :
( ( ( ! [SY2153: $i] :
~ ( c_member @ ( tc_prod @ SY2153 @ SY2153 ) @ ( c_Product__Type_OPair @ SY2153 @ SY2153 @ SV667 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY2153 @ SV283 ) @ SV135 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV667 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2583,plain,
! [SV283: $i,SV477: $i,SV668: $i,SV135: $i,SV385: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV668 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 ) )
= $true )
| ( ( ! [SY2154: $i] : ( c_member @ ( tc_prod @ SY2154 @ SY2154 ) @ ( c_Product__Type_OPair @ SY2154 @ SY2154 @ SV668 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY2154 @ SV283 ) @ SV135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2584,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2585,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i,SV601: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV601 @ SV601 ) @ ( c_Product__Type_OPair @ SV601 @ SV601 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2586,plain,
! [SV138: $i,SV554: $i,SV285: $i,SV479: $i,SV387: $i,SV601: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2587,plain,
! [SV140: $i,SV286: $i,SV602: $i,SV638: $i] :
( ( ( SV638 = SV602 )
= $false )
| ( ( ~ ( c_member @ SV286 @ SV140 @ SV638 )
| ( c_member @ SV286 @ SV140 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2588,plain,
! [SV140: $i,SV286: $i,SV603: $i,SV639: $i] :
( ( ( SV639 = SV603 )
= $false )
| ( ( ~ ( c_member @ SV286 @ SV140 @ SV603 )
| ( c_member @ SV286 @ SV140 @ SV639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2589,plain,
! [SV141: $i,SV287: $i,SV604: $i,SV640: $i] :
( ( ( SV640 = SV604 )
= $false )
| ( ( ~ ( c_member @ SV287 @ SV640 @ SV141 )
| ( c_member @ SV287 @ SV604 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2590,plain,
! [SV141: $i,SV287: $i,SV605: $i,SV641: $i] :
( ( ( SV641 = SV605 )
= $false )
| ( ( ~ ( c_member @ SV287 @ SV605 @ SV141 )
| ( c_member @ SV287 @ SV641 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2591,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2592,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ~ ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2593,plain,
! [SV143: $i] :
( ( ~ ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2594,plain,
! [SV143: $i] :
( ( ~ ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2595,plain,
! [SV143: $i] :
( ( ~ ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2440]) ).
thf(2596,plain,
! [SV143: $i] :
( ( ~ ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2440]) ).
thf(2597,plain,
! [SV143: $i] :
( ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2598,plain,
! [SV143: $i] :
( ( ~ ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2599,plain,
! [SV143: $i] :
( ( ~ ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2600,plain,
! [SV143: $i] :
( ( ~ ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2601,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2602,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2603,plain,
! [SV606: $i,SV290: $i,SV145: $i,SV642: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV642 @ SV145 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV290 @ SV606 ) @ ( c_Transitive__Closure_Ortrancl @ SV642 @ SV145 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV642 @ ( c_Set_Oinsert @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV606 @ SV290 ) @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2604,plain,
! [SV145: $i,SV290: $i,SV707: $i] :
( ( ! [SY2183: $i] :
( ~ ( c_Wellfounded_Owf @ SY2183 @ ( c_Set_Oinsert @ ( tc_prod @ SY2183 @ SY2183 ) @ ( c_Product__Type_OPair @ SY2183 @ SY2183 @ SV707 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SY2183 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2605,plain,
! [SV145: $i,SV290: $i,SV708: $i] :
( ( ! [SY2184: $i] :
( ~ ( c_Wellfounded_Owf @ SY2184 @ ( c_Set_Oinsert @ ( tc_prod @ SY2184 @ SY2184 ) @ ( c_Product__Type_OPair @ SY2184 @ SY2184 @ SV708 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SY2184 @ SY2184 ) @ ( c_Product__Type_OPair @ SY2184 @ SY2184 @ SV290 @ SV708 ) @ ( c_Transitive__Closure_Ortrancl @ SY2184 @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2606,plain,
! [SV146: $i,SV559: $i,SV607: $i] :
( ( ( c_Relation_Orefl__on @ SV607 @ SV559 @ SV146 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV607 @ SV146 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV607 @ SV559 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2607,plain,
! [SV146: $i,SV673: $i,SV709: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV709 @ SV673 @ SV146 )
| ( c_Relation_Orefl__on @ SV709 @ SV673 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2608,plain,
! [SV146: $i,SV674: $i,SV710: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV710 @ SV674 @ SV146 )
| ( c_Relation_Otrans @ SV710 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2609,plain,
! [SV148: $i,SV292: $i,SV711: $i] :
( ( ! [SY2185: $i] :
( ( SY2185 != SV711 )
| ( c_member @ SV292 @ SV148 @ SY2185 )
| ~ ( c_member @ SV292 @ SV148 @ SY2185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2610,plain,
! [SV148: $i,SV292: $i,SV712: $i] :
( ( ! [SY2186: $i] :
( ( SY2186 != SV712 )
| ( c_member @ SV292 @ SV148 @ SY2186 )
| ~ ( c_member @ SV292 @ SV148 @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2611,plain,
! [SV148: $i,SV292: $i,SV713: $i] :
( ( ! [SY2187: $i] :
( ( SY2187 != SV713 )
| ( c_member @ SV292 @ SV148 @ SV713 )
| ~ ( c_member @ SV292 @ SV148 @ SY2187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2612,plain,
! [SV148: $i,SV292: $i,SV714: $i] :
( ( ! [SY2188: $i] : ( SY2188 != SV714 )
| ( c_member @ SV292 @ SV148 @ SV714 )
| ~ ( c_member @ SV292 @ SV148 @ SV714 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2613,plain,
! [SV149: $i,SV293: $i,SV608: $i,SV643: $i] :
( ( ( c_member @ SV643 @ SV608 @ ( c_Set_Oinsert @ SV643 @ SV293 @ SV149 ) )
= $false )
| ( ( ( SV608 = SV293 )
| ( c_member @ SV643 @ SV608 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2614,plain,
! [SV149: $i,SV293: $i,SV715: $i] :
( ( ( SV715 != SV293 )
| ! [SY2189: $i] : ( c_member @ SY2189 @ SV715 @ ( c_Set_Oinsert @ SY2189 @ SV293 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2615,plain,
! [SV293: $i,SV149: $i,SV716: $i] :
( ( ! [SY2190: $i] :
( ~ ( c_member @ SY2190 @ SV716 @ SV149 )
| ( c_member @ SY2190 @ SV716 @ ( c_Set_Oinsert @ SY2190 @ SV293 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2616,plain,
! [SV294: $i,SV483: $i,SV560: $i,SV391: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ SV483 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2617,plain,
! [SV393: $i,SV152: $i,SV296: $i,SV644: $i,SV675: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV675 @ SV644 ) @ ( c_Product__Type_OPair @ SV675 @ SV644 @ SV296 @ SV152 ) @ SV393 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV675 @ SV644 @ SV393 ) @ SV296 ) @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2618,plain,
! [SV152: $i,SV296: $i,SV393: $i,SV645: $i,SV676: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV676 @ SV645 @ SV393 ) @ SV296 ) @ SV152 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV676 @ SV645 ) @ ( c_Product__Type_OPair @ SV676 @ SV645 @ SV296 @ SV152 ) @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2619,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 ) )
= $false )
| ( ( SV394 = SV297 )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2620,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) ) )
= $false )
| ( ( SV394 = SV297 )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2621,plain,
! [SV298: $i,SV395: $i,SV561: $i,SV485: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV154 @ SV395 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2622,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) ) @ SV155 )
= $true )
| ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2623,plain,
! [SV155: $i,SV299: $i,SV396: $i,SV486: $i] :
( ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK41_B_z @ SV486 @ SV396 @ SV299 @ SV155 ) @ SV299 ) @ ( c_Transitive__Closure_Ortrancl @ SV486 @ SV155 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SV396 @ SV299 ) @ ( c_Transitive__Closure_Otrancl @ SV486 @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2624,plain,
! [SV156: $i,SV300: $i,SV609: $i,SV677: $i] :
( ( ( c_member @ ( tc_prod @ SV677 @ SV677 ) @ ( c_Product__Type_OPair @ SV677 @ SV677 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV677 @ SV156 ) )
= $false )
| ( ( ( SV609 != SV300 )
| ( SV609 = SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2625,plain,
! [SV156: $i,SV300: $i,SV610: $i,SV646: $i] :
( ( ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV646 @ SV156 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SV646 @ SV156 ) )
| ( SV610 = SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2626,plain,
! [SV157: $i,SV301: $i,SV611: $i,SV647: $i] :
( ( ( c_member @ SV647 @ SV611 @ SV301 )
= $false )
| ( ( c_member @ SV647 @ SV611 @ ( c_Set_Oinsert @ SV647 @ SV157 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2627,plain,
! [SV301: $i,SV157: $i,SV612: $i,SV717: $i] :
( ( ( c_member @ SV717 @ SV612 @ ( c_Set_Oinsert @ SV717 @ SV157 @ SV301 ) )
= $true )
| ( ( SV612 = SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2628,plain,
! [SV158: $i,SV302: $i] :
( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ ( sK27_SY720 @ SV302 @ SV158 ) @ ( sK26_B_x @ SV302 @ SV158 ) ) @ SV158 )
= $true )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2629,plain,
! [SV158: $i,SV302: $i] :
( ( ( ( ( sK26_B_x @ SV302 @ SV158 )
!= ( sK27_SY720 @ SV302 @ SV158 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2472]) ).
thf(2630,plain,
! [SV489: $i,SV564: $i] :
( ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK33_B_x @ SV564 @ SV489 ) @ ( sK34_SY725 @ SV564 @ SV489 ) ) @ SV489 )
= $true )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2631,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2632,plain,
! [SV490: $i,SV718: $i,SV678: $i,SV565: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SV718 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV718 @ SV678 ) @ SV490 )
| ( SV678 = SV718 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2633,plain,
! [SV159: $i,SV566: $i,SV613: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV613 @ SV566 @ SV159 )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV613 @ SV159 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV613 @ SV566 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2634,plain,
! [SV159: $i,SV679: $i,SV719: $i] :
( ( ~ ( c_Order__Relation_Opartial__order__on @ SV719 @ SV679 @ SV159 )
| ( c_Order__Relation_Opreorder__on @ SV719 @ SV679 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2635,plain,
! [SV159: $i,SV680: $i,SV720: $i] :
( ( ~ ( c_Order__Relation_Opartial__order__on @ SV720 @ SV680 @ SV159 )
| ( c_Relation_Oantisym @ SV720 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2636,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i,SV721: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV721 @ SV721 ) @ ( c_Product__Type_OPair @ SV721 @ SV721 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2637,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV682: $i,SV722: $i] :
( ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) )
| ! [SY2191: $i] :
( ~ ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SY2191 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2191 )
= ( hAPP @ SV160 @ SY2191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2638,plain,
! [SV305: $i,SV399: $i,SV1: $i,SV162: $i,SV492: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 )
= $true )
| ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
= $false )
| ( ( c_Relation_Otrans @ SV492 @ SV399 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2639,plain,
! [SV19: $i,SV416: $i,SV180: $i,SV322: $i,SV499: $i,SV569: $i] :
( ( ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
| ( SV180 = SV19 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2640,plain,
! [SV184: $i,SV418: $i,SV23: $i,SV326: $i,SV501: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2641,plain,
! [SV344: $i,SV208: $i,SV48: $i,SV435: $i] :
( ( ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV48 @ SV208 ) @ SV344 )
= $false )
| ( ( SV208 = SV48 )
= $true )
| ( ( c_member @ ( tc_prod @ SV435 @ SV435 ) @ ( c_Product__Type_OPair @ SV435 @ SV435 @ SV208 @ SV48 ) @ SV344 )
= $false )
| ( ( c_Relation_Oantisym @ SV435 @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2642,plain,
! [SV443: $i,SV62: $i,SV222: $i,SV517: $i,SV357: $i,SV573: $i] :
( ( ( c_member @ ( tc_prod @ SV573 @ SV357 ) @ ( c_Product__Type_OPair @ SV573 @ SV357 @ SV517 @ SV222 ) @ SV62 )
= $false )
| ( ( c_member @ SV357 @ SV222 @ ( c_Relation_OImage @ SV573 @ SV357 @ SV62 @ SV443 ) )
= $true )
| ( ( c_member @ SV573 @ SV517 @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2643,plain,
! [SV63: $i,SV223: $i,SV358: $i,SV444: $i,SV518: $i,SV574: $i,SV614: $i,SV648: $i] :
( ( ( c_member @ ( tc_prod @ SV648 @ SV614 ) @ ( c_Product__Type_OPair @ SV648 @ SV614 @ SV574 @ SV518 ) @ SV444 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV648 @ SV358 ) @ ( c_Product__Type_OPair @ SV648 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SV648 @ SV614 @ SV358 @ SV444 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2644,plain,
! [SV615: $i,SV65: $i,SV575: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SV615 @ SV225 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV615 @ SV575 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2645,plain,
! [SV451: $i,SV246: $i,SV88: $i,SV576: $i,SV366: $i,SV523: $i] :
( ( ( c_Wellfounded_Owf @ SV523 @ SV366 )
= $false )
| ( ( ( hAPP @ SV576 @ SV88 )
= ( hAPP @ ( hAPP @ SV246 @ ( c_Recdef_Ocut @ SV523 @ SV451 @ SV576 @ SV366 @ SV88 ) ) @ SV88 ) )
= $true )
| ( ( SV576
= ( c_Recdef_Owfrec @ SV523 @ SV451 @ SV366 @ SV246 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2646,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
| ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2647,plain,
! [SV455: $i,SV649: $i,SV724: $i,SV526: $i] :
( ( ( ~ ( c_member @ SV526 @ SV724 @ SV649 ) )
= $true )
| ( ( ~ ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2648,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK52_SY730 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2649,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2650,plain,
! [SV107: $i,SV725: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 )
| ! [SY2192: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SY2192 ) @ SV107 )
| ( SV725 = SY2192 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2651,plain,
! [SV261: $i,SV617: $i,SV650: $i,SV108: $i,SV726: $i,SV372: $i] :
( ( ( ~ ( c_member @ SV372 @ SV726 @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SV726 @ SV617 ) @ SV261 ) )
= $true )
| ( ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2652,plain,
! [SV108: $i,SV261: $i,SV372: $i,SV618: $i,SV651: $i] :
( ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2653,plain,
! [SV109: $i,SV262: $i] :
( ( ( c_member @ ( tc_prod @ SV262 @ SV262 ) @ ( c_Product__Type_OPair @ SV262 @ SV262 @ ( sK69_B_x @ SV262 @ SV109 ) @ ( sK71_SY738 @ SV262 @ SV109 ) ) @ SV109 )
= $false )
| ( ( c_Relation_Otrans @ SV262 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2654,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) )
| ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2655,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV456: $i,SV579: $i] :
( ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) )
| ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2656,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV684: $i] :
( ( ( ! [SY2165: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SY2165 @ ( sK60_B_z @ SY2165 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SY2165 ) @ SV264 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2657,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV653: $i,SV685: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2658,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( c_member @ ( tc_prod @ SV580 @ SV580 ) @ ( c_Product__Type_OPair @ SV580 @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ SV530 ) @ SV112 )
= $true )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2659,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( ~ ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) ) )
= $true )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2520]) ).
thf(2660,plain,
! [SV112: $i,SV531: $i,SV686: $i,SV581: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SV686 @ SV531 ) @ SV112 ) )
= $true )
| ( ( c_member @ SV581 @ SV686 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $true )
| ( ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2661,plain,
! [SV114: $i,SV687: $i,SV582: $i,SV266: $i,SV619: $i] :
( ( ( c_member @ ( tc_prod @ SV619 @ SV266 ) @ ( c_Product__Type_OPair @ SV619 @ SV266 @ SV582 @ SV687 ) @ SV114 )
= $false )
| ( ( c_member @ SV619 @ SV582 @ ( c_Relation_ODomain @ SV619 @ SV266 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2662,plain,
! [SV584: $i,SV267: $i,SV115: $i,SV621: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV621 @ SV115 )
= $false )
| ( ( c_member @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV267 @ SV584 ) @ ( c_Transitive__Closure_Ortrancl @ SV621 @ SV115 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV621 @ ( c_Set_Oinsert @ ( tc_prod @ SV621 @ SV621 ) @ ( c_Product__Type_OPair @ SV621 @ SV621 @ SV584 @ SV267 ) @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2663,plain,
! [SV115: $i,SV267: $i,SV688: $i,SV727: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV727 @ ( c_Set_Oinsert @ ( tc_prod @ SV727 @ SV727 ) @ ( c_Product__Type_OPair @ SV727 @ SV727 @ SV688 @ SV267 ) @ SV115 ) )
| ( c_Wellfounded_Oacyclic @ SV727 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2664,plain,
! [SV115: $i,SV267: $i,SV689: $i,SV728: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV728 @ ( c_Set_Oinsert @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV689 @ SV267 ) @ SV115 ) )
| ~ ( c_member @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV267 @ SV689 ) @ ( c_Transitive__Closure_Ortrancl @ SV728 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2665,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(2666,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( c_member @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ SV535 )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2667,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2668,plain,
! [SV117: $i,SV536: $i,SV690: $i,SV587: $i] :
( ( ( ~ ( c_member @ SV587 @ SV690 @ SV536 ) )
= $true )
| ( ( ! [SY2169: $i] :
( ~ ( c_member @ SV587 @ SY2169 @ SV536 )
| ( SV690 = SY2169 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SY2169 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2169 @ SV690 ) @ SV117 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2669,plain,
! [SV118: $i,SV269: $i,SV464: $i,SV539: $i,SV377: $i] :
( ( ( c_member @ ( tc_prod @ SV377 @ SV539 ) @ ( c_Product__Type_OPair @ SV377 @ SV539 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV464 ) @ SV269 )
= $true )
| ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2670,plain,
! [SV118: $i,SV269: $i,SV464: $i,SV539: $i,SV377: $i] :
( ( ( c_member @ SV377 @ ( sK23_B_x @ SV539 @ SV464 @ SV377 @ SV269 @ SV118 ) @ SV118 )
= $true )
| ( ( c_member @ SV539 @ SV464 @ ( c_Relation_OImage @ SV377 @ SV539 @ SV269 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2671,plain,
! [SV656: $i,SV270: $i,SV119: $i,SV588: $i] :
( ( ( SV588 = SV119 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV656 @ SV588 @ SV270 ) @ SV119 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2672,plain,
! [SV270: $i,SV119: $i,SV691: $i] :
( ( ( ( SV691 != SV119 ) )
= $true )
| ( ( ! [SY2170: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2170 @ SV691 @ SV270 ) @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2673,plain,
! [SV119: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
= $false )
| ( ( ! [SY1542: $i,SY1543: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY1543 @ SY1542 @ SV270 ) @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2674,plain,
! [SV120: $i,SV378: $i,SV271: $i,SV465: $i] :
( ( ( SV465 = SV271 )
= $false )
| ( ( ( SV378 != SV120 ) )
= $true )
| ( ( ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2675,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) )
| ( SV465 = SV271 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2676,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) )
| ( SV378 = SV120 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2540]) ).
thf(2677,plain,
! [SV122: $i,SV272: $i,SV692: $i] :
( ( ( ! [SY2171: $i] :
~ ( c_member @ ( tc_prod @ SY2171 @ SY2171 ) @ ( c_Product__Type_OPair @ SY2171 @ SY2171 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2171 @ SV122 ) ) )
= $true )
| ( ( ( SV692 != SV272 )
| ( SV692 = SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2678,plain,
! [SV122: $i,SV272: $i,SV693: $i,SV729: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV729 @ SV122 ) )
| ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV729 @ SV122 ) )
| ( SV693 = SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2679,plain,
! [SV122: $i,SV730: $i,SV272: $i,SV694: $i] :
( ( ( SV694 = SV272 )
| ~ ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV730 @ SV122 ) )
| ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV730 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2680,plain,
! [SV122: $i,SV272: $i,SV695: $i] :
( ( ( ( SV695 != SV272 ) )
= $true )
| ( ( ! [SY2174: $i] : ( c_member @ ( tc_prod @ SY2174 @ SY2174 ) @ ( c_Product__Type_OPair @ SY2174 @ SY2174 @ SV695 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2174 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2681,plain,
! [SV624: $i,SV658: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV658 @ SV624 )
= $false )
| ( ( ( SV658 != SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2682,plain,
! [SV659: $i,SV625: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV625 @ SV659 )
= $false )
| ( ( ( SV659 != SV625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2683,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ( c_Relation_Oirrefl @ SV589 @ SV123 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV589 @ SV123 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2684,plain,
! [SV123: $i] :
( ( ! [SY1116: $i,SY1117: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1117 @ SY1116 @ SV123 )
| ( c_Relation_Oirrefl @ SY1117 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2685,plain,
! [SV123: $i] :
( ( ! [SY1118: $i,SY1119: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY1119 @ SY1118 @ SV123 )
| ( c_Relation_Otrans @ SY1119 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2686,plain,
! [SV123: $i,SV660: $i,SV696: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV696 @ SV660 @ SV123 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV696 @ SV660 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2687,plain,
! [SV731: $i,SV697: $i,SV124: $i,SV544: $i,SV590: $i] :
( ( ( hBOOL @ ( hAPP @ SV590 @ ( c_Product__Type_OPair @ SV544 @ SV124 @ SV697 @ SV731 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV590 @ ( sK75_B_x1 @ SV590 @ SV544 @ SV124 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2688,plain,
! [SV626: $i,SV661: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV661 @ SV626 ) @ v_L )
= $true )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV626 @ SV661 ) @ v_L )
= $true )
| ( ( SV626 = SV661 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2689,plain,
! [SV732: $i] :
( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV732 @ SV732 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2690,plain,
( ( ( ~ ( ( sK2_B_x != sK3_SY704 ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2691,plain,
( ( ( ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2692,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
| ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2693,plain,
! [SV470: $i,SV699: $i,SV663: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 ) )
= $true )
| ( ( ! [SY2176: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SY2176 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SY2176 ) @ SV470 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2694,plain,
! [SV125: $i,SV627: $i,SV273: $i,SV592: $i] :
( ( ( SV592 = SV273 )
= $false )
| ( ( ~ ( c_member @ SV627 @ SV592 @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV627 @ SV627 ) @ ( c_Product__Type_OPair @ SV627 @ SV627 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SV627 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2695,plain,
! [SV125: $i,SV273: $i,SV700: $i] :
( ( ( ! [SY2177: $i] :
~ ( c_member @ ( tc_prod @ SY2177 @ SY2177 ) @ ( c_Product__Type_OPair @ SY2177 @ SY2177 @ SV700 @ SV273 ) @ ( c_Relation_OId__on @ SY2177 @ SV125 ) ) )
= $true )
| ( ( SV700 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2696,plain,
! [SV125: $i,SV273: $i,SV701: $i,SV733: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV733 @ SV733 ) @ ( c_Product__Type_OPair @ SV733 @ SV733 @ SV701 @ SV273 ) @ ( c_Relation_OId__on @ SV733 @ SV125 ) )
| ( c_member @ SV733 @ SV701 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2697,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $true )
| ( ( SV379 = SV274 )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2698,plain,
! [SV126: $i,SV274: $i,SV379: $i,SV471: $i] :
( ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ ( sK45_B_y @ SV471 @ SV379 @ SV274 @ SV126 ) @ SV274 ) @ SV126 )
= $true )
| ( ( SV379 = SV274 )
= $true )
| ( ( c_member @ ( tc_prod @ SV471 @ SV471 ) @ ( c_Product__Type_OPair @ SV471 @ SV471 @ SV379 @ SV274 ) @ ( c_Transitive__Closure_Ortrancl @ SV471 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2699,plain,
! [SV127: $i,SV275: $i,SV593: $i,SV628: $i] :
( ( ( ( ( c_Set_Oinsert @ SV628 @ SV593 @ SV275 )
!= ( c_Set_Oinsert @ SV628 @ SV593 @ SV127 ) ) )
= $true )
| ( ( SV275 = SV127 )
= $true )
| ( ( c_member @ SV628 @ SV593 @ SV127 )
= $true )
| ( ( c_member @ SV628 @ SV593 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2700,plain,
! [SV594: $i,SV629: $i,SV127: $i,SV275: $i] :
( ( ( ( SV275 != SV127 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV629 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SV629 @ SV594 @ SV127 ) )
= $true )
| ( ( c_member @ SV629 @ SV594 @ SV127 )
= $true )
| ( ( c_member @ SV629 @ SV594 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2701,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2702,plain,
! [SV128: $i,SV276: $i,SV380: $i,SV472: $i] :
( ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ ( sK37_B_c @ SV472 @ SV380 @ SV276 @ SV128 ) @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ SV128 )
= $true )
| ( ( c_member @ ( tc_prod @ SV472 @ SV472 ) @ ( c_Product__Type_OPair @ SV472 @ SV472 @ SV380 @ SV276 ) @ ( c_Transitive__Closure_Otrancl @ SV472 @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2703,plain,
! [SV277: $i,SV630: $i,SV129: $i,SV595: $i] :
( ( ( SV595 = SV129 )
= $false )
| ( ( c_member @ ( tc_prod @ SV630 @ SV630 ) @ ( c_Product__Type_OPair @ SV630 @ SV630 @ SV595 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV630 @ SV277 ) )
= $true )
| ( ( c_member @ SV630 @ SV595 @ ( c_Relation_ODomain @ SV630 @ SV630 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2704,plain,
! [SV277: $i,SV129: $i,SV596: $i,SV631: $i] :
( ( ( c_member @ ( tc_prod @ SV631 @ SV631 ) @ ( c_Product__Type_OPair @ SV631 @ SV631 @ SV596 @ SV129 ) @ ( c_Transitive__Closure_Ortrancl @ SV631 @ SV277 ) )
= $false )
| ( ( SV596 = SV129 )
= $true )
| ( ( c_member @ SV631 @ SV596 @ ( c_Relation_ODomain @ SV631 @ SV631 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2705,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV702: $i,SV734: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV734 @ SV702 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SV734 @ SV702 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV473 = SV278 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2706,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV703: $i,SV735: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV735 @ SV703 @ SV473 @ SV381 )
!= ( c_Product__Type_OPair @ SV735 @ SV703 @ SV278 @ SV130 ) ) )
= $true )
| ( ( SV381 = SV130 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2707,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2708,plain,
! [SV132: $i,SV598: $i,SV704: $i,SV633: $i,SV280: $i] :
( ( ( c_member @ ( tc_prod @ SV280 @ SV633 ) @ ( c_Product__Type_OPair @ SV280 @ SV633 @ SV704 @ SV598 ) @ SV132 )
= $false )
| ( ( c_member @ SV633 @ SV598 @ ( c_Relation_ORange @ SV280 @ SV633 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2709,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV705: $i] :
( ( ( ! [SY2181: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SY2181 @ ( sK55_B_z @ SY2181 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SY2181 ) @ SV281 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2710,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV666: $i,SV706: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) )
= $true )
| ( ( ~ ( ~ ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2711,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i,SV667: $i,SV736: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV736 @ SV736 ) @ ( c_Product__Type_OPair @ SV736 @ SV736 @ SV667 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SV736 @ SV283 ) @ SV135 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV667 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(2712,plain,
! [SV283: $i,SV477: $i,SV668: $i,SV135: $i,SV385: $i] :
( ( ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV668 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
= $false )
| ( ( ! [SY2154: $i] : ( c_member @ ( tc_prod @ SY2154 @ SY2154 ) @ ( c_Product__Type_OPair @ SY2154 @ SY2154 @ SV668 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SY2154 @ SV283 ) @ SV135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2713,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2714,plain,
! [SV138: $i,SV285: $i,SV387: $i,SV479: $i,SV554: $i,SV601: $i] :
( ( ( c_member @ ( tc_prod @ SV601 @ SV601 ) @ ( c_Product__Type_OPair @ SV601 @ SV601 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ SV554 ) @ SV479 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2715,plain,
! [SV138: $i,SV554: $i,SV285: $i,SV479: $i,SV387: $i,SV601: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2716,plain,
! [SV602: $i,SV638: $i,SV140: $i,SV286: $i] :
( ( ( ~ ( c_member @ SV286 @ SV140 @ SV638 ) )
= $true )
| ( ( c_member @ SV286 @ SV140 @ SV602 )
= $true )
| ( ( SV638 = SV602 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2717,plain,
! [SV639: $i,SV603: $i,SV140: $i,SV286: $i] :
( ( ( ~ ( c_member @ SV286 @ SV140 @ SV603 ) )
= $true )
| ( ( c_member @ SV286 @ SV140 @ SV639 )
= $true )
| ( ( SV639 = SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2718,plain,
! [SV604: $i,SV141: $i,SV640: $i,SV287: $i] :
( ( ( ~ ( c_member @ SV287 @ SV640 @ SV141 ) )
= $true )
| ( ( c_member @ SV287 @ SV604 @ SV141 )
= $true )
| ( ( SV640 = SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2719,plain,
! [SV641: $i,SV141: $i,SV605: $i,SV287: $i] :
( ( ( ~ ( c_member @ SV287 @ SV605 @ SV141 ) )
= $true )
| ( ( c_member @ SV287 @ SV641 @ SV141 )
= $true )
| ( ( SV641 = SV605 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2720,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( c_member @ ( tc_prod @ SV388 @ SV288 ) @ ( c_Product__Type_OPair @ SV388 @ SV288 @ ( sK48_B_x @ SV388 @ SV288 @ SV142 ) @ ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) @ SV142 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2721,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
!= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2722,plain,
! [SV143: $i] :
( ( ! [SY1223: $i,SY1224: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1224 @ SY1223 )
| ( SY1224 = SY1223 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1223 @ SY1224 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1223 ) @ SY1224 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2593]) ).
thf(2723,plain,
! [SV143: $i] :
( ( ! [SY1225: $i,SY1226: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1226 @ SY1225 )
| ( SY1226 = SY1225 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1225 ) @ SY1226 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2594]) ).
thf(2724,plain,
! [SV143: $i] :
( ( ! [SY1227: $i,SY1228: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1228 @ SY1227 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1227 @ SY1228 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1227 ) @ SY1228 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2725,plain,
! [SV143: $i] :
( ( ! [SY1229: $i,SY1230: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1230 @ SY1229 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1229 ) @ SY1230 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2726,plain,
! [SV143: $i] :
( ( ! [SY1231: $i,SY1232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) )
| ( SY1232 = SY1231 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1231 @ SY1232 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1231 ) @ SY1232 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2597]) ).
thf(2727,plain,
! [SV143: $i] :
( ( ! [SY1233: $i,SY1234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( SY1234 = SY1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1233 ) @ SY1234 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2728,plain,
! [SV143: $i] :
( ( ! [SY1235: $i,SY1236: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY1235 @ SY1236 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1235 ) @ SY1236 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2729,plain,
! [SV143: $i] :
( ( ! [SY1237: $i,SY1238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1237 ) @ SY1238 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2730,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2601]) ).
thf(2731,plain,
! [SV144: $i,SV289: $i,SV389: $i,SV482: $i] :
( ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ ( sK38_B_y @ SV482 @ SV389 @ SV289 @ SV144 ) @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ SV144 )
= $true )
| ( ( c_member @ ( tc_prod @ SV482 @ SV482 ) @ ( c_Product__Type_OPair @ SV482 @ SV482 @ SV389 @ SV289 ) @ ( c_Transitive__Closure_Otrancl @ SV482 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2732,plain,
! [SV606: $i,SV290: $i,SV145: $i,SV642: $i] :
( ( ( c_Wellfounded_Owf @ SV642 @ SV145 )
= $false )
| ( ( c_member @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV290 @ SV606 ) @ ( c_Transitive__Closure_Ortrancl @ SV642 @ SV145 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV642 @ ( c_Set_Oinsert @ ( tc_prod @ SV642 @ SV642 ) @ ( c_Product__Type_OPair @ SV642 @ SV642 @ SV606 @ SV290 ) @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2733,plain,
! [SV145: $i,SV290: $i,SV707: $i,SV737: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV737 @ ( c_Set_Oinsert @ ( tc_prod @ SV737 @ SV737 ) @ ( c_Product__Type_OPair @ SV737 @ SV737 @ SV707 @ SV290 ) @ SV145 ) )
| ( c_Wellfounded_Owf @ SV737 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2734,plain,
! [SV145: $i,SV290: $i,SV708: $i,SV738: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV738 @ ( c_Set_Oinsert @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV708 @ SV290 ) @ SV145 ) )
| ~ ( c_member @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV290 @ SV708 ) @ ( c_Transitive__Closure_Ortrancl @ SV738 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(2735,plain,
! [SV559: $i,SV146: $i,SV607: $i] :
( ( ( c_Relation_Otrans @ SV607 @ SV146 )
= $false )
| ( ( c_Relation_Orefl__on @ SV607 @ SV559 @ SV146 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV607 @ SV559 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2736,plain,
! [SV146: $i,SV673: $i,SV709: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV709 @ SV673 @ SV146 ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV709 @ SV673 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2737,plain,
! [SV146: $i,SV674: $i,SV710: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV710 @ SV674 @ SV146 ) )
= $true )
| ( ( c_Relation_Otrans @ SV710 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2738,plain,
! [SV148: $i,SV292: $i,SV711: $i,SV739: $i] :
( ( ( SV739 != SV711 )
| ( c_member @ SV292 @ SV148 @ SV739 )
| ~ ( c_member @ SV292 @ SV148 @ SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(2739,plain,
! [SV148: $i,SV292: $i,SV712: $i,SV740: $i] :
( ( ( SV740 != SV712 )
| ( c_member @ SV292 @ SV148 @ SV740 )
| ~ ( c_member @ SV292 @ SV148 @ SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2740,plain,
! [SV148: $i,SV292: $i,SV713: $i,SV741: $i] :
( ( ( SV741 != SV713 )
| ( c_member @ SV292 @ SV148 @ SV713 )
| ~ ( c_member @ SV292 @ SV148 @ SV741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2741,plain,
! [SV148: $i,SV292: $i,SV714: $i] :
( ( ( ! [SY2188: $i] : ( SY2188 != SV714 ) )
= $true )
| ( ( ( c_member @ SV292 @ SV148 @ SV714 )
| ~ ( c_member @ SV292 @ SV148 @ SV714 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2742,plain,
! [SV149: $i,SV643: $i,SV293: $i,SV608: $i] :
( ( ( SV608 = SV293 )
= $true )
| ( ( c_member @ SV643 @ SV608 @ SV149 )
= $true )
| ( ( c_member @ SV643 @ SV608 @ ( c_Set_Oinsert @ SV643 @ SV293 @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2743,plain,
! [SV149: $i,SV293: $i,SV715: $i] :
( ( ( ( SV715 != SV293 ) )
= $true )
| ( ( ! [SY2189: $i] : ( c_member @ SY2189 @ SV715 @ ( c_Set_Oinsert @ SY2189 @ SV293 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2744,plain,
! [SV293: $i,SV149: $i,SV716: $i,SV742: $i] :
( ( ~ ( c_member @ SV742 @ SV716 @ SV149 )
| ( c_member @ SV742 @ SV716 @ ( c_Set_Oinsert @ SV742 @ SV293 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2745,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2746,plain,
! [SV393: $i,SV152: $i,SV296: $i,SV644: $i,SV675: $i] :
( ( ( c_member @ ( tc_prod @ SV675 @ SV644 ) @ ( c_Product__Type_OPair @ SV675 @ SV644 @ SV296 @ SV152 ) @ SV393 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV675 @ SV644 @ SV393 ) @ SV296 ) @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2747,plain,
! [SV152: $i,SV296: $i,SV393: $i,SV645: $i,SV676: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV676 @ SV645 @ SV393 ) @ SV296 ) @ SV152 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV676 @ SV645 ) @ ( c_Product__Type_OPair @ SV676 @ SV645 @ SV296 @ SV152 ) @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2748,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) ) @ SV153 )
= $true )
| ( ( SV394 = SV297 )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2619]) ).
thf(2749,plain,
! [SV153: $i,SV297: $i,SV394: $i,SV484: $i] :
( ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ ( sK44_B_y @ SV484 @ SV394 @ SV297 @ SV153 ) @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $true )
| ( ( SV394 = SV297 )
= $true )
| ( ( c_member @ ( tc_prod @ SV484 @ SV484 ) @ ( c_Product__Type_OPair @ SV484 @ SV484 @ SV394 @ SV297 ) @ ( c_Transitive__Closure_Ortrancl @ SV484 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2620]) ).
thf(2750,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2751,plain,
! [SV156: $i,SV677: $i,SV300: $i,SV609: $i] :
( ( ( ( SV609 != SV300 ) )
= $true )
| ( ( SV609 = SV300 )
= $true )
| ( ( c_member @ ( tc_prod @ SV677 @ SV677 ) @ ( c_Product__Type_OPair @ SV677 @ SV677 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV677 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2752,plain,
! [SV156: $i,SV300: $i,SV610: $i,SV646: $i] :
( ( ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Otrancl @ SV646 @ SV156 ) )
= $true )
| ( ( SV610 = SV300 )
= $true )
| ( ( c_member @ ( tc_prod @ SV646 @ SV646 ) @ ( c_Product__Type_OPair @ SV646 @ SV646 @ SV610 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV646 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2753,plain,
! [SV158: $i,SV302: $i] :
( ( ( ( sK26_B_x @ SV302 @ SV158 )
= ( sK27_SY720 @ SV302 @ SV158 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV302 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2754,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
| ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2755,plain,
! [SV490: $i,SV718: $i,SV678: $i,SV565: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SV718 ) @ SV490 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV718 @ SV678 ) @ SV490 )
| ( SV678 = SV718 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2756,plain,
! [SV566: $i,SV159: $i,SV613: $i] :
( ( ( c_Relation_Oantisym @ SV613 @ SV159 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV613 @ SV566 @ SV159 )
= $false )
| ( ( c_Order__Relation_Opartial__order__on @ SV613 @ SV566 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2757,plain,
! [SV159: $i,SV679: $i,SV719: $i] :
( ( ( ~ ( c_Order__Relation_Opartial__order__on @ SV719 @ SV679 @ SV159 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV719 @ SV679 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2758,plain,
! [SV159: $i,SV680: $i,SV720: $i] :
( ( ( ~ ( c_Order__Relation_Opartial__order__on @ SV720 @ SV680 @ SV159 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV720 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2759,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i,SV721: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV721 @ SV721 ) @ ( c_Product__Type_OPair @ SV721 @ SV721 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2760,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV682: $i,SV722: $i] :
( ( ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
!= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) ) )
= $true )
| ( ( ! [SY2191: $i] :
( ~ ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SY2191 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2191 )
= ( hAPP @ SV160 @ SY2191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2761,plain,
! [SV305: $i,SV399: $i,SV1: $i,SV162: $i,SV492: $i] :
( ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV162 @ SV1 ) @ SV399 )
= $false )
| ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV1 ) @ SV399 )
= $true )
| ( ( c_member @ ( tc_prod @ SV492 @ SV492 ) @ ( c_Product__Type_OPair @ SV492 @ SV492 @ SV305 @ SV162 ) @ SV399 )
= $false )
| ( ( c_Relation_Otrans @ SV492 @ SV399 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2762,plain,
! [SV180: $i,SV416: $i,SV19: $i,SV322: $i,SV499: $i,SV569: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 ) )
= $true )
| ( ( SV180 = SV19 )
= $true )
| ( ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2763,plain,
! [SV184: $i,SV418: $i,SV23: $i,SV326: $i,SV501: $i] :
( ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
| ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2764,plain,
! [SV444: $i,SV574: $i,SV648: $i,SV63: $i,SV223: $i,SV518: $i,SV358: $i,SV614: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV648 @ SV358 ) @ ( c_Product__Type_OPair @ SV648 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SV648 @ SV614 @ SV358 @ SV444 @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV648 @ SV614 ) @ ( c_Product__Type_OPair @ SV648 @ SV614 @ SV574 @ SV518 ) @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2765,plain,
! [SV615: $i,SV65: $i,SV575: $i,SV225: $i,SV359: $i,SV445: $i,SV519: $i] :
( ( ( c_member @ ( tc_prod @ SV519 @ SV519 ) @ ( c_Product__Type_OPair @ SV519 @ SV519 @ SV445 @ SV359 ) @ ( hAPP @ SV225 @ SV575 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV65 @ SV519 ) @ ( tc_prod @ SV65 @ SV519 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV445 ) @ ( c_Product__Type_OPair @ SV65 @ SV519 @ SV575 @ SV359 ) ) @ ( c_Recdef_Osame__fst @ SV65 @ SV519 @ SV615 @ SV225 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV615 @ SV575 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2766,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) ) )
= $true )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2767,plain,
! [SV455: $i,SV649: $i,SV724: $i,SV526: $i] :
( ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( ~ ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2768,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
| ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2769,plain,
! [SV107: $i,SV725: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 ) )
= $true )
| ( ( ! [SY2192: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SY2192 ) @ SV107 )
| ( SV725 = SY2192 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2770,plain,
! [SV261: $i,SV617: $i,SV650: $i,SV108: $i,SV726: $i,SV372: $i] :
( ( ( ~ ( c_member @ SV372 @ SV726 @ SV108 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SV726 @ SV617 ) @ SV261 ) )
= $true )
| ( ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2771,plain,
! [SV108: $i,SV261: $i,SV618: $i,SV651: $i,SV372: $i] :
( ( ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
| ~ ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) )
= $false )
| ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2772,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2773,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ~ ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2774,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV456: $i,SV579: $i] :
( ( ~ ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2655]) ).
thf(2775,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV263: $i,SV456: $i,SV579: $i] :
( ( ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2655]) ).
thf(2776,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV743: $i,SV684: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2777,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV653: $i,SV685: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false )
| ( ( ~ ( ~ ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2778,plain,
! [SV112: $i,SV530: $i,SV580: $i] :
( ( ( c_member @ SV580 @ ( sK61_B_x @ SV580 @ SV530 @ SV112 ) @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $false )
| ( ( c_member @ SV580 @ SV530 @ ( c_Wellfounded_Oacc @ SV580 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2779,plain,
! [SV112: $i,SV531: $i,SV686: $i,SV581: $i] :
( ( ( c_member @ ( tc_prod @ SV581 @ SV581 ) @ ( c_Product__Type_OPair @ SV581 @ SV581 @ SV686 @ SV531 ) @ SV112 )
= $false )
| ( ( c_member @ SV581 @ SV686 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $true )
| ( ( c_member @ SV581 @ SV531 @ ( c_Wellfounded_Oacc @ SV581 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2780,plain,
! [SV115: $i,SV267: $i,SV688: $i,SV727: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV727 @ ( c_Set_Oinsert @ ( tc_prod @ SV727 @ SV727 ) @ ( c_Product__Type_OPair @ SV727 @ SV727 @ SV688 @ SV267 ) @ SV115 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV727 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2781,plain,
! [SV115: $i,SV267: $i,SV689: $i,SV728: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV728 @ ( c_Set_Oinsert @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV689 @ SV267 ) @ SV115 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV267 @ SV689 ) @ ( c_Transitive__Closure_Ortrancl @ SV728 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(2782,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2783,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2784,plain,
! [SV117: $i,SV536: $i,SV690: $i,SV587: $i] :
( ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( ! [SY2169: $i] :
( ~ ( c_member @ SV587 @ SY2169 @ SV536 )
| ( SV690 = SY2169 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SY2169 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SY2169 @ SV690 ) @ SV117 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2785,plain,
! [SV270: $i,SV119: $i,SV691: $i] :
( ( ( SV691 = SV119 )
= $false )
| ( ( ! [SY2170: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2170 @ SV691 @ SV270 ) @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2786,plain,
! [SV119: $i,SV270: $i,SV744: $i] :
( ( ( ! [SY2193: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2193 @ SV744 @ SV270 ) @ SV119 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(2787,plain,
! [SV271: $i,SV465: $i,SV120: $i,SV378: $i] :
( ( ( SV378 = SV120 )
= $false )
| ( ( SV465 = SV271 )
= $false )
| ( ( ! [SY1953: $i,SY1954: $i] :
( ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY1954 @ SY1953 @ SV271 @ SV120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2788,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ( ! [SY1955: $i,SY1956: $i] :
( ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1956 @ SY1955 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV465 = SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2789,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i] :
( ( ( ! [SY1957: $i,SY1958: $i] :
( ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY1958 @ SY1957 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV378 = SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2790,plain,
! [SV122: $i,SV272: $i,SV692: $i,SV745: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV745 @ SV745 ) @ ( c_Product__Type_OPair @ SV745 @ SV745 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV745 @ SV122 ) ) )
= $true )
| ( ( ( SV692 != SV272 )
| ( SV692 = SV272 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(2791,plain,
! [SV122: $i,SV272: $i,SV693: $i,SV729: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV729 @ SV122 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV729 @ SV122 ) )
| ( SV693 = SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2792,plain,
! [SV122: $i,SV730: $i,SV272: $i,SV694: $i] :
( ( ( ( SV694 = SV272 )
| ~ ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV730 @ SV122 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV730 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2793,plain,
! [SV122: $i,SV272: $i,SV695: $i] :
( ( ( SV695 = SV272 )
= $false )
| ( ( ! [SY2174: $i] : ( c_member @ ( tc_prod @ SY2174 @ SY2174 ) @ ( c_Product__Type_OPair @ SY2174 @ SY2174 @ SV695 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SY2174 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2794,plain,
! [SV624: $i,SV658: $i] :
( ( ( SV658 = SV624 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV658 @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2795,plain,
! [SV625: $i,SV659: $i] :
( ( ( SV659 = SV625 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV625 @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2796,plain,
! [SV543: $i,SV123: $i,SV589: $i] :
( ( ( c_Relation_Otrans @ SV589 @ SV123 )
= $false )
| ( ( c_Relation_Oirrefl @ SV589 @ SV123 )
= $false )
| ( ( ~ ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2797,plain,
! [SV123: $i,SV746: $i] :
( ( ! [SY2194: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2194 @ SV746 @ SV123 )
| ( c_Relation_Oirrefl @ SY2194 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(2798,plain,
! [SV123: $i,SV747: $i] :
( ( ! [SY2195: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2195 @ SV747 @ SV123 )
| ( c_Relation_Otrans @ SY2195 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(2799,plain,
! [SV123: $i,SV660: $i,SV696: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV696 @ SV660 @ SV123 )
= $false )
| ( ( c_Relation_Ototal__on @ SV696 @ SV660 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2800,plain,
! [SV732: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV732 @ SV732 ) @ v_L )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2801,plain,
( ( ( ( sK2_B_x != sK3_SY704 ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2802,plain,
( ( ( ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2803,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2692]) ).
thf(2804,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2692]) ).
thf(2805,plain,
! [SV470: $i,SV699: $i,SV663: $i,SV549: $i] :
( ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 )
= $false )
| ( ( ! [SY2176: $i] :
( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SY2176 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SY2176 ) @ SV470 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2806,plain,
! [SV273: $i,SV125: $i,SV592: $i,SV627: $i] :
( ( ( c_member @ SV627 @ SV592 @ SV125 )
= $false )
| ( ( SV592 = SV273 )
= $false )
| ( ( c_member @ ( tc_prod @ SV627 @ SV627 ) @ ( c_Product__Type_OPair @ SV627 @ SV627 @ SV592 @ SV273 ) @ ( c_Relation_OId__on @ SV627 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2807,plain,
! [SV125: $i,SV273: $i,SV700: $i,SV748: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV748 @ SV748 ) @ ( c_Product__Type_OPair @ SV748 @ SV748 @ SV700 @ SV273 ) @ ( c_Relation_OId__on @ SV748 @ SV125 ) ) )
= $true )
| ( ( SV700 = SV273 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(2808,plain,
! [SV125: $i,SV273: $i,SV701: $i,SV733: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV733 @ SV733 ) @ ( c_Product__Type_OPair @ SV733 @ SV733 @ SV701 @ SV273 ) @ ( c_Relation_OId__on @ SV733 @ SV125 ) ) )
= $true )
| ( ( c_member @ SV733 @ SV701 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2696]) ).
thf(2809,plain,
! [SV127: $i,SV275: $i,SV593: $i,SV628: $i] :
( ( ( ( c_Set_Oinsert @ SV628 @ SV593 @ SV275 )
= ( c_Set_Oinsert @ SV628 @ SV593 @ SV127 ) )
= $false )
| ( ( SV275 = SV127 )
= $true )
| ( ( c_member @ SV628 @ SV593 @ SV127 )
= $true )
| ( ( c_member @ SV628 @ SV593 @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2810,plain,
! [SV594: $i,SV629: $i,SV127: $i,SV275: $i] :
( ( ( SV275 = SV127 )
= $false )
| ( ( ( c_Set_Oinsert @ SV629 @ SV594 @ SV275 )
= ( c_Set_Oinsert @ SV629 @ SV594 @ SV127 ) )
= $true )
| ( ( c_member @ SV629 @ SV594 @ SV127 )
= $true )
| ( ( c_member @ SV629 @ SV594 @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2811,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV702: $i,SV734: $i] :
( ( ( ( c_Product__Type_OPair @ SV734 @ SV702 @ SV473 @ SV381 )
= ( c_Product__Type_OPair @ SV734 @ SV702 @ SV278 @ SV130 ) )
= $false )
| ( ( SV473 = SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2812,plain,
! [SV130: $i,SV278: $i,SV381: $i,SV473: $i,SV703: $i,SV735: $i] :
( ( ( ( c_Product__Type_OPair @ SV735 @ SV703 @ SV473 @ SV381 )
= ( c_Product__Type_OPair @ SV735 @ SV703 @ SV278 @ SV130 ) )
= $false )
| ( ( SV381 = SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2813,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV632: $i,SV664: $i,SV550: $i,SV597: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2814,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV749: $i,SV705: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(2815,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV666: $i,SV706: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false )
| ( ( ~ ( ~ ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2816,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i,SV667: $i,SV736: $i] :
( ( ( c_member @ ( tc_prod @ SV736 @ SV736 ) @ ( c_Product__Type_OPair @ SV736 @ SV736 @ SV667 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SV736 @ SV283 ) @ SV135 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV667 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2817,plain,
! [SV135: $i,SV283: $i,SV385: $i,SV477: $i,SV668: $i,SV750: $i] :
( ( ( c_member @ ( tc_prod @ SV750 @ SV750 ) @ ( c_Product__Type_OPair @ SV750 @ SV750 @ SV668 @ SV477 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV385 @ SV750 @ SV283 ) @ SV135 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV385 @ SV385 ) @ ( c_Product__Type_OPair @ SV385 @ SV385 @ ( hAPP @ SV135 @ SV668 ) @ ( hAPP @ SV135 @ SV477 ) ) @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(2818,plain,
! [SV284: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV386: $i,SV478: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2819,plain,
! [SV138: $i,SV554: $i,SV285: $i,SV479: $i,SV387: $i,SV601: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) @ ( hAPP @ SV138 @ ( sK56_B_z @ SV601 @ SV554 @ SV479 @ SV387 @ SV285 @ SV138 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV601 @ SV387 @ SV479 @ SV285 @ SV554 @ ( hAPP @ ( hAPP @ SV285 @ SV138 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2820,plain,
! [SV602: $i,SV638: $i,SV140: $i,SV286: $i] :
( ( ( c_member @ SV286 @ SV140 @ SV638 )
= $false )
| ( ( c_member @ SV286 @ SV140 @ SV602 )
= $true )
| ( ( SV638 = SV602 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2821,plain,
! [SV639: $i,SV603: $i,SV140: $i,SV286: $i] :
( ( ( c_member @ SV286 @ SV140 @ SV603 )
= $false )
| ( ( c_member @ SV286 @ SV140 @ SV639 )
= $true )
| ( ( SV639 = SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2822,plain,
! [SV604: $i,SV141: $i,SV640: $i,SV287: $i] :
( ( ( c_member @ SV287 @ SV640 @ SV141 )
= $false )
| ( ( c_member @ SV287 @ SV604 @ SV141 )
= $true )
| ( ( SV640 = SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2823,plain,
! [SV641: $i,SV141: $i,SV605: $i,SV287: $i] :
( ( ( c_member @ SV287 @ SV605 @ SV141 )
= $false )
| ( ( c_member @ SV287 @ SV641 @ SV141 )
= $true )
| ( ( SV641 = SV605 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2824,plain,
! [SV142: $i,SV288: $i,SV388: $i] :
( ( ( ( sK49_SY727 @ SV388 @ SV288 @ SV142 )
= ( sK50_SY729 @ SV388 @ SV288 @ SV142 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV388 @ SV288 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2825,plain,
! [SV143: $i,SV751: $i] :
( ( ! [SY2196: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2196 @ SV751 )
| ( SY2196 = SV751 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV751 @ SY2196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV751 ) @ SY2196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2826,plain,
! [SV143: $i,SV752: $i] :
( ( ! [SY2197: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2197 @ SV752 )
| ( SY2197 = SV752 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SY2197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SY2197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(2827,plain,
! [SV143: $i,SV753: $i] :
( ( ! [SY2198: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2198 @ SV753 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SY2198 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SY2198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SY2198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(2828,plain,
! [SV143: $i,SV754: $i] :
( ( ! [SY2199: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2199 @ SV754 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SY2199 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SY2199 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SY2199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2829,plain,
! [SV755: $i,SV143: $i] :
( ( ! [SY2200: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SY2200 ) )
| ( SY2200 = SV755 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SY2200 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SY2200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2830,plain,
! [SV756: $i,SV143: $i] :
( ( ! [SY2201: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SY2201 ) )
| ( SY2201 = SV756 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SY2201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SY2201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(2831,plain,
! [SV757: $i,SV143: $i] :
( ( ! [SY2202: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SY2202 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SY2202 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SY2202 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SY2202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(2832,plain,
! [SV758: $i,SV143: $i] :
( ( ! [SY2203: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SY2203 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SY2203 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SY2203 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SY2203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2833,plain,
! [SV145: $i,SV290: $i,SV707: $i,SV737: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV737 @ ( c_Set_Oinsert @ ( tc_prod @ SV737 @ SV737 ) @ ( c_Product__Type_OPair @ SV737 @ SV737 @ SV707 @ SV290 ) @ SV145 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV737 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2834,plain,
! [SV145: $i,SV290: $i,SV708: $i,SV738: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV738 @ ( c_Set_Oinsert @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV708 @ SV290 ) @ SV145 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV290 @ SV708 ) @ ( c_Transitive__Closure_Ortrancl @ SV738 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(2835,plain,
! [SV146: $i,SV673: $i,SV709: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV709 @ SV673 @ SV146 )
= $false )
| ( ( c_Relation_Orefl__on @ SV709 @ SV673 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2836,plain,
! [SV146: $i,SV674: $i,SV710: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV710 @ SV674 @ SV146 )
= $false )
| ( ( c_Relation_Otrans @ SV710 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2837,plain,
! [SV148: $i,SV292: $i,SV711: $i,SV739: $i] :
( ( ( ( SV739 != SV711 ) )
= $true )
| ( ( ( c_member @ SV292 @ SV148 @ SV739 )
| ~ ( c_member @ SV292 @ SV148 @ SV739 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2838,plain,
! [SV148: $i,SV292: $i,SV712: $i,SV740: $i] :
( ( ( ( SV740 != SV712 ) )
= $true )
| ( ( ( c_member @ SV292 @ SV148 @ SV740 )
| ~ ( c_member @ SV292 @ SV148 @ SV712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2839,plain,
! [SV148: $i,SV292: $i,SV713: $i,SV741: $i] :
( ( ( ( SV741 != SV713 ) )
= $true )
| ( ( ( c_member @ SV292 @ SV148 @ SV713 )
| ~ ( c_member @ SV292 @ SV148 @ SV741 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2840,plain,
! [SV148: $i,SV292: $i,SV714: $i,SV759: $i] :
( ( ( ( SV759 != SV714 ) )
= $true )
| ( ( ( c_member @ SV292 @ SV148 @ SV714 )
| ~ ( c_member @ SV292 @ SV148 @ SV714 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2841,plain,
! [SV149: $i,SV293: $i,SV715: $i] :
( ( ( SV715 = SV293 )
= $false )
| ( ( ! [SY2189: $i] : ( c_member @ SY2189 @ SV715 @ ( c_Set_Oinsert @ SY2189 @ SV293 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2842,plain,
! [SV293: $i,SV149: $i,SV716: $i,SV742: $i] :
( ( ( ~ ( c_member @ SV742 @ SV716 @ SV149 ) )
= $true )
| ( ( c_member @ SV742 @ SV716 @ ( c_Set_Oinsert @ SV742 @ SV293 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(2843,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2844,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2845,plain,
! [SV156: $i,SV677: $i,SV300: $i,SV609: $i] :
( ( ( SV609 = SV300 )
= $false )
| ( ( SV609 = SV300 )
= $true )
| ( ( c_member @ ( tc_prod @ SV677 @ SV677 ) @ ( c_Product__Type_OPair @ SV677 @ SV677 @ SV609 @ SV300 ) @ ( c_Transitive__Closure_Ortrancl @ SV677 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2846,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2847,plain,
! [SV489: $i,SV564: $i] :
( ( ( ~ ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2848,plain,
! [SV490: $i,SV718: $i,SV678: $i,SV565: $i] :
( ( ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SV718 ) @ SV490 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV718 @ SV678 ) @ SV490 )
| ( SV678 = SV718 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2849,plain,
! [SV159: $i,SV679: $i,SV719: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ SV719 @ SV679 @ SV159 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV719 @ SV679 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2850,plain,
! [SV159: $i,SV680: $i,SV720: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ SV720 @ SV680 @ SV159 )
= $false )
| ( ( c_Relation_Oantisym @ SV720 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2851,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i,SV721: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV721 @ SV721 ) @ ( c_Product__Type_OPair @ SV721 @ SV721 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
| ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2852,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV682: $i,SV722: $i] :
( ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) )
= $false )
| ( ( ! [SY2191: $i] :
( ~ ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SY2191 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SY2191 )
= ( hAPP @ SV160 @ SY2191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2853,plain,
! [SV180: $i,SV416: $i,SV19: $i,SV322: $i,SV499: $i,SV569: $i] :
( ( ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV19 ) @ SV416 )
= $false )
| ( ( SV180 = SV19 )
= $true )
| ( ( c_member @ ( tc_prod @ SV569 @ SV499 ) @ ( c_Product__Type_OPair @ SV569 @ SV499 @ SV322 @ SV180 ) @ SV416 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV569 @ SV499 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2854,plain,
! [SV326: $i,SV418: $i,SV23: $i,SV184: $i,SV501: $i] :
( ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV184 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV23 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV23 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV501 @ SV501 ) @ ( c_Product__Type_OPair @ SV501 @ SV501 @ SV326 @ SV184 ) @ ( c_Transitive__Closure_Ortrancl @ SV501 @ SV418 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV501 @ SV501 @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2855,plain,
! [SV444: $i,SV574: $i,SV648: $i,SV63: $i,SV223: $i,SV518: $i,SV358: $i,SV614: $i] :
( ( ( c_member @ ( tc_prod @ SV614 @ SV358 ) @ ( c_Product__Type_OPair @ SV614 @ SV358 @ SV518 @ SV223 ) @ SV63 )
= $false )
| ( ( c_member @ ( tc_prod @ SV648 @ SV358 ) @ ( c_Product__Type_OPair @ SV648 @ SV358 @ SV574 @ SV223 ) @ ( c_Relation_Orel__comp @ SV648 @ SV614 @ SV358 @ SV444 @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV648 @ SV614 ) @ ( c_Product__Type_OPair @ SV648 @ SV614 @ SV574 @ SV518 ) @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2856,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 )
| ~ ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $false )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2857,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV526: $i] :
( ( ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) )
| ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) )
= $false )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2858,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2859,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2860,plain,
! [SV107: $i,SV725: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 )
= $false )
| ( ( ! [SY2192: $i] :
( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SY2192 ) @ SV107 )
| ( SV725 = SY2192 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2861,plain,
! [SV261: $i,SV617: $i,SV650: $i,SV108: $i,SV726: $i,SV372: $i] :
( ( ( c_member @ SV372 @ SV726 @ SV108 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SV726 @ SV617 ) @ SV261 ) )
= $true )
| ( ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2862,plain,
! [SV108: $i,SV261: $i,SV618: $i,SV651: $i,SV372: $i] :
( ( ( ~ ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 ) )
= $false )
| ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2863,plain,
! [SV108: $i,SV261: $i,SV618: $i,SV651: $i,SV372: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 ) )
= $false )
| ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2864,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ! [SY2084: $i,SY2085: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2085 @ SY2084 ) @ ( tc_prod @ SY2085 @ SY2084 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2084 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2085 @ SY2084 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2085 @ SY2085 ) @ ( c_Product__Type_OPair @ SY2085 @ SY2085 @ SV579 @ SV456 ) @ SV263 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2865,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i] :
( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2087 @ SY2086 ) @ ( tc_prod @ SY2087 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2086 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2087 @ SY2086 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SY2086 @ SY2086 ) @ ( c_Product__Type_OPair @ SY2086 @ SY2086 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2087 @ SY2087 ) @ ( c_Product__Type_OPair @ SY2087 @ SY2087 @ SV579 @ SV456 ) @ SV263 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2773]) ).
thf(2866,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV456: $i,SV579: $i] :
( ( ! [SY2088: $i] :
( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SY2088 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2088 @ SY2088 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2089: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2089 @ SY2088 ) @ ( tc_prod @ SY2089 @ SY2088 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2089 @ SY2088 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2089 @ SY2088 @ SV263 @ SV110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2867,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV263: $i,SV456: $i,SV579: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ~ ( c_member @ ( tc_prod @ SY2091 @ SY2091 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2091 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2091 @ SY2090 ) @ ( tc_prod @ SY2091 @ SY2090 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2091 @ SY2090 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2091 @ SY2090 @ SV263 @ SV110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2868,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV743: $i,SV684: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2869,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV685: $i] :
( ( ( ~ ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) )
| ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(2870,plain,
! [SV115: $i,SV267: $i,SV688: $i,SV727: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV727 @ ( c_Set_Oinsert @ ( tc_prod @ SV727 @ SV727 ) @ ( c_Product__Type_OPair @ SV727 @ SV727 @ SV688 @ SV267 ) @ SV115 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV727 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2871,plain,
! [SV115: $i,SV267: $i,SV689: $i,SV728: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV728 @ ( c_Set_Oinsert @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV689 @ SV267 ) @ SV115 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV267 @ SV689 ) @ ( c_Transitive__Closure_Ortrancl @ SV728 @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2872,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2873,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2874,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2875,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2876,plain,
! [SV117: $i,SV690: $i,SV536: $i,SV760: $i,SV587: $i] :
( ( ( ~ ( c_member @ SV587 @ SV760 @ SV536 )
| ( SV690 = SV760 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SV760 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV760 @ SV690 ) @ SV117 ) )
= $true )
| ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(2877,plain,
! [SV119: $i,SV270: $i,SV691: $i,SV761: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV761 @ SV691 @ SV270 ) @ SV119 ) )
= $true )
| ( ( SV691 = SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(2878,plain,
! [SV119: $i,SV270: $i,SV744: $i,SV762: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV762 @ SV744 @ SV270 ) @ SV119 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV119 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(2879,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV763: $i] :
( ( ( ! [SY2204: $i] :
( ( c_Product__Type_OPair @ SY2204 @ SV763 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SY2204 @ SV763 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV465 = SV271 )
= $false )
| ( ( SV378 = SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(2880,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV764: $i] :
( ( ( ! [SY2205: $i] :
( ( c_Product__Type_OPair @ SY2205 @ SV764 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY2205 @ SV764 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV465 = SV271 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(2881,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV765: $i] :
( ( ( ! [SY2206: $i] :
( ( c_Product__Type_OPair @ SY2206 @ SV765 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SY2206 @ SV765 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV378 = SV120 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(2882,plain,
! [SV122: $i,SV272: $i,SV692: $i,SV745: $i] :
( ( ( c_member @ ( tc_prod @ SV745 @ SV745 ) @ ( c_Product__Type_OPair @ SV745 @ SV745 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV745 @ SV122 ) )
= $false )
| ( ( ( SV692 != SV272 )
| ( SV692 = SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2883,plain,
! [SV122: $i,SV272: $i,SV693: $i,SV729: $i] :
( ( ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV729 @ SV122 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV729 @ SV122 ) )
| ( SV693 = SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2884,plain,
! [SV122: $i,SV730: $i,SV272: $i,SV694: $i] :
( ( ( SV694 = SV272 )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV730 @ SV122 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV730 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(2885,plain,
! [SV122: $i,SV272: $i,SV695: $i,SV766: $i] :
( ( ( c_member @ ( tc_prod @ SV766 @ SV766 ) @ ( c_Product__Type_OPair @ SV766 @ SV766 @ SV695 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV766 @ SV122 ) )
= $true )
| ( ( SV695 = SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(2886,plain,
! [SV123: $i,SV543: $i,SV589: $i] :
( ( ( c_Relation_Ototal__on @ SV589 @ SV543 @ SV123 )
= $false )
| ( ( c_Relation_Oirrefl @ SV589 @ SV123 )
= $false )
| ( ( c_Relation_Otrans @ SV589 @ SV123 )
= $false )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV589 @ SV543 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2887,plain,
! [SV123: $i,SV746: $i,SV767: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV767 @ SV746 @ SV123 )
| ( c_Relation_Oirrefl @ SV767 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(2888,plain,
! [SV123: $i,SV747: $i,SV768: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV768 @ SV747 @ SV123 )
| ( c_Relation_Otrans @ SV768 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(2889,plain,
( ( ( sK2_B_x = sK3_SY704 )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2890,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2891,plain,
! [SV469: $i,SV548: $i] :
( ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK78_SY740 @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
= $true )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2892,plain,
! [SV469: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 ) )
= $true )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2893,plain,
! [SV663: $i,SV470: $i,SV769: $i,SV699: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SV769 ) @ SV470 )
| ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV769 ) @ SV470 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 )
= $false )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(2894,plain,
! [SV125: $i,SV273: $i,SV700: $i,SV748: $i] :
( ( ( c_member @ ( tc_prod @ SV748 @ SV748 ) @ ( c_Product__Type_OPair @ SV748 @ SV748 @ SV700 @ SV273 ) @ ( c_Relation_OId__on @ SV748 @ SV125 ) )
= $false )
| ( ( SV700 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2895,plain,
! [SV125: $i,SV273: $i,SV701: $i,SV733: $i] :
( ( ( c_member @ ( tc_prod @ SV733 @ SV733 ) @ ( c_Product__Type_OPair @ SV733 @ SV733 @ SV701 @ SV273 ) @ ( c_Relation_OId__on @ SV733 @ SV125 ) )
= $false )
| ( ( c_member @ SV733 @ SV701 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2896,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV632: $i,SV664: $i,SV550: $i,SV597: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2897,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV749: $i,SV705: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) ) )
= $true )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(2898,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV706: $i] :
( ( ( ~ ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) )
| ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2899,plain,
! [SV284: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV386: $i,SV478: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2900,plain,
! [SV143: $i,SV751: $i,SV770: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV770 @ SV751 )
| ( SV770 = SV751 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV751 @ SV770 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV751 ) @ SV770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(2901,plain,
! [SV143: $i,SV752: $i,SV771: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV771 @ SV752 )
| ( SV771 = SV752 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(2902,plain,
! [SV143: $i,SV753: $i,SV772: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV772 @ SV753 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SV772 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(2903,plain,
! [SV143: $i,SV754: $i,SV773: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(2904,plain,
! [SV774: $i,SV755: $i,SV143: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) )
| ( SV774 = SV755 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SV774 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(2905,plain,
! [SV775: $i,SV756: $i,SV143: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
| ( SV775 = SV756 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(2906,plain,
! [SV776: $i,SV757: $i,SV143: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2907,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2908,plain,
! [SV145: $i,SV290: $i,SV707: $i,SV737: $i] :
( ( ( c_Wellfounded_Owf @ SV737 @ ( c_Set_Oinsert @ ( tc_prod @ SV737 @ SV737 ) @ ( c_Product__Type_OPair @ SV737 @ SV737 @ SV707 @ SV290 ) @ SV145 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV737 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2909,plain,
! [SV145: $i,SV290: $i,SV708: $i,SV738: $i] :
( ( ( c_Wellfounded_Owf @ SV738 @ ( c_Set_Oinsert @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV708 @ SV290 ) @ SV145 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV290 @ SV708 ) @ ( c_Transitive__Closure_Ortrancl @ SV738 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2910,plain,
! [SV148: $i,SV292: $i,SV711: $i,SV739: $i] :
( ( ( SV739 = SV711 )
= $false )
| ( ( ( c_member @ SV292 @ SV148 @ SV739 )
| ~ ( c_member @ SV292 @ SV148 @ SV739 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2911,plain,
! [SV148: $i,SV292: $i,SV712: $i,SV740: $i] :
( ( ( SV740 = SV712 )
= $false )
| ( ( ( c_member @ SV292 @ SV148 @ SV740 )
| ~ ( c_member @ SV292 @ SV148 @ SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2912,plain,
! [SV148: $i,SV292: $i,SV713: $i,SV741: $i] :
( ( ( SV741 = SV713 )
= $false )
| ( ( ( c_member @ SV292 @ SV148 @ SV713 )
| ~ ( c_member @ SV292 @ SV148 @ SV741 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2913,plain,
! [SV148: $i,SV292: $i,SV714: $i,SV759: $i] :
( ( ( SV759 = SV714 )
= $false )
| ( ( ( c_member @ SV292 @ SV148 @ SV714 )
| ~ ( c_member @ SV292 @ SV148 @ SV714 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2914,plain,
! [SV149: $i,SV293: $i,SV715: $i,SV778: $i] :
( ( ( c_member @ SV778 @ SV715 @ ( c_Set_Oinsert @ SV778 @ SV293 @ SV149 ) )
= $true )
| ( ( SV715 = SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(2915,plain,
! [SV293: $i,SV149: $i,SV716: $i,SV742: $i] :
( ( ( c_member @ SV742 @ SV716 @ SV149 )
= $false )
| ( ( c_member @ SV742 @ SV716 @ ( c_Set_Oinsert @ SV742 @ SV293 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2916,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2917,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2918,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2919,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2920,plain,
! [SV489: $i,SV564: $i] :
( ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK34_SY725 @ SV564 @ SV489 ) @ ( sK33_B_x @ SV564 @ SV489 ) ) @ SV489 )
= $true )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2846]) ).
thf(2921,plain,
! [SV489: $i,SV564: $i] :
( ( ( ( ( sK33_B_x @ SV564 @ SV489 )
!= ( sK34_SY725 @ SV564 @ SV489 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(2922,plain,
! [SV490: $i,SV678: $i,SV718: $i,SV565: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV718 @ SV678 ) @ SV490 ) )
= $true )
| ( ( SV678 = SV718 )
= $true )
| ( ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SV718 ) @ SV490 )
= $false )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(2923,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i,SV721: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV721 @ SV721 ) @ ( c_Product__Type_OPair @ SV721 @ SV721 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2851]) ).
thf(2924,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV681: $i,SV721: $i,SV491: $i] :
( ( ( ~ ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2851]) ).
thf(2925,plain,
! [SV682: $i,SV160: $i,SV491: $i,SV397: $i,SV303: $i,SV779: $i,SV722: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SV779 @ SV303 ) @ SV397 )
| ( ( hAPP @ SV491 @ SV779 )
= ( hAPP @ SV160 @ SV779 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(2926,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 ) )
= $false )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2927,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( ~ ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $false )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2928,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV526: $i] :
( ( ( ~ ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) ) )
= $false )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2929,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV526: $i] :
( ( ( ~ ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 ) )
= $false )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2930,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( c_member @ ( tc_prod @ SV577 @ SV527 ) @ ( c_Product__Type_OPair @ SV577 @ SV527 @ ( sK51_B_x @ SV577 @ SV527 @ SV107 ) @ ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) @ SV107 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2858]) ).
thf(2931,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
!= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2932,plain,
! [SV725: $i,SV107: $i,SV780: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV780 ) @ SV107 )
| ( SV725 = SV780 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(2933,plain,
! [SV108: $i,SV261: $i,SV617: $i,SV726: $i,SV650: $i,SV372: $i] :
( ( ( c_member @ ( tc_prod @ SV372 @ SV650 ) @ ( c_Product__Type_OPair @ SV372 @ SV650 @ SV726 @ SV617 ) @ SV261 )
= $false )
| ( ( c_member @ SV372 @ SV726 @ SV108 )
= $false )
| ( ( c_member @ SV650 @ SV617 @ ( c_Relation_OImage @ SV372 @ SV650 @ SV261 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2934,plain,
! [SV108: $i,SV261: $i,SV618: $i,SV651: $i,SV372: $i] :
( ( ( c_member @ SV372 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV108 )
= $true )
| ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2935,plain,
! [SV108: $i,SV261: $i,SV618: $i,SV651: $i,SV372: $i] :
( ( ( c_member @ ( tc_prod @ SV372 @ SV651 ) @ ( c_Product__Type_OPair @ SV372 @ SV651 @ ( sK24_B_x @ SV651 @ SV618 @ SV372 @ SV261 @ SV108 ) @ SV618 ) @ SV261 )
= $true )
| ( ( c_member @ SV651 @ SV618 @ ( c_Relation_OImage @ SV372 @ SV651 @ SV261 @ SV108 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2936,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV781: $i] :
( ( ! [SY2207: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2207 @ SV781 ) @ ( tc_prod @ SY2207 @ SV781 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2207 @ SV781 ) @ ( tc_prod @ SY2207 @ SV781 ) @ ( c_Product__Type_OPair @ SY2207 @ SV781 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2207 @ SV781 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2207 @ SV781 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SY2207 @ SY2207 ) @ ( c_Product__Type_OPair @ SY2207 @ SY2207 @ SV579 @ SV456 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2937,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV782: $i] :
( ( ! [SY2208: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2208 @ SV782 ) @ ( tc_prod @ SY2208 @ SV782 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2208 @ SV782 ) @ ( tc_prod @ SY2208 @ SV782 ) @ ( c_Product__Type_OPair @ SY2208 @ SV782 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2208 @ SV782 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2208 @ SV782 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SV782 @ SV782 ) @ ( c_Product__Type_OPair @ SV782 @ SV782 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SY2208 @ SY2208 ) @ ( c_Product__Type_OPair @ SY2208 @ SY2208 @ SV579 @ SV456 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(2938,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV783: $i,SV456: $i,SV579: $i] :
( ( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 )
| ! [SY2209: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2209 @ SV783 @ SV263 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(2939,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV784: $i,SV263: $i,SV456: $i,SV579: $i] :
( ( ! [SY2210: $i] :
( ~ ( c_member @ ( tc_prod @ SY2210 @ SY2210 ) @ ( c_Product__Type_OPair @ SY2210 @ SY2210 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2210 @ SV784 ) @ ( tc_prod @ SY2210 @ SV784 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2210 @ SV784 ) @ ( tc_prod @ SY2210 @ SV784 ) @ ( c_Product__Type_OPair @ SY2210 @ SV784 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2210 @ SV784 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2210 @ SV784 @ SV263 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(2940,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV743: $i,SV684: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(2941,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV685: $i] :
( ( ( ~ ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(2942,plain,
! [SV457: $i,SV653: $i,SV685: $i,SV264: $i,SV111: $i,SV374: $i] :
( ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(2943,plain,
! [SV115: $i,SV689: $i,SV267: $i,SV728: $i] :
( ( ( c_member @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV267 @ SV689 ) @ ( c_Transitive__Closure_Ortrancl @ SV728 @ SV115 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV728 @ ( c_Set_Oinsert @ ( tc_prod @ SV728 @ SV728 ) @ ( c_Product__Type_OPair @ SV728 @ SV728 @ SV689 @ SV267 ) @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2944,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) ) @ SV116 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2945,plain,
! [SV116: $i,SV268: $i,SV376: $i,SV461: $i,SV534: $i,SV585: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ ( sK46_B_a @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) @ ( sK47_SY726 @ SV622 @ SV585 @ SV534 @ SV461 @ SV376 @ SV268 @ SV116 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 )
= ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV585 ) @ ( tc_prod @ SV622 @ SV585 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV534 @ SV461 ) @ ( c_Product__Type_OPair @ SV622 @ SV585 @ SV376 @ SV268 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV585 ) @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2873]) ).
thf(2946,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( c_member @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ SV535 )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(2947,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(2948,plain,
! [SV117: $i,SV690: $i,SV536: $i,SV760: $i,SV587: $i] :
( ( ( ~ ( c_member @ SV587 @ SV760 @ SV536 ) )
= $true )
| ( ( ( SV690 = SV760 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SV760 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV760 @ SV690 ) @ SV117 ) )
= $true )
| ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(2949,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV763: $i,SV785: $i] :
( ( ( ( c_Product__Type_OPair @ SV785 @ SV763 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SV785 @ SV763 @ SV271 @ SV120 ) )
= $true )
| ( ( SV465 = SV271 )
= $false )
| ( ( SV378 = SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(2950,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV764: $i,SV786: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV786 @ SV764 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SV786 @ SV764 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV465 = SV271 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(2951,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV765: $i,SV787: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV787 @ SV765 @ SV465 @ SV378 )
!= ( c_Product__Type_OPair @ SV787 @ SV765 @ SV271 @ SV120 ) ) )
= $true )
| ( ( SV378 = SV120 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(2952,plain,
! [SV122: $i,SV745: $i,SV272: $i,SV692: $i] :
( ( ( ( SV692 != SV272 ) )
= $true )
| ( ( SV692 = SV272 )
= $true )
| ( ( c_member @ ( tc_prod @ SV745 @ SV745 ) @ ( c_Product__Type_OPair @ SV745 @ SV745 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV745 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(2953,plain,
! [SV122: $i,SV272: $i,SV693: $i,SV729: $i] :
( ( ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV729 @ SV122 ) )
= $true )
| ( ( SV693 = SV272 )
= $true )
| ( ( c_member @ ( tc_prod @ SV729 @ SV729 ) @ ( c_Product__Type_OPair @ SV729 @ SV729 @ SV693 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV729 @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(2954,plain,
! [SV122: $i,SV272: $i,SV694: $i,SV730: $i] :
( ( ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Otrancl @ SV730 @ SV122 ) )
= $false )
| ( ( SV694 = SV272 )
= $true )
| ( ( c_member @ ( tc_prod @ SV730 @ SV730 ) @ ( c_Product__Type_OPair @ SV730 @ SV730 @ SV694 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV730 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2955,plain,
! [SV123: $i,SV746: $i,SV767: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV767 @ SV746 @ SV123 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV767 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(2956,plain,
! [SV123: $i,SV747: $i,SV768: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV768 @ SV747 @ SV123 ) )
= $true )
| ( ( c_Relation_Otrans @ SV768 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(2957,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2958,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2959,plain,
! [SV469: $i,SV548: $i] :
( ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK77_B_x @ SV548 @ SV469 ) @ ( sK79_SY742 @ SV548 @ SV469 ) ) @ SV469 )
= $false )
| ( ( c_Relation_Otrans @ SV548 @ SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2960,plain,
! [SV663: $i,SV470: $i,SV769: $i,SV699: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SV769 ) @ SV470 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV769 ) @ SV470 )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 )
= $false )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(2961,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(2962,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV749: $i,SV705: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
= $false )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2963,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV706: $i] :
( ( ( ~ ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2964,plain,
! [SV281: $i,SV475: $i,SV666: $i,SV706: $i,SV383: $i,SV133: $i] :
( ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2965,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(2966,plain,
! [SV143: $i,SV751: $i,SV770: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV770 @ SV751 )
= $true )
| ( ( ( SV770 = SV751 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV751 @ SV770 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV751 ) @ SV770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(2967,plain,
! [SV143: $i,SV752: $i,SV771: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV771 @ SV752 )
= $true )
| ( ( ( SV771 = SV752 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(2968,plain,
! [SV143: $i,SV753: $i,SV772: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV772 @ SV753 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SV772 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(2969,plain,
! [SV143: $i,SV754: $i,SV773: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2903]) ).
thf(2970,plain,
! [SV774: $i,SV755: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) ) )
= $true )
| ( ( ( SV774 = SV755 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SV774 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2971,plain,
! [SV775: $i,SV756: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true )
| ( ( ( SV775 = SV756 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(2972,plain,
! [SV776: $i,SV757: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2906]) ).
thf(2973,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(2974,plain,
! [SV145: $i,SV708: $i,SV290: $i,SV738: $i] :
( ( ( c_member @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV290 @ SV708 ) @ ( c_Transitive__Closure_Ortrancl @ SV738 @ SV145 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV738 @ ( c_Set_Oinsert @ ( tc_prod @ SV738 @ SV738 ) @ ( c_Product__Type_OPair @ SV738 @ SV738 @ SV708 @ SV290 ) @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2975,plain,
! [SV711: $i,SV739: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV739 )
= $true )
| ( ( ~ ( c_member @ SV292 @ SV148 @ SV739 ) )
= $true )
| ( ( SV739 = SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(2976,plain,
! [SV712: $i,SV740: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV740 )
= $true )
| ( ( ~ ( c_member @ SV292 @ SV148 @ SV712 ) )
= $true )
| ( ( SV740 = SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(2977,plain,
! [SV741: $i,SV713: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV713 )
= $true )
| ( ( ~ ( c_member @ SV292 @ SV148 @ SV741 ) )
= $true )
| ( ( SV741 = SV713 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(2978,plain,
! [SV759: $i,SV714: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV714 )
= $true )
| ( ( ~ ( c_member @ SV292 @ SV148 @ SV714 ) )
= $true )
| ( ( SV759 = SV714 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(2979,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) @ SV294 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(2980,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(2981,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(2982,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(2983,plain,
! [SV489: $i,SV564: $i] :
( ( ( ( sK33_B_x @ SV564 @ SV489 )
= ( sK34_SY725 @ SV564 @ SV489 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV564 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2984,plain,
! [SV490: $i,SV678: $i,SV718: $i,SV565: $i] :
( ( ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV718 @ SV678 ) @ SV490 )
= $false )
| ( ( SV678 = SV718 )
= $true )
| ( ( c_member @ ( tc_prod @ SV565 @ SV565 ) @ ( c_Product__Type_OPair @ SV565 @ SV565 @ SV678 @ SV718 ) @ SV490 )
= $false )
| ( ( c_Relation_Oantisym @ SV565 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2985,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV491: $i,SV681: $i,SV721: $i] :
( ( ( c_member @ ( tc_prod @ SV721 @ SV721 ) @ ( c_Product__Type_OPair @ SV721 @ SV721 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) @ SV303 ) @ SV397 )
= $true )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2986,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV681: $i,SV721: $i,SV491: $i] :
( ( ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
!= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2924]) ).
thf(2987,plain,
! [SV682: $i,SV160: $i,SV491: $i,SV397: $i,SV303: $i,SV779: $i,SV722: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SV779 @ SV303 ) @ SV397 ) )
= $true )
| ( ( ( hAPP @ SV491 @ SV779 )
= ( hAPP @ SV160 @ SV779 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(2988,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 )
= $true )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(2989,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
= $true )
| ( ( ~ ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(2990,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV526: $i] :
( ( ( ! [SY2140: $i] :
( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SY2140 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SY2140 @ SV649 ) ) )
= $true )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2991,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV526: $i] :
( ( ( c_member @ SV526 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) @ SV649 )
= $true )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2992,plain,
! [SV107: $i,SV527: $i,SV577: $i] :
( ( ( ( sK52_SY730 @ SV577 @ SV527 @ SV107 )
= ( sK53_SY732 @ SV577 @ SV527 @ SV107 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV577 @ SV527 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(2993,plain,
! [SV725: $i,SV107: $i,SV780: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV780 ) @ SV107 ) )
= $true )
| ( ( SV725 = SV780 )
= $true )
| ( ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(2994,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV781: $i,SV788: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV788 @ SV781 @ SV263 @ SV110 ) )
| ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SV788 @ SV788 ) @ ( c_Product__Type_OPair @ SV788 @ SV788 @ SV579 @ SV456 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(2995,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV782: $i,SV789: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV789 @ SV782 @ SV263 @ SV110 ) )
| ( c_member @ ( tc_prod @ SV782 @ SV782 ) @ ( c_Product__Type_OPair @ SV782 @ SV782 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SV789 @ SV789 ) @ ( c_Product__Type_OPair @ SV789 @ SV789 @ SV579 @ SV456 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(2996,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV783: $i,SV456: $i,SV579: $i] :
( ( ( ( SV579 != SV456 )
| ~ ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 ) )
= $true )
| ( ( ! [SY2209: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2209 @ SV783 @ SV263 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(2997,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV784: $i,SV263: $i,SV456: $i,SV579: $i,SV790: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV790 @ SV790 ) @ ( c_Product__Type_OPair @ SV790 @ SV790 @ SV579 @ SV456 ) @ SV263 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV790 @ SV784 @ SV263 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(2998,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV743: $i,SV684: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2940]) ).
thf(2999,plain,
! [SV111: $i,SV264: $i,SV743: $i,SV374: $i,SV457: $i,SV652: $i,SV684: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2940]) ).
thf(3000,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV685: $i] :
( ( ( ! [SY2166: $i] :
( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SY2166 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SY2166 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SY2166 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2941]) ).
thf(3001,plain,
! [SV457: $i,SV653: $i,SV685: $i,SV264: $i,SV111: $i,SV374: $i] :
( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
= ( hAPP @ ( hAPP @ SV374 @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) ) @ SV264 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(3002,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3003,plain,
! [SV117: $i,SV690: $i,SV536: $i,SV760: $i,SV587: $i] :
( ( ( c_member @ SV587 @ SV760 @ SV536 )
= $false )
| ( ( ( SV690 = SV760 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SV760 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV760 @ SV690 ) @ SV117 ) )
= $true )
| ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3004,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV764: $i,SV786: $i] :
( ( ( ( c_Product__Type_OPair @ SV786 @ SV764 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SV786 @ SV764 @ SV271 @ SV120 ) )
= $false )
| ( ( SV465 = SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3005,plain,
! [SV120: $i,SV271: $i,SV378: $i,SV465: $i,SV765: $i,SV787: $i] :
( ( ( ( c_Product__Type_OPair @ SV787 @ SV765 @ SV465 @ SV378 )
= ( c_Product__Type_OPair @ SV787 @ SV765 @ SV271 @ SV120 ) )
= $false )
| ( ( SV378 = SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3006,plain,
! [SV122: $i,SV745: $i,SV272: $i,SV692: $i] :
( ( ( SV692 = SV272 )
= $false )
| ( ( SV692 = SV272 )
= $true )
| ( ( c_member @ ( tc_prod @ SV745 @ SV745 ) @ ( c_Product__Type_OPair @ SV745 @ SV745 @ SV692 @ SV272 ) @ ( c_Transitive__Closure_Ortrancl @ SV745 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3007,plain,
! [SV123: $i,SV746: $i,SV767: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV767 @ SV746 @ SV123 )
= $false )
| ( ( c_Relation_Oirrefl @ SV767 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3008,plain,
! [SV123: $i,SV747: $i,SV768: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV768 @ SV747 @ SV123 )
= $false )
| ( ( c_Relation_Otrans @ SV768 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3009,plain,
( ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2957]) ).
thf(3010,plain,
( ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(3011,plain,
! [SV663: $i,SV470: $i,SV769: $i,SV699: $i,SV549: $i] :
( ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV699 @ SV769 ) @ SV470 )
= $false )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV769 ) @ SV470 )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV663 @ SV699 ) @ SV470 )
= $false )
| ( ( c_Relation_Otrans @ SV549 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3012,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3013,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV749: $i,SV705: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 ) )
= $false )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(3014,plain,
! [SV133: $i,SV281: $i,SV749: $i,SV383: $i,SV475: $i,SV665: $i,SV705: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
= $false )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(3015,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV706: $i] :
( ( ( ! [SY2182: $i] :
( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SY2182 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SY2182 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SY2182 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3016,plain,
! [SV281: $i,SV475: $i,SV666: $i,SV706: $i,SV383: $i,SV133: $i] :
( ( ( SV133
= ( hAPP @ ( hAPP @ SV383 @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) ) @ SV281 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2964]) ).
thf(3017,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3018,plain,
! [SV143: $i,SV751: $i,SV770: $i] :
( ( ( SV770 = SV751 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV751 @ SV770 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV751 ) @ SV770 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV770 @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3019,plain,
! [SV143: $i,SV752: $i,SV771: $i] :
( ( ( SV771 = SV752 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV771 @ SV752 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3020,plain,
! [SV772: $i,SV753: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SV772 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV772 @ SV753 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3021,plain,
! [SV773: $i,SV754: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3022,plain,
! [SV774: $i,SV755: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) )
= $false )
| ( ( ( SV774 = SV755 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SV774 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3023,plain,
! [SV775: $i,SV756: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $false )
| ( ( ( SV775 = SV756 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3024,plain,
! [SV776: $i,SV757: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3025,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3026,plain,
! [SV711: $i,SV739: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV739 )
= $false )
| ( ( c_member @ SV292 @ SV148 @ SV739 )
= $true )
| ( ( SV739 = SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3027,plain,
! [SV740: $i,SV712: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV712 )
= $false )
| ( ( c_member @ SV292 @ SV148 @ SV740 )
= $true )
| ( ( SV740 = SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3028,plain,
! [SV713: $i,SV741: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV741 )
= $false )
| ( ( c_member @ SV292 @ SV148 @ SV713 )
= $true )
| ( ( SV741 = SV713 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3029,plain,
! [SV759: $i,SV714: $i,SV148: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV148 @ SV714 )
= $false )
| ( ( c_member @ SV292 @ SV148 @ SV714 )
= $true )
| ( ( SV759 = SV714 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3030,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3031,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3032,plain,
! [SV160: $i,SV303: $i,SV397: $i,SV681: $i,SV721: $i,SV491: $i] :
( ( ( ( hAPP @ SV491 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) )
= ( hAPP @ SV160 @ ( sK43_B_y @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 @ SV160 ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV721 @ SV681 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV721 @ SV681 @ SV160 @ SV397 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3033,plain,
! [SV682: $i,SV160: $i,SV491: $i,SV397: $i,SV303: $i,SV779: $i,SV722: $i] :
( ( ( c_member @ ( tc_prod @ SV722 @ SV722 ) @ ( c_Product__Type_OPair @ SV722 @ SV722 @ SV779 @ SV303 ) @ SV397 )
= $false )
| ( ( ( hAPP @ SV491 @ SV779 )
= ( hAPP @ SV160 @ SV779 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV722 @ SV682 @ SV491 @ SV397 @ SV303 )
= ( c_Recdef_Ocut @ SV722 @ SV682 @ SV160 @ SV397 @ SV303 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3034,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV525 @ SV525 ) @ ( c_Product__Type_OPair @ SV525 @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ SV723 ) @ SV454 )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3035,plain,
! [SV454: $i,SV723: $i,SV525: $i] :
( ( ( c_member @ SV525 @ SV723 @ ( sK29_B_Q @ SV525 @ SV454 ) )
= $false )
| ( ( c_member @ SV525 @ ( sK30_SY724 @ SV723 @ SV525 @ SV454 ) @ ( sK29_B_Q @ SV525 @ SV454 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV525 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3036,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV791: $i,SV526: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SV791 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
| ~ ( c_member @ SV526 @ SV791 @ SV649 ) )
= $true )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3037,plain,
! [SV725: $i,SV107: $i,SV780: $i,SV683: $i,SV528: $i,SV578: $i] :
( ( ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV780 ) @ SV107 )
= $false )
| ( ( SV725 = SV780 )
= $true )
| ( ( c_member @ ( tc_prod @ SV578 @ SV528 ) @ ( c_Product__Type_OPair @ SV578 @ SV528 @ SV683 @ SV725 ) @ SV107 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV578 @ SV528 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3038,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV781: $i,SV788: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV788 @ SV781 @ SV263 @ SV110 ) ) )
= $true )
| ( ( ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SV788 @ SV788 ) @ ( c_Product__Type_OPair @ SV788 @ SV788 @ SV579 @ SV456 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3039,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV782: $i,SV789: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV789 @ SV782 @ SV263 @ SV110 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV782 @ SV782 ) @ ( c_Product__Type_OPair @ SV782 @ SV782 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SV789 @ SV789 ) @ ( c_Product__Type_OPair @ SV789 @ SV789 @ SV579 @ SV456 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3040,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV783: $i,SV456: $i,SV579: $i] :
( ( ( ( SV579 != SV456 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 ) )
= $true )
| ( ( ! [SY2209: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2209 @ SV783 @ SV263 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3041,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV784: $i,SV263: $i,SV456: $i,SV579: $i,SV790: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV790 @ SV790 ) @ ( c_Product__Type_OPair @ SV790 @ SV790 @ SV579 @ SV456 ) @ SV263 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV790 @ SV784 @ SV263 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3042,plain,
! [SV111: $i,SV264: $i,SV374: $i,SV457: $i,SV652: $i,SV743: $i,SV684: $i] :
( ( ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2998]) ).
thf(3043,plain,
! [SV111: $i,SV264: $i,SV743: $i,SV374: $i,SV457: $i,SV652: $i,SV684: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3044,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV792: $i,SV685: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SV792 @ SV264 ) @ SV457 )
| ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV792 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV792 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3045,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3002]) ).
thf(3046,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3002]) ).
thf(3047,plain,
! [SV536: $i,SV117: $i,SV587: $i,SV760: $i,SV690: $i] :
( ( ( SV690 = SV760 )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SV760 ) @ SV117 )
| ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV760 @ SV690 ) @ SV117 ) )
= $true )
| ( ( c_member @ SV587 @ SV760 @ SV536 )
= $false )
| ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3003]) ).
thf(3048,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK2_B_x @ sK3_SY704 ) @ v_L )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3049,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK3_SY704 @ sK2_B_x ) @ v_L )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3050,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3012]) ).
thf(3051,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3012]) ).
thf(3052,plain,
! [SV133: $i,SV281: $i,SV383: $i,SV475: $i,SV665: $i,SV749: $i,SV705: $i] :
( ( ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
= $true )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3013]) ).
thf(3053,plain,
! [SV133: $i,SV281: $i,SV749: $i,SV383: $i,SV475: $i,SV665: $i,SV705: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) ) )
= $true )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3014]) ).
thf(3054,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV793: $i,SV706: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SV793 @ SV281 ) @ SV475 )
| ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV793 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV793 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3055,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3017]) ).
thf(3056,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3017]) ).
thf(3057,plain,
! [SV143: $i,SV770: $i,SV751: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV751 @ SV770 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV751 ) @ SV770 ) )
= $true )
| ( ( SV770 = SV751 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV770 @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3058,plain,
! [SV771: $i,SV752: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
= $true )
| ( ( SV771 = SV752 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV771 @ SV752 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3059,plain,
! [SV772: $i,SV753: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SV772 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV772 @ SV753 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3060,plain,
! [SV773: $i,SV754: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3061,plain,
! [SV143: $i,SV755: $i,SV774: $i] :
( ( ( SV774 = SV755 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SV774 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3062,plain,
! [SV143: $i,SV756: $i,SV775: $i] :
( ( ( SV775 = SV756 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3063,plain,
! [SV776: $i,SV757: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3064,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3065,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3066,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3067,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3068,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3069,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV791: $i,SV526: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SV791 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 ) )
= $true )
| ( ( ~ ( c_member @ SV526 @ SV791 @ SV649 ) )
= $true )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3070,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV781: $i,SV788: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV788 @ SV781 @ SV263 @ SV110 ) )
= $false )
| ( ( ( SV579 = SV456 )
| ( c_member @ ( tc_prod @ SV788 @ SV788 ) @ ( c_Product__Type_OPair @ SV788 @ SV788 @ SV579 @ SV456 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3071,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV782: $i,SV789: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV789 @ SV782 @ SV263 @ SV110 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV782 @ SV782 ) @ ( c_Product__Type_OPair @ SV782 @ SV782 @ SV529 @ SV373 ) @ SV110 )
| ( c_member @ ( tc_prod @ SV789 @ SV789 ) @ ( c_Product__Type_OPair @ SV789 @ SV789 @ SV579 @ SV456 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3072,plain,
! [SV263: $i,SV110: $i,SV373: $i,SV529: $i,SV783: $i,SV456: $i,SV579: $i] :
( ( ( SV579 = SV456 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 ) )
= $true )
| ( ( ! [SY2209: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2209 @ SV783 @ SV263 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3073,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV784: $i,SV263: $i,SV456: $i,SV579: $i,SV790: $i] :
( ( ( c_member @ ( tc_prod @ SV790 @ SV790 ) @ ( c_Product__Type_OPair @ SV790 @ SV790 @ SV579 @ SV456 ) @ SV263 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV790 @ SV784 ) @ ( tc_prod @ SV790 @ SV784 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV790 @ SV784 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV790 @ SV784 @ SV263 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3074,plain,
! [SV457: $i,SV652: $i,SV684: $i,SV743: $i,SV264: $i,SV111: $i,SV374: $i] :
( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV684 @ SV684 ) @ ( c_Product__Type_OPair @ SV684 @ SV684 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV264 ) @ SV457 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3042]) ).
thf(3075,plain,
! [SV111: $i,SV264: $i,SV743: $i,SV374: $i,SV457: $i,SV652: $i,SV684: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
!= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3076,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV792: $i,SV685: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SV792 @ SV264 ) @ SV457 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV792 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV792 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3077,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
!= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3078,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3046]) ).
thf(3079,plain,
! [SV536: $i,SV117: $i,SV760: $i,SV690: $i,SV587: $i] :
( ( ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV690 @ SV760 ) @ SV117 )
= $true )
| ( ( c_member @ ( tc_prod @ SV587 @ SV587 ) @ ( c_Product__Type_OPair @ SV587 @ SV587 @ SV760 @ SV690 ) @ SV117 )
= $true )
| ( ( SV690 = SV760 )
= $true )
| ( ( c_member @ SV587 @ SV760 @ SV536 )
= $false )
| ( ( c_member @ SV587 @ SV690 @ SV536 )
= $false )
| ( ( c_Relation_Ototal__on @ SV587 @ SV536 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3080,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3081,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3082,plain,
! [SV475: $i,SV665: $i,SV705: $i,SV281: $i,SV749: $i,SV383: $i,SV133: $i] :
( ( ( SV133
= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV705 @ SV705 ) @ ( c_Product__Type_OPair @ SV705 @ SV705 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV281 ) @ SV475 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3083,plain,
! [SV133: $i,SV281: $i,SV749: $i,SV383: $i,SV475: $i,SV665: $i,SV705: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) )
= $false )
| ( ( ( SV133
!= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3084,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV793: $i,SV706: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SV793 @ SV281 ) @ SV475 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV793 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV793 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3085,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) @ SV284 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3086,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3087,plain,
! [SV771: $i,SV752: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV752 ) @ SV771 ) )
= $true )
| ( ( SV771 = SV752 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV771 @ SV752 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3088,plain,
! [SV143: $i,SV772: $i,SV753: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV753 @ SV772 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV753 ) @ SV772 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV772 @ SV753 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3089,plain,
! [SV773: $i,SV754: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3090,plain,
! [SV143: $i,SV774: $i,SV755: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV755 @ SV774 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) )
= $true )
| ( ( SV774 = SV755 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV755 ) @ SV774 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3091,plain,
! [SV775: $i,SV756: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $true )
| ( ( SV775 = SV756 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3092,plain,
! [SV776: $i,SV757: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3093,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3094,plain,
! [SV150: $i,SV294: $i,SV391: $i,SV483: $i,SV560: $i] :
( ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3095,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3096,plain,
! [SV154: $i,SV298: $i,SV395: $i,SV485: $i,SV561: $i] :
( ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) @ SV298 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3067]) ).
thf(3097,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3068]) ).
thf(3098,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV791: $i,SV526: $i] :
( ( ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SV791 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
= $false )
| ( ( ~ ( c_member @ SV526 @ SV791 @ SV649 ) )
= $true )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3099,plain,
! [SV110: $i,SV373: $i,SV529: $i,SV781: $i,SV263: $i,SV788: $i,SV456: $i,SV579: $i] :
( ( ( SV579 = SV456 )
= $true )
| ( ( c_member @ ( tc_prod @ SV788 @ SV788 ) @ ( c_Product__Type_OPair @ SV788 @ SV788 @ SV579 @ SV456 ) @ SV263 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV788 @ SV781 ) @ ( tc_prod @ SV788 @ SV781 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV788 @ SV781 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV788 @ SV781 @ SV263 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3100,plain,
! [SV263: $i,SV456: $i,SV579: $i,SV789: $i,SV110: $i,SV373: $i,SV529: $i,SV782: $i] :
( ( ( c_member @ ( tc_prod @ SV782 @ SV782 ) @ ( c_Product__Type_OPair @ SV782 @ SV782 @ SV529 @ SV373 ) @ SV110 )
= $true )
| ( ( c_member @ ( tc_prod @ SV789 @ SV789 ) @ ( c_Product__Type_OPair @ SV789 @ SV789 @ SV579 @ SV456 ) @ SV263 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV789 @ SV782 ) @ ( tc_prod @ SV789 @ SV782 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV789 @ SV782 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV789 @ SV782 @ SV263 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3101,plain,
! [SV263: $i,SV456: $i,SV579: $i,SV110: $i,SV373: $i,SV529: $i,SV783: $i] :
( ( ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 )
= $false )
| ( ( SV579 = SV456 )
= $false )
| ( ( ! [SY2209: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2209 @ SV783 ) @ ( tc_prod @ SY2209 @ SV783 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SY2209 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SY2209 @ SV783 @ SV263 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3102,plain,
! [SV457: $i,SV652: $i,SV684: $i,SV743: $i,SV264: $i,SV111: $i,SV374: $i] :
( ( ( ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 )
= ( hAPP @ ( hAPP @ SV374 @ SV743 ) @ SV264 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) @ ( hAPP @ SV743 @ ( sK60_B_z @ SV743 @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ SV111 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV684 @ SV652 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3103,plain,
! [SV111: $i,SV374: $i,SV653: $i,SV457: $i,SV264: $i,SV792: $i,SV685: $i] :
( ( ( c_member @ ( tc_prod @ SV685 @ SV685 ) @ ( c_Product__Type_OPair @ SV685 @ SV685 @ SV792 @ SV264 ) @ SV457 )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV792 @ ( hAPP @ ( sK59_B_g @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ SV111 ) @ SV792 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV685 @ SV653 @ SV457 @ SV374 @ SV264 @ ( hAPP @ ( hAPP @ SV374 @ SV111 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3104,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ( sK67_B_x @ SV586 @ SV535 @ SV117 )
= ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3105,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
| ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3106,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3107,plain,
! [SV475: $i,SV665: $i,SV705: $i,SV281: $i,SV749: $i,SV383: $i,SV133: $i] :
( ( ( SV133
= ( hAPP @ ( hAPP @ SV383 @ SV749 ) @ SV281 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) @ ( hAPP @ SV749 @ ( sK55_B_z @ SV749 @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV705 @ SV665 @ SV475 @ SV383 @ SV281 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3108,plain,
! [SV133: $i,SV383: $i,SV666: $i,SV475: $i,SV281: $i,SV793: $i,SV706: $i] :
( ( ( c_member @ ( tc_prod @ SV706 @ SV706 ) @ ( c_Product__Type_OPair @ SV706 @ SV706 @ SV793 @ SV281 ) @ SV475 )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV793 @ ( hAPP @ ( sK54_B_g @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 ) @ SV793 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV706 @ SV666 @ SV475 @ SV383 @ SV281 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3109,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3110,plain,
! [SV773: $i,SV754: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV754 ) @ SV773 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV773 @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3111,plain,
! [SV775: $i,SV756: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $true )
| ( ( SV775 = SV756 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV756 ) @ SV775 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3112,plain,
! [SV143: $i,SV776: $i,SV757: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV757 @ SV776 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV757 ) @ SV776 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3113,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3114,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3115,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3116,plain,
! [SV724: $i,SV455: $i,SV649: $i,SV791: $i,SV526: $i] :
( ( ( c_member @ SV526 @ SV791 @ SV649 )
= $false )
| ( ( c_member @ ( tc_prod @ SV526 @ SV526 ) @ ( c_Product__Type_OPair @ SV526 @ SV526 @ SV791 @ ( sK28_B_x @ SV649 @ SV526 @ SV455 ) ) @ SV455 )
= $false )
| ( ( c_member @ SV526 @ SV724 @ SV649 )
= $false )
| ( ( c_Wellfounded_Owf @ SV526 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3117,plain,
! [SV110: $i,SV263: $i,SV373: $i,SV456: $i,SV529: $i,SV579: $i,SV783: $i,SV794: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV794 @ SV783 ) @ ( tc_prod @ SV794 @ SV783 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV794 @ SV783 ) @ ( tc_prod @ SV794 @ SV783 ) @ ( c_Product__Type_OPair @ SV794 @ SV783 @ SV579 @ SV529 ) @ ( c_Product__Type_OPair @ SV794 @ SV783 @ SV456 @ SV373 ) ) @ ( c_Wellfounded_Olex__prod @ SV794 @ SV783 @ SV263 @ SV110 ) )
= $true )
| ( ( SV579 = SV456 )
= $false )
| ( ( c_member @ ( tc_prod @ SV783 @ SV783 ) @ ( c_Product__Type_OPair @ SV783 @ SV783 @ SV529 @ SV373 ) @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3118,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3119,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3120,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3121,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3122,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3123,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3124,plain,
! [SV777: $i,SV758: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV758 ) @ SV777 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3125,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3126,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3127,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3128,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3129,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3118]) ).
thf(3130,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3131,plain,
! [SV131: $i,SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) @ SV279 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3132,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3133,plain,
! [SV137: $i,SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3134,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3123]) ).
thf(3135,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ SV150 @ ( sK13_SY707 @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3136,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3126]) ).
thf(3137,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ SV154 @ ( sK10_B_y @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3127]) ).
thf(3138,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3139,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3140,plain,
! [SV117: $i,SV535: $i,SV586: $i] :
( ( ( c_member @ ( tc_prod @ SV586 @ SV586 ) @ ( c_Product__Type_OPair @ SV586 @ SV586 @ ( sK68_SY735 @ SV586 @ SV535 @ SV117 ) @ ( sK67_B_x @ SV586 @ SV535 @ SV117 ) ) @ SV117 )
= $false )
| ( ( c_Relation_Ototal__on @ SV586 @ SV535 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3141,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3142,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3143,plain,
! [SV294: $i,SV391: $i,SV483: $i,SV560: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ SV150 @ ( sK12_B_y @ SV560 @ SV483 @ SV391 @ SV294 @ SV150 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ SV391 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV560 @ SV560 ) @ ( c_Product__Type_OPair @ SV560 @ SV560 @ SV483 @ SV391 ) @ ( c_Transitive__Closure_Ortrancl @ SV560 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3144,plain,
! [SV298: $i,SV395: $i,SV485: $i,SV561: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ SV154 @ ( sK11_SY706 @ SV561 @ SV485 @ SV395 @ SV298 @ SV154 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV395 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV154 @ SV485 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV561 @ SV561 ) @ ( c_Product__Type_OPair @ SV561 @ SV561 @ SV485 @ SV395 ) @ ( c_Transitive__Closure_Ortrancl @ SV561 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3145,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3146,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3147,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3148,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3149,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK18_B_a @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK19_SY714 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3145]) ).
thf(3150,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3151,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK16_SY711 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK17_SY713 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3147]) ).
thf(3152,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3153,plain,
! [SV279: $i,SV382: $i,SV474: $i,SV550: $i,SV597: $i,SV632: $i,SV664: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ ( sK20_SY717 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) @ ( sK21_SY719 @ SV664 @ SV632 @ SV597 @ SV550 @ SV474 @ SV382 @ SV279 @ SV131 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV474 ) @ SV382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV597 ) @ SV550 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV664 @ SV632 ) @ ( tc_prod @ SV664 @ SV632 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV597 @ SV550 ) @ ( c_Product__Type_OPair @ SV664 @ SV632 @ SV474 @ SV382 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV664 @ SV632 ) @ SV279 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3154,plain,
! [SV284: $i,SV386: $i,SV478: $i,SV553: $i,SV600: $i,SV636: $i,SV670: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ ( sK14_B_a @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) @ ( sK15_SY708 @ SV670 @ SV636 @ SV600 @ SV553 @ SV478 @ SV386 @ SV284 @ SV137 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV600 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV478 ) @ SV386 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV670 @ SV636 ) @ ( tc_prod @ SV670 @ SV636 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV600 @ SV553 ) @ ( c_Product__Type_OPair @ SV670 @ SV636 @ SV478 @ SV386 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV670 @ SV636 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3155,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[960,3154,3153,3151,3149,3144,3143,3140,3139,3137,3135,3133,3131,3124,3117,3116,3112,3111,3110,3108,3107,3104,3103,3102,3100,3099,3096,3094,3090,3088,3087,3085,3082,3080,3079,3074,3073,3057,3049,3048,3037,3035,3034,3033,3032,3029,3028,3027,3026,3016,3011,3008,3007,3006,3005,3004,3001,2992,2991,2985,2984,2983,2981,2979,2974,2959,2954,2953,2949,2946,2945,2944,2943,2935,2934,2933,2930,2920,2915,2914,2908,2895,2894,2891,2889,2886,2885,2878,2877,2870,2855,2854,2853,2850,2849,2845,2836,2835,2824,2823,2822,2821,2820,2819,2817,2816,2812,2811,2810,2809,2806,2800,2799,2795,2794,2779,2778,2765,2761,2756,2753,2752,2749,2748,2747,2746,2742,2735,2732,2731,2730,2720,2714,2708,2704,2703,2702,2701,2698,2697,2688,2687,2671,2670,2669,2666,2662,2661,2658,2653,2648,2645,2642,2641,2630,2628,2627,2626,2623,2622,2581,2580,2577,2559,2558,2556,2555,2552,2525,2524,2522,2513,2505,2500,2499,2497,2496,2495,2494,2493,2492,2491,2490,2489,2488,2487,2484,2483,2481,2460,2451,2450,2433,2432,2431,2428,2427,2386,2385,2378,2367,2345,2343,2342,2333,2327,2326,2323,2322,2321,2320,2319,2316,2303,2302,2295,2272,2266,2226,2212,2188,2187,2186,2184,2183,2182,2175,2150,2148,2135,2070,2040,2030,2023,2018,2011,2008,2006,1993,1991,1986,1978,1977,1976,1971,1970,1857,1856,1855,1844,1838,1836,1835,1822,1814,1693,1692,1689,1686,1681,1680,1678,1677,1672,1669,1656,1645,1528,1524,1512,1494,1488,1467,1370,1362,1360,1355,1351,1347,1346,1345,1344,1343,1342,1338,1337,1336,1315,1303,1298,1280,1198,1191,1182,1178,1145,1032,1031,1030,1029,1028,1027,1026,1025,1023,1022,1008,1007,1004]) ).
thf(3156,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK78_SY740 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK78_SY740 @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK77_B_x @ T_a @ V_r_2 ) @ ( sK79_SY742 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_z ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_z ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(3157,plain,
( ( ! [V_c_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(3158,plain,
( ( ! [V_c_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_A_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_A_2 ) )
& ! [V_B_2: $i] :
( ! [V_A_2: $i] : ( V_A_2 != V_B_2 )
| ( c_member @ T_a @ V_c_2 @ V_B_2 )
| ~ ( c_member @ T_a @ V_c_2 @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(3159,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK76_B_x @ T_a @ V_r_2 ) @ ( sK76_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Nitpick_Orefl_H @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Nitpick_Orefl_H @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(3160,plain,
( ( ! [T_b: $i] :
( ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK75_B_x1 @ V_P_2 @ T_a @ T_b ) ) )
| ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ B_a @ B_b ) ) ) )
& ! [T_a: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK73_B_a @ V_P_2 @ T_a @ T_b ) @ ( sK74_SY739 @ V_P_2 @ T_a @ T_b ) ) ) )
| ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(3161,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ( ( V_a_2 != V_a_H_2 )
| ( V_b_2 != V_b_H_2 )
| ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_a_2 = V_a_H_2 ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) )
| ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(3162,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i] :
( ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_a = V_a_H ) )
& ( ! [T_b: $i,T_a: $i] :
( ( c_Product__Type_OPair @ T_a @ T_b @ V_a @ V_b )
!= ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H @ V_b_H ) )
| ( V_b = V_b_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(3163,plain,
( ( ! [V_A_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(3164,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_b_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(3165,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_y_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(3166,plain,
( ( ! [V_x_2: $i,T_a: $i] :
( ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 ) )
& ! [V_B_2: $i,V_A_2: $i] :
( ( V_A_2 != V_B_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(3167,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f1_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ T_b @ T_c @ T_a @ V_f1_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_f1_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(3168,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK72_B_x @ T_a @ V_r_2 ) @ ( sK72_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(3169,plain,
( ( ! [V_s_2: $i,V_r_2: $i,V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( V_a_2 = V_a_H_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 ) )
& ! [T_b: $i] :
( ( V_a_2 != V_a_H_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_b_2 @ V_b_H_2 ) @ V_s_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_H_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_H_2 @ V_b_H_2 ) ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_r_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(3170,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_c_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ointernal__split @ T_b @ T_c @ T_a @ V_c_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) )
= ( hAPP @ ( hAPP @ V_c_2 @ V_a_2 ) @ V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(3171,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_ORange @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(3172,plain,
( ( ! [V_A_2: $i,V_y_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 != V_y_2 )
| ~ ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(3173,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(3174,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(3175,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK70_SY736 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK70_SY736 @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK69_B_x @ T_a @ V_r_2 ) @ ( sK71_SY738 @ T_a @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(3176,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( c_member @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ V_A_2 )
& ( ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 )
!= ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 )
& ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK68_SY735 @ T_a @ V_A_2 @ V_r_2 ) @ ( sK67_B_x @ T_a @ V_A_2 @ V_r_2 ) ) @ V_r_2 ) )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ! [B_x: $i] :
( ~ ( c_member @ T_a @ B_x @ V_A_2 )
| ! [B_xa: $i] :
( ~ ( c_member @ T_a @ B_xa @ V_A_2 )
| ( B_x = B_xa )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_xa ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_xa @ B_x ) @ V_r_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(3177,plain,
( ( ! [V_f_2: $i,V_r_2: $i,T_b: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 ) )
& ! [V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_y_2 ) ) @ V_r_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( hAPP @ ( c_Relation_Oinv__image @ T_b @ T_a @ V_r_2 ) @ V_f_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(3178,plain,
( ( ! [V_R2_2: $i,T_b: $i,V_R1_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_R1_2 )
| ~ ( c_Relation_Otrans @ T_b @ V_R2_2 )
| ( c_Relation_Otrans @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_R1_2 @ V_R2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(3179,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(3180,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Relation_Otrans @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(3181,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ B_y ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK66_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(3182,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ! [B_y: $i] :
~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_y @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK65_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) @ V_a_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(3183,plain,
( ( ! [V_A_2: $i,V_c_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_c_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
| ( ( c_member @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ V_A_2 )
& ( V_c_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) @ ( sK64_B_x @ T_a @ V_c_2 @ V_A_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(3184,plain,
( ( ! [V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK63_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(3185,plain,
( ( ! [V_r_2: $i,T_b: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ ( sK62_B_y @ T_a @ V_a_2 @ T_b @ V_r_2 ) ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(3186,plain,
( ( ! [V_r_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ V_a_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK61_B_x @ T_a @ V_a_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ! [B_x: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ V_a_2 ) @ V_r_2 )
| ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(3187,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(3188,plain,
( ( ! [V_a_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(3189,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(3190,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( c_member @ T_a @ V_y_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(3191,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK60_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 ) )
| ( ! [SY734: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY734 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY734 @ ( hAPP @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY734 ) ) )
& ( ( hAPP @ ( hAPP @ V_F_2 @ V_a2_2 ) @ V_a1_2 )
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK59_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(3192,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Orefl__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(3193,plain,
( ( ! [V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_member @ T_a @ ( sK58_B_z @ T_a @ V_x_2 @ V_R_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(3194,plain,
( ( ! [V_r_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ V_x_2 ) @ V_r_2 )
& ~ ( c_member @ T_a @ ( sK57_B_y @ T_a @ V_x_2 @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(3195,plain,
( ( ! [V_g_2: $i,V_F_2: $i,T_b: $i,V_R_2: $i,V_x_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ V_x_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) @ ( hAPP @ V_g_2 @ ( sK56_B_z @ T_a @ V_x_2 @ V_R_2 @ T_b @ V_F_2 @ V_g_2 ) ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_x_2 @ ( hAPP @ ( hAPP @ V_F_2 @ V_g_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(3196,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,V_F_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ! [B_g: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ V_a1_2 ) @ V_R_2 )
& ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ ( hAPP @ B_g @ ( sK55_B_z @ B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) ) )
| ( V_a2_2
!= ( hAPP @ ( hAPP @ V_F_2 @ B_g ) @ V_a1_2 ) ) )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 )
| ( ! [SY733: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY733 @ V_a1_2 ) @ V_R_2 )
| ( c_Recdef_Owfrec__rel @ T_a @ T_b @ V_R_2 @ V_F_2 @ SY733 @ ( hAPP @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) @ SY733 ) ) )
& ( V_a2_2
= ( hAPP @ ( hAPP @ V_F_2 @ ( sK54_B_g @ T_a @ T_b @ V_R_2 @ V_F_2 @ V_a1_2 @ V_a2_2 ) ) @ V_a1_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(3197,plain,
( ( ! [V_r_2: $i,V_a_2: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(3198,plain,
( ( ! [V_b_2: $i,V_r_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(3199,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( V_y_2 = V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(3200,plain,
( ( ! [V_r_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK52_SY730 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK51_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK52_SY730 @ T_a @ T_b @ V_r_2 )
!= ( sK53_SY732 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_y ) @ V_r_2 )
| ! [B_z: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ B_x @ B_z ) @ V_r_2 )
| ( B_y = B_z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(3201,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Product__Type_Ocurry @ T_b @ T_c @ T_a @ V_f_2 @ V_a_2 @ V_b_2 )
= ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_b @ T_c @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(3202,plain,
( ( ! [V_r_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(3203,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(3204,plain,
( ( ! [V_y_2: $i,V_R_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ ( c_Relation_ODomain @ T_a @ T_a @ V_R_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(3205,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Osingle__valued @ T_a @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_z_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(3206,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(3207,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(3208,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(3209,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(3210,plain,
( ( ! [V_r_2: $i,T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK49_SY727 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK48_B_x @ T_a @ T_b @ V_r_2 ) @ ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) @ V_r_2 )
& ( ( sK49_SY727 @ T_a @ T_b @ V_r_2 )
!= ( sK50_SY729 @ T_a @ T_b @ V_r_2 ) ) )
| ( c_Relation_Osingle__valued @ T_a @ T_b @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(3211,plain,
( ( ! [V_r_2: $i,V_zb_2: $i,V_za_2: $i,V_xb_2: $i,V_xa_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ( ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 )
= ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_xa_2 @ V_xb_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK46_B_a @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) @ ( sK47_SY726 @ T_a @ T_b @ V_xa_2 @ V_xb_2 @ V_za_2 @ V_zb_2 @ V_r_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_za_2 @ V_zb_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(3212,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_a_2 = V_b_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK45_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(3213,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( V_x_2 = V_z_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK44_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(3214,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(3215,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,V_a_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(3216,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(3217,plain,
( ( ! [V_r_2: $i,V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(3218,plain,
( ( ! [V_r_2: $i,T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(3219,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ( ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 )
= V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(3220,plain,
( ( ! [V_c_2: $i,V_R_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_R_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_R_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(3221,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(3222,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(3223,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(3224,plain,
( ( ! [V_R_2: $i,V_y_2: $i] :
( ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_x_2 != V_y_2 )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_x_2 = V_y_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( V_x_2 = V_y_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
& ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(3225,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(3226,plain,
( ( ! [V_R_2: $i,V_b_2: $i] :
( ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( V_a_2 != V_b_2 )
| ( V_a_2 = V_b_2 ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(3227,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(3228,plain,
( ( ! [V_c_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_c_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_c_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(3229,plain,
( ( ! [V_z_2: $i,V_r_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(3230,plain,
( ( ! [T_b: $i,V_a_2: $i,V_x_2: $i,T_a: $i,B_f: $i,B_R: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ B_R )
| ( ( hAPP @ ( c_Recdef_Ocut @ T_a @ T_b @ B_f @ B_R @ V_a_2 ) @ V_x_2 )
= ( hAPP @ B_f @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(3231,plain,
( ( ! [V_g_2: $i,V_x_2: $i,V_r_2: $i,V_f_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) @ V_x_2 ) @ V_r_2 )
& ( ( hAPP @ V_f_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK43_B_y @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 @ V_g_2 ) ) ) )
| ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ( ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_x_2 )
!= ( c_Recdef_Ocut @ T_a @ T_b @ V_g_2 @ V_r_2 @ V_x_2 ) )
| ! [B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ V_x_2 ) @ V_r_2 )
| ( ( hAPP @ V_f_2 @ B_y )
= ( hAPP @ V_g_2 @ B_y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(3232,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK42_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(3233,plain,
( ( ! [V_R_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) ) @ V_R_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK41_B_z @ T_a @ V_x_2 @ V_y_2 @ V_R_2 ) @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(3234,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK40_B_x @ T_a @ V_r_2 ) @ ( sK40_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_x ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(3235,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) @ ( sK39_B_x @ T_a @ V_r_2 @ V_x_2 @ V_y_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ V_r_2 )
| ( V_x_2 != V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(3236,plain,
( ( ! [V_r_2: $i,V_z_2: $i,V_x_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_z_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK38_B_y @ T_a @ V_x_2 @ V_z_2 @ V_r_2 ) @ V_z_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(3237,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK37_B_c @ T_a @ V_a_2 @ V_b_2 @ V_r_2 ) @ V_b_2 ) @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(3238,plain,
( ( ! [V_a_2: $i,T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(3239,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(3240,plain,
( ( ! [V_b_2: $i] :
( ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) ) )
& ! [V_a_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Relation_OId @ T_a ) )
| ( V_a_2 = V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(3241,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK36_B_x @ T_a @ V_r_2 ) @ ( sK36_B_x @ T_a @ V_r_2 ) ) @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(3242,plain,
( ( ! [V_p_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ V_p_2 @ ( c_Relation_OId @ T_a ) )
| ( V_p_2
= ( c_Product__Type_OPair @ T_a @ T_a @ ( sK35_B_x @ T_a @ V_p_2 ) @ ( sK35_B_x @ T_a @ V_p_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(3243,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_b_2 @ V_a_2 ) @ V_r_2 )
| ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(3244,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(3245,plain,
( ( ! [V_b_2: $i,V_B_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(3246,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_b @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_a_2 @ ( c_Relation_ODomain @ T_a @ T_b @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(3247,plain,
( ( ! [V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ T_b @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ V_a_2 @ V_b_2 ) @ V_r_2 ) )
= ( c_Set_Oinsert @ T_a @ V_b_2 @ ( c_Relation_ORange @ T_b @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(3248,plain,
( ( ! [V_B_2: $i,V_a_2: $i,T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_a_2 @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(3249,plain,
( ( ! [V_A_2: $i,V_b_2: $i] :
( ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) )
| ( V_a_2 = V_b_2 )
| ( c_member @ T_a @ V_a_2 @ V_A_2 ) )
& ! [V_a_2: $i] :
( ( V_a_2 != V_b_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) )
& ! [V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(3250,plain,
( ( ! [V_B_2: $i,V_A_2: $i] :
( ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
!= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) )
& ! [V_x_2: $i,T_a: $i] :
( ( c_member @ T_a @ V_x_2 @ V_A_2 )
| ( c_member @ T_a @ V_x_2 @ V_B_2 )
| ( V_A_2 != V_B_2 )
| ( ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(3251,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_B_2 )
| ( c_member @ T_a @ V_a_2 @ ( c_Set_Oinsert @ T_a @ V_b_2 @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(3252,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ( ( c_Set_Oinsert @ T_a @ V_a_2 @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(3253,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK33_B_x @ T_a @ V_r_2 ) @ ( sK34_SY725 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK34_SY725 @ T_a @ V_r_2 ) @ ( sK33_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK33_B_x @ T_a @ V_r_2 )
!= ( sK34_SY725 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ! [B_x: $i,B_y: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_x @ B_y ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ B_y @ B_x ) @ V_r_2 )
| ( B_x = B_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(3254,plain,
( ( ! [V_rb_2: $i,T_b: $i,V_ra_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_ra_2 )
| ~ ( c_Wellfounded_Owf @ T_b @ V_rb_2 )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Wellfounded_Olex__prod @ T_a @ T_b @ V_ra_2 @ V_rb_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(3255,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(3256,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(3257,plain,
( ( ! [V_x_2: $i,V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_x_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(3258,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_a_2 ) @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(3259,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ T_a @ V_x_2 @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(3260,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK32_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_x: $i] : ( c_member @ T_a @ B_x @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(3261,plain,
( ( ! [V_y_2: $i] :
( ! [V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ! [T_a: $i] : ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) ) )
& ! [V_x_2: $i] :
( ! [T_a: $i] :
~ ( c_member @ T_a @ V_x_2 @ ( c_fequal @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(3262,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ T_a @ ( sK31_SY722 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) )
& ! [SY723: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ SY723 ) @ V_r_2 )
& ( c_member @ T_a @ ( sK30_SY724 @ SY723 @ T_a @ V_r_2 ) @ ( sK29_B_Q @ T_a @ V_r_2 ) ) )
| ~ ( c_member @ T_a @ SY723 @ ( sK29_B_Q @ T_a @ V_r_2 ) ) ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ! [B_Q: $i] :
( ! [B_x: $i] :
~ ( c_member @ T_a @ B_x @ B_Q )
| ( ! [SY721: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ SY721 @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) ) @ V_r_2 )
| ~ ( c_member @ T_a @ SY721 @ B_Q ) )
& ( c_member @ T_a @ ( sK28_B_x @ B_Q @ T_a @ V_r_2 ) @ B_Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(3263,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK26_B_x @ T_a @ V_r_2 ) @ ( sK27_SY720 @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK27_SY720 @ T_a @ V_r_2 ) @ ( sK26_B_x @ T_a @ V_r_2 ) ) @ V_r_2 )
& ( ( sK26_B_x @ T_a @ V_r_2 )
!= ( sK27_SY720 @ T_a @ V_r_2 ) ) )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(3264,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ ( sK25_B_x @ T_a @ V_r_2 ) @ ( c_Wellfounded_Oacc @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(3265,plain,
( ( c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(3266,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i] :
( ! [V_b_2: $i,T_a: $i] :
( ! [B_x: $i] :
( ~ ( c_member @ T_b @ B_x @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ B_x @ V_b_2 ) @ V_r_2 ) )
| ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) ) )
& ! [V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ T_b @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 )
& ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK24_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(3267,plain,
( ( ! [V_r_2: $i,V_b_2: $i,T_b: $i,V_A_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_a_2 @ V_A_2 )
| ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ( c_member @ T_b @ V_b_2 @ ( c_Relation_OImage @ T_a @ T_b @ V_r_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(3268,plain,
( ( ! [V_A_2: $i,V_r_2: $i,T_b: $i,V_b_2: $i,T_a: $i] :
( ~ ( c_member @ T_a @ V_b_2 @ ( c_Relation_OImage @ T_b @ T_a @ V_r_2 @ V_A_2 ) )
| ( ( c_member @ ( tc_prod @ T_b @ T_a ) @ ( c_Product__Type_OPair @ T_b @ T_a @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_b_2 ) @ V_r_2 )
& ( c_member @ T_b @ ( sK23_B_x @ T_a @ V_b_2 @ T_b @ V_r_2 @ V_A_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(3269,plain,
( ( ! [V_s_2: $i,V_c_2: $i,T_c: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) @ V_r_2 )
| ~ ( c_member @ ( tc_prod @ T_b @ T_c ) @ ( c_Product__Type_OPair @ T_b @ T_c @ V_b_2 @ V_c_2 ) @ V_s_2 )
| ( c_member @ ( tc_prod @ T_a @ T_c ) @ ( c_Product__Type_OPair @ T_a @ T_c @ V_a_2 @ V_c_2 ) @ ( c_Relation_Orel__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(3270,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) )
!= ( hAPP @ V_g_2 @ ( sK22_B_x @ V_f_2 @ V_g_2 ) ) )
| ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(3271,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i] :
( ! [T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) ) )
& ! [T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ T_a @ T_b @ V_R_2 ) @ V_x_2 ) @ V_y_2 ) )
| ( c_member @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(3272,plain,
( ( ! [T_a: $i,V_R_2: $i,V_y_2: $i,V_y_H_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
| ~ ( c_member @ ( tc_prod @ T_b @ T_b ) @ ( c_Product__Type_OPair @ T_b @ T_b @ V_y_H_2 @ V_y_2 ) @ ( hAPP @ V_R_2 @ V_x_2 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_H_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_x_2 @ V_y_2 ) ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(3273,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(3274,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(3275,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Relation_Oirrefl @ T_a @ V_r_2 )
| ~ ( c_Relation_Otrans @ T_a @ V_r_2 )
| ~ ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oirrefl @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Otrans @ T_a @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Ototal__on @ T_a @ V_A_2 @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(3276,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Orefl__on @ T_a @ V_A_2 @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(3277,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(3278,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(3279,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ T_a @ T_b @ tc_HOL_Obool @ V_f_2 @ V_a_2 @ V_b_2 ) )
| ( hBOOL @ ( hAPP @ V_f_2 @ ( c_Product__Type_OPair @ T_a @ T_b @ V_a_2 @ V_b_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(3280,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(3281,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(3282,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK18_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK19_SY714 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK20_SY717 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK21_SY719 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(3283,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_by_2: $i,V_bx_2: $i,V_ay_2: $i,V_ax_2: $i,T_b: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_ax_2 @ V_ay_2 ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_bx_2 ) @ V_by_2 ) )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) @ ( c_Product__Type_OPair @ T_a @ T_b @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Product__Type_OPair @ T_a @ T_b @ V_bx_2 @ V_by_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ T_a @ T_b ) @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK16_SY711 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK17_SY713 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ ( sK14_B_a @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) @ ( sK15_SY708 @ T_a @ T_b @ V_ax_2 @ V_ay_2 @ V_bx_2 @ V_by_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_ax_2 ) @ V_ay_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(3284,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK13_SY707 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK12_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(3285,plain,
( ( ! [V_P_2: $i,V_r_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ V_b_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ~ ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
| ( ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_a_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
& ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) @ V_r_2 )
& ( hBOOL @ ( hAPP @ V_P_2 @ ( sK10_B_y @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) )
& ~ ( hBOOL @ ( hAPP @ V_P_2 @ ( sK11_SY706 @ T_a @ V_a_2 @ V_b_2 @ V_r_2 @ V_P_2 ) ) ) )
| ( hBOOL @ ( hAPP @ V_P_2 @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(3286,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(3287,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) )
= ( c_Transitive__Closure_Ortrancl @ T_a @ V_R_2 ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(3288,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ODomain @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ODomain @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(3289,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ( c_Relation_ORange @ T_a @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) )
= ( c_Relation_ORange @ T_a @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(3290,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ T_a @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(3291,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(3292,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(3293,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(3294,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( c_Set_Oinsert @ T_a @ V_x_2 @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) )
= ( c_Set_Oinsert @ T_a @ V_y_2 @ ( c_Set_Oinsert @ T_a @ V_x_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(3295,plain,
( ( ! [V_x_2: $i,V_A_2: $i] :
( ! [V_y_2: $i] :
( ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) )
| ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
& ! [V_y_2: $i] :
( ( V_y_2 != V_x_2 )
| ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) )
& ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
| ! [V_y_2: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ T_a @ V_y_2 @ V_A_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(3296,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(3297,plain,
( ( ! [V_A_2: $i,T_a: $i] : ( c_Relation_Oantisym @ T_a @ ( c_Relation_OId__on @ T_a @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(3298,plain,
( ( ! [V_r_2: $i] :
( ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 )
| ~ ( c_Relation_Oantisym @ T_a @ V_r_2 )
| ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Order__Relation_Opreorder__on @ T_a @ V_A_2 @ V_r_2 ) )
& ! [V_A_2: $i,T_a: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ T_a @ V_A_2 @ V_r_2 )
| ( c_Relation_Oantisym @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(3299,plain,
( ( ! [V_r_2: $i,V_x_2: $i] :
( ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ( c_Wellfounded_Owf @ T_a @ V_r_2 ) )
& ! [V_y_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ ( c_Set_Oinsert @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_y_2 @ V_x_2 ) @ V_r_2 ) )
| ~ ( c_member @ ( tc_prod @ T_a @ T_a ) @ ( c_Product__Type_OPair @ T_a @ T_a @ V_x_2 @ V_y_2 ) @ ( c_Transitive__Closure_Ortrancl @ T_a @ V_r_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(3300,plain,
( ( ! [V_f_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_b @ ( hAPP @ ( c_Relation_Oinv__image @ T_a @ T_b @ V_r_2 ) @ V_f_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(3301,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Transitive__Closure_Otrancl @ T_a @ V_r_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(3302,plain,
( ( ! [V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( c_Wellfounded_Oacyclic @ T_a @ V_r_2 ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(3303,plain,
( ( ! [V_f_2: $i,T_a: $i] : ( c_Wellfounded_Owf @ T_a @ ( hAPP @ ( c_Wellfounded_Omeasure @ T_a ) @ V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(3304,plain,
( ( ! [V_a_2: $i,V_H_2: $i,V_r_2: $i,T_b: $i,T_a: $i,V_f_2: $i] :
( ( V_f_2
!= ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) )
| ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ V_f_2 @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ V_f_2 @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(3305,plain,
( ( ! [V_a_2: $i,V_H_2: $i,T_b: $i,V_r_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_r_2 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ V_H_2 @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ V_r_2 @ V_H_2 ) @ V_r_2 @ V_a_2 ) ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(3306,plain,
( ( ! [T_b: $i,T_a: $i,B_M: $i,B_R: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ B_R )
| ! [B_x: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_x )
= ( hAPP @ ( hAPP @ B_M @ ( c_Recdef_Ocut @ T_a @ T_b @ ( c_Recdef_Owfrec @ T_a @ T_b @ B_R @ B_M ) @ B_R @ B_x ) ) @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(3307,plain,
( ( ! [T_a: $i,V_R_2: $i,T_b: $i,V_P_2: $i] :
( ( ( hBOOL @ ( hAPP @ V_P_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) )
& ~ ( c_Wellfounded_Owf @ T_b @ ( hAPP @ V_R_2 @ ( sK9_B_x @ V_P_2 @ T_b @ V_R_2 @ T_a ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ T_a @ T_b ) @ ( c_Recdef_Osame__fst @ T_a @ T_b @ V_P_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(3308,plain,
( ( ! [T_a: $i] :
( ( c_Wellfounded_Omeasure @ T_a )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ T_a @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(3309,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(3310,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than ) )
& ! [V_y_2: $i,V_x_2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x_2 @ V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(3311,plain,
( ( ! [V_f_2: $i,V_R_2: $i,T_a: $i] :
( ~ ( c_Wellfounded_Owf @ T_a @ V_R_2 )
| ( c_Wellfounded_Owf @ T_a @ ( c_Wellfounded_Omlex__prod @ T_a @ V_f_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(3312,plain,
( ( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(3313,plain,
( ( c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(3314,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(3315,plain,
( ( ! [V_n_2: $i,V_m_2: $i] :
( ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 != V_n_2 ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( V_m_2 != V_n_2 ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(3316,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( V_x = V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_x @ V_y )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_y @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(3317,plain,
( ( ! [V_n: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(3318,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m != V_n ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(3319,plain,
( ( ! [V_t: $i,V_s: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_s @ V_t )
| ( V_s != V_t ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(3320,plain,
( ( ! [V_P_2: $i] :
( ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_m_2 @ V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( V_m_2 = V_n_2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ V_n_2 @ V_m_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) )
& ! [V_n_2: $i,V_m_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_n_2 ) @ V_m_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(3321,plain,
( ( ! [V_n: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_n ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(3322,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(3323,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m != V_n )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(3324,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_j )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_j @ V_k )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_i @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(3325,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_m @ V_n )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ V_n @ V_m )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(3326,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_j ) @ V_k )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ V_i @ V_k ) @ V_j ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(3327,plain,
( ( c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(3328,plain,
( ( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(3329,plain,
( ( ! [V_A_2: $i,T_a: $i] :
( ( c_Relation_OImage @ T_a @ T_a @ ( c_Relation_OId @ T_a ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(3330,plain,
( ( class_Lattices_Osemilattice__sup @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(3331,plain,
( ( class_Orderings_Opreorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(3332,plain,
( ( class_Orderings_Olinorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(3333,plain,
( ( class_Lattices_Olattice @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(3334,plain,
( ( class_Orderings_Oorder @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(3335,plain,
( ( class_Orderings_Oord @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(3336,plain,
( ( class_Orderings_Obot @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(3337,plain,
( ( class_Groups_Ominus @ tc_Nat_Onat )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(3338,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(3339,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(3340,plain,
( ( ! [B_x: $i,B_y: $i] :
( ( B_x = B_y )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_y ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_y @ B_x ) @ v_L ) )
& ! [B_x: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B_x @ B_x ) @ v_L )
& ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
& ( sK8_REN
=> ( ( sK6_B_x != sK7_SY705 )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
& ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(3341,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK69_B_x @ SX1 @ SX0 ) @ ( sK70_SY736 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK70_SY736 @ SX1 @ SX0 ) @ ( sK71_SY738 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK69_B_x @ SX1 @ SX0 ) @ ( sK71_SY738 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3175]) ).
thf(3342,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK12_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK13_SY707 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK12_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3284]) ).
thf(3343,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
!= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 )
| ( SX1 != SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3250]) ).
thf(3344,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX5 ) @ SX4 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK20_SY717 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK21_SY719 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK18_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK19_SY714 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK20_SY717 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK21_SY719 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3282]) ).
thf(3345,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK61_B_x @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK61_B_x @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX1 ) @ SX0 )
| ( c_member @ SX2 @ SX3 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3186]) ).
thf(3346,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ SX2 @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( c_member @ SX2 @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SX2 @ SX1 @ SX0 )
!= ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK68_SY735 @ SX2 @ SX1 @ SX0 ) @ ( sK67_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 )
| ! [SX3: $i] :
( ~ ( c_member @ SX2 @ SX3 @ SX1 )
| ! [SX4: $i] :
( ~ ( c_member @ SX2 @ SX4 @ SX1 )
| ( SX3 = SX4 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX4 @ SX3 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3176]) ).
thf(3347,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX3 = SX1 ) )
| ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3162]) ).
thf(3348,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK26_B_x @ SX1 @ SX0 ) @ ( sK27_SY720 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK27_SY720 @ SX1 @ SX0 ) @ ( sK26_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK26_B_x @ SX1 @ SX0 )
!= ( sK27_SY720 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3263]) ).
thf(3349,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ ( sK75_B_x1 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( c_Product__Type_OPair @ SX1 @ SX0 @ SX3 @ SX4 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ ( c_Product__Type_OPair @ SX1 @ SX0 @ ( sK73_B_a @ SX2 @ SX1 @ SX0 ) @ ( sK74_SY739 @ SX2 @ SX1 @ SX0 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3160]) ).
thf(3350,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK51_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK52_SY730 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK51_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK53_SY732 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK52_SY730 @ SX2 @ SX1 @ SX0 )
!= ( sK53_SY732 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ! [SX5: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ SX3 @ SX5 ) @ SX0 )
| ( SX4 = SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3200]) ).
thf(3351,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ~ ( ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) )
| ( SX5 = SX3 )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 ) )
| ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX6: $i] :
( ( SX5 != SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 )
| ! [SX7: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) ) )
| ~ ! [SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Wellfounded_Olex__prod @ SX7 @ SX6 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3169]) ).
thf(3352,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK48_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY727 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX1 ) @ ( c_Product__Type_OPair @ SX2 @ SX1 @ ( sK48_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK50_SY729 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK49_SY727 @ SX2 @ SX1 @ SX0 )
!= ( sK50_SY729 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3210]) ).
thf(3353,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3156]) ).
thf(3354,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3253]) ).
thf(3355,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Orefl__on @ SX2 @ SX1 @ SX0 )
| ~ ( c_Relation_Otrans @ SX2 @ SX0 )
| ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Orefl__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Otrans @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3192]) ).
thf(3356,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( c_member @ SX2 @ SX5 @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 ) )
| ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_member @ SX2 @ ( sK24_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ ( sK24_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3266]) ).
thf(3357,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK45_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK45_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3212]) ).
thf(3358,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3240]) ).
thf(3359,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3165]) ).
thf(3360,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3234]) ).
thf(3361,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX1 @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3271]) ).
thf(3362,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ! [SX6: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX6 @ ( sK60_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ SX2 @ SX6 ) @ SX1 ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ~ ( ~ ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX3 )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX6 @ ( hAPP @ ( sK59_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 ) ) )
| ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ SX2 @ ( sK59_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3191]) ).
thf(3363,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ( SX2 = SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ( SX2 = SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( SX2 = SX1 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( SX2 = SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3320]) ).
thf(3364,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i] :
( ! [SX5: $i] :
~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX4 @ SX3 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SX2 @ SX5 @ SX1 ) @ SX0 ) )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( hAPP @ SX0 @ SX4 ) @ ( hAPP @ SX0 @ SX3 ) ) @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( hAPP @ SX0 @ SX4 ) @ ( hAPP @ SX0 @ SX3 ) ) @ SX1 )
| ! [SX5: $i] : ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX4 @ SX3 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SX2 @ SX5 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3177]) ).
thf(3365,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3261]) ).
thf(3366,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK44_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK44_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3213]) ).
thf(3367,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK41_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK41_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3233]) ).
thf(3368,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Relation_OId__on @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ SX2 @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( SX1
!= ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) @ ( sK64_B_x @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3183]) ).
thf(3369,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3310]) ).
thf(3370,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ ( sK66_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3181]) ).
thf(3371,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX3 @ SX1 ) )
| ( SX2 != SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX3 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX1 ) )
| ( SX2 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3204]) ).
thf(3372,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ SX0 ) )
| ! [SX2: $i,SX3: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3295]) ).
thf(3373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX2 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK14_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY708 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX7 @ SX6 ) @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX3 @ SX2 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX7 @ SX6 ) @ SX1 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK16_SY711 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK17_SY713 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ ( sK14_B_a @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK15_SY708 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX5 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3283]) ).
thf(3374,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX3 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3291]) ).
thf(3375,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ ( sK65_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3182]) ).
thf(3376,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) )
| ( ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 )
= ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ ( sK46_B_a @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK47_SY726 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SX6 @ SX5 ) @ ( tc_prod @ SX6 @ SX5 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ ( sK46_B_a @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK47_SY726 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3211]) ).
thf(3377,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3262]) ).
thf(3378,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX2 )
| ~ ( ( ( hAPP @ SX3 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( hAPP @ SX0 @ ( sK43_B_y @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
= ( c_Recdef_Ocut @ SX5 @ SX4 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( c_Recdef_Ocut @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
!= ( c_Recdef_Ocut @ SX5 @ SX4 @ SX0 @ SX2 @ SX1 ) )
| ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX2 )
| ( ( hAPP @ SX3 @ SX6 )
= ( hAPP @ SX0 @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3231]) ).
thf(3379,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3166]) ).
thf(3380,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK37_B_c @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK37_B_c @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3237]) ).
thf(3381,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 )
| ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX3 = SX1 ) )
| ~ ( ! [SX4: $i,SX5: $i] :
( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
!= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3161]) ).
thf(3382,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] : ( SX3 != SX2 )
| ( c_member @ SX1 @ SX0 @ SX2 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3158]) ).
thf(3383,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ ( sK9_B_x @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SX2 @ ( hAPP @ SX1 @ ( sK9_B_x @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SX0 @ SX2 ) @ ( c_Recdef_Osame__fst @ SX0 @ SX2 @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3307]) ).
thf(3384,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( c_member @ SX2 @ SX1 @ SX0 )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ! [SX2: $i] : ( c_member @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3163]) ).
thf(3385,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX1 )
| ~ ( c_member @ SX3 @ SX2 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Relation_OId__on @ SX3 @ SX0 ) )
| ( c_member @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3172]) ).
thf(3386,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK57_B_y @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK57_B_y @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3194]) ).
thf(3387,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK38_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK38_B_y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3236]) ).
thf(3388,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 != SX1 )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 = SX1 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ( SX2 != SX1 )
| ! [SX3: $i] : ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3224]) ).
thf(3389,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ ( sK42_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ ( sK42_B_z @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3232]) ).
thf(3390,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3159]) ).
thf(3391,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX2 @ SX3 @ SX1 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX0 @ ( sK56_B_z @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX2 @ SX3 @ SX1 @ SX4 @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3195]) ).
thf(3392,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 )
| ~ ( c_Relation_Oantisym @ SX2 @ SX0 )
| ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Order__Relation_Opreorder__on @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Oantisym @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3298]) ).
thf(3393,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
| ~ ~ ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3340]) ).
thf(3394,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Relation_Oirrefl @ SX2 @ SX0 )
| ~ ( c_Relation_Otrans @ SX2 @ SX0 )
| ~ ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Oirrefl @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Otrans @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SX2 @ SX1 @ SX0 )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3275]) ).
thf(3395,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) )
| ( SX2 = SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX1 )
| ! [SX3: $i] : ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX0 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3249]) ).
thf(3396,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3168]) ).
thf(3397,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ! [SX6: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX3 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( hAPP @ SX6 @ ( sK55_B_z @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0
!= ( hAPP @ ( hAPP @ SX2 @ SX6 ) @ SX1 ) ) )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ! [SX6: $i] :
( ~ ( c_member @ ( tc_prod @ SX5 @ SX5 ) @ ( c_Product__Type_OPair @ SX5 @ SX5 @ SX6 @ SX1 ) @ SX3 )
| ( c_Recdef_Owfrec__rel @ SX5 @ SX4 @ SX3 @ SX2 @ SX6 @ ( hAPP @ ( sK54_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 ) ) )
| ( SX0
!= ( hAPP @ ( hAPP @ SX2 @ ( sK54_B_g @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3196]) ).
thf(3398,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ! [SX3: $i] : ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3245]) ).
thf(3399,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY706 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK10_B_y @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX0 @ ( sK11_SY706 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3285]) ).
thf(3400,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( SX2 != SX1 )
| ( SX2 = SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3226]) ).
thf(3401,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ ( sK23_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX1 )
| ~ ( c_member @ SX2 @ ( sK23_B_x @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3268]) ).
thf(3402,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3315]) ).
thf(3403,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3260]) ).
thf(3404,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ ( sK58_B_z @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ~ ( c_member @ SX2 @ ( sK58_B_z @ SX2 @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3193]) ).
thf(3405,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( c_Wellfounded_Owf @ SX3 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ ( c_Set_Oinsert @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX2 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3299]) ).
thf(3406,plain,
! [SV795: $i] :
( ( ! [SY2211: $i,SY2212: $i,SY2213: $i,SY2214: $i] :
( ~ ( c_Relation_Otrans @ SY2214 @ SY2213 )
| ~ ( c_member @ ( tc_prod @ SY2214 @ SY2214 ) @ ( c_Product__Type_OPair @ SY2214 @ SY2214 @ SY2212 @ SY2211 ) @ SY2213 )
| ~ ( c_member @ ( tc_prod @ SY2214 @ SY2214 ) @ ( c_Product__Type_OPair @ SY2214 @ SY2214 @ SY2211 @ SV795 ) @ SY2213 )
| ( c_member @ ( tc_prod @ SY2214 @ SY2214 ) @ ( c_Product__Type_OPair @ SY2214 @ SY2214 @ SY2212 @ SV795 ) @ SY2213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3407,plain,
! [SV796: $i] :
( ( ! [SY2215: $i,SY2216: $i,SY2217: $i] :
( ( SY2217 != SY2216 )
| ~ ( c_member @ SY2215 @ SY2216 @ SV796 )
| ( c_member @ SY2215 @ SY2217 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3408,plain,
! [SV797: $i] :
( ( ! [SY2218: $i,SY2219: $i,SY2220: $i,SY2221: $i,SY2222: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY2222 @ SY2221 @ SY2220 @ SY2219 @ ( c_Product__Type_OPair @ SY2222 @ SY2221 @ SY2218 @ SV797 ) )
= ( hAPP @ ( hAPP @ SY2219 @ SY2218 ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3409,plain,
! [SV798: $i] :
( ( ! [SY2223: $i,SY2224: $i,SY2225: $i,SY2226: $i,SY2227: $i] :
( ( c_Product__Type_Ointernal__split @ SY2227 @ SY2226 @ SY2225 @ SY2224 @ ( c_Product__Type_OPair @ SY2227 @ SY2226 @ SY2223 @ SV798 ) )
= ( hAPP @ ( hAPP @ SY2224 @ SY2223 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3410,plain,
! [SV799: $i] :
( ( ! [SY2228: $i,SY2229: $i,SY2230: $i,SY2231: $i] :
( ~ ( c_member @ ( tc_prod @ SY2231 @ SY2230 ) @ ( c_Product__Type_OPair @ SY2231 @ SY2230 @ SY2229 @ SY2228 ) @ SV799 )
| ( c_member @ SY2230 @ SY2228 @ ( c_Relation_ORange @ SY2231 @ SY2230 @ SV799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3411,plain,
! [SV800: $i] :
( ( ! [SY2232: $i,SY2233: $i,SY2234: $i] :
( ( SY2234 != SY2233 )
| ~ ( c_member @ SY2232 @ SY2234 @ SV800 )
| ( c_member @ ( tc_prod @ SY2232 @ SY2232 ) @ ( c_Product__Type_OPair @ SY2232 @ SY2232 @ SY2234 @ SY2233 ) @ ( c_Relation_OId__on @ SY2232 @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3412,plain,
! [SV801: $i] :
( ( ! [SY2235: $i,SY2236: $i,SY2237: $i,SY2238: $i] :
( ~ ( c_member @ ( tc_prod @ SY2238 @ SY2237 ) @ ( c_Product__Type_OPair @ SY2238 @ SY2237 @ SY2236 @ SY2235 ) @ SV801 )
| ( c_member @ SY2238 @ SY2236 @ ( c_Relation_ODomain @ SY2238 @ SY2237 @ SV801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3413,plain,
! [SV802: $i] :
( ( ! [SY2239: $i,SY2240: $i,SY2241: $i] :
( ~ ( c_Relation_Otrans @ SY2241 @ SY2240 )
| ~ ( c_Relation_Otrans @ SY2239 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SY2241 @ SY2239 ) @ ( c_Wellfounded_Olex__prod @ SY2241 @ SY2239 @ SY2240 @ SV802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3414,plain,
! [SV803: $i] :
( ( ! [SY2242: $i] : ( c_Relation_Otrans @ SY2242 @ ( c_Relation_OId__on @ SY2242 @ SV803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3415,plain,
! [SV804: $i] :
( ( ! [SY2243: $i,SY2244: $i,SY2245: $i] :
( ~ ( c_Relation_Otrans @ SY2245 @ SY2244 )
| ( c_Relation_Otrans @ SY2243 @ ( hAPP @ ( c_Relation_Oinv__image @ SY2245 @ SY2243 @ SY2244 ) @ SV804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3416,plain,
! [SV805: $i] :
( ( ! [SY2246: $i,SY2247: $i,SY2248: $i] :
( ~ ( c_member @ SY2248 @ SY2247 @ ( c_Relation_ORange @ SY2246 @ SY2248 @ SV805 ) )
| ( c_member @ ( tc_prod @ SY2246 @ SY2248 ) @ ( c_Product__Type_OPair @ SY2246 @ SY2248 @ ( sK63_B_x @ SY2248 @ SY2247 @ SY2246 @ SV805 ) @ SY2247 ) @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3417,plain,
! [SV806: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i] :
( ~ ( c_member @ SY2251 @ SY2250 @ ( c_Relation_ODomain @ SY2251 @ SY2249 @ SV806 ) )
| ( c_member @ ( tc_prod @ SY2251 @ SY2249 ) @ ( c_Product__Type_OPair @ SY2251 @ SY2249 @ SY2250 @ ( sK62_B_y @ SY2251 @ SY2250 @ SY2249 @ SV806 ) ) @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3418,plain,
! [SV807: $i] :
( ( ! [SY2252: $i,SY2253: $i,SY2254: $i] :
( ~ ( c_member @ SY2254 @ SY2253 @ ( c_Wellfounded_Oacc @ SY2254 @ SY2252 ) )
| ~ ( c_member @ ( tc_prod @ SY2254 @ SY2254 ) @ ( c_Product__Type_OPair @ SY2254 @ SY2254 @ SV807 @ SY2253 ) @ SY2252 )
| ( c_member @ SY2254 @ SV807 @ ( c_Wellfounded_Oacc @ SY2254 @ SY2252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3419,plain,
! [SV808: $i] :
( ( ! [SY2255: $i,SY2256: $i,SY2257: $i] :
( ~ ( c_Relation_Orefl__on @ SY2257 @ SY2256 @ SY2255 )
| ~ ( c_member @ SY2257 @ SV808 @ SY2256 )
| ( c_member @ ( tc_prod @ SY2257 @ SY2257 ) @ ( c_Product__Type_OPair @ SY2257 @ SY2257 @ SV808 @ SV808 ) @ SY2255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3420,plain,
! [SV809: $i] :
( ( ! [SY2258: $i,SY2259: $i,SY2260: $i,SY2261: $i] :
( ~ ( c_Relation_Orefl__on @ SY2261 @ SY2260 @ SY2259 )
| ~ ( c_member @ ( tc_prod @ SY2261 @ SY2261 ) @ ( c_Product__Type_OPair @ SY2261 @ SY2261 @ SY2258 @ SV809 ) @ SY2259 )
| ( c_member @ SY2261 @ SY2258 @ SY2260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3421,plain,
! [SV810: $i] :
( ( ! [SY2262: $i,SY2263: $i,SY2264: $i,SY2265: $i] :
( ~ ( c_Relation_Orefl__on @ SY2265 @ SY2264 @ SY2263 )
| ~ ( c_member @ ( tc_prod @ SY2265 @ SY2265 ) @ ( c_Product__Type_OPair @ SY2265 @ SY2265 @ SY2262 @ SV810 ) @ SY2263 )
| ( c_member @ SY2265 @ SV810 @ SY2264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3422,plain,
! [SV811: $i] :
( ( ! [SY2266: $i,SY2267: $i,SY2268: $i] :
( ~ ( c_member @ ( tc_prod @ SY2268 @ SY2268 ) @ ( c_Product__Type_OPair @ SY2268 @ SY2268 @ SY2267 @ SY2266 ) @ ( c_Transitive__Closure_Ortrancl @ SY2268 @ SV811 ) )
| ~ ( c_member @ SY2268 @ SY2266 @ ( c_Wellfounded_Oacc @ SY2268 @ SV811 ) )
| ( c_member @ SY2268 @ SY2267 @ ( c_Wellfounded_Oacc @ SY2268 @ SV811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3423,plain,
! [SV812: $i] :
( ( ! [SY2269: $i,SY2270: $i,SY2271: $i] :
( ~ ( c_member @ SY2271 @ SY2270 @ ( c_Wellfounded_Oacc @ SY2271 @ SY2269 ) )
| ~ ( c_member @ ( tc_prod @ SY2271 @ SY2271 ) @ ( c_Product__Type_OPair @ SY2271 @ SY2271 @ SV812 @ SY2270 ) @ ( c_Transitive__Closure_Ortrancl @ SY2271 @ SY2269 ) )
| ( c_member @ SY2271 @ SV812 @ ( c_Wellfounded_Oacc @ SY2271 @ SY2269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3424,plain,
! [SV813: $i] :
( ( ! [SY2272: $i,SY2273: $i,SY2274: $i,SY2275: $i,SY2276: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2276 @ SY2275 @ SY2274 )
| ~ ( c_member @ ( tc_prod @ SY2276 @ SY2275 ) @ ( c_Product__Type_OPair @ SY2276 @ SY2275 @ SY2273 @ SY2272 ) @ SY2274 )
| ~ ( c_member @ ( tc_prod @ SY2276 @ SY2275 ) @ ( c_Product__Type_OPair @ SY2276 @ SY2275 @ SY2273 @ SV813 ) @ SY2274 )
| ( SY2272 = SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3425,plain,
! [SV814: $i] :
( ( ! [SY2277: $i,SY2278: $i,SY2279: $i,SY2280: $i,SY2281: $i] :
( ( c_Product__Type_Ocurry @ SY2281 @ SY2280 @ SY2279 @ SY2278 @ SY2277 @ SV814 )
= ( hAPP @ SY2278 @ ( c_Product__Type_OPair @ SY2281 @ SY2280 @ SY2277 @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3426,plain,
! [SV815: $i] :
( ( ! [SY2282: $i,SY2283: $i] : ( c_member @ ( tc_prod @ SY2283 @ SY2283 ) @ ( c_Product__Type_OPair @ SY2283 @ SY2283 @ SY2282 @ SY2282 ) @ ( c_Transitive__Closure_Ortrancl @ SY2283 @ SV815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3427,plain,
! [SV816: $i] :
( ( ! [SY2284: $i,SY2285: $i] :
( ~ ( c_member @ ( tc_prod @ SY2285 @ SY2285 ) @ SY2284 @ SV816 )
| ( c_member @ ( tc_prod @ SY2285 @ SY2285 ) @ SY2284 @ ( c_Transitive__Closure_Ortrancl @ SY2285 @ SV816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3428,plain,
! [SV817: $i] :
( ( ! [SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2289 @ SY2289 @ SY2288 )
| ~ ( c_member @ ( tc_prod @ SY2289 @ SY2289 ) @ ( c_Product__Type_OPair @ SY2289 @ SY2289 @ SY2287 @ SY2286 ) @ ( c_Transitive__Closure_Ortrancl @ SY2289 @ SY2288 ) )
| ~ ( c_member @ ( tc_prod @ SY2289 @ SY2289 ) @ ( c_Product__Type_OPair @ SY2289 @ SY2289 @ SY2287 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY2289 @ SY2288 ) )
| ( c_member @ ( tc_prod @ SY2289 @ SY2289 ) @ ( c_Product__Type_OPair @ SY2289 @ SY2289 @ SY2286 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY2289 @ SY2288 ) )
| ( c_member @ ( tc_prod @ SY2289 @ SY2289 ) @ ( c_Product__Type_OPair @ SY2289 @ SY2289 @ SV817 @ SY2286 ) @ ( c_Transitive__Closure_Ortrancl @ SY2289 @ SY2288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3429,plain,
! [SV818: $i] :
( ( ! [SY2290: $i,SY2291: $i,SY2292: $i,SY2293: $i] :
( ~ ( c_member @ ( tc_prod @ SY2293 @ SY2293 ) @ ( c_Product__Type_OPair @ SY2293 @ SY2293 @ SY2292 @ SY2291 ) @ SY2290 )
| ~ ( c_member @ ( tc_prod @ SY2293 @ SY2293 ) @ ( c_Product__Type_OPair @ SY2293 @ SY2293 @ SY2291 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY2293 @ SY2290 ) )
| ( c_member @ ( tc_prod @ SY2293 @ SY2293 ) @ ( c_Product__Type_OPair @ SY2293 @ SY2293 @ SY2292 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY2293 @ SY2290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3430,plain,
! [SV819: $i] :
( ( ! [SY2294: $i,SY2295: $i,SY2296: $i,SY2297: $i] :
( ~ ( c_member @ ( tc_prod @ SY2297 @ SY2297 ) @ ( c_Product__Type_OPair @ SY2297 @ SY2297 @ SY2296 @ SY2295 ) @ ( c_Transitive__Closure_Ortrancl @ SY2297 @ SY2294 ) )
| ~ ( c_member @ ( tc_prod @ SY2297 @ SY2297 ) @ ( c_Product__Type_OPair @ SY2297 @ SY2297 @ SY2295 @ SV819 ) @ SY2294 )
| ( c_member @ ( tc_prod @ SY2297 @ SY2297 ) @ ( c_Product__Type_OPair @ SY2297 @ SY2297 @ SY2296 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SY2297 @ SY2294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3431,plain,
! [SV820: $i] :
( ( ! [SY2298: $i,SY2299: $i,SY2300: $i,SY2301: $i] :
( ~ ( c_member @ ( tc_prod @ SY2301 @ SY2301 ) @ ( c_Product__Type_OPair @ SY2301 @ SY2301 @ SY2300 @ SY2299 ) @ ( c_Transitive__Closure_Ortrancl @ SY2301 @ SY2298 ) )
| ~ ( c_member @ ( tc_prod @ SY2301 @ SY2301 ) @ ( c_Product__Type_OPair @ SY2301 @ SY2301 @ SY2299 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY2301 @ SY2298 ) )
| ( c_member @ ( tc_prod @ SY2301 @ SY2301 ) @ ( c_Product__Type_OPair @ SY2301 @ SY2301 @ SY2300 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY2301 @ SY2298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3432,plain,
! [SV821: $i] :
( ( ! [SY2302: $i] : ( c_Relation_Otrans @ SY2302 @ ( c_Transitive__Closure_Ortrancl @ SY2302 @ SV821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3433,plain,
! [SV822: $i] :
( ( ! [SY2303: $i,SY2304: $i,SY2305: $i] :
( ~ ( c_member @ ( tc_prod @ SY2305 @ SY2305 ) @ ( c_Product__Type_OPair @ SY2305 @ SY2305 @ SY2304 @ SY2303 ) @ ( c_Transitive__Closure_Otrancl @ SY2305 @ SV822 ) )
| ( c_member @ ( tc_prod @ SY2305 @ SY2305 ) @ ( c_Product__Type_OPair @ SY2305 @ SY2305 @ SY2304 @ SY2303 ) @ ( c_Transitive__Closure_Ortrancl @ SY2305 @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3434,plain,
! [SV823: $i] :
( ( ! [SY2306: $i,SY2307: $i,SY2308: $i,SY2309: $i,SY2310: $i] :
( ~ ( c_member @ ( tc_prod @ SY2310 @ SY2310 ) @ ( c_Product__Type_OPair @ SY2310 @ SY2310 @ SY2309 @ SY2308 ) @ SY2307 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY2310 @ SY2306 @ SV823 @ SY2307 @ SY2308 ) @ SY2309 )
= ( hAPP @ SV823 @ SY2309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3435,plain,
! [SV824: $i] :
( ( ! [SY2311: $i,SY2312: $i,SY2313: $i] :
( ~ ( c_member @ ( tc_prod @ SY2313 @ SY2313 ) @ ( c_Product__Type_OPair @ SY2313 @ SY2313 @ SY2312 @ SY2311 ) @ SV824 )
| ( c_member @ ( tc_prod @ SY2313 @ SY2313 ) @ ( c_Product__Type_OPair @ SY2313 @ SY2313 @ SY2312 @ SY2311 ) @ ( c_Transitive__Closure_Otrancl @ SY2313 @ SV824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3436,plain,
! [SV825: $i] :
( ( ! [SY2314: $i,SY2315: $i] :
( ~ ( c_member @ ( tc_prod @ SY2315 @ SY2315 ) @ SY2314 @ SV825 )
| ( c_member @ ( tc_prod @ SY2315 @ SY2315 ) @ SY2314 @ ( c_Transitive__Closure_Otrancl @ SY2315 @ SV825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3437,plain,
! [SV826: $i] :
( ( ! [SY2316: $i] : ( c_Relation_Otrans @ SY2316 @ ( c_Transitive__Closure_Otrancl @ SY2316 @ SV826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3438,plain,
! [SV827: $i] :
( ( ! [SY2317: $i] :
( ~ ( c_Relation_Otrans @ SY2317 @ SV827 )
| ( ( c_Transitive__Closure_Otrancl @ SY2317 @ SV827 )
= SV827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3439,plain,
! [SV828: $i] :
( ( ! [SY2318: $i,SY2319: $i,SY2320: $i,SY2321: $i] :
( ~ ( c_member @ ( tc_prod @ SY2321 @ SY2321 ) @ ( c_Product__Type_OPair @ SY2321 @ SY2321 @ SY2320 @ SY2319 ) @ SY2318 )
| ~ ( c_member @ ( tc_prod @ SY2321 @ SY2321 ) @ ( c_Product__Type_OPair @ SY2321 @ SY2321 @ SY2319 @ SV828 ) @ SY2318 )
| ( c_member @ ( tc_prod @ SY2321 @ SY2321 ) @ ( c_Product__Type_OPair @ SY2321 @ SY2321 @ SY2320 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SY2321 @ SY2318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3440,plain,
! [SV829: $i] :
( ( ! [SY2322: $i,SY2323: $i,SY2324: $i,SY2325: $i] :
( ~ ( c_member @ ( tc_prod @ SY2325 @ SY2325 ) @ ( c_Product__Type_OPair @ SY2325 @ SY2325 @ SY2324 @ SY2323 ) @ SY2322 )
| ~ ( c_member @ ( tc_prod @ SY2325 @ SY2325 ) @ ( c_Product__Type_OPair @ SY2325 @ SY2325 @ SY2323 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY2325 @ SY2322 ) )
| ( c_member @ ( tc_prod @ SY2325 @ SY2325 ) @ ( c_Product__Type_OPair @ SY2325 @ SY2325 @ SY2324 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY2325 @ SY2322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3441,plain,
! [SV830: $i] :
( ( ! [SY2326: $i,SY2327: $i,SY2328: $i,SY2329: $i] :
( ~ ( c_member @ ( tc_prod @ SY2329 @ SY2329 ) @ ( c_Product__Type_OPair @ SY2329 @ SY2329 @ SY2328 @ SY2327 ) @ ( c_Transitive__Closure_Otrancl @ SY2329 @ SY2326 ) )
| ~ ( c_member @ ( tc_prod @ SY2329 @ SY2329 ) @ ( c_Product__Type_OPair @ SY2329 @ SY2329 @ SY2327 @ SV830 ) @ SY2326 )
| ( c_member @ ( tc_prod @ SY2329 @ SY2329 ) @ ( c_Product__Type_OPair @ SY2329 @ SY2329 @ SY2328 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SY2329 @ SY2326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3442,plain,
! [SV831: $i] :
( ( ! [SY2330: $i,SY2331: $i,SY2332: $i,SY2333: $i] :
( ~ ( c_member @ ( tc_prod @ SY2333 @ SY2333 ) @ ( c_Product__Type_OPair @ SY2333 @ SY2333 @ SY2332 @ SY2331 ) @ ( c_Transitive__Closure_Otrancl @ SY2333 @ SY2330 ) )
| ~ ( c_member @ ( tc_prod @ SY2333 @ SY2333 ) @ ( c_Product__Type_OPair @ SY2333 @ SY2333 @ SY2331 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY2333 @ SY2330 ) )
| ( c_member @ ( tc_prod @ SY2333 @ SY2333 ) @ ( c_Product__Type_OPair @ SY2333 @ SY2333 @ SY2332 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY2333 @ SY2330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3443,plain,
! [SV832: $i] :
( ( ! [SY2334: $i,SY2335: $i,SY2336: $i,SY2337: $i] :
( ~ ( c_member @ ( tc_prod @ SY2337 @ SY2337 ) @ ( c_Product__Type_OPair @ SY2337 @ SY2337 @ SY2336 @ SY2335 ) @ SY2334 )
| ~ ( c_member @ ( tc_prod @ SY2337 @ SY2337 ) @ ( c_Product__Type_OPair @ SY2337 @ SY2337 @ SY2335 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SY2337 @ SY2334 ) )
| ( c_member @ ( tc_prod @ SY2337 @ SY2337 ) @ ( c_Product__Type_OPair @ SY2337 @ SY2337 @ SY2336 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SY2337 @ SY2334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3444,plain,
! [SV833: $i] :
( ( ! [SY2338: $i,SY2339: $i,SY2340: $i,SY2341: $i] :
( ~ ( c_member @ ( tc_prod @ SY2341 @ SY2341 ) @ ( c_Product__Type_OPair @ SY2341 @ SY2341 @ SY2340 @ SY2339 ) @ ( c_Transitive__Closure_Ortrancl @ SY2341 @ SY2338 ) )
| ~ ( c_member @ ( tc_prod @ SY2341 @ SY2341 ) @ ( c_Product__Type_OPair @ SY2341 @ SY2341 @ SY2339 @ SV833 ) @ SY2338 )
| ( c_member @ ( tc_prod @ SY2341 @ SY2341 ) @ ( c_Product__Type_OPair @ SY2341 @ SY2341 @ SY2340 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SY2341 @ SY2338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3445,plain,
! [SV834: $i] :
( ( ! [SY2342: $i,SY2343: $i,SY2344: $i,SY2345: $i] :
( ~ ( c_member @ ( tc_prod @ SY2345 @ SY2345 ) @ ( c_Product__Type_OPair @ SY2345 @ SY2345 @ SY2344 @ SY2343 ) @ ( c_Transitive__Closure_Otrancl @ SY2345 @ SY2342 ) )
| ~ ( c_member @ ( tc_prod @ SY2345 @ SY2345 ) @ ( c_Product__Type_OPair @ SY2345 @ SY2345 @ SY2343 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SY2345 @ SY2342 ) )
| ( c_member @ ( tc_prod @ SY2345 @ SY2345 ) @ ( c_Product__Type_OPair @ SY2345 @ SY2345 @ SY2344 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SY2345 @ SY2342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3446,plain,
! [SV835: $i] :
( ( ! [SY2346: $i,SY2347: $i,SY2348: $i,SY2349: $i] :
( ~ ( c_member @ ( tc_prod @ SY2349 @ SY2349 ) @ ( c_Product__Type_OPair @ SY2349 @ SY2349 @ SY2348 @ SY2347 ) @ ( c_Transitive__Closure_Ortrancl @ SY2349 @ SY2346 ) )
| ~ ( c_member @ ( tc_prod @ SY2349 @ SY2349 ) @ ( c_Product__Type_OPair @ SY2349 @ SY2349 @ SY2347 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY2349 @ SY2346 ) )
| ( c_member @ ( tc_prod @ SY2349 @ SY2349 ) @ ( c_Product__Type_OPair @ SY2349 @ SY2349 @ SY2348 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY2349 @ SY2346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3447,plain,
! [SV836: $i] :
( ( ! [SY2350: $i,SY2351: $i,SY2352: $i,SY2353: $i,SY2354: $i] :
( ~ ( c_member @ ( tc_prod @ SY2352 @ SY2352 ) @ ( c_Product__Type_OPair @ SY2352 @ SY2352 @ SY2351 @ SY2350 ) @ SY2354 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY2352 @ SV836 @ SY2353 @ SY2354 @ SY2350 ) @ SY2351 )
= ( hAPP @ SY2353 @ SY2351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3448,plain,
! [SV837: $i] :
( ( ! [SY2355: $i,SY2356: $i,SY2357: $i] :
( ( c_member @ ( tc_prod @ SY2357 @ SY2357 ) @ ( c_Product__Type_OPair @ SY2357 @ SY2357 @ ( sK39_B_x @ SY2357 @ SY2356 @ SY2355 @ SV837 ) @ ( sK39_B_x @ SY2357 @ SY2356 @ SY2355 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SY2357 @ SY2356 ) )
| ~ ( c_member @ ( tc_prod @ SY2357 @ SY2357 ) @ ( c_Product__Type_OPair @ SY2357 @ SY2357 @ SY2355 @ SV837 ) @ SY2356 )
| ( SY2355 != SV837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3449,plain,
! [SV838: $i] :
( ( ! [SY2358: $i] : ( c_member @ ( tc_prod @ SY2358 @ SY2358 ) @ ( c_Product__Type_OPair @ SY2358 @ SY2358 @ SV838 @ SV838 ) @ ( c_Relation_OId @ SY2358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3450,plain,
! [SV839: $i] :
( ( c_Relation_Otrans @ SV839 @ ( c_Relation_OId @ SV839 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3451,plain,
! [SV840: $i] :
( ( ! [SY2359: $i] :
( ( c_member @ ( tc_prod @ SY2359 @ SY2359 ) @ ( c_Product__Type_OPair @ SY2359 @ SY2359 @ ( sK36_B_x @ SY2359 @ SV840 ) @ ( sK36_B_x @ SY2359 @ SV840 ) ) @ ( c_Transitive__Closure_Otrancl @ SY2359 @ SV840 ) )
| ( c_Wellfounded_Oacyclic @ SY2359 @ SV840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3452,plain,
! [SV841: $i] :
( ( ! [SY2360: $i] :
( ~ ( c_member @ ( tc_prod @ SY2360 @ SY2360 ) @ SV841 @ ( c_Relation_OId @ SY2360 ) )
| ( SV841
= ( c_Product__Type_OPair @ SY2360 @ SY2360 @ ( sK35_B_x @ SY2360 @ SV841 ) @ ( sK35_B_x @ SY2360 @ SV841 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3453,plain,
! [SV842: $i] :
( ( ! [SY2361: $i,SY2362: $i,SY2363: $i] :
( ~ ( c_Relation_Oantisym @ SY2363 @ SY2362 )
| ~ ( c_member @ ( tc_prod @ SY2363 @ SY2363 ) @ ( c_Product__Type_OPair @ SY2363 @ SY2363 @ SY2361 @ SV842 ) @ SY2362 )
| ~ ( c_member @ ( tc_prod @ SY2363 @ SY2363 ) @ ( c_Product__Type_OPair @ SY2363 @ SY2363 @ SV842 @ SY2361 ) @ SY2362 )
| ( SY2361 = SV842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3454,plain,
! [SV843: $i] :
( ( ! [SY2364: $i,SY2365: $i,SY2366: $i] :
( ~ ( c_member @ SY2366 @ SY2365 @ ( c_Set_Oinsert @ SY2366 @ SY2364 @ SV843 ) )
| ( SY2365 = SY2364 )
| ( c_member @ SY2366 @ SY2365 @ SV843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3455,plain,
! [SV844: $i] :
( ( ! [SY2367: $i,SY2368: $i,SY2369: $i,SY2370: $i] :
( ( c_Relation_ODomain @ SY2370 @ SY2369 @ ( c_Set_Oinsert @ ( tc_prod @ SY2370 @ SY2369 ) @ ( c_Product__Type_OPair @ SY2370 @ SY2369 @ SY2368 @ SY2367 ) @ SV844 ) )
= ( c_Set_Oinsert @ SY2370 @ SY2368 @ ( c_Relation_ODomain @ SY2370 @ SY2369 @ SV844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3456,plain,
! [SV845: $i] :
( ( ! [SY2371: $i,SY2372: $i,SY2373: $i,SY2374: $i] :
( ( c_Relation_ORange @ SY2374 @ SY2373 @ ( c_Set_Oinsert @ ( tc_prod @ SY2374 @ SY2373 ) @ ( c_Product__Type_OPair @ SY2374 @ SY2373 @ SY2372 @ SY2371 ) @ SV845 ) )
= ( c_Set_Oinsert @ SY2373 @ SY2371 @ ( c_Relation_ORange @ SY2374 @ SY2373 @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3457,plain,
! [SV846: $i] :
( ( ! [SY2375: $i,SY2376: $i] : ( c_member @ SY2376 @ SY2375 @ ( c_Set_Oinsert @ SY2376 @ SY2375 @ SV846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3458,plain,
! [SV847: $i] :
( ( ! [SY2377: $i,SY2378: $i,SY2379: $i] :
( ~ ( c_member @ SY2379 @ SY2378 @ SY2377 )
| ( c_member @ SY2379 @ SY2378 @ ( c_Set_Oinsert @ SY2379 @ SV847 @ SY2377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3459,plain,
! [SV848: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ~ ( c_member @ SY2381 @ SY2380 @ SV848 )
| ( ( c_Set_Oinsert @ SY2381 @ SY2380 @ SV848 )
= SV848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3460,plain,
! [SV849: $i] :
( ( ! [SY2382: $i,SY2383: $i,SY2384: $i] :
( ~ ( c_Wellfounded_Owf @ SY2384 @ SY2383 )
| ~ ( c_Wellfounded_Owf @ SY2382 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY2384 @ SY2382 ) @ ( c_Wellfounded_Olex__prod @ SY2384 @ SY2382 @ SY2383 @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3461,plain,
! [SV850: $i] :
( ( ! [SY2385: $i,SY2386: $i] :
( ~ ( c_Wellfounded_Owf @ SY2386 @ SY2385 )
| ~ ( c_member @ ( tc_prod @ SY2386 @ SY2386 ) @ ( c_Product__Type_OPair @ SY2386 @ SY2386 @ SV850 @ SV850 ) @ SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3462,plain,
! [SV851: $i] :
( ( ! [SY2387: $i,SY2388: $i,SY2389: $i] :
( ~ ( c_Wellfounded_Owf @ SY2389 @ SY2388 )
| ~ ( c_member @ ( tc_prod @ SY2389 @ SY2389 ) @ ( c_Product__Type_OPair @ SY2389 @ SY2389 @ SY2387 @ SV851 ) @ SY2388 )
| ~ ( c_member @ ( tc_prod @ SY2389 @ SY2389 ) @ ( c_Product__Type_OPair @ SY2389 @ SY2389 @ SV851 @ SY2387 ) @ SY2388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3463,plain,
! [SV852: $i] :
( ( ! [SY2390: $i,SY2391: $i,SY2392: $i] :
( ~ ( c_Wellfounded_Owf @ SY2392 @ SY2391 )
| ~ ( c_member @ ( tc_prod @ SY2392 @ SY2392 ) @ ( c_Product__Type_OPair @ SY2392 @ SY2392 @ SY2390 @ SV852 ) @ SY2391 )
| ~ ( c_member @ ( tc_prod @ SY2392 @ SY2392 ) @ ( c_Product__Type_OPair @ SY2392 @ SY2392 @ SV852 @ SY2390 ) @ SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(3464,plain,
! [SV853: $i] :
( ( ! [SY2393: $i,SY2394: $i] :
( ~ ( c_Wellfounded_Owf @ SY2394 @ SY2393 )
| ~ ( c_member @ ( tc_prod @ SY2394 @ SY2394 ) @ ( c_Product__Type_OPair @ SY2394 @ SY2394 @ SV853 @ SV853 ) @ SY2393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(3465,plain,
! [SV854: $i] :
( ( ! [SY2395: $i,SY2396: $i] :
( ~ ( c_Wellfounded_Owf @ SY2396 @ SY2395 )
| ( c_member @ SY2396 @ SV854 @ ( c_Wellfounded_Oacc @ SY2396 @ SY2395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3466,plain,
! [SV855: $i] :
( ( ! [SY2397: $i] :
( ~ ( c_member @ SY2397 @ ( sK25_B_x @ SY2397 @ SV855 ) @ ( c_Wellfounded_Oacc @ SY2397 @ SV855 ) )
| ( c_Wellfounded_Owf @ SY2397 @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3467,plain,
! [SV856: $i] :
( ( ! [SY2398: $i,SY2399: $i,SY2400: $i,SY2401: $i,SY2402: $i] :
( ~ ( c_member @ SY2402 @ SY2401 @ SY2400 )
| ~ ( c_member @ ( tc_prod @ SY2402 @ SY2399 ) @ ( c_Product__Type_OPair @ SY2402 @ SY2399 @ SY2401 @ SY2398 ) @ SV856 )
| ( c_member @ SY2399 @ SY2398 @ ( c_Relation_OImage @ SY2402 @ SY2399 @ SV856 @ SY2400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3468,plain,
! [SV857: $i] :
( ( ! [SY2403: $i,SY2404: $i,SY2405: $i,SY2406: $i,SY2407: $i,SY2408: $i,SY2409: $i] :
( ~ ( c_member @ ( tc_prod @ SY2409 @ SY2408 ) @ ( c_Product__Type_OPair @ SY2409 @ SY2408 @ SY2407 @ SY2406 ) @ SY2405 )
| ~ ( c_member @ ( tc_prod @ SY2408 @ SY2404 ) @ ( c_Product__Type_OPair @ SY2408 @ SY2404 @ SY2406 @ SY2403 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY2409 @ SY2404 ) @ ( c_Product__Type_OPair @ SY2409 @ SY2404 @ SY2407 @ SY2403 ) @ ( c_Relation_Orel__comp @ SY2409 @ SY2408 @ SY2404 @ SY2405 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3469,plain,
! [SV858: $i] :
( ( ! [SY2410: $i] :
( ( ( hAPP @ SY2410 @ ( sK22_B_x @ SY2410 @ SV858 ) )
!= ( hAPP @ SV858 @ ( sK22_B_x @ SY2410 @ SV858 ) ) )
| ( SY2410 = SV858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3470,plain,
! [SV859: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i,SY2414: $i,SY2415: $i,SY2416: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2416 @ SY2415 ) )
| ~ ( c_member @ ( tc_prod @ SY2414 @ SY2414 ) @ ( c_Product__Type_OPair @ SY2414 @ SY2414 @ SY2413 @ SY2412 ) @ ( hAPP @ SY2411 @ SY2415 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SY2414 ) @ ( tc_prod @ SV859 @ SY2414 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SY2414 ) @ ( tc_prod @ SV859 @ SY2414 ) @ ( c_Product__Type_OPair @ SV859 @ SY2414 @ SY2415 @ SY2413 ) @ ( c_Product__Type_OPair @ SV859 @ SY2414 @ SY2415 @ SY2412 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SY2414 @ SY2416 @ SY2411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3471,plain,
! [SV860: $i] :
( ( ! [SY2417: $i] :
( ( c_Relation_ORange @ SY2417 @ SY2417 @ ( c_Relation_OId__on @ SY2417 @ SV860 ) )
= SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3472,plain,
! [SV861: $i] :
( ( ! [SY2418: $i] :
( ( c_Relation_ODomain @ SY2418 @ SY2418 @ ( c_Relation_OId__on @ SY2418 @ SV861 ) )
= SV861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3473,plain,
! [SV862: $i] :
( ( ! [SY2419: $i] : ( c_Relation_Orefl__on @ SY2419 @ SV862 @ ( c_Relation_OId__on @ SY2419 @ SV862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3474,plain,
! [SV863: $i] :
( ( ! [SY2420: $i,SY2421: $i,SY2422: $i,SY2423: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2423 @ ( c_Product__Type_OPair @ SY2422 @ SY2421 @ SY2420 @ SV863 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY2422 @ SY2421 @ tc_HOL_Obool @ SY2423 @ SY2420 @ SV863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3475,plain,
! [SV864: $i] :
( ( ! [SY2424: $i,SY2425: $i,SY2426: $i,SY2427: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY2427 @ SY2426 @ tc_HOL_Obool @ SY2425 @ SY2424 @ SV864 ) )
| ( hBOOL @ ( hAPP @ SY2425 @ ( c_Product__Type_OPair @ SY2427 @ SY2426 @ SY2424 @ SV864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3476,plain,
! [SV865: $i] :
( ( ! [SY2428: $i,SY2429: $i,SY2430: $i,SY2431: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY2431 @ SY2430 @ tc_HOL_Obool @ SY2429 @ SY2428 @ SV865 ) )
| ( hBOOL @ ( hAPP @ SY2429 @ ( c_Product__Type_OPair @ SY2431 @ SY2430 @ SY2428 @ SV865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3477,plain,
! [SV866: $i] :
( ( ! [SY2432: $i] : ( c_Relation_Osingle__valued @ SY2432 @ SY2432 @ ( c_Relation_OId__on @ SY2432 @ SV866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3478,plain,
! [SV867: $i] :
( ( ! [SY2433: $i] :
( ( c_Transitive__Closure_Ortrancl @ SY2433 @ ( c_Transitive__Closure_Ortrancl @ SY2433 @ SV867 ) )
= ( c_Transitive__Closure_Ortrancl @ SY2433 @ SV867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3479,plain,
! [SV868: $i] :
( ( ! [SY2434: $i] :
( ( c_Transitive__Closure_Ortrancl @ SY2434 @ ( c_Transitive__Closure_Otrancl @ SY2434 @ SV868 ) )
= ( c_Transitive__Closure_Ortrancl @ SY2434 @ SV868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(3480,plain,
! [SV869: $i] :
( ( ! [SY2435: $i] :
( ( c_Transitive__Closure_Otrancl @ SY2435 @ ( c_Transitive__Closure_Ortrancl @ SY2435 @ SV869 ) )
= ( c_Transitive__Closure_Ortrancl @ SY2435 @ SV869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3481,plain,
! [SV870: $i] :
( ( ! [SY2436: $i] :
( ( c_Relation_ODomain @ SY2436 @ SY2436 @ ( c_Transitive__Closure_Otrancl @ SY2436 @ SV870 ) )
= ( c_Relation_ODomain @ SY2436 @ SY2436 @ SV870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3482,plain,
! [SV871: $i] :
( ( ! [SY2437: $i] :
( ( c_Relation_ORange @ SY2437 @ SY2437 @ ( c_Transitive__Closure_Otrancl @ SY2437 @ SV871 ) )
= ( c_Relation_ORange @ SY2437 @ SY2437 @ SV871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3483,plain,
! [SV872: $i] :
( ( c_Relation_Osingle__valued @ SV872 @ SV872 @ ( c_Relation_OId @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3484,plain,
! [SV873: $i] :
( ( ! [SY2438: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2438 @ SV873 )
| ( c_Relation_Oantisym @ SY2438 @ ( c_Transitive__Closure_Ortrancl @ SY2438 @ SV873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3485,plain,
! [SV874: $i] :
( ( ! [SY2439: $i,SY2440: $i] :
( ( c_Set_Oinsert @ SY2440 @ SY2439 @ ( c_Set_Oinsert @ SY2440 @ SY2439 @ SV874 ) )
= ( c_Set_Oinsert @ SY2440 @ SY2439 @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(3486,plain,
! [SV875: $i] :
( ( ! [SY2441: $i,SY2442: $i,SY2443: $i] :
( ( c_Set_Oinsert @ SY2443 @ SY2442 @ ( c_Set_Oinsert @ SY2443 @ SY2441 @ SV875 ) )
= ( c_Set_Oinsert @ SY2443 @ SY2441 @ ( c_Set_Oinsert @ SY2443 @ SY2442 @ SV875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3487,plain,
! [SV876: $i] :
( ( c_Relation_Oantisym @ SV876 @ ( c_Relation_OId @ SV876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3488,plain,
! [SV877: $i] :
( ( ! [SY2444: $i] : ( c_Relation_Oantisym @ SY2444 @ ( c_Relation_OId__on @ SY2444 @ SV877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3489,plain,
! [SV878: $i] :
( ( ! [SY2445: $i,SY2446: $i,SY2447: $i] :
( ~ ( c_Wellfounded_Owf @ SY2447 @ SY2446 )
| ( c_Wellfounded_Owf @ SY2445 @ ( hAPP @ ( c_Relation_Oinv__image @ SY2447 @ SY2445 @ SY2446 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3490,plain,
! [SV879: $i] :
( ( ! [SY2448: $i] :
( ~ ( c_Wellfounded_Owf @ SY2448 @ SV879 )
| ( c_Wellfounded_Owf @ SY2448 @ ( c_Transitive__Closure_Otrancl @ SY2448 @ SV879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3491,plain,
! [SV880: $i] :
( ( ! [SY2449: $i] :
( ~ ( c_Wellfounded_Owf @ SY2449 @ SV880 )
| ( c_Wellfounded_Oacyclic @ SY2449 @ SV880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3492,plain,
! [SV881: $i] :
( ( ! [SY2450: $i] : ( c_Wellfounded_Owf @ SY2450 @ ( hAPP @ ( c_Wellfounded_Omeasure @ SY2450 ) @ SV881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3493,plain,
! [SV882: $i] :
( ( ! [SY2451: $i,SY2452: $i,SY2453: $i,SY2454: $i,SY2455: $i] :
( ( SY2455
!= ( c_Recdef_Owfrec @ SY2454 @ SY2453 @ SY2452 @ SY2451 ) )
| ~ ( c_Wellfounded_Owf @ SY2454 @ SY2452 )
| ( ( hAPP @ SY2455 @ SV882 )
= ( hAPP @ ( hAPP @ SY2451 @ ( c_Recdef_Ocut @ SY2454 @ SY2453 @ SY2455 @ SY2452 @ SV882 ) ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3494,plain,
! [SV883: $i] :
( ( ! [SY2456: $i,SY2457: $i,SY2458: $i,SY2459: $i] :
( ~ ( c_Wellfounded_Owf @ SY2459 @ SY2458 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY2459 @ SY2457 @ SY2458 @ SY2456 ) @ SV883 )
= ( hAPP @ ( hAPP @ SY2456 @ ( c_Recdef_Ocut @ SY2459 @ SY2457 @ ( c_Recdef_Owfrec @ SY2459 @ SY2457 @ SY2458 @ SY2456 ) @ SY2458 @ SV883 ) ) @ SV883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3495,plain,
! [SV884: $i] :
( ( ! [SY2460: $i,SY2461: $i,SY2462: $i] :
( ~ ( c_Wellfounded_Owf @ SY2460 @ SY2462 )
| ! [SY2463: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SY2460 @ SV884 @ SY2462 @ SY2461 ) @ SY2463 )
= ( hAPP @ ( hAPP @ SY2461 @ ( c_Recdef_Ocut @ SY2460 @ SV884 @ ( c_Recdef_Owfrec @ SY2460 @ SV884 @ SY2462 @ SY2461 ) @ SY2462 @ SY2463 ) ) @ SY2463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3496,plain,
! [SV885: $i] :
( ( ( c_Wellfounded_Omeasure @ SV885 )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ SV885 @ c_Wellfounded_Oless__than ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3497,plain,
! [SV886: $i] :
( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( c_Wellfounded_Owf @ SY2465 @ SY2464 )
| ( c_Wellfounded_Owf @ SY2465 @ ( c_Wellfounded_Omlex__prod @ SY2465 @ SV886 @ SY2464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3498,plain,
! [SV887: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV887 @ SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3499,plain,
! [SV888: $i] :
( ( ! [SY2466: $i] :
( ( SY2466 = SV888 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2466 @ SV888 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV888 @ SY2466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3500,plain,
! [SV889: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV889 @ SV889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3501,plain,
! [SV890: $i] :
( ( ! [SY2467: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2467 @ SV890 )
| ( SV890 != SY2467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3502,plain,
! [SV891: $i] :
( ( ! [SY2468: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2468 @ SV891 )
| ( SY2468 != SV891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3503,plain,
! [SV892: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV892 @ SV892 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3504,plain,
! [SV893: $i] :
( ( ! [SY2469: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2469 @ SV893 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV893 @ SY2469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3505,plain,
! [SV894: $i] :
( ( ! [SY2470: $i] :
( ( SY2470 != SV894 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2470 @ SV894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3506,plain,
! [SV895: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2472 @ SY2471 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2471 @ SV895 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2472 @ SV895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3507,plain,
! [SV896: $i] :
( ( ! [SY2473: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2473 @ SV896 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SY2473 )
| ( SY2473 = SV896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3508,plain,
! [SV897: $i] :
( ( ! [SY2474: $i,SY2475: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY2475 @ SY2474 ) @ SV897 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY2475 @ SV897 ) @ SY2474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3509,plain,
! [SV898: $i] :
( ( ! [SY2476: $i] :
( ( c_Relation_OImage @ SY2476 @ SY2476 @ ( c_Relation_OId @ SY2476 ) @ SV898 )
= SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3510,plain,
! [SV899: $i] :
( ( ! [SY2477: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SY2477 ) @ SV899 ) )
| ( SY2477 = SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3511,plain,
! [SV900: $i] :
( ( ! [SY2478: $i] :
( ( SY2478 != SV900 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ SY2478 ) @ SV900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(3512,plain,
! [SV901: $i] :
( ( ! [SY2479: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2479 @ SY2479 ) @ ( c_Product__Type_OPair @ SY2479 @ SY2479 @ ( sK69_B_x @ SY2479 @ SV901 ) @ ( sK70_SY736 @ SY2479 @ SV901 ) ) @ SV901 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2479 @ SY2479 ) @ ( c_Product__Type_OPair @ SY2479 @ SY2479 @ ( sK70_SY736 @ SY2479 @ SV901 ) @ ( sK71_SY738 @ SY2479 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SY2479 @ SY2479 ) @ ( c_Product__Type_OPair @ SY2479 @ SY2479 @ ( sK69_B_x @ SY2479 @ SV901 ) @ ( sK71_SY738 @ SY2479 @ SV901 ) ) @ SV901 ) ) )
| ( c_Relation_Otrans @ SY2479 @ SV901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(3513,plain,
! [SV902: $i] :
( ( ! [SY2480: $i,SY2481: $i,SY2482: $i,SY2483: $i] :
( ~ ( c_member @ ( tc_prod @ SY2483 @ SY2483 ) @ ( c_Product__Type_OPair @ SY2483 @ SY2483 @ SY2482 @ SY2481 ) @ ( c_Transitive__Closure_Ortrancl @ SY2483 @ SY2480 ) )
| ~ ( hBOOL @ ( hAPP @ SV902 @ SY2481 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2483 @ SY2483 ) @ ( c_Product__Type_OPair @ SY2483 @ SY2483 @ ( sK12_B_y @ SY2483 @ SY2482 @ SY2481 @ SY2480 @ SV902 ) @ ( sK13_SY707 @ SY2483 @ SY2482 @ SY2481 @ SY2480 @ SV902 ) ) @ SY2480 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2483 @ SY2483 ) @ ( c_Product__Type_OPair @ SY2483 @ SY2483 @ ( sK13_SY707 @ SY2483 @ SY2482 @ SY2481 @ SY2480 @ SV902 ) @ SY2481 ) @ ( c_Transitive__Closure_Ortrancl @ SY2483 @ SY2480 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SY2483 @ SY2482 @ SY2481 @ SY2480 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SY2483 @ SY2482 @ SY2481 @ SY2480 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SY2482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3514,plain,
! [SV903: $i] :
( ( ! [SY2484: $i] :
~ ( ~ ! [SY2485: $i,SY2486: $i] :
( ( c_member @ SY2486 @ SY2485 @ SY2484 )
| ( c_member @ SY2486 @ SY2485 @ SV903 )
| ( ( c_Set_Oinsert @ SY2486 @ SY2485 @ SY2484 )
!= ( c_Set_Oinsert @ SY2486 @ SY2485 @ SV903 ) )
| ( SY2484 = SV903 ) )
| ~ ! [SY2487: $i,SY2488: $i] :
( ( c_member @ SY2488 @ SY2487 @ SY2484 )
| ( c_member @ SY2488 @ SY2487 @ SV903 )
| ( SY2484 != SV903 )
| ( ( c_Set_Oinsert @ SY2488 @ SY2487 @ SY2484 )
= ( c_Set_Oinsert @ SY2488 @ SY2487 @ SV903 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3515,plain,
! [SV904: $i] :
( ( ! [SY2489: $i,SY2490: $i,SY2491: $i,SY2492: $i,SY2493: $i,SY2494: $i,SY2495: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ SY2493 @ SY2492 ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ SY2491 @ SY2490 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2495 @ SY2494 ) @ SY2489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY2493 ) @ SY2492 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ SY2493 @ SY2492 ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ ( sK18_B_a @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) @ ( sK19_SY714 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2495 @ SY2494 ) @ SY2489 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2495 @ SY2494 ) @ ( tc_prod @ SY2495 @ SY2494 ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ ( sK18_B_a @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) @ ( sK19_SY714 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY2495 @ SY2494 @ ( sK20_SY717 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) @ ( sK21_SY719 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) ) @ SY2489 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) @ ( sK19_SY714 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) @ ( sK21_SY719 @ SY2495 @ SY2494 @ SY2493 @ SY2492 @ SY2491 @ SY2490 @ SY2489 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY2491 ) @ SY2490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3516,plain,
! [SV905: $i] :
( ( ~ ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2497 @ SY2497 ) @ ( c_Product__Type_OPair @ SY2497 @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ SY2496 ) @ SV905 )
| ~ ~ ( c_member @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ( c_member @ SY2497 @ SY2496 @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ~ ! [SY2498: $i,SY2499: $i] :
( ~ ( c_member @ SY2499 @ SY2498 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) )
| ! [SY2500: $i] :
( ~ ( c_member @ ( tc_prod @ SY2499 @ SY2499 ) @ ( c_Product__Type_OPair @ SY2499 @ SY2499 @ SY2500 @ SY2498 ) @ SV905 )
| ( c_member @ SY2499 @ SY2500 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3517,plain,
! [SV906: $i] :
( ( ~ ( ~ ! [SY2501: $i,SY2502: $i] :
( ~ ( ~ ( c_member @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( c_member @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY2502 @ SY2501 @ SV906 )
!= ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY2502 @ SY2501 @ SV906 ) )
| ~ ! [SY2503: $i,SY2504: $i] :
( ~ ( c_Relation_Ototal__on @ SY2504 @ SY2503 @ SV906 )
| ! [SY2505: $i] :
( ~ ( c_member @ SY2504 @ SY2505 @ SY2503 )
| ! [SY2506: $i] :
( ~ ( c_member @ SY2504 @ SY2506 @ SY2503 )
| ( SY2505 = SY2506 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2505 @ SY2506 ) @ SV906 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2506 @ SY2505 ) @ SV906 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3518,plain,
! [SV907: $i] :
( ( ! [SY2507: $i,SY2508: $i,SY2509: $i] :
~ ( ~ ( ! [SY2510: $i,SY2511: $i] :
( ( c_Product__Type_OPair @ SY2511 @ SY2510 @ SY2509 @ SY2508 )
!= ( c_Product__Type_OPair @ SY2511 @ SY2510 @ SY2507 @ SV907 ) )
| ( SY2509 = SY2507 ) )
| ~ ( ! [SY2512: $i,SY2513: $i] :
( ( c_Product__Type_OPair @ SY2513 @ SY2512 @ SY2509 @ SY2508 )
!= ( c_Product__Type_OPair @ SY2513 @ SY2512 @ SY2507 @ SV907 ) )
| ( SY2508 = SV907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3519,plain,
! [SV908: $i] :
( ( ! [SY2514: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2514 @ SY2514 ) @ ( c_Product__Type_OPair @ SY2514 @ SY2514 @ ( sK26_B_x @ SY2514 @ SV908 ) @ ( sK27_SY720 @ SY2514 @ SV908 ) ) @ SV908 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2514 @ SY2514 ) @ ( c_Product__Type_OPair @ SY2514 @ SY2514 @ ( sK27_SY720 @ SY2514 @ SV908 ) @ ( sK26_B_x @ SY2514 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SY2514 @ SV908 )
!= ( sK27_SY720 @ SY2514 @ SV908 ) ) ) ) )
| ( c_Relation_Oantisym @ SY2514 @ SV908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3520,plain,
! [SV909: $i] :
( ( ~ ( ~ ! [SY2515: $i,SY2516: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2516 @ ( sK75_B_x1 @ SY2516 @ SY2515 @ SV909 ) ) )
| ! [SY2517: $i,SY2518: $i] : ( hBOOL @ ( hAPP @ SY2516 @ ( c_Product__Type_OPair @ SY2515 @ SV909 @ SY2517 @ SY2518 ) ) ) )
| ~ ! [SY2519: $i,SY2520: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2520 @ ( c_Product__Type_OPair @ SY2519 @ SV909 @ ( sK73_B_a @ SY2520 @ SY2519 @ SV909 ) @ ( sK74_SY739 @ SY2520 @ SY2519 @ SV909 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2520 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3521,plain,
! [SV910: $i] :
( ( ~ ( ~ ! [SY2522: $i,SY2523: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 )
!= ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2523 @ SY2522 @ SV910 ) )
| ~ ! [SY2524: $i,SY2525: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2525 @ SY2524 @ SV910 )
| ! [SY2526: $i,SY2527: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2527 ) @ SV910 )
| ! [SY2528: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2528 ) @ SV910 )
| ( SY2527 = SY2528 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3522,plain,
! [SV911: $i] :
( ( ! [SY2529: $i,SY2530: $i,SY2531: $i,SY2532: $i,SY2533: $i] :
~ ( ~ ~ ( ~ ! [SY2534: $i,SY2535: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2535 @ SY2534 ) @ ( tc_prod @ SY2535 @ SY2534 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2535 @ SY2534 ) @ ( tc_prod @ SY2535 @ SY2534 ) @ ( c_Product__Type_OPair @ SY2535 @ SY2534 @ SY2533 @ SY2532 ) @ ( c_Product__Type_OPair @ SY2535 @ SY2534 @ SY2531 @ SY2530 ) ) @ ( c_Wellfounded_Olex__prod @ SY2535 @ SY2534 @ SY2529 @ SV911 ) )
| ( SY2533 = SY2531 )
| ( c_member @ ( tc_prod @ SY2535 @ SY2535 ) @ ( c_Product__Type_OPair @ SY2535 @ SY2535 @ SY2533 @ SY2531 ) @ SY2529 ) )
| ~ ! [SY2536: $i,SY2537: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2537 @ SY2536 ) @ ( tc_prod @ SY2537 @ SY2536 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2537 @ SY2536 ) @ ( tc_prod @ SY2537 @ SY2536 ) @ ( c_Product__Type_OPair @ SY2537 @ SY2536 @ SY2533 @ SY2532 ) @ ( c_Product__Type_OPair @ SY2537 @ SY2536 @ SY2531 @ SY2530 ) ) @ ( c_Wellfounded_Olex__prod @ SY2537 @ SY2536 @ SY2529 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY2536 @ SY2536 ) @ ( c_Product__Type_OPair @ SY2536 @ SY2536 @ SY2532 @ SY2530 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY2537 @ SY2537 ) @ ( c_Product__Type_OPair @ SY2537 @ SY2537 @ SY2533 @ SY2531 ) @ SY2529 ) ) )
| ~ ~ ( ~ ! [SY2538: $i] :
( ( SY2533 != SY2531 )
| ~ ( c_member @ ( tc_prod @ SY2538 @ SY2538 ) @ ( c_Product__Type_OPair @ SY2538 @ SY2538 @ SY2532 @ SY2530 ) @ SV911 )
| ! [SY2539: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2539 @ SY2538 ) @ ( tc_prod @ SY2539 @ SY2538 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2539 @ SY2538 ) @ ( tc_prod @ SY2539 @ SY2538 ) @ ( c_Product__Type_OPair @ SY2539 @ SY2538 @ SY2533 @ SY2532 ) @ ( c_Product__Type_OPair @ SY2539 @ SY2538 @ SY2531 @ SY2530 ) ) @ ( c_Wellfounded_Olex__prod @ SY2539 @ SY2538 @ SY2529 @ SV911 ) ) )
| ~ ! [SY2540: $i,SY2541: $i] :
( ~ ( c_member @ ( tc_prod @ SY2541 @ SY2541 ) @ ( c_Product__Type_OPair @ SY2541 @ SY2541 @ SY2533 @ SY2531 ) @ SY2529 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2541 @ SY2540 ) @ ( tc_prod @ SY2541 @ SY2540 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2541 @ SY2540 ) @ ( tc_prod @ SY2541 @ SY2540 ) @ ( c_Product__Type_OPair @ SY2541 @ SY2540 @ SY2533 @ SY2532 ) @ ( c_Product__Type_OPair @ SY2541 @ SY2540 @ SY2531 @ SY2530 ) ) @ ( c_Wellfounded_Olex__prod @ SY2541 @ SY2540 @ SY2529 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3523,plain,
! [SV912: $i] :
( ( ! [SY2542: $i,SY2543: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2543 @ SY2542 ) @ ( c_Product__Type_OPair @ SY2543 @ SY2542 @ ( sK48_B_x @ SY2543 @ SY2542 @ SV912 ) @ ( sK49_SY727 @ SY2543 @ SY2542 @ SV912 ) ) @ SV912 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2543 @ SY2542 ) @ ( c_Product__Type_OPair @ SY2543 @ SY2542 @ ( sK48_B_x @ SY2543 @ SY2542 @ SV912 ) @ ( sK50_SY729 @ SY2543 @ SY2542 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SY2543 @ SY2542 @ SV912 )
!= ( sK50_SY729 @ SY2543 @ SY2542 @ SV912 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2543 @ SY2542 @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3525,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3526,plain,
! [SV913: $i] :
( ( ~ ( ~ ! [SY2544: $i,SY2545: $i] :
( ~ ( c_Relation_Orefl__on @ SY2545 @ SY2544 @ SV913 )
| ~ ( c_Relation_Otrans @ SY2545 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SY2545 @ SY2544 @ SV913 ) )
| ~ ~ ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) )
| ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3527,plain,
! [SV914: $i] :
( ( ! [SY2550: $i,SY2551: $i] :
~ ( ~ ! [SY2552: $i,SY2553: $i] :
( ! [SY2554: $i] :
( ~ ( c_member @ SY2551 @ SY2554 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SY2551 @ SY2553 ) @ ( c_Product__Type_OPair @ SY2551 @ SY2553 @ SY2554 @ SY2552 ) @ SY2550 ) )
| ( c_member @ SY2553 @ SY2552 @ ( c_Relation_OImage @ SY2551 @ SY2553 @ SY2550 @ SV914 ) ) )
| ~ ! [SY2555: $i,SY2556: $i] :
( ~ ( c_member @ SY2556 @ SY2555 @ ( c_Relation_OImage @ SY2551 @ SY2556 @ SY2550 @ SV914 ) )
| ~ ( ~ ( c_member @ SY2551 @ ( sK24_B_x @ SY2556 @ SY2555 @ SY2551 @ SY2550 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SY2551 @ SY2556 ) @ ( c_Product__Type_OPair @ SY2551 @ SY2556 @ ( sK24_B_x @ SY2556 @ SY2555 @ SY2551 @ SY2550 @ SV914 ) @ SY2555 ) @ SY2550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3528,plain,
! [SV915: $i] :
( ( ! [SY2557: $i,SY2558: $i,SY2559: $i] :
( ~ ( c_member @ ( tc_prod @ SY2559 @ SY2559 ) @ ( c_Product__Type_OPair @ SY2559 @ SY2559 @ SY2558 @ SY2557 ) @ ( c_Transitive__Closure_Ortrancl @ SY2559 @ SV915 ) )
| ( SY2558 = SY2557 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2559 @ SY2559 ) @ ( c_Product__Type_OPair @ SY2559 @ SY2559 @ SY2558 @ ( sK45_B_y @ SY2559 @ SY2558 @ SY2557 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY2559 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SY2559 @ SY2559 ) @ ( c_Product__Type_OPair @ SY2559 @ SY2559 @ ( sK45_B_y @ SY2559 @ SY2558 @ SY2557 @ SV915 ) @ SY2557 ) @ SV915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3529,plain,
! [SV916: $i] :
( ( ~ ( ~ ! [SY2560: $i] :
( ( SY2560 != SV916 )
| ! [SY2561: $i] : ( c_member @ ( tc_prod @ SY2561 @ SY2561 ) @ ( c_Product__Type_OPair @ SY2561 @ SY2561 @ SY2560 @ SV916 ) @ ( c_Relation_OId @ SY2561 ) ) )
| ~ ! [SY2562: $i] :
( ! [SY2563: $i] :
~ ( c_member @ ( tc_prod @ SY2563 @ SY2563 ) @ ( c_Product__Type_OPair @ SY2563 @ SY2563 @ SY2562 @ SV916 ) @ ( c_Relation_OId @ SY2563 ) )
| ( SY2562 = SV916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3530,plain,
! [SV917: $i] :
( ( ! [SY2564: $i] :
~ ( ~ ! [SY2565: $i,SY2566: $i] :
( ( SY2566 != SY2565 )
| ~ ( c_member @ SY2564 @ SY2566 @ SV917 )
| ( c_member @ SY2564 @ SY2565 @ SV917 ) )
| ~ ! [SY2567: $i,SY2568: $i] :
( ( SY2568 != SY2567 )
| ~ ( c_member @ SY2564 @ SY2567 @ SV917 )
| ( c_member @ SY2564 @ SY2568 @ SV917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3531,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3532,plain,
! [SV918: $i] :
( ( ! [SY2569: $i,SY2570: $i] :
~ ( ~ ! [SY2571: $i,SY2572: $i] :
( ~ ( c_member @ ( tc_prod @ SY2572 @ SY2571 ) @ ( c_Product__Type_OPair @ SY2572 @ SY2571 @ SY2569 @ SV918 ) @ SY2570 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY2572 @ SY2571 @ SY2570 ) @ SY2569 ) @ SV918 ) ) )
| ~ ! [SY2573: $i,SY2574: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY2574 @ SY2573 @ SY2570 ) @ SY2569 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY2574 @ SY2573 ) @ ( c_Product__Type_OPair @ SY2574 @ SY2573 @ SY2569 @ SV918 ) @ SY2570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3533,plain,
! [SV919: $i] :
( ( ! [SY2575: $i,SY2576: $i,SY2577: $i] :
~ ( ~ ! [SY2578: $i,SY2579: $i] :
( ! [SY2580: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2579 @ SY2579 ) @ ( c_Product__Type_OPair @ SY2579 @ SY2579 @ ( sK60_B_z @ SY2580 @ SY2579 @ SY2578 @ SY2577 @ SY2576 @ SY2575 @ SV919 ) @ SY2575 ) @ SY2577 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2579 @ SY2578 @ SY2577 @ SY2576 @ ( sK60_B_z @ SY2580 @ SY2579 @ SY2578 @ SY2577 @ SY2576 @ SY2575 @ SV919 ) @ ( hAPP @ SY2580 @ ( sK60_B_z @ SY2580 @ SY2579 @ SY2578 @ SY2577 @ SY2576 @ SY2575 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SY2576 @ SV919 ) @ SY2575 )
!= ( hAPP @ ( hAPP @ SY2576 @ SY2580 ) @ SY2575 ) ) )
| ( c_Recdef_Owfrec__rel @ SY2579 @ SY2578 @ SY2577 @ SY2576 @ SY2575 @ ( hAPP @ ( hAPP @ SY2576 @ SV919 ) @ SY2575 ) ) )
| ~ ! [SY2581: $i,SY2582: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY2582 @ SY2581 @ SY2577 @ SY2576 @ SY2575 @ ( hAPP @ ( hAPP @ SY2576 @ SV919 ) @ SY2575 ) )
| ~ ( ~ ! [SY2583: $i] :
( ~ ( c_member @ ( tc_prod @ SY2582 @ SY2582 ) @ ( c_Product__Type_OPair @ SY2582 @ SY2582 @ SY2583 @ SY2575 ) @ SY2577 )
| ( c_Recdef_Owfrec__rel @ SY2582 @ SY2581 @ SY2577 @ SY2576 @ SY2583 @ ( hAPP @ ( sK59_B_g @ SY2582 @ SY2581 @ SY2577 @ SY2576 @ SY2575 @ SV919 ) @ SY2583 ) ) )
| ( ( hAPP @ ( hAPP @ SY2576 @ SV919 ) @ SY2575 )
!= ( hAPP @ ( hAPP @ SY2576 @ ( sK59_B_g @ SY2582 @ SY2581 @ SY2577 @ SY2576 @ SY2575 @ SV919 ) ) @ SY2575 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3534,plain,
! [SV920: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
| ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
| ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3535,plain,
! [SV921: $i] :
( ( ! [SY2600: $i,SY2601: $i,SY2602: $i] :
~ ( ~ ! [SY2603: $i] :
( ! [SY2604: $i] :
~ ( c_member @ ( tc_prod @ SY2604 @ SY2604 ) @ ( c_Product__Type_OPair @ SY2604 @ SY2604 @ SY2603 @ SY2602 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY2601 @ SY2604 @ SY2600 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SY2601 @ SY2601 ) @ ( c_Product__Type_OPair @ SY2601 @ SY2601 @ ( hAPP @ SV921 @ SY2603 ) @ ( hAPP @ SV921 @ SY2602 ) ) @ SY2600 ) )
| ~ ! [SY2605: $i] :
( ~ ( c_member @ ( tc_prod @ SY2601 @ SY2601 ) @ ( c_Product__Type_OPair @ SY2601 @ SY2601 @ ( hAPP @ SV921 @ SY2605 ) @ ( hAPP @ SV921 @ SY2602 ) ) @ SY2600 )
| ! [SY2606: $i] : ( c_member @ ( tc_prod @ SY2606 @ SY2606 ) @ ( c_Product__Type_OPair @ SY2606 @ SY2606 @ SY2605 @ SY2602 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY2601 @ SY2606 @ SY2600 ) @ SV921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3536,plain,
! [SV922: $i] :
( ( ~ ( ~ ! [SY2607: $i] :
( ( SY2607 != SV922 )
| ! [SY2608: $i] : ( c_member @ SY2608 @ SY2607 @ ( c_fequal @ SV922 ) ) )
| ~ ! [SY2609: $i] :
( ! [SY2610: $i] :
~ ( c_member @ SY2610 @ SY2609 @ ( c_fequal @ SV922 ) )
| ( SY2609 = SV922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3537,plain,
! [SV923: $i] :
( ( ! [SY2611: $i,SY2612: $i,SY2613: $i] :
( ~ ( c_member @ ( tc_prod @ SY2613 @ SY2613 ) @ ( c_Product__Type_OPair @ SY2613 @ SY2613 @ SY2612 @ SY2611 ) @ ( c_Transitive__Closure_Ortrancl @ SY2613 @ SV923 ) )
| ( SY2612 = SY2611 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2613 @ SY2613 ) @ ( c_Product__Type_OPair @ SY2613 @ SY2613 @ SY2612 @ ( sK44_B_y @ SY2613 @ SY2612 @ SY2611 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SY2613 @ SY2613 ) @ ( c_Product__Type_OPair @ SY2613 @ SY2613 @ ( sK44_B_y @ SY2613 @ SY2612 @ SY2611 @ SV923 ) @ SY2611 ) @ ( c_Transitive__Closure_Ortrancl @ SY2613 @ SV923 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3538,plain,
! [SV924: $i] :
( ( ! [SY2614: $i,SY2615: $i,SY2616: $i] :
( ~ ( c_member @ ( tc_prod @ SY2616 @ SY2616 ) @ ( c_Product__Type_OPair @ SY2616 @ SY2616 @ SY2615 @ SY2614 ) @ ( c_Transitive__Closure_Otrancl @ SY2616 @ SV924 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2616 @ SY2616 ) @ ( c_Product__Type_OPair @ SY2616 @ SY2616 @ SY2615 @ ( sK41_B_z @ SY2616 @ SY2615 @ SY2614 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SY2616 @ SY2616 ) @ ( c_Product__Type_OPair @ SY2616 @ SY2616 @ ( sK41_B_z @ SY2616 @ SY2615 @ SY2614 @ SV924 ) @ SY2614 ) @ ( c_Transitive__Closure_Ortrancl @ SY2616 @ SV924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3539,plain,
! [SV925: $i] :
( ( ! [SY2617: $i,SY2618: $i] :
( ~ ( c_member @ ( tc_prod @ SY2618 @ SY2618 ) @ SY2617 @ ( c_Relation_OId__on @ SY2618 @ SV925 ) )
| ~ ( ~ ( c_member @ SY2618 @ ( sK64_B_x @ SY2618 @ SY2617 @ SV925 ) @ SV925 )
| ( SY2617
!= ( c_Product__Type_OPair @ SY2618 @ SY2618 @ ( sK64_B_x @ SY2618 @ SY2617 @ SV925 ) @ ( sK64_B_x @ SY2618 @ SY2617 @ SV925 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3541,plain,
! [SV926: $i] :
( ( ! [SY2619: $i] :
~ ( ~ ! [SY2620: $i,SY2621: $i] :
( ! [SY2622: $i] :
~ ( c_member @ ( tc_prod @ SY2621 @ SY2619 ) @ ( c_Product__Type_OPair @ SY2621 @ SY2619 @ SY2620 @ SY2622 ) @ SV926 )
| ( c_member @ SY2621 @ SY2620 @ ( c_Relation_ODomain @ SY2621 @ SY2619 @ SV926 ) ) )
| ~ ! [SY2623: $i,SY2624: $i] :
( ~ ( c_member @ SY2624 @ SY2623 @ ( c_Relation_ODomain @ SY2624 @ SY2619 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY2624 @ SY2619 ) @ ( c_Product__Type_OPair @ SY2624 @ SY2619 @ SY2623 @ ( sK66_B_y @ SY2624 @ SY2623 @ SY2619 @ SV926 ) ) @ SV926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3542,plain,
! [SV927: $i] :
( ( ! [SY2625: $i] :
~ ( ~ ! [SY2626: $i,SY2627: $i] :
( ( c_member @ SY2627 @ SY2626 @ ( c_Relation_ODomain @ SY2627 @ SY2627 @ SY2625 ) )
| ( SY2626 != SV927 )
| ( c_member @ ( tc_prod @ SY2627 @ SY2627 ) @ ( c_Product__Type_OPair @ SY2627 @ SY2627 @ SY2626 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY2627 @ SY2625 ) ) )
| ~ ! [SY2628: $i,SY2629: $i] :
( ( c_member @ SY2629 @ SY2628 @ ( c_Relation_ODomain @ SY2629 @ SY2629 @ SY2625 ) )
| ~ ( c_member @ ( tc_prod @ SY2629 @ SY2629 ) @ ( c_Product__Type_OPair @ SY2629 @ SY2629 @ SY2628 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY2629 @ SY2625 ) )
| ( SY2628 = SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3543,plain,
! [SV928: $i] :
( ( ! [SY2630: $i] :
~ ( ~ ! [SY2631: $i] :
( ! [SY2632: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2632 @ SY2631 @ SY2630 ) @ SV928 ) )
| ( SY2631 = SV928 )
| ( hBOOL @ ( hAPP @ SY2630 @ SV928 ) ) )
| ~ ~ ( ~ ! [SY2633: $i] :
( ( SY2633 != SV928 )
| ! [SY2634: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2634 @ SY2633 @ SY2630 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY2630 @ SV928 ) )
| ! [SY2635: $i,SY2636: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2636 @ SY2635 @ SY2630 ) @ SV928 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3544,plain,
! [SV929: $i] :
( ( ! [SY2637: $i,SY2638: $i,SY2639: $i,SY2640: $i,SY2641: $i,SY2642: $i,SY2643: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ SY2641 @ SY2640 ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ SY2639 @ SY2638 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2643 @ SY2642 ) @ SY2637 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY2639 ) @ SY2638 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ ( sK14_B_a @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) @ ( sK15_SY708 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ ( sK16_SY711 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) @ ( sK17_SY713 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) ) @ SY2637 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2643 @ SY2642 ) @ ( tc_prod @ SY2643 @ SY2642 ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ ( sK16_SY711 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) @ ( sK17_SY713 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY2643 @ SY2642 @ SY2639 @ SY2638 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2643 @ SY2642 ) @ SY2637 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) @ ( sK17_SY713 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) @ ( sK15_SY708 @ SY2643 @ SY2642 @ SY2641 @ SY2640 @ SY2639 @ SY2638 @ SY2637 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY2641 ) @ SY2640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3545,plain,
! [SV930: $i] :
( ( ! [SY2644: $i] :
~ ( ~ ! [SY2645: $i,SY2646: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2646 @ SV930 )
| ( c_member @ ( tc_prod @ SY2646 @ SY2646 ) @ ( c_Product__Type_OPair @ SY2646 @ SY2646 @ SY2644 @ SY2645 ) @ ( c_Transitive__Closure_Ortrancl @ SY2646 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY2646 @ ( c_Set_Oinsert @ ( tc_prod @ SY2646 @ SY2646 ) @ ( c_Product__Type_OPair @ SY2646 @ SY2646 @ SY2645 @ SY2644 ) @ SV930 ) ) )
| ~ ~ ( ~ ! [SY2647: $i,SY2648: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2648 @ ( c_Set_Oinsert @ ( tc_prod @ SY2648 @ SY2648 ) @ ( c_Product__Type_OPair @ SY2648 @ SY2648 @ SY2647 @ SY2644 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY2648 @ SV930 ) )
| ~ ! [SY2649: $i,SY2650: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY2650 @ ( c_Set_Oinsert @ ( tc_prod @ SY2650 @ SY2650 ) @ ( c_Product__Type_OPair @ SY2650 @ SY2650 @ SY2649 @ SY2644 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY2650 @ SY2650 ) @ ( c_Product__Type_OPair @ SY2650 @ SY2650 @ SY2644 @ SY2649 ) @ ( c_Transitive__Closure_Ortrancl @ SY2650 @ SV930 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3546,plain,
! [SV931: $i] :
( ( ! [SY2651: $i] :
~ ( ~ ! [SY2652: $i,SY2653: $i] :
( ! [SY2654: $i] :
~ ( c_member @ ( tc_prod @ SY2651 @ SY2653 ) @ ( c_Product__Type_OPair @ SY2651 @ SY2653 @ SY2654 @ SY2652 ) @ SV931 )
| ( c_member @ SY2653 @ SY2652 @ ( c_Relation_ORange @ SY2651 @ SY2653 @ SV931 ) ) )
| ~ ! [SY2655: $i,SY2656: $i] :
( ~ ( c_member @ SY2656 @ SY2655 @ ( c_Relation_ORange @ SY2651 @ SY2656 @ SV931 ) )
| ( c_member @ ( tc_prod @ SY2651 @ SY2656 ) @ ( c_Product__Type_OPair @ SY2651 @ SY2656 @ ( sK65_B_y @ SY2656 @ SY2655 @ SY2651 @ SV931 ) @ SY2655 ) @ SV931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3547,plain,
! [SV932: $i] :
( ( ! [SY2657: $i,SY2658: $i,SY2659: $i,SY2660: $i,SY2661: $i,SY2662: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2660 @ SY2659 ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2658 @ SY2657 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2662 @ SY2661 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2660 @ SY2659 )
= ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2658 @ SY2657 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2660 @ SY2659 ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ ( sK46_B_a @ SY2662 @ SY2661 @ SY2660 @ SY2659 @ SY2658 @ SY2657 @ SV932 ) @ ( sK47_SY726 @ SY2662 @ SY2661 @ SY2660 @ SY2659 @ SY2658 @ SY2657 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2662 @ SY2661 ) @ ( tc_prod @ SY2662 @ SY2661 ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ ( sK46_B_a @ SY2662 @ SY2661 @ SY2660 @ SY2659 @ SY2658 @ SY2657 @ SV932 ) @ ( sK47_SY726 @ SY2662 @ SY2661 @ SY2660 @ SY2659 @ SY2658 @ SY2657 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY2662 @ SY2661 @ SY2658 @ SY2657 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2662 @ SY2661 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3548,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3549,plain,
! [SV933: $i] :
( ( ! [SY2663: $i,SY2664: $i,SY2665: $i] :
~ ( ~ ! [SY2666: $i,SY2667: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2667 @ SY2667 ) @ ( c_Product__Type_OPair @ SY2667 @ SY2667 @ ( sK43_B_y @ SY2667 @ SY2666 @ SY2665 @ SY2664 @ SY2663 @ SV933 ) @ SY2663 ) @ SY2664 )
| ~ ( ( ( hAPP @ SY2665 @ ( sK43_B_y @ SY2667 @ SY2666 @ SY2665 @ SY2664 @ SY2663 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY2667 @ SY2666 @ SY2665 @ SY2664 @ SY2663 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY2667 @ SY2666 @ SY2665 @ SY2664 @ SY2663 )
= ( c_Recdef_Ocut @ SY2667 @ SY2666 @ SV933 @ SY2664 @ SY2663 ) ) )
| ~ ! [SY2668: $i,SY2669: $i] :
( ( ( c_Recdef_Ocut @ SY2669 @ SY2668 @ SY2665 @ SY2664 @ SY2663 )
!= ( c_Recdef_Ocut @ SY2669 @ SY2668 @ SV933 @ SY2664 @ SY2663 ) )
| ! [SY2670: $i] :
( ~ ( c_member @ ( tc_prod @ SY2669 @ SY2669 ) @ ( c_Product__Type_OPair @ SY2669 @ SY2669 @ SY2670 @ SY2663 ) @ SY2664 )
| ( ( hAPP @ SY2665 @ SY2670 )
= ( hAPP @ SV933 @ SY2670 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3550,plain,
! [SV934: $i] :
( ( ! [SY2671: $i] :
~ ( ~ ! [SY2672: $i,SY2673: $i] :
( ( SY2673 != SY2672 )
| ~ ( c_member @ SY2671 @ SV934 @ SY2673 )
| ( c_member @ SY2671 @ SV934 @ SY2672 ) )
| ~ ! [SY2674: $i,SY2675: $i] :
( ( SY2675 != SY2674 )
| ~ ( c_member @ SY2671 @ SV934 @ SY2674 )
| ( c_member @ SY2671 @ SV934 @ SY2675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3551,plain,
! [SV935: $i] :
( ( ! [SY2676: $i,SY2677: $i,SY2678: $i] :
( ~ ( c_member @ ( tc_prod @ SY2678 @ SY2678 ) @ ( c_Product__Type_OPair @ SY2678 @ SY2678 @ SY2677 @ SY2676 ) @ ( c_Transitive__Closure_Otrancl @ SY2678 @ SV935 ) )
| ( c_member @ ( tc_prod @ SY2678 @ SY2678 ) @ ( c_Product__Type_OPair @ SY2678 @ SY2678 @ SY2677 @ SY2676 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2678 @ SY2678 ) @ ( c_Product__Type_OPair @ SY2678 @ SY2678 @ SY2677 @ ( sK37_B_c @ SY2678 @ SY2677 @ SY2676 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SY2678 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SY2678 @ SY2678 ) @ ( c_Product__Type_OPair @ SY2678 @ SY2678 @ ( sK37_B_c @ SY2678 @ SY2677 @ SY2676 @ SV935 ) @ SY2676 ) @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3552,plain,
! [SV936: $i] :
( ( ! [SY2679: $i,SY2680: $i,SY2681: $i] :
~ ( ~ ( ( SY2681 != SY2679 )
| ( SY2680 != SV936 )
| ! [SY2682: $i,SY2683: $i] :
( ( c_Product__Type_OPair @ SY2683 @ SY2682 @ SY2681 @ SY2680 )
= ( c_Product__Type_OPair @ SY2683 @ SY2682 @ SY2679 @ SV936 ) ) )
| ~ ~ ( ~ ( ! [SY2684: $i,SY2685: $i] :
( ( c_Product__Type_OPair @ SY2685 @ SY2684 @ SY2681 @ SY2680 )
!= ( c_Product__Type_OPair @ SY2685 @ SY2684 @ SY2679 @ SV936 ) )
| ( SY2681 = SY2679 ) )
| ~ ( ! [SY2686: $i,SY2687: $i] :
( ( c_Product__Type_OPair @ SY2687 @ SY2686 @ SY2681 @ SY2680 )
!= ( c_Product__Type_OPair @ SY2687 @ SY2686 @ SY2679 @ SV936 ) )
| ( SY2680 = SV936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3553,plain,
! [SV937: $i] :
( ( ! [SY2688: $i] :
~ ( ~ ~ ( ~ ! [SY2689: $i,SY2690: $i] :
( ( SY2690 != SY2689 )
| ( c_member @ SY2688 @ SV937 @ SY2690 )
| ~ ( c_member @ SY2688 @ SV937 @ SY2690 ) )
| ~ ! [SY2691: $i,SY2692: $i] :
( ( SY2692 != SY2691 )
| ( c_member @ SY2688 @ SV937 @ SY2692 )
| ~ ( c_member @ SY2688 @ SV937 @ SY2691 ) ) )
| ~ ~ ( ~ ! [SY2693: $i,SY2694: $i] :
( ( SY2694 != SY2693 )
| ( c_member @ SY2688 @ SV937 @ SY2693 )
| ~ ( c_member @ SY2688 @ SV937 @ SY2694 ) )
| ~ ! [SY2695: $i] :
( ! [SX3: $i] : ( SX3 != SY2695 )
| ( c_member @ SY2688 @ SV937 @ SY2695 )
| ~ ( c_member @ SY2688 @ SV937 @ SY2695 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3554,plain,
! [SV938: $i] :
( ( ! [SY2697: $i,SY2698: $i,SY2699: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY2699 @ ( sK9_B_x @ SY2699 @ SY2698 @ SY2697 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SY2698 @ ( hAPP @ SY2697 @ ( sK9_B_x @ SY2699 @ SY2698 @ SY2697 @ SV938 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SY2698 ) @ ( c_Recdef_Osame__fst @ SV938 @ SY2698 @ SY2699 @ SY2697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3555,plain,
! [SV939: $i] :
( ( ~ ( ~ ! [SY2700: $i] :
( ! [SY2701: $i] :
~ ( c_member @ SY2701 @ SY2700 @ SV939 )
| ( hBOOL @ ( hAPP @ SV939 @ SY2700 ) ) )
| ~ ! [SY2702: $i] :
( ~ ( hBOOL @ ( hAPP @ SV939 @ SY2702 ) )
| ! [SY2703: $i] : ( c_member @ SY2703 @ SY2702 @ SV939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3556,plain,
! [SV940: $i] :
( ( ! [SY2704: $i] :
~ ( ~ ! [SY2705: $i,SY2706: $i] :
( ( SY2705 != SY2704 )
| ~ ( c_member @ SY2706 @ SY2705 @ SV940 )
| ( c_member @ ( tc_prod @ SY2706 @ SY2706 ) @ ( c_Product__Type_OPair @ SY2706 @ SY2706 @ SY2705 @ SY2704 ) @ ( c_Relation_OId__on @ SY2706 @ SV940 ) ) )
| ~ ~ ( ~ ! [SY2707: $i] :
( ! [SY2708: $i] :
~ ( c_member @ ( tc_prod @ SY2708 @ SY2708 ) @ ( c_Product__Type_OPair @ SY2708 @ SY2708 @ SY2707 @ SY2704 ) @ ( c_Relation_OId__on @ SY2708 @ SV940 ) )
| ( SY2707 = SY2704 ) )
| ~ ! [SY2709: $i,SY2710: $i] :
( ~ ( c_member @ ( tc_prod @ SY2710 @ SY2710 ) @ ( c_Product__Type_OPair @ SY2710 @ SY2710 @ SY2709 @ SY2704 ) @ ( c_Relation_OId__on @ SY2710 @ SV940 ) )
| ( c_member @ SY2710 @ SY2709 @ SV940 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3557,plain,
! [SV941: $i] :
( ( ! [SY2711: $i,SY2712: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2712 @ SY2712 ) @ ( c_Product__Type_OPair @ SY2712 @ SY2712 @ ( sK57_B_y @ SY2712 @ SY2711 @ SV941 ) @ SY2711 ) @ SV941 )
| ~ ~ ( c_member @ SY2712 @ ( sK57_B_y @ SY2712 @ SY2711 @ SV941 ) @ ( c_Wellfounded_Oacc @ SY2712 @ SV941 ) ) )
| ( c_member @ SY2712 @ SY2711 @ ( c_Wellfounded_Oacc @ SY2712 @ SV941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3558,plain,
! [SV942: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i] :
( ~ ( c_member @ ( tc_prod @ SY2715 @ SY2715 ) @ ( c_Product__Type_OPair @ SY2715 @ SY2715 @ SY2714 @ SY2713 ) @ ( c_Transitive__Closure_Otrancl @ SY2715 @ SV942 ) )
| ( c_member @ ( tc_prod @ SY2715 @ SY2715 ) @ ( c_Product__Type_OPair @ SY2715 @ SY2715 @ SY2714 @ SY2713 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2715 @ SY2715 ) @ ( c_Product__Type_OPair @ SY2715 @ SY2715 @ SY2714 @ ( sK38_B_y @ SY2715 @ SY2714 @ SY2713 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SY2715 @ SY2715 ) @ ( c_Product__Type_OPair @ SY2715 @ SY2715 @ ( sK38_B_y @ SY2715 @ SY2714 @ SY2713 @ SV942 ) @ SY2713 ) @ ( c_Transitive__Closure_Otrancl @ SY2715 @ SV942 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3559,plain,
! [SV943: $i] :
( ( ! [SY2716: $i] :
~ ( ~ ~ ( ~ ! [SY2717: $i] :
( ! [SY2718: $i] :
~ ( c_member @ ( tc_prod @ SY2718 @ SY2718 ) @ ( c_Product__Type_OPair @ SY2718 @ SY2718 @ SY2717 @ SY2716 ) @ ( c_Transitive__Closure_Ortrancl @ SY2718 @ SV943 ) )
| ( SY2717 != SY2716 )
| ( SY2717 = SY2716 ) )
| ~ ! [SY2719: $i,SY2720: $i] :
( ~ ( c_member @ ( tc_prod @ SY2720 @ SY2720 ) @ ( c_Product__Type_OPair @ SY2720 @ SY2720 @ SY2719 @ SY2716 ) @ ( c_Transitive__Closure_Ortrancl @ SY2720 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY2720 @ SY2720 ) @ ( c_Product__Type_OPair @ SY2720 @ SY2720 @ SY2719 @ SY2716 ) @ ( c_Transitive__Closure_Otrancl @ SY2720 @ SV943 ) )
| ( SY2719 = SY2716 ) ) )
| ~ ~ ( ~ ! [SY2721: $i,SY2722: $i] :
( ( SY2721 = SY2716 )
| ~ ( c_member @ ( tc_prod @ SY2722 @ SY2722 ) @ ( c_Product__Type_OPair @ SY2722 @ SY2722 @ SY2721 @ SY2716 ) @ ( c_Transitive__Closure_Otrancl @ SY2722 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY2722 @ SY2722 ) @ ( c_Product__Type_OPair @ SY2722 @ SY2722 @ SY2721 @ SY2716 ) @ ( c_Transitive__Closure_Ortrancl @ SY2722 @ SV943 ) ) )
| ~ ! [SY2723: $i] :
( ( SY2723 != SY2716 )
| ! [SY2724: $i] : ( c_member @ ( tc_prod @ SY2724 @ SY2724 ) @ ( c_Product__Type_OPair @ SY2724 @ SY2724 @ SY2723 @ SY2716 ) @ ( c_Transitive__Closure_Ortrancl @ SY2724 @ SV943 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3560,plain,
! [SV944: $i] :
( ( ! [SY2725: $i,SY2726: $i,SY2727: $i] :
( ~ ( c_member @ ( tc_prod @ SY2727 @ SY2727 ) @ ( c_Product__Type_OPair @ SY2727 @ SY2727 @ SY2726 @ SY2725 ) @ ( c_Transitive__Closure_Otrancl @ SY2727 @ SV944 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2727 @ SY2727 ) @ ( c_Product__Type_OPair @ SY2727 @ SY2727 @ SY2726 @ ( sK42_B_z @ SY2727 @ SY2726 @ SY2725 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY2727 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SY2727 @ SY2727 ) @ ( c_Product__Type_OPair @ SY2727 @ SY2727 @ ( sK42_B_z @ SY2727 @ SY2726 @ SY2725 @ SV944 ) @ SY2725 ) @ SV944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3561,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3562,plain,
! [SV945: $i] :
( ( ! [SY2728: $i,SY2729: $i,SY2730: $i,SY2731: $i,SY2732: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2732 @ SY2732 ) @ ( c_Product__Type_OPair @ SY2732 @ SY2732 @ ( sK56_B_z @ SY2732 @ SY2731 @ SY2730 @ SY2729 @ SY2728 @ SV945 ) @ SY2731 ) @ SY2730 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2732 @ SY2729 @ SY2730 @ SY2728 @ ( sK56_B_z @ SY2732 @ SY2731 @ SY2730 @ SY2729 @ SY2728 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SY2732 @ SY2731 @ SY2730 @ SY2729 @ SY2728 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY2732 @ SY2729 @ SY2730 @ SY2728 @ SY2731 @ ( hAPP @ ( hAPP @ SY2728 @ SV945 ) @ SY2731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3563,plain,
! [SV946: $i] :
( ( ~ ( ~ ! [SY2733: $i,SY2734: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2734 @ SY2733 @ SV946 )
| ~ ( c_Relation_Oantisym @ SY2734 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SY2734 @ SY2733 @ SV946 ) )
| ~ ~ ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) )
| ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3564,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
| ~ ~ ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3565,plain,
! [SV947: $i] :
( ( ~ ( ~ ! [SY2739: $i,SY2740: $i] :
( ~ ( c_Relation_Oirrefl @ SY2740 @ SV947 )
| ~ ( c_Relation_Otrans @ SY2740 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SY2740 @ SY2739 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY2740 @ SY2739 @ SV947 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
| ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3566,plain,
! [SV948: $i] :
( ( ! [SY2747: $i] :
~ ( ~ ! [SY2748: $i,SY2749: $i] :
( ~ ( c_member @ SY2749 @ SY2748 @ ( c_Set_Oinsert @ SY2749 @ SY2747 @ SV948 ) )
| ( SY2748 = SY2747 )
| ( c_member @ SY2749 @ SY2748 @ SV948 ) )
| ~ ~ ( ~ ! [SY2750: $i] :
( ( SY2750 != SY2747 )
| ! [SY2751: $i] : ( c_member @ SY2751 @ SY2750 @ ( c_Set_Oinsert @ SY2751 @ SY2747 @ SV948 ) ) )
| ~ ! [SY2752: $i,SY2753: $i] :
( ~ ( c_member @ SY2753 @ SY2752 @ SV948 )
| ( c_member @ SY2753 @ SY2752 @ ( c_Set_Oinsert @ SY2753 @ SY2747 @ SV948 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3567,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3568,plain,
! [SV949: $i] :
( ( ! [SY2754: $i,SY2755: $i,SY2756: $i] :
~ ( ~ ! [SY2757: $i,SY2758: $i] :
( ! [SY2759: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2758 @ SY2758 ) @ ( c_Product__Type_OPair @ SY2758 @ SY2758 @ ( sK55_B_z @ SY2759 @ SY2758 @ SY2757 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) @ SY2754 ) @ SY2756 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY2758 @ SY2757 @ SY2756 @ SY2755 @ ( sK55_B_z @ SY2759 @ SY2758 @ SY2757 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) @ ( hAPP @ SY2759 @ ( sK55_B_z @ SY2759 @ SY2758 @ SY2757 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SY2755 @ SY2759 ) @ SY2754 ) ) )
| ( c_Recdef_Owfrec__rel @ SY2758 @ SY2757 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) )
| ~ ! [SY2760: $i,SY2761: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY2761 @ SY2760 @ SY2756 @ SY2755 @ SY2754 @ SV949 )
| ~ ( ~ ! [SY2762: $i] :
( ~ ( c_member @ ( tc_prod @ SY2761 @ SY2761 ) @ ( c_Product__Type_OPair @ SY2761 @ SY2761 @ SY2762 @ SY2754 ) @ SY2756 )
| ( c_Recdef_Owfrec__rel @ SY2761 @ SY2760 @ SY2756 @ SY2755 @ SY2762 @ ( hAPP @ ( sK54_B_g @ SY2761 @ SY2760 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) @ SY2762 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SY2755 @ ( sK54_B_g @ SY2761 @ SY2760 @ SY2756 @ SY2755 @ SY2754 @ SV949 ) ) @ SY2754 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3569,plain,
! [SV950: $i] :
( ( ! [SY2763: $i] :
~ ( ~ ! [SY2764: $i,SY2765: $i] :
( ~ ( c_member @ SY2765 @ SY2764 @ SY2763 )
| ( c_member @ SY2765 @ SY2764 @ ( c_Set_Oinsert @ SY2765 @ SV950 @ SY2763 ) ) )
| ~ ! [SY2766: $i] :
( ( SY2766 != SV950 )
| ! [SY2767: $i] : ( c_member @ SY2767 @ SY2766 @ ( c_Set_Oinsert @ SY2767 @ SV950 @ SY2763 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3570,plain,
! [SV951: $i] :
( ( ! [SY2768: $i,SY2769: $i,SY2770: $i,SY2771: $i] :
( ~ ( c_member @ ( tc_prod @ SY2771 @ SY2771 ) @ ( c_Product__Type_OPair @ SY2771 @ SY2771 @ SY2770 @ SY2769 ) @ ( c_Transitive__Closure_Ortrancl @ SY2771 @ SY2768 ) )
| ~ ( hBOOL @ ( hAPP @ SV951 @ SY2770 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2771 @ SY2771 ) @ ( c_Product__Type_OPair @ SY2771 @ SY2771 @ SY2770 @ ( sK10_B_y @ SY2771 @ SY2770 @ SY2769 @ SY2768 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY2771 @ SY2768 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2771 @ SY2771 ) @ ( c_Product__Type_OPair @ SY2771 @ SY2771 @ ( sK10_B_y @ SY2771 @ SY2770 @ SY2769 @ SY2768 @ SV951 ) @ ( sK11_SY706 @ SY2771 @ SY2770 @ SY2769 @ SY2768 @ SV951 ) ) @ SY2768 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SY2771 @ SY2770 @ SY2769 @ SY2768 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SY2771 @ SY2770 @ SY2769 @ SY2768 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SY2769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3571,plain,
! [SV952: $i] :
( ( ! [SY2772: $i] :
~ ( ~ ! [SY2773: $i] :
( ! [SY2774: $i] :
~ ( c_member @ ( tc_prod @ SY2774 @ SY2774 ) @ ( c_Product__Type_OPair @ SY2774 @ SY2774 @ SY2773 @ SY2772 ) @ ( c_Transitive__Closure_Ortrancl @ SY2774 @ SV952 ) )
| ( SY2773 != SY2772 )
| ( SY2773 = SY2772 ) )
| ~ ! [SY2775: $i,SY2776: $i] :
( ~ ( c_member @ ( tc_prod @ SY2776 @ SY2776 ) @ ( c_Product__Type_OPair @ SY2776 @ SY2776 @ SY2775 @ SY2772 ) @ ( c_Transitive__Closure_Ortrancl @ SY2776 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY2776 @ SY2776 ) @ ( c_Product__Type_OPair @ SY2776 @ SY2776 @ SY2775 @ SY2772 ) @ ( c_Transitive__Closure_Otrancl @ SY2776 @ SV952 ) )
| ( SY2775 = SY2772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(3572,plain,
! [SV953: $i] :
( ( ! [SY2777: $i,SY2778: $i,SY2779: $i,SY2780: $i] :
( ~ ( c_member @ SY2780 @ SY2779 @ ( c_Relation_OImage @ SY2778 @ SY2780 @ SY2777 @ SV953 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2778 @ SY2780 ) @ ( c_Product__Type_OPair @ SY2778 @ SY2780 @ ( sK23_B_x @ SY2780 @ SY2779 @ SY2778 @ SY2777 @ SV953 ) @ SY2779 ) @ SY2777 )
| ~ ( c_member @ SY2778 @ ( sK23_B_x @ SY2780 @ SY2779 @ SY2778 @ SY2777 @ SV953 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3573,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3574,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3575,plain,
! [SV954: $i] :
( ( ! [SY2781: $i,SY2782: $i] :
( ( c_member @ SY2782 @ SY2781 @ ( c_Wellfounded_Oacc @ SY2782 @ SV954 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2782 @ SY2782 ) @ ( c_Product__Type_OPair @ SY2782 @ SY2782 @ ( sK58_B_z @ SY2782 @ SY2781 @ SV954 ) @ SY2781 ) @ SV954 )
| ~ ~ ( c_member @ SY2782 @ ( sK58_B_z @ SY2782 @ SY2781 @ SV954 ) @ ( c_Wellfounded_Oacc @ SY2782 @ SV954 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3576,plain,
! [SV955: $i] :
( ( ! [SY2783: $i] :
~ ( ~ ! [SY2784: $i,SY2785: $i] :
( ~ ( c_Wellfounded_Owf @ SY2785 @ SV955 )
| ( c_member @ ( tc_prod @ SY2785 @ SY2785 ) @ ( c_Product__Type_OPair @ SY2785 @ SY2785 @ SY2783 @ SY2784 ) @ ( c_Transitive__Closure_Ortrancl @ SY2785 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY2785 @ ( c_Set_Oinsert @ ( tc_prod @ SY2785 @ SY2785 ) @ ( c_Product__Type_OPair @ SY2785 @ SY2785 @ SY2784 @ SY2783 ) @ SV955 ) ) )
| ~ ~ ( ~ ! [SY2786: $i,SY2787: $i] :
( ~ ( c_Wellfounded_Owf @ SY2787 @ ( c_Set_Oinsert @ ( tc_prod @ SY2787 @ SY2787 ) @ ( c_Product__Type_OPair @ SY2787 @ SY2787 @ SY2786 @ SY2783 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY2787 @ SV955 ) )
| ~ ! [SY2788: $i,SY2789: $i] :
( ~ ( c_Wellfounded_Owf @ SY2789 @ ( c_Set_Oinsert @ ( tc_prod @ SY2789 @ SY2789 ) @ ( c_Product__Type_OPair @ SY2789 @ SY2789 @ SY2788 @ SY2783 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY2789 @ SY2789 ) @ ( c_Product__Type_OPair @ SY2789 @ SY2789 @ SY2783 @ SY2788 ) @ ( c_Transitive__Closure_Ortrancl @ SY2789 @ SV955 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3577,plain,
! [SV795: $i,SV956: $i] :
( ( ! [SY2790: $i,SY2791: $i,SY2792: $i] :
( ~ ( c_Relation_Otrans @ SY2792 @ SY2791 )
| ~ ( c_member @ ( tc_prod @ SY2792 @ SY2792 ) @ ( c_Product__Type_OPair @ SY2792 @ SY2792 @ SY2790 @ SV956 ) @ SY2791 )
| ~ ( c_member @ ( tc_prod @ SY2792 @ SY2792 ) @ ( c_Product__Type_OPair @ SY2792 @ SY2792 @ SV956 @ SV795 ) @ SY2791 )
| ( c_member @ ( tc_prod @ SY2792 @ SY2792 ) @ ( c_Product__Type_OPair @ SY2792 @ SY2792 @ SY2790 @ SV795 ) @ SY2791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3578,plain,
! [SV796: $i,SV957: $i] :
( ( ! [SY2793: $i,SY2794: $i] :
( ( SY2794 != SY2793 )
| ~ ( c_member @ SV957 @ SY2793 @ SV796 )
| ( c_member @ SV957 @ SY2794 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3579,plain,
! [SV797: $i,SV958: $i] :
( ( ! [SY2795: $i,SY2796: $i,SY2797: $i,SY2798: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY2798 @ SY2797 @ SY2796 @ SY2795 @ ( c_Product__Type_OPair @ SY2798 @ SY2797 @ SV958 @ SV797 ) )
= ( hAPP @ ( hAPP @ SY2795 @ SV958 ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3580,plain,
! [SV798: $i,SV959: $i] :
( ( ! [SY2799: $i,SY2800: $i,SY2801: $i,SY2802: $i] :
( ( c_Product__Type_Ointernal__split @ SY2802 @ SY2801 @ SY2800 @ SY2799 @ ( c_Product__Type_OPair @ SY2802 @ SY2801 @ SV959 @ SV798 ) )
= ( hAPP @ ( hAPP @ SY2799 @ SV959 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(3581,plain,
! [SV799: $i,SV960: $i] :
( ( ! [SY2803: $i,SY2804: $i,SY2805: $i] :
( ~ ( c_member @ ( tc_prod @ SY2805 @ SY2804 ) @ ( c_Product__Type_OPair @ SY2805 @ SY2804 @ SY2803 @ SV960 ) @ SV799 )
| ( c_member @ SY2804 @ SV960 @ ( c_Relation_ORange @ SY2805 @ SY2804 @ SV799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3582,plain,
! [SV800: $i,SV961: $i] :
( ( ! [SY2806: $i,SY2807: $i] :
( ( SY2807 != SY2806 )
| ~ ( c_member @ SV961 @ SY2807 @ SV800 )
| ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SY2807 @ SY2806 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3583,plain,
! [SV801: $i,SV962: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i] :
( ~ ( c_member @ ( tc_prod @ SY2810 @ SY2809 ) @ ( c_Product__Type_OPair @ SY2810 @ SY2809 @ SY2808 @ SV962 ) @ SV801 )
| ( c_member @ SY2810 @ SY2808 @ ( c_Relation_ODomain @ SY2810 @ SY2809 @ SV801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3584,plain,
! [SV802: $i,SV963: $i] :
( ( ! [SY2811: $i,SY2812: $i] :
( ~ ( c_Relation_Otrans @ SY2812 @ SY2811 )
| ~ ( c_Relation_Otrans @ SV963 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SY2812 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SY2812 @ SV963 @ SY2811 @ SV802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3585,plain,
! [SV803: $i,SV964: $i] :
( ( c_Relation_Otrans @ SV964 @ ( c_Relation_OId__on @ SV964 @ SV803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(3586,plain,
! [SV804: $i,SV965: $i] :
( ( ! [SY2813: $i,SY2814: $i] :
( ~ ( c_Relation_Otrans @ SY2814 @ SY2813 )
| ( c_Relation_Otrans @ SV965 @ ( hAPP @ ( c_Relation_Oinv__image @ SY2814 @ SV965 @ SY2813 ) @ SV804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3587,plain,
! [SV805: $i,SV966: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ~ ( c_member @ SY2816 @ SY2815 @ ( c_Relation_ORange @ SV966 @ SY2816 @ SV805 ) )
| ( c_member @ ( tc_prod @ SV966 @ SY2816 ) @ ( c_Product__Type_OPair @ SV966 @ SY2816 @ ( sK63_B_x @ SY2816 @ SY2815 @ SV966 @ SV805 ) @ SY2815 ) @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3588,plain,
! [SV806: $i,SV967: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ~ ( c_member @ SY2818 @ SY2817 @ ( c_Relation_ODomain @ SY2818 @ SV967 @ SV806 ) )
| ( c_member @ ( tc_prod @ SY2818 @ SV967 ) @ ( c_Product__Type_OPair @ SY2818 @ SV967 @ SY2817 @ ( sK62_B_y @ SY2818 @ SY2817 @ SV967 @ SV806 ) ) @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3589,plain,
! [SV807: $i,SV968: $i] :
( ( ! [SY2819: $i,SY2820: $i] :
( ~ ( c_member @ SY2820 @ SY2819 @ ( c_Wellfounded_Oacc @ SY2820 @ SV968 ) )
| ~ ( c_member @ ( tc_prod @ SY2820 @ SY2820 ) @ ( c_Product__Type_OPair @ SY2820 @ SY2820 @ SV807 @ SY2819 ) @ SV968 )
| ( c_member @ SY2820 @ SV807 @ ( c_Wellfounded_Oacc @ SY2820 @ SV968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3590,plain,
! [SV808: $i,SV969: $i] :
( ( ! [SY2821: $i,SY2822: $i] :
( ~ ( c_Relation_Orefl__on @ SY2822 @ SY2821 @ SV969 )
| ~ ( c_member @ SY2822 @ SV808 @ SY2821 )
| ( c_member @ ( tc_prod @ SY2822 @ SY2822 ) @ ( c_Product__Type_OPair @ SY2822 @ SY2822 @ SV808 @ SV808 ) @ SV969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3591,plain,
! [SV809: $i,SV970: $i] :
( ( ! [SY2823: $i,SY2824: $i,SY2825: $i] :
( ~ ( c_Relation_Orefl__on @ SY2825 @ SY2824 @ SY2823 )
| ~ ( c_member @ ( tc_prod @ SY2825 @ SY2825 ) @ ( c_Product__Type_OPair @ SY2825 @ SY2825 @ SV970 @ SV809 ) @ SY2823 )
| ( c_member @ SY2825 @ SV970 @ SY2824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3592,plain,
! [SV810: $i,SV971: $i] :
( ( ! [SY2826: $i,SY2827: $i,SY2828: $i] :
( ~ ( c_Relation_Orefl__on @ SY2828 @ SY2827 @ SY2826 )
| ~ ( c_member @ ( tc_prod @ SY2828 @ SY2828 ) @ ( c_Product__Type_OPair @ SY2828 @ SY2828 @ SV971 @ SV810 ) @ SY2826 )
| ( c_member @ SY2828 @ SV810 @ SY2827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3593,plain,
! [SV811: $i,SV972: $i] :
( ( ! [SY2829: $i,SY2830: $i] :
( ~ ( c_member @ ( tc_prod @ SY2830 @ SY2830 ) @ ( c_Product__Type_OPair @ SY2830 @ SY2830 @ SY2829 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SY2830 @ SV811 ) )
| ~ ( c_member @ SY2830 @ SV972 @ ( c_Wellfounded_Oacc @ SY2830 @ SV811 ) )
| ( c_member @ SY2830 @ SY2829 @ ( c_Wellfounded_Oacc @ SY2830 @ SV811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3594,plain,
! [SV812: $i,SV973: $i] :
( ( ! [SY2831: $i,SY2832: $i] :
( ~ ( c_member @ SY2832 @ SY2831 @ ( c_Wellfounded_Oacc @ SY2832 @ SV973 ) )
| ~ ( c_member @ ( tc_prod @ SY2832 @ SY2832 ) @ ( c_Product__Type_OPair @ SY2832 @ SY2832 @ SV812 @ SY2831 ) @ ( c_Transitive__Closure_Ortrancl @ SY2832 @ SV973 ) )
| ( c_member @ SY2832 @ SV812 @ ( c_Wellfounded_Oacc @ SY2832 @ SV973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3595,plain,
! [SV813: $i,SV974: $i] :
( ( ! [SY2833: $i,SY2834: $i,SY2835: $i,SY2836: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2836 @ SY2835 @ SY2834 )
| ~ ( c_member @ ( tc_prod @ SY2836 @ SY2835 ) @ ( c_Product__Type_OPair @ SY2836 @ SY2835 @ SY2833 @ SV974 ) @ SY2834 )
| ~ ( c_member @ ( tc_prod @ SY2836 @ SY2835 ) @ ( c_Product__Type_OPair @ SY2836 @ SY2835 @ SY2833 @ SV813 ) @ SY2834 )
| ( SV974 = SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3596,plain,
! [SV814: $i,SV975: $i] :
( ( ! [SY2837: $i,SY2838: $i,SY2839: $i,SY2840: $i] :
( ( c_Product__Type_Ocurry @ SY2840 @ SY2839 @ SY2838 @ SY2837 @ SV975 @ SV814 )
= ( hAPP @ SY2837 @ ( c_Product__Type_OPair @ SY2840 @ SY2839 @ SV975 @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3597,plain,
! [SV815: $i,SV976: $i] :
( ( ! [SY2841: $i] : ( c_member @ ( tc_prod @ SY2841 @ SY2841 ) @ ( c_Product__Type_OPair @ SY2841 @ SY2841 @ SV976 @ SV976 ) @ ( c_Transitive__Closure_Ortrancl @ SY2841 @ SV815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(3598,plain,
! [SV816: $i,SV977: $i] :
( ( ! [SY2842: $i] :
( ~ ( c_member @ ( tc_prod @ SY2842 @ SY2842 ) @ SV977 @ SV816 )
| ( c_member @ ( tc_prod @ SY2842 @ SY2842 ) @ SV977 @ ( c_Transitive__Closure_Ortrancl @ SY2842 @ SV816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3599,plain,
! [SV817: $i,SV978: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2845 @ SY2845 @ SY2844 )
| ~ ( c_member @ ( tc_prod @ SY2845 @ SY2845 ) @ ( c_Product__Type_OPair @ SY2845 @ SY2845 @ SY2843 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY2845 @ SY2844 ) )
| ~ ( c_member @ ( tc_prod @ SY2845 @ SY2845 ) @ ( c_Product__Type_OPair @ SY2845 @ SY2845 @ SY2843 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY2845 @ SY2844 ) )
| ( c_member @ ( tc_prod @ SY2845 @ SY2845 ) @ ( c_Product__Type_OPair @ SY2845 @ SY2845 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY2845 @ SY2844 ) )
| ( c_member @ ( tc_prod @ SY2845 @ SY2845 ) @ ( c_Product__Type_OPair @ SY2845 @ SY2845 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY2845 @ SY2844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3600,plain,
! [SV818: $i,SV979: $i] :
( ( ! [SY2846: $i,SY2847: $i,SY2848: $i] :
( ~ ( c_member @ ( tc_prod @ SY2848 @ SY2848 ) @ ( c_Product__Type_OPair @ SY2848 @ SY2848 @ SY2847 @ SY2846 ) @ SV979 )
| ~ ( c_member @ ( tc_prod @ SY2848 @ SY2848 ) @ ( c_Product__Type_OPair @ SY2848 @ SY2848 @ SY2846 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY2848 @ SV979 ) )
| ( c_member @ ( tc_prod @ SY2848 @ SY2848 ) @ ( c_Product__Type_OPair @ SY2848 @ SY2848 @ SY2847 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY2848 @ SV979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3601,plain,
! [SV819: $i,SV980: $i] :
( ( ! [SY2849: $i,SY2850: $i,SY2851: $i] :
( ~ ( c_member @ ( tc_prod @ SY2851 @ SY2851 ) @ ( c_Product__Type_OPair @ SY2851 @ SY2851 @ SY2850 @ SY2849 ) @ ( c_Transitive__Closure_Ortrancl @ SY2851 @ SV980 ) )
| ~ ( c_member @ ( tc_prod @ SY2851 @ SY2851 ) @ ( c_Product__Type_OPair @ SY2851 @ SY2851 @ SY2849 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SY2851 @ SY2851 ) @ ( c_Product__Type_OPair @ SY2851 @ SY2851 @ SY2850 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SY2851 @ SV980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3602,plain,
! [SV820: $i,SV981: $i] :
( ( ! [SY2852: $i,SY2853: $i,SY2854: $i] :
( ~ ( c_member @ ( tc_prod @ SY2854 @ SY2854 ) @ ( c_Product__Type_OPair @ SY2854 @ SY2854 @ SY2853 @ SY2852 ) @ ( c_Transitive__Closure_Ortrancl @ SY2854 @ SV981 ) )
| ~ ( c_member @ ( tc_prod @ SY2854 @ SY2854 ) @ ( c_Product__Type_OPair @ SY2854 @ SY2854 @ SY2852 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY2854 @ SV981 ) )
| ( c_member @ ( tc_prod @ SY2854 @ SY2854 ) @ ( c_Product__Type_OPair @ SY2854 @ SY2854 @ SY2853 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY2854 @ SV981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(3603,plain,
! [SV821: $i,SV982: $i] :
( ( c_Relation_Otrans @ SV982 @ ( c_Transitive__Closure_Ortrancl @ SV982 @ SV821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(3604,plain,
! [SV822: $i,SV983: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ~ ( c_member @ ( tc_prod @ SY2856 @ SY2856 ) @ ( c_Product__Type_OPair @ SY2856 @ SY2856 @ SY2855 @ SV983 ) @ ( c_Transitive__Closure_Otrancl @ SY2856 @ SV822 ) )
| ( c_member @ ( tc_prod @ SY2856 @ SY2856 ) @ ( c_Product__Type_OPair @ SY2856 @ SY2856 @ SY2855 @ SV983 ) @ ( c_Transitive__Closure_Ortrancl @ SY2856 @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3605,plain,
! [SV823: $i,SV984: $i] :
( ( ! [SY2857: $i,SY2858: $i,SY2859: $i,SY2860: $i] :
( ~ ( c_member @ ( tc_prod @ SY2860 @ SY2860 ) @ ( c_Product__Type_OPair @ SY2860 @ SY2860 @ SY2859 @ SY2858 ) @ SY2857 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY2860 @ SV984 @ SV823 @ SY2857 @ SY2858 ) @ SY2859 )
= ( hAPP @ SV823 @ SY2859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3606,plain,
! [SV824: $i,SV985: $i] :
( ( ! [SY2861: $i,SY2862: $i] :
( ~ ( c_member @ ( tc_prod @ SY2862 @ SY2862 ) @ ( c_Product__Type_OPair @ SY2862 @ SY2862 @ SY2861 @ SV985 ) @ SV824 )
| ( c_member @ ( tc_prod @ SY2862 @ SY2862 ) @ ( c_Product__Type_OPair @ SY2862 @ SY2862 @ SY2861 @ SV985 ) @ ( c_Transitive__Closure_Otrancl @ SY2862 @ SV824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3607,plain,
! [SV825: $i,SV986: $i] :
( ( ! [SY2863: $i] :
( ~ ( c_member @ ( tc_prod @ SY2863 @ SY2863 ) @ SV986 @ SV825 )
| ( c_member @ ( tc_prod @ SY2863 @ SY2863 ) @ SV986 @ ( c_Transitive__Closure_Otrancl @ SY2863 @ SV825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(3608,plain,
! [SV826: $i,SV987: $i] :
( ( c_Relation_Otrans @ SV987 @ ( c_Transitive__Closure_Otrancl @ SV987 @ SV826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(3609,plain,
! [SV827: $i,SV988: $i] :
( ( ~ ( c_Relation_Otrans @ SV988 @ SV827 )
| ( ( c_Transitive__Closure_Otrancl @ SV988 @ SV827 )
= SV827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(3610,plain,
! [SV828: $i,SV989: $i] :
( ( ! [SY2864: $i,SY2865: $i,SY2866: $i] :
( ~ ( c_member @ ( tc_prod @ SY2866 @ SY2866 ) @ ( c_Product__Type_OPair @ SY2866 @ SY2866 @ SY2865 @ SY2864 ) @ SV989 )
| ~ ( c_member @ ( tc_prod @ SY2866 @ SY2866 ) @ ( c_Product__Type_OPair @ SY2866 @ SY2866 @ SY2864 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SY2866 @ SY2866 ) @ ( c_Product__Type_OPair @ SY2866 @ SY2866 @ SY2865 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SY2866 @ SV989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(3611,plain,
! [SV829: $i,SV990: $i] :
( ( ! [SY2867: $i,SY2868: $i,SY2869: $i] :
( ~ ( c_member @ ( tc_prod @ SY2869 @ SY2869 ) @ ( c_Product__Type_OPair @ SY2869 @ SY2869 @ SY2868 @ SY2867 ) @ SV990 )
| ~ ( c_member @ ( tc_prod @ SY2869 @ SY2869 ) @ ( c_Product__Type_OPair @ SY2869 @ SY2869 @ SY2867 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY2869 @ SV990 ) )
| ( c_member @ ( tc_prod @ SY2869 @ SY2869 ) @ ( c_Product__Type_OPair @ SY2869 @ SY2869 @ SY2868 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY2869 @ SV990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3612,plain,
! [SV830: $i,SV991: $i] :
( ( ! [SY2870: $i,SY2871: $i,SY2872: $i] :
( ~ ( c_member @ ( tc_prod @ SY2872 @ SY2872 ) @ ( c_Product__Type_OPair @ SY2872 @ SY2872 @ SY2871 @ SY2870 ) @ ( c_Transitive__Closure_Otrancl @ SY2872 @ SV991 ) )
| ~ ( c_member @ ( tc_prod @ SY2872 @ SY2872 ) @ ( c_Product__Type_OPair @ SY2872 @ SY2872 @ SY2870 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SY2872 @ SY2872 ) @ ( c_Product__Type_OPair @ SY2872 @ SY2872 @ SY2871 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SY2872 @ SV991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3613,plain,
! [SV831: $i,SV992: $i] :
( ( ! [SY2873: $i,SY2874: $i,SY2875: $i] :
( ~ ( c_member @ ( tc_prod @ SY2875 @ SY2875 ) @ ( c_Product__Type_OPair @ SY2875 @ SY2875 @ SY2874 @ SY2873 ) @ ( c_Transitive__Closure_Otrancl @ SY2875 @ SV992 ) )
| ~ ( c_member @ ( tc_prod @ SY2875 @ SY2875 ) @ ( c_Product__Type_OPair @ SY2875 @ SY2875 @ SY2873 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY2875 @ SV992 ) )
| ( c_member @ ( tc_prod @ SY2875 @ SY2875 ) @ ( c_Product__Type_OPair @ SY2875 @ SY2875 @ SY2874 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY2875 @ SV992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(3614,plain,
! [SV832: $i,SV993: $i] :
( ( ! [SY2876: $i,SY2877: $i,SY2878: $i] :
( ~ ( c_member @ ( tc_prod @ SY2878 @ SY2878 ) @ ( c_Product__Type_OPair @ SY2878 @ SY2878 @ SY2877 @ SY2876 ) @ SV993 )
| ~ ( c_member @ ( tc_prod @ SY2878 @ SY2878 ) @ ( c_Product__Type_OPair @ SY2878 @ SY2878 @ SY2876 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SY2878 @ SV993 ) )
| ( c_member @ ( tc_prod @ SY2878 @ SY2878 ) @ ( c_Product__Type_OPair @ SY2878 @ SY2878 @ SY2877 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SY2878 @ SV993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(3615,plain,
! [SV833: $i,SV994: $i] :
( ( ! [SY2879: $i,SY2880: $i,SY2881: $i] :
( ~ ( c_member @ ( tc_prod @ SY2881 @ SY2881 ) @ ( c_Product__Type_OPair @ SY2881 @ SY2881 @ SY2880 @ SY2879 ) @ ( c_Transitive__Closure_Ortrancl @ SY2881 @ SV994 ) )
| ~ ( c_member @ ( tc_prod @ SY2881 @ SY2881 ) @ ( c_Product__Type_OPair @ SY2881 @ SY2881 @ SY2879 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SY2881 @ SY2881 ) @ ( c_Product__Type_OPair @ SY2881 @ SY2881 @ SY2880 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SY2881 @ SV994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(3616,plain,
! [SV834: $i,SV995: $i] :
( ( ! [SY2882: $i,SY2883: $i,SY2884: $i] :
( ~ ( c_member @ ( tc_prod @ SY2884 @ SY2884 ) @ ( c_Product__Type_OPair @ SY2884 @ SY2884 @ SY2883 @ SY2882 ) @ ( c_Transitive__Closure_Otrancl @ SY2884 @ SV995 ) )
| ~ ( c_member @ ( tc_prod @ SY2884 @ SY2884 ) @ ( c_Product__Type_OPair @ SY2884 @ SY2884 @ SY2882 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SY2884 @ SV995 ) )
| ( c_member @ ( tc_prod @ SY2884 @ SY2884 ) @ ( c_Product__Type_OPair @ SY2884 @ SY2884 @ SY2883 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SY2884 @ SV995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3617,plain,
! [SV835: $i,SV996: $i] :
( ( ! [SY2885: $i,SY2886: $i,SY2887: $i] :
( ~ ( c_member @ ( tc_prod @ SY2887 @ SY2887 ) @ ( c_Product__Type_OPair @ SY2887 @ SY2887 @ SY2886 @ SY2885 ) @ ( c_Transitive__Closure_Ortrancl @ SY2887 @ SV996 ) )
| ~ ( c_member @ ( tc_prod @ SY2887 @ SY2887 ) @ ( c_Product__Type_OPair @ SY2887 @ SY2887 @ SY2885 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY2887 @ SV996 ) )
| ( c_member @ ( tc_prod @ SY2887 @ SY2887 ) @ ( c_Product__Type_OPair @ SY2887 @ SY2887 @ SY2886 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY2887 @ SV996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(3618,plain,
! [SV836: $i,SV997: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i,SY2891: $i] :
( ~ ( c_member @ ( tc_prod @ SY2889 @ SY2889 ) @ ( c_Product__Type_OPair @ SY2889 @ SY2889 @ SY2888 @ SV997 ) @ SY2891 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY2889 @ SV836 @ SY2890 @ SY2891 @ SV997 ) @ SY2888 )
= ( hAPP @ SY2890 @ SY2888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(3619,plain,
! [SV837: $i,SV998: $i] :
( ( ! [SY2892: $i,SY2893: $i] :
( ( c_member @ ( tc_prod @ SY2893 @ SY2893 ) @ ( c_Product__Type_OPair @ SY2893 @ SY2893 @ ( sK39_B_x @ SY2893 @ SY2892 @ SV998 @ SV837 ) @ ( sK39_B_x @ SY2893 @ SY2892 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SY2893 @ SY2892 ) )
| ~ ( c_member @ ( tc_prod @ SY2893 @ SY2893 ) @ ( c_Product__Type_OPair @ SY2893 @ SY2893 @ SV998 @ SV837 ) @ SY2892 )
| ( SV998 != SV837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(3620,plain,
! [SV838: $i,SV999: $i] :
( ( c_member @ ( tc_prod @ SV999 @ SV999 ) @ ( c_Product__Type_OPair @ SV999 @ SV999 @ SV838 @ SV838 ) @ ( c_Relation_OId @ SV999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(3621,plain,
! [SV840: $i,SV1000: $i] :
( ( ( c_member @ ( tc_prod @ SV1000 @ SV1000 ) @ ( c_Product__Type_OPair @ SV1000 @ SV1000 @ ( sK36_B_x @ SV1000 @ SV840 ) @ ( sK36_B_x @ SV1000 @ SV840 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1000 @ SV840 ) )
| ( c_Wellfounded_Oacyclic @ SV1000 @ SV840 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(3622,plain,
! [SV841: $i,SV1001: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1001 @ SV1001 ) @ SV841 @ ( c_Relation_OId @ SV1001 ) )
| ( SV841
= ( c_Product__Type_OPair @ SV1001 @ SV1001 @ ( sK35_B_x @ SV1001 @ SV841 ) @ ( sK35_B_x @ SV1001 @ SV841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(3623,plain,
! [SV842: $i,SV1002: $i] :
( ( ! [SY2894: $i,SY2895: $i] :
( ~ ( c_Relation_Oantisym @ SY2895 @ SY2894 )
| ~ ( c_member @ ( tc_prod @ SY2895 @ SY2895 ) @ ( c_Product__Type_OPair @ SY2895 @ SY2895 @ SV1002 @ SV842 ) @ SY2894 )
| ~ ( c_member @ ( tc_prod @ SY2895 @ SY2895 ) @ ( c_Product__Type_OPair @ SY2895 @ SY2895 @ SV842 @ SV1002 ) @ SY2894 )
| ( SV1002 = SV842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3624,plain,
! [SV843: $i,SV1003: $i] :
( ( ! [SY2896: $i,SY2897: $i] :
( ~ ( c_member @ SY2897 @ SY2896 @ ( c_Set_Oinsert @ SY2897 @ SV1003 @ SV843 ) )
| ( SY2896 = SV1003 )
| ( c_member @ SY2897 @ SY2896 @ SV843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3625,plain,
! [SV844: $i,SV1004: $i] :
( ( ! [SY2898: $i,SY2899: $i,SY2900: $i] :
( ( c_Relation_ODomain @ SY2900 @ SY2899 @ ( c_Set_Oinsert @ ( tc_prod @ SY2900 @ SY2899 ) @ ( c_Product__Type_OPair @ SY2900 @ SY2899 @ SY2898 @ SV1004 ) @ SV844 ) )
= ( c_Set_Oinsert @ SY2900 @ SY2898 @ ( c_Relation_ODomain @ SY2900 @ SY2899 @ SV844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(3626,plain,
! [SV845: $i,SV1005: $i] :
( ( ! [SY2901: $i,SY2902: $i,SY2903: $i] :
( ( c_Relation_ORange @ SY2903 @ SY2902 @ ( c_Set_Oinsert @ ( tc_prod @ SY2903 @ SY2902 ) @ ( c_Product__Type_OPair @ SY2903 @ SY2902 @ SY2901 @ SV1005 ) @ SV845 ) )
= ( c_Set_Oinsert @ SY2902 @ SV1005 @ ( c_Relation_ORange @ SY2903 @ SY2902 @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3627,plain,
! [SV846: $i,SV1006: $i] :
( ( ! [SY2904: $i] : ( c_member @ SY2904 @ SV1006 @ ( c_Set_Oinsert @ SY2904 @ SV1006 @ SV846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3628,plain,
! [SV847: $i,SV1007: $i] :
( ( ! [SY2905: $i,SY2906: $i] :
( ~ ( c_member @ SY2906 @ SY2905 @ SV1007 )
| ( c_member @ SY2906 @ SY2905 @ ( c_Set_Oinsert @ SY2906 @ SV847 @ SV1007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3629,plain,
! [SV848: $i,SV1008: $i] :
( ( ! [SY2907: $i] :
( ~ ( c_member @ SY2907 @ SV1008 @ SV848 )
| ( ( c_Set_Oinsert @ SY2907 @ SV1008 @ SV848 )
= SV848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3630,plain,
! [SV849: $i,SV1009: $i] :
( ( ! [SY2908: $i,SY2909: $i] :
( ~ ( c_Wellfounded_Owf @ SY2909 @ SY2908 )
| ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY2909 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SY2909 @ SV1009 @ SY2908 @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3631,plain,
! [SV850: $i,SV1010: $i] :
( ( ! [SY2910: $i] :
( ~ ( c_Wellfounded_Owf @ SY2910 @ SV1010 )
| ~ ( c_member @ ( tc_prod @ SY2910 @ SY2910 ) @ ( c_Product__Type_OPair @ SY2910 @ SY2910 @ SV850 @ SV850 ) @ SV1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(3632,plain,
! [SV851: $i,SV1011: $i] :
( ( ! [SY2911: $i,SY2912: $i] :
( ~ ( c_Wellfounded_Owf @ SY2912 @ SY2911 )
| ~ ( c_member @ ( tc_prod @ SY2912 @ SY2912 ) @ ( c_Product__Type_OPair @ SY2912 @ SY2912 @ SV1011 @ SV851 ) @ SY2911 )
| ~ ( c_member @ ( tc_prod @ SY2912 @ SY2912 ) @ ( c_Product__Type_OPair @ SY2912 @ SY2912 @ SV851 @ SV1011 ) @ SY2911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3633,plain,
! [SV852: $i,SV1012: $i] :
( ( ! [SY2913: $i,SY2914: $i] :
( ~ ( c_Wellfounded_Owf @ SY2914 @ SY2913 )
| ~ ( c_member @ ( tc_prod @ SY2914 @ SY2914 ) @ ( c_Product__Type_OPair @ SY2914 @ SY2914 @ SV1012 @ SV852 ) @ SY2913 )
| ~ ( c_member @ ( tc_prod @ SY2914 @ SY2914 ) @ ( c_Product__Type_OPair @ SY2914 @ SY2914 @ SV852 @ SV1012 ) @ SY2913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3634,plain,
! [SV853: $i,SV1013: $i] :
( ( ! [SY2915: $i] :
( ~ ( c_Wellfounded_Owf @ SY2915 @ SV1013 )
| ~ ( c_member @ ( tc_prod @ SY2915 @ SY2915 ) @ ( c_Product__Type_OPair @ SY2915 @ SY2915 @ SV853 @ SV853 ) @ SV1013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(3635,plain,
! [SV854: $i,SV1014: $i] :
( ( ! [SY2916: $i] :
( ~ ( c_Wellfounded_Owf @ SY2916 @ SV1014 )
| ( c_member @ SY2916 @ SV854 @ ( c_Wellfounded_Oacc @ SY2916 @ SV1014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3636,plain,
! [SV855: $i,SV1015: $i] :
( ( ~ ( c_member @ SV1015 @ ( sK25_B_x @ SV1015 @ SV855 ) @ ( c_Wellfounded_Oacc @ SV1015 @ SV855 ) )
| ( c_Wellfounded_Owf @ SV1015 @ SV855 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(3637,plain,
! [SV856: $i,SV1016: $i] :
( ( ! [SY2917: $i,SY2918: $i,SY2919: $i,SY2920: $i] :
( ~ ( c_member @ SY2920 @ SY2919 @ SY2918 )
| ~ ( c_member @ ( tc_prod @ SY2920 @ SY2917 ) @ ( c_Product__Type_OPair @ SY2920 @ SY2917 @ SY2919 @ SV1016 ) @ SV856 )
| ( c_member @ SY2917 @ SV1016 @ ( c_Relation_OImage @ SY2920 @ SY2917 @ SV856 @ SY2918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3638,plain,
! [SV857: $i,SV1017: $i] :
( ( ! [SY2921: $i,SY2922: $i,SY2923: $i,SY2924: $i,SY2925: $i,SY2926: $i] :
( ~ ( c_member @ ( tc_prod @ SY2926 @ SY2925 ) @ ( c_Product__Type_OPair @ SY2926 @ SY2925 @ SY2924 @ SY2923 ) @ SY2922 )
| ~ ( c_member @ ( tc_prod @ SY2925 @ SY2921 ) @ ( c_Product__Type_OPair @ SY2925 @ SY2921 @ SY2923 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY2926 @ SY2921 ) @ ( c_Product__Type_OPair @ SY2926 @ SY2921 @ SY2924 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY2926 @ SY2925 @ SY2921 @ SY2922 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3639,plain,
! [SV858: $i,SV1018: $i] :
( ( ( ( hAPP @ SV1018 @ ( sK22_B_x @ SV1018 @ SV858 ) )
!= ( hAPP @ SV858 @ ( sK22_B_x @ SV1018 @ SV858 ) ) )
| ( SV1018 = SV858 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3640,plain,
! [SV859: $i,SV1019: $i] :
( ( ! [SY2927: $i,SY2928: $i,SY2929: $i,SY2930: $i,SY2931: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2931 @ SY2930 ) )
| ~ ( c_member @ ( tc_prod @ SY2929 @ SY2929 ) @ ( c_Product__Type_OPair @ SY2929 @ SY2929 @ SY2928 @ SY2927 ) @ ( hAPP @ SV1019 @ SY2930 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SY2929 ) @ ( tc_prod @ SV859 @ SY2929 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SY2929 ) @ ( tc_prod @ SV859 @ SY2929 ) @ ( c_Product__Type_OPair @ SV859 @ SY2929 @ SY2930 @ SY2928 ) @ ( c_Product__Type_OPair @ SV859 @ SY2929 @ SY2930 @ SY2927 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SY2929 @ SY2931 @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(3641,plain,
! [SV860: $i,SV1020: $i] :
( ( ( c_Relation_ORange @ SV1020 @ SV1020 @ ( c_Relation_OId__on @ SV1020 @ SV860 ) )
= SV860 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(3642,plain,
! [SV861: $i,SV1021: $i] :
( ( ( c_Relation_ODomain @ SV1021 @ SV1021 @ ( c_Relation_OId__on @ SV1021 @ SV861 ) )
= SV861 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(3643,plain,
! [SV862: $i,SV1022: $i] :
( ( c_Relation_Orefl__on @ SV1022 @ SV862 @ ( c_Relation_OId__on @ SV1022 @ SV862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(3644,plain,
! [SV863: $i,SV1023: $i] :
( ( ! [SY2932: $i,SY2933: $i,SY2934: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2934 @ ( c_Product__Type_OPair @ SY2933 @ SY2932 @ SV1023 @ SV863 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY2933 @ SY2932 @ tc_HOL_Obool @ SY2934 @ SV1023 @ SV863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3645,plain,
! [SV864: $i,SV1024: $i] :
( ( ! [SY2935: $i,SY2936: $i,SY2937: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY2937 @ SY2936 @ tc_HOL_Obool @ SY2935 @ SV1024 @ SV864 ) )
| ( hBOOL @ ( hAPP @ SY2935 @ ( c_Product__Type_OPair @ SY2937 @ SY2936 @ SV1024 @ SV864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3646,plain,
! [SV865: $i,SV1025: $i] :
( ( ! [SY2938: $i,SY2939: $i,SY2940: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY2940 @ SY2939 @ tc_HOL_Obool @ SY2938 @ SV1025 @ SV865 ) )
| ( hBOOL @ ( hAPP @ SY2938 @ ( c_Product__Type_OPair @ SY2940 @ SY2939 @ SV1025 @ SV865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(3647,plain,
! [SV866: $i,SV1026: $i] :
( ( c_Relation_Osingle__valued @ SV1026 @ SV1026 @ ( c_Relation_OId__on @ SV1026 @ SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(3648,plain,
! [SV867: $i,SV1027: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV1027 @ ( c_Transitive__Closure_Ortrancl @ SV1027 @ SV867 ) )
= ( c_Transitive__Closure_Ortrancl @ SV1027 @ SV867 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3649,plain,
! [SV868: $i,SV1028: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV1028 @ ( c_Transitive__Closure_Otrancl @ SV1028 @ SV868 ) )
= ( c_Transitive__Closure_Ortrancl @ SV1028 @ SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3650,plain,
! [SV869: $i,SV1029: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV1029 @ ( c_Transitive__Closure_Ortrancl @ SV1029 @ SV869 ) )
= ( c_Transitive__Closure_Ortrancl @ SV1029 @ SV869 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(3651,plain,
! [SV870: $i,SV1030: $i] :
( ( ( c_Relation_ODomain @ SV1030 @ SV1030 @ ( c_Transitive__Closure_Otrancl @ SV1030 @ SV870 ) )
= ( c_Relation_ODomain @ SV1030 @ SV1030 @ SV870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3652,plain,
! [SV871: $i,SV1031: $i] :
( ( ( c_Relation_ORange @ SV1031 @ SV1031 @ ( c_Transitive__Closure_Otrancl @ SV1031 @ SV871 ) )
= ( c_Relation_ORange @ SV1031 @ SV1031 @ SV871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(3653,plain,
! [SV873: $i,SV1032: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV1032 @ SV873 )
| ( c_Relation_Oantisym @ SV1032 @ ( c_Transitive__Closure_Ortrancl @ SV1032 @ SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3654,plain,
! [SV874: $i,SV1033: $i] :
( ( ! [SY2941: $i] :
( ( c_Set_Oinsert @ SY2941 @ SV1033 @ ( c_Set_Oinsert @ SY2941 @ SV1033 @ SV874 ) )
= ( c_Set_Oinsert @ SY2941 @ SV1033 @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(3655,plain,
! [SV875: $i,SV1034: $i] :
( ( ! [SY2942: $i,SY2943: $i] :
( ( c_Set_Oinsert @ SY2943 @ SY2942 @ ( c_Set_Oinsert @ SY2943 @ SV1034 @ SV875 ) )
= ( c_Set_Oinsert @ SY2943 @ SV1034 @ ( c_Set_Oinsert @ SY2943 @ SY2942 @ SV875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(3656,plain,
! [SV877: $i,SV1035: $i] :
( ( c_Relation_Oantisym @ SV1035 @ ( c_Relation_OId__on @ SV1035 @ SV877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(3657,plain,
! [SV878: $i,SV1036: $i] :
( ( ! [SY2944: $i,SY2945: $i] :
( ~ ( c_Wellfounded_Owf @ SY2945 @ SY2944 )
| ( c_Wellfounded_Owf @ SV1036 @ ( hAPP @ ( c_Relation_Oinv__image @ SY2945 @ SV1036 @ SY2944 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3658,plain,
! [SV879: $i,SV1037: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1037 @ SV879 )
| ( c_Wellfounded_Owf @ SV1037 @ ( c_Transitive__Closure_Otrancl @ SV1037 @ SV879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3659,plain,
! [SV880: $i,SV1038: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1038 @ SV880 )
| ( c_Wellfounded_Oacyclic @ SV1038 @ SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(3660,plain,
! [SV881: $i,SV1039: $i] :
( ( c_Wellfounded_Owf @ SV1039 @ ( hAPP @ ( c_Wellfounded_Omeasure @ SV1039 ) @ SV881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(3661,plain,
! [SV882: $i,SV1040: $i] :
( ( ! [SY2946: $i,SY2947: $i,SY2948: $i,SY2949: $i] :
( ( SY2949
!= ( c_Recdef_Owfrec @ SY2948 @ SY2947 @ SY2946 @ SV1040 ) )
| ~ ( c_Wellfounded_Owf @ SY2948 @ SY2946 )
| ( ( hAPP @ SY2949 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SY2948 @ SY2947 @ SY2949 @ SY2946 @ SV882 ) ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(3662,plain,
! [SV883: $i,SV1041: $i] :
( ( ! [SY2950: $i,SY2951: $i,SY2952: $i] :
( ~ ( c_Wellfounded_Owf @ SY2952 @ SY2951 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY2952 @ SY2950 @ SY2951 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SY2952 @ SY2950 @ ( c_Recdef_Owfrec @ SY2952 @ SY2950 @ SY2951 @ SV1041 ) @ SY2951 @ SV883 ) ) @ SV883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(3663,plain,
! [SV884: $i,SV1042: $i] :
( ( ! [SY2953: $i,SY2954: $i] :
( ~ ( c_Wellfounded_Owf @ SV1042 @ SY2954 )
| ! [SY2955: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SY2954 @ SY2953 ) @ SY2955 )
= ( hAPP @ ( hAPP @ SY2953 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SY2954 @ SY2953 ) @ SY2954 @ SY2955 ) ) @ SY2955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3664,plain,
! [SV886: $i,SV1043: $i] :
( ( ! [SY2956: $i] :
( ~ ( c_Wellfounded_Owf @ SY2956 @ SV1043 )
| ( c_Wellfounded_Owf @ SY2956 @ ( c_Wellfounded_Omlex__prod @ SY2956 @ SV886 @ SV1043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(3665,plain,
! [SV887: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV887 @ SV887 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3666,plain,
! [SV888: $i,SV1044: $i] :
( ( ( SV1044 = SV888 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1044 @ SV888 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV888 @ SV1044 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3667,plain,
! [SV889: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV889 @ SV889 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3668,plain,
! [SV890: $i,SV1045: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1045 @ SV890 )
| ( SV890 != SV1045 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(3669,plain,
! [SV891: $i,SV1046: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1046 @ SV891 )
| ( SV1046 != SV891 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(3670,plain,
! [SV893: $i,SV1047: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1047 @ SV893 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV893 @ SV1047 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(3671,plain,
! [SV894: $i,SV1048: $i] :
( ( ( SV1048 != SV894 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1048 @ SV894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(3672,plain,
! [SV895: $i,SV1049: $i] :
( ( ! [SY2957: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2957 @ SV1049 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SY2957 @ SV895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(3673,plain,
! [SV896: $i,SV1050: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1050 @ SV896 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SV1050 )
| ( SV1050 = SV896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3674,plain,
! [SV897: $i,SV1051: $i] :
( ( ! [SY2958: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY2958 @ SV1051 ) @ SV897 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SY2958 @ SV897 ) @ SV1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3675,plain,
! [SV898: $i,SV1052: $i] :
( ( ( c_Relation_OImage @ SV1052 @ SV1052 @ ( c_Relation_OId @ SV1052 ) @ SV898 )
= SV898 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(3676,plain,
! [SV899: $i,SV1053: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SV1053 ) @ SV899 ) )
| ( SV1053 = SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(3677,plain,
! [SV900: $i,SV1054: $i] :
( ( ( SV1054 != SV900 )
| ( hBOOL @ ( hAPP @ ( c_fequal @ SV1054 ) @ SV900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(3678,plain,
! [SV901: $i,SV1055: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK70_SY736 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) ) )
| ( c_Relation_Otrans @ SV1055 @ SV901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(3679,plain,
! [SV902: $i,SV1056: $i] :
( ( ! [SY2959: $i,SY2960: $i,SY2961: $i] :
( ~ ( c_member @ ( tc_prod @ SY2961 @ SY2961 ) @ ( c_Product__Type_OPair @ SY2961 @ SY2961 @ SY2960 @ SY2959 ) @ ( c_Transitive__Closure_Ortrancl @ SY2961 @ SV1056 ) )
| ~ ( hBOOL @ ( hAPP @ SV902 @ SY2959 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2961 @ SY2961 ) @ ( c_Product__Type_OPair @ SY2961 @ SY2961 @ ( sK12_B_y @ SY2961 @ SY2960 @ SY2959 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SY2961 @ SY2960 @ SY2959 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2961 @ SY2961 ) @ ( c_Product__Type_OPair @ SY2961 @ SY2961 @ ( sK13_SY707 @ SY2961 @ SY2960 @ SY2959 @ SV1056 @ SV902 ) @ SY2959 ) @ ( c_Transitive__Closure_Ortrancl @ SY2961 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SY2961 @ SY2960 @ SY2959 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SY2961 @ SY2960 @ SY2959 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SY2960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(3680,plain,
! [SV903: $i,SV1057: $i] :
( ( ~ ( ~ ! [SY2962: $i,SY2963: $i] :
( ( c_member @ SY2963 @ SY2962 @ SV1057 )
| ( c_member @ SY2963 @ SY2962 @ SV903 )
| ( ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV1057 )
!= ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV903 ) )
| ( SV1057 = SV903 ) )
| ~ ! [SY2964: $i,SY2965: $i] :
( ( c_member @ SY2965 @ SY2964 @ SV1057 )
| ( c_member @ SY2965 @ SY2964 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV1057 )
= ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV903 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(3681,plain,
! [SV904: $i,SV1058: $i] :
( ( ! [SY2966: $i,SY2967: $i,SY2968: $i,SY2969: $i,SY2970: $i,SY2971: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ SY2969 @ SY2968 ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ SY2967 @ SY2966 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2971 @ SY2970 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY2969 ) @ SY2968 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ SY2969 @ SY2968 ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ ( sK18_B_a @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY2971 @ SY2970 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2971 @ SY2970 ) @ ( tc_prod @ SY2971 @ SY2970 ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ ( sK18_B_a @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY2971 @ SY2970 @ ( sK20_SY717 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY2971 @ SY2970 @ SY2969 @ SY2968 @ SY2967 @ SY2966 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY2967 ) @ SY2966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(3682,plain,
! [SV905: $i] :
( ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2497 @ SY2497 ) @ ( c_Product__Type_OPair @ SY2497 @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ SY2496 ) @ SV905 )
| ~ ~ ( c_member @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ( c_member @ SY2497 @ SY2496 @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ~ ! [SY2498: $i,SY2499: $i] :
( ~ ( c_member @ SY2499 @ SY2498 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) )
| ! [SY2500: $i] :
( ~ ( c_member @ ( tc_prod @ SY2499 @ SY2499 ) @ ( c_Product__Type_OPair @ SY2499 @ SY2499 @ SY2500 @ SY2498 ) @ SV905 )
| ( c_member @ SY2499 @ SY2500 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3683,plain,
! [SV906: $i] :
( ( ~ ! [SY2501: $i,SY2502: $i] :
( ~ ( ~ ( c_member @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( c_member @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY2502 @ SY2501 @ SV906 )
!= ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY2502 @ SY2501 @ SV906 ) )
| ~ ! [SY2503: $i,SY2504: $i] :
( ~ ( c_Relation_Ototal__on @ SY2504 @ SY2503 @ SV906 )
| ! [SY2505: $i] :
( ~ ( c_member @ SY2504 @ SY2505 @ SY2503 )
| ! [SY2506: $i] :
( ~ ( c_member @ SY2504 @ SY2506 @ SY2503 )
| ( SY2505 = SY2506 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2505 @ SY2506 ) @ SV906 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2506 @ SY2505 ) @ SV906 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(3684,plain,
! [SV907: $i,SV1059: $i] :
( ( ! [SY2972: $i,SY2973: $i] :
~ ( ~ ( ! [SY2974: $i,SY2975: $i] :
( ( c_Product__Type_OPair @ SY2975 @ SY2974 @ SY2973 @ SY2972 )
!= ( c_Product__Type_OPair @ SY2975 @ SY2974 @ SV1059 @ SV907 ) )
| ( SY2973 = SV1059 ) )
| ~ ( ! [SY2976: $i,SY2977: $i] :
( ( c_Product__Type_OPair @ SY2977 @ SY2976 @ SY2973 @ SY2972 )
!= ( c_Product__Type_OPair @ SY2977 @ SY2976 @ SV1059 @ SV907 ) )
| ( SY2972 = SV907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(3685,plain,
! [SV908: $i,SV1060: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK26_B_x @ SV1060 @ SV908 ) @ ( sK27_SY720 @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) ) )
| ( c_Relation_Oantisym @ SV1060 @ SV908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(3686,plain,
! [SV909: $i] :
( ( ~ ! [SY2515: $i,SY2516: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2516 @ ( sK75_B_x1 @ SY2516 @ SY2515 @ SV909 ) ) )
| ! [SY2517: $i,SY2518: $i] : ( hBOOL @ ( hAPP @ SY2516 @ ( c_Product__Type_OPair @ SY2515 @ SV909 @ SY2517 @ SY2518 ) ) ) )
| ~ ! [SY2519: $i,SY2520: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2520 @ ( c_Product__Type_OPair @ SY2519 @ SV909 @ ( sK73_B_a @ SY2520 @ SY2519 @ SV909 ) @ ( sK74_SY739 @ SY2520 @ SY2519 @ SV909 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2520 @ SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3687,plain,
! [SV910: $i] :
( ( ~ ! [SY2522: $i,SY2523: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 )
!= ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2523 @ SY2522 @ SV910 ) )
| ~ ! [SY2524: $i,SY2525: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2525 @ SY2524 @ SV910 )
| ! [SY2526: $i,SY2527: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2527 ) @ SV910 )
| ! [SY2528: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2528 ) @ SV910 )
| ( SY2527 = SY2528 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3688,plain,
! [SV911: $i,SV1061: $i] :
( ( ! [SY2978: $i,SY2979: $i,SY2980: $i,SY2981: $i] :
~ ( ~ ~ ( ~ ! [SY2982: $i,SY2983: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2983 @ SY2982 ) @ ( tc_prod @ SY2983 @ SY2982 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2983 @ SY2982 ) @ ( tc_prod @ SY2983 @ SY2982 ) @ ( c_Product__Type_OPair @ SY2983 @ SY2982 @ SY2981 @ SY2980 ) @ ( c_Product__Type_OPair @ SY2983 @ SY2982 @ SY2979 @ SY2978 ) ) @ ( c_Wellfounded_Olex__prod @ SY2983 @ SY2982 @ SV1061 @ SV911 ) )
| ( SY2981 = SY2979 )
| ( c_member @ ( tc_prod @ SY2983 @ SY2983 ) @ ( c_Product__Type_OPair @ SY2983 @ SY2983 @ SY2981 @ SY2979 ) @ SV1061 ) )
| ~ ! [SY2984: $i,SY2985: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY2985 @ SY2984 ) @ ( tc_prod @ SY2985 @ SY2984 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2985 @ SY2984 ) @ ( tc_prod @ SY2985 @ SY2984 ) @ ( c_Product__Type_OPair @ SY2985 @ SY2984 @ SY2981 @ SY2980 ) @ ( c_Product__Type_OPair @ SY2985 @ SY2984 @ SY2979 @ SY2978 ) ) @ ( c_Wellfounded_Olex__prod @ SY2985 @ SY2984 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY2984 @ SY2984 ) @ ( c_Product__Type_OPair @ SY2984 @ SY2984 @ SY2980 @ SY2978 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY2985 @ SY2985 ) @ ( c_Product__Type_OPair @ SY2985 @ SY2985 @ SY2981 @ SY2979 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY2986: $i] :
( ( SY2981 != SY2979 )
| ~ ( c_member @ ( tc_prod @ SY2986 @ SY2986 ) @ ( c_Product__Type_OPair @ SY2986 @ SY2986 @ SY2980 @ SY2978 ) @ SV911 )
| ! [SY2987: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY2987 @ SY2986 ) @ ( tc_prod @ SY2987 @ SY2986 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2987 @ SY2986 ) @ ( tc_prod @ SY2987 @ SY2986 ) @ ( c_Product__Type_OPair @ SY2987 @ SY2986 @ SY2981 @ SY2980 ) @ ( c_Product__Type_OPair @ SY2987 @ SY2986 @ SY2979 @ SY2978 ) ) @ ( c_Wellfounded_Olex__prod @ SY2987 @ SY2986 @ SV1061 @ SV911 ) ) )
| ~ ! [SY2988: $i,SY2989: $i] :
( ~ ( c_member @ ( tc_prod @ SY2989 @ SY2989 ) @ ( c_Product__Type_OPair @ SY2989 @ SY2989 @ SY2981 @ SY2979 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY2989 @ SY2988 ) @ ( tc_prod @ SY2989 @ SY2988 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY2989 @ SY2988 ) @ ( tc_prod @ SY2989 @ SY2988 ) @ ( c_Product__Type_OPair @ SY2989 @ SY2988 @ SY2981 @ SY2980 ) @ ( c_Product__Type_OPair @ SY2989 @ SY2988 @ SY2979 @ SY2978 ) ) @ ( c_Wellfounded_Olex__prod @ SY2989 @ SY2988 @ SV1061 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(3689,plain,
! [SV912: $i,SV1062: $i] :
( ( ! [SY2990: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2990 @ SV1062 ) @ ( c_Product__Type_OPair @ SY2990 @ SV1062 @ ( sK48_B_x @ SY2990 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SY2990 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2990 @ SV1062 ) @ ( c_Product__Type_OPair @ SY2990 @ SV1062 @ ( sK48_B_x @ SY2990 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SY2990 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SY2990 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SY2990 @ SV1062 @ SV912 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2990 @ SV1062 @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(3690,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3524]) ).
thf(3691,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3524]) ).
thf(3692,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3693,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3694,plain,
! [SV913: $i] :
( ( ~ ! [SY2544: $i,SY2545: $i] :
( ~ ( c_Relation_Orefl__on @ SY2545 @ SY2544 @ SV913 )
| ~ ( c_Relation_Otrans @ SY2545 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SY2545 @ SY2544 @ SV913 ) )
| ~ ~ ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) )
| ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3526]) ).
thf(3695,plain,
! [SV1063: $i,SV914: $i] :
( ( ! [SY2991: $i] :
~ ( ~ ! [SY2992: $i,SY2993: $i] :
( ! [SY2994: $i] :
( ~ ( c_member @ SY2991 @ SY2994 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SY2991 @ SY2993 ) @ ( c_Product__Type_OPair @ SY2991 @ SY2993 @ SY2994 @ SY2992 ) @ SV1063 ) )
| ( c_member @ SY2993 @ SY2992 @ ( c_Relation_OImage @ SY2991 @ SY2993 @ SV1063 @ SV914 ) ) )
| ~ ! [SY2995: $i,SY2996: $i] :
( ~ ( c_member @ SY2996 @ SY2995 @ ( c_Relation_OImage @ SY2991 @ SY2996 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SY2991 @ ( sK24_B_x @ SY2996 @ SY2995 @ SY2991 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SY2991 @ SY2996 ) @ ( c_Product__Type_OPair @ SY2991 @ SY2996 @ ( sK24_B_x @ SY2996 @ SY2995 @ SY2991 @ SV1063 @ SV914 ) @ SY2995 ) @ SV1063 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3696,plain,
! [SV915: $i,SV1064: $i] :
( ( ! [SY2997: $i,SY2998: $i] :
( ~ ( c_member @ ( tc_prod @ SY2998 @ SY2998 ) @ ( c_Product__Type_OPair @ SY2998 @ SY2998 @ SY2997 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SY2998 @ SV915 ) )
| ( SY2997 = SV1064 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY2998 @ SY2998 ) @ ( c_Product__Type_OPair @ SY2998 @ SY2998 @ SY2997 @ ( sK45_B_y @ SY2998 @ SY2997 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY2998 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SY2998 @ SY2998 ) @ ( c_Product__Type_OPair @ SY2998 @ SY2998 @ ( sK45_B_y @ SY2998 @ SY2997 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(3697,plain,
! [SV916: $i] :
( ( ~ ! [SY2560: $i] :
( ( SY2560 != SV916 )
| ! [SY2561: $i] : ( c_member @ ( tc_prod @ SY2561 @ SY2561 ) @ ( c_Product__Type_OPair @ SY2561 @ SY2561 @ SY2560 @ SV916 ) @ ( c_Relation_OId @ SY2561 ) ) )
| ~ ! [SY2562: $i] :
( ! [SY2563: $i] :
~ ( c_member @ ( tc_prod @ SY2563 @ SY2563 ) @ ( c_Product__Type_OPair @ SY2563 @ SY2563 @ SY2562 @ SV916 ) @ ( c_Relation_OId @ SY2563 ) )
| ( SY2562 = SV916 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3698,plain,
! [SV917: $i,SV1065: $i] :
( ( ~ ( ~ ! [SY2999: $i,SY3000: $i] :
( ( SY3000 != SY2999 )
| ~ ( c_member @ SV1065 @ SY3000 @ SV917 )
| ( c_member @ SV1065 @ SY2999 @ SV917 ) )
| ~ ! [SY3001: $i,SY3002: $i] :
( ( SY3002 != SY3001 )
| ~ ( c_member @ SV1065 @ SY3001 @ SV917 )
| ( c_member @ SV1065 @ SY3002 @ SV917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(3699,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3531]) ).
thf(3700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3531]) ).
thf(3701,plain,
! [SV918: $i,SV1066: $i] :
( ( ! [SY3003: $i] :
~ ( ~ ! [SY3004: $i,SY3005: $i] :
( ~ ( c_member @ ( tc_prod @ SY3005 @ SY3004 ) @ ( c_Product__Type_OPair @ SY3005 @ SY3004 @ SV1066 @ SV918 ) @ SY3003 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3005 @ SY3004 @ SY3003 ) @ SV1066 ) @ SV918 ) ) )
| ~ ! [SY3006: $i,SY3007: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3007 @ SY3006 @ SY3003 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3007 @ SY3006 ) @ ( c_Product__Type_OPair @ SY3007 @ SY3006 @ SV1066 @ SV918 ) @ SY3003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(3702,plain,
! [SV919: $i,SV1067: $i] :
( ( ! [SY3008: $i,SY3009: $i] :
~ ( ~ ! [SY3010: $i,SY3011: $i] :
( ! [SY3012: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3011 @ SY3011 ) @ ( c_Product__Type_OPair @ SY3011 @ SY3011 @ ( sK60_B_z @ SY3012 @ SY3011 @ SY3010 @ SY3009 @ SY3008 @ SV1067 @ SV919 ) @ SV1067 ) @ SY3009 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3011 @ SY3010 @ SY3009 @ SY3008 @ ( sK60_B_z @ SY3012 @ SY3011 @ SY3010 @ SY3009 @ SY3008 @ SV1067 @ SV919 ) @ ( hAPP @ SY3012 @ ( sK60_B_z @ SY3012 @ SY3011 @ SY3010 @ SY3009 @ SY3008 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SY3008 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SY3008 @ SY3012 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3011 @ SY3010 @ SY3009 @ SY3008 @ SV1067 @ ( hAPP @ ( hAPP @ SY3008 @ SV919 ) @ SV1067 ) ) )
| ~ ! [SY3013: $i,SY3014: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3014 @ SY3013 @ SY3009 @ SY3008 @ SV1067 @ ( hAPP @ ( hAPP @ SY3008 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3015: $i] :
( ~ ( c_member @ ( tc_prod @ SY3014 @ SY3014 ) @ ( c_Product__Type_OPair @ SY3014 @ SY3014 @ SY3015 @ SV1067 ) @ SY3009 )
| ( c_Recdef_Owfrec__rel @ SY3014 @ SY3013 @ SY3009 @ SY3008 @ SY3015 @ ( hAPP @ ( sK59_B_g @ SY3014 @ SY3013 @ SY3009 @ SY3008 @ SV1067 @ SV919 ) @ SY3015 ) ) )
| ( ( hAPP @ ( hAPP @ SY3008 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SY3008 @ ( sK59_B_g @ SY3014 @ SY3013 @ SY3009 @ SY3008 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3703,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
| ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
| ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3704,plain,
! [SV921: $i,SV1068: $i] :
( ( ! [SY3016: $i,SY3017: $i] :
~ ( ~ ! [SY3018: $i] :
( ! [SY3019: $i] :
~ ( c_member @ ( tc_prod @ SY3019 @ SY3019 ) @ ( c_Product__Type_OPair @ SY3019 @ SY3019 @ SY3018 @ SY3017 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY3016 @ SY3019 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SY3016 @ SY3016 ) @ ( c_Product__Type_OPair @ SY3016 @ SY3016 @ ( hAPP @ SV921 @ SY3018 ) @ ( hAPP @ SV921 @ SY3017 ) ) @ SV1068 ) )
| ~ ! [SY3020: $i] :
( ~ ( c_member @ ( tc_prod @ SY3016 @ SY3016 ) @ ( c_Product__Type_OPair @ SY3016 @ SY3016 @ ( hAPP @ SV921 @ SY3020 ) @ ( hAPP @ SV921 @ SY3017 ) ) @ SV1068 )
| ! [SY3021: $i] : ( c_member @ ( tc_prod @ SY3021 @ SY3021 ) @ ( c_Product__Type_OPair @ SY3021 @ SY3021 @ SY3020 @ SY3017 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SY3016 @ SY3021 @ SV1068 ) @ SV921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3705,plain,
! [SV922: $i] :
( ( ~ ! [SY2607: $i] :
( ( SY2607 != SV922 )
| ! [SY2608: $i] : ( c_member @ SY2608 @ SY2607 @ ( c_fequal @ SV922 ) ) )
| ~ ! [SY2609: $i] :
( ! [SY2610: $i] :
~ ( c_member @ SY2610 @ SY2609 @ ( c_fequal @ SV922 ) )
| ( SY2609 = SV922 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3706,plain,
! [SV923: $i,SV1069: $i] :
( ( ! [SY3022: $i,SY3023: $i] :
( ~ ( c_member @ ( tc_prod @ SY3023 @ SY3023 ) @ ( c_Product__Type_OPair @ SY3023 @ SY3023 @ SY3022 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SY3023 @ SV923 ) )
| ( SY3022 = SV1069 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3023 @ SY3023 ) @ ( c_Product__Type_OPair @ SY3023 @ SY3023 @ SY3022 @ ( sK44_B_y @ SY3023 @ SY3022 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SY3023 @ SY3023 ) @ ( c_Product__Type_OPair @ SY3023 @ SY3023 @ ( sK44_B_y @ SY3023 @ SY3022 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SY3023 @ SV923 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3707,plain,
! [SV924: $i,SV1070: $i] :
( ( ! [SY3024: $i,SY3025: $i] :
( ~ ( c_member @ ( tc_prod @ SY3025 @ SY3025 ) @ ( c_Product__Type_OPair @ SY3025 @ SY3025 @ SY3024 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SY3025 @ SV924 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3025 @ SY3025 ) @ ( c_Product__Type_OPair @ SY3025 @ SY3025 @ SY3024 @ ( sK41_B_z @ SY3025 @ SY3024 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SY3025 @ SY3025 ) @ ( c_Product__Type_OPair @ SY3025 @ SY3025 @ ( sK41_B_z @ SY3025 @ SY3024 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SY3025 @ SV924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(3708,plain,
! [SV925: $i,SV1071: $i] :
( ( ! [SY3026: $i] :
( ~ ( c_member @ ( tc_prod @ SY3026 @ SY3026 ) @ SV1071 @ ( c_Relation_OId__on @ SY3026 @ SV925 ) )
| ~ ( ~ ( c_member @ SY3026 @ ( sK64_B_x @ SY3026 @ SV1071 @ SV925 ) @ SV925 )
| ( SV1071
!= ( c_Product__Type_OPair @ SY3026 @ SY3026 @ ( sK64_B_x @ SY3026 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SY3026 @ SV1071 @ SV925 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3709,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3711,plain,
! [SV926: $i,SV1072: $i] :
( ( ~ ( ~ ! [SY3027: $i,SY3028: $i] :
( ! [SY3029: $i] :
~ ( c_member @ ( tc_prod @ SY3028 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3028 @ SV1072 @ SY3027 @ SY3029 ) @ SV926 )
| ( c_member @ SY3028 @ SY3027 @ ( c_Relation_ODomain @ SY3028 @ SV1072 @ SV926 ) ) )
| ~ ! [SY3030: $i,SY3031: $i] :
( ~ ( c_member @ SY3031 @ SY3030 @ ( c_Relation_ODomain @ SY3031 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY3031 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3031 @ SV1072 @ SY3030 @ ( sK66_B_y @ SY3031 @ SY3030 @ SV1072 @ SV926 ) ) @ SV926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(3712,plain,
! [SV927: $i,SV1073: $i] :
( ( ~ ( ~ ! [SY3032: $i,SY3033: $i] :
( ( c_member @ SY3033 @ SY3032 @ ( c_Relation_ODomain @ SY3033 @ SY3033 @ SV1073 ) )
| ( SY3032 != SV927 )
| ( c_member @ ( tc_prod @ SY3033 @ SY3033 ) @ ( c_Product__Type_OPair @ SY3033 @ SY3033 @ SY3032 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3033 @ SV1073 ) ) )
| ~ ! [SY3034: $i,SY3035: $i] :
( ( c_member @ SY3035 @ SY3034 @ ( c_Relation_ODomain @ SY3035 @ SY3035 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SY3035 @ SY3035 ) @ ( c_Product__Type_OPair @ SY3035 @ SY3035 @ SY3034 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3035 @ SV1073 ) )
| ( SY3034 = SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(3713,plain,
! [SV928: $i,SV1074: $i] :
( ( ~ ( ~ ! [SY3036: $i] :
( ! [SY3037: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3037 @ SY3036 @ SV1074 ) @ SV928 ) )
| ( SY3036 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
| ~ ~ ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(3714,plain,
! [SV929: $i,SV1075: $i] :
( ( ! [SY3042: $i,SY3043: $i,SY3044: $i,SY3045: $i,SY3046: $i,SY3047: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ SY3045 @ SY3044 ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ SY3043 @ SY3042 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3047 @ SY3046 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3043 ) @ SY3042 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ ( sK14_B_a @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ ( sK16_SY711 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3047 @ SY3046 ) @ ( tc_prod @ SY3047 @ SY3046 ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ ( sK16_SY711 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3047 @ SY3046 @ SY3043 @ SY3042 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3047 @ SY3046 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3047 @ SY3046 @ SY3045 @ SY3044 @ SY3043 @ SY3042 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3045 ) @ SY3044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(3715,plain,
! [SV1076: $i,SV930: $i] :
( ( ~ ( ~ ! [SY3048: $i,SY3049: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3049 @ SV930 )
| ( c_member @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SV1076 @ SY3048 ) @ ( c_Transitive__Closure_Ortrancl @ SY3049 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3049 @ ( c_Set_Oinsert @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SY3048 @ SV1076 ) @ SV930 ) ) )
| ~ ~ ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) )
| ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(3716,plain,
! [SV931: $i,SV1077: $i] :
( ( ~ ( ~ ! [SY3054: $i,SY3055: $i] :
( ! [SY3056: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SY3055 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3055 @ SY3056 @ SY3054 ) @ SV931 )
| ( c_member @ SY3055 @ SY3054 @ ( c_Relation_ORange @ SV1077 @ SY3055 @ SV931 ) ) )
| ~ ! [SY3057: $i,SY3058: $i] :
( ~ ( c_member @ SY3058 @ SY3057 @ ( c_Relation_ORange @ SV1077 @ SY3058 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SY3058 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3058 @ ( sK65_B_y @ SY3058 @ SY3057 @ SV1077 @ SV931 ) @ SY3057 ) @ SV931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(3717,plain,
! [SV932: $i,SV1078: $i] :
( ( ! [SY3059: $i,SY3060: $i,SY3061: $i,SY3062: $i,SY3063: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3061 @ SY3060 ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3059 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3063 @ SY3062 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3061 @ SY3060 )
= ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3059 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3061 @ SY3060 ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ ( sK46_B_a @ SY3063 @ SY3062 @ SY3061 @ SY3060 @ SY3059 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3063 @ SY3062 @ SY3061 @ SY3060 @ SY3059 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3063 @ SY3062 ) @ ( tc_prod @ SY3063 @ SY3062 ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ ( sK46_B_a @ SY3063 @ SY3062 @ SY3061 @ SY3060 @ SY3059 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3063 @ SY3062 @ SY3061 @ SY3060 @ SY3059 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY3063 @ SY3062 @ SY3059 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3063 @ SY3062 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3719,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3720,plain,
! [SV933: $i,SV1079: $i] :
( ( ! [SY3064: $i,SY3065: $i] :
~ ( ~ ! [SY3066: $i,SY3067: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3067 @ SY3067 ) @ ( c_Product__Type_OPair @ SY3067 @ SY3067 @ ( sK43_B_y @ SY3067 @ SY3066 @ SY3065 @ SY3064 @ SV1079 @ SV933 ) @ SV1079 ) @ SY3064 )
| ~ ( ( ( hAPP @ SY3065 @ ( sK43_B_y @ SY3067 @ SY3066 @ SY3065 @ SY3064 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3067 @ SY3066 @ SY3065 @ SY3064 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3067 @ SY3066 @ SY3065 @ SY3064 @ SV1079 )
= ( c_Recdef_Ocut @ SY3067 @ SY3066 @ SV933 @ SY3064 @ SV1079 ) ) )
| ~ ! [SY3068: $i,SY3069: $i] :
( ( ( c_Recdef_Ocut @ SY3069 @ SY3068 @ SY3065 @ SY3064 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3069 @ SY3068 @ SV933 @ SY3064 @ SV1079 ) )
| ! [SY3070: $i] :
( ~ ( c_member @ ( tc_prod @ SY3069 @ SY3069 ) @ ( c_Product__Type_OPair @ SY3069 @ SY3069 @ SY3070 @ SV1079 ) @ SY3064 )
| ( ( hAPP @ SY3065 @ SY3070 )
= ( hAPP @ SV933 @ SY3070 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(3721,plain,
! [SV934: $i,SV1080: $i] :
( ( ~ ( ~ ! [SY3071: $i,SY3072: $i] :
( ( SY3072 != SY3071 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3072 )
| ( c_member @ SV1080 @ SV934 @ SY3071 ) )
| ~ ! [SY3073: $i,SY3074: $i] :
( ( SY3074 != SY3073 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3073 )
| ( c_member @ SV1080 @ SV934 @ SY3074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3722,plain,
! [SV935: $i,SV1081: $i] :
( ( ! [SY3075: $i,SY3076: $i] :
( ~ ( c_member @ ( tc_prod @ SY3076 @ SY3076 ) @ ( c_Product__Type_OPair @ SY3076 @ SY3076 @ SY3075 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SY3076 @ SV935 ) )
| ( c_member @ ( tc_prod @ SY3076 @ SY3076 ) @ ( c_Product__Type_OPair @ SY3076 @ SY3076 @ SY3075 @ SV1081 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3076 @ SY3076 ) @ ( c_Product__Type_OPair @ SY3076 @ SY3076 @ SY3075 @ ( sK37_B_c @ SY3076 @ SY3075 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SY3076 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SY3076 @ SY3076 ) @ ( c_Product__Type_OPair @ SY3076 @ SY3076 @ ( sK37_B_c @ SY3076 @ SY3075 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(3723,plain,
! [SV936: $i,SV1082: $i] :
( ( ! [SY3077: $i,SY3078: $i] :
~ ( ~ ( ( SY3078 != SV1082 )
| ( SY3077 != SV936 )
| ! [SY3079: $i,SY3080: $i] :
( ( c_Product__Type_OPair @ SY3080 @ SY3079 @ SY3078 @ SY3077 )
= ( c_Product__Type_OPair @ SY3080 @ SY3079 @ SV1082 @ SV936 ) ) )
| ~ ~ ( ~ ( ! [SY3081: $i,SY3082: $i] :
( ( c_Product__Type_OPair @ SY3082 @ SY3081 @ SY3078 @ SY3077 )
!= ( c_Product__Type_OPair @ SY3082 @ SY3081 @ SV1082 @ SV936 ) )
| ( SY3078 = SV1082 ) )
| ~ ( ! [SY3083: $i,SY3084: $i] :
( ( c_Product__Type_OPair @ SY3084 @ SY3083 @ SY3078 @ SY3077 )
!= ( c_Product__Type_OPair @ SY3084 @ SY3083 @ SV1082 @ SV936 ) )
| ( SY3077 = SV936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(3724,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) )
| ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) )
| ~ ~ ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) )
| ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(3725,plain,
! [SV938: $i,SV1084: $i] :
( ( ! [SY3093: $i,SY3094: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY3094 @ ( sK9_B_x @ SY3094 @ SY3093 @ SV1084 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SY3093 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SY3094 @ SY3093 @ SV1084 @ SV938 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SY3093 ) @ ( c_Recdef_Osame__fst @ SV938 @ SY3093 @ SY3094 @ SV1084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3726,plain,
! [SV939: $i] :
( ( ~ ! [SY2700: $i] :
( ! [SY2701: $i] :
~ ( c_member @ SY2701 @ SY2700 @ SV939 )
| ( hBOOL @ ( hAPP @ SV939 @ SY2700 ) ) )
| ~ ! [SY2702: $i] :
( ~ ( hBOOL @ ( hAPP @ SV939 @ SY2702 ) )
| ! [SY2703: $i] : ( c_member @ SY2703 @ SY2702 @ SV939 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3727,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ( ~ ! [SY3095: $i,SY3096: $i] :
( ( SY3095 != SV1085 )
| ~ ( c_member @ SY3096 @ SY3095 @ SV940 )
| ( c_member @ ( tc_prod @ SY3096 @ SY3096 ) @ ( c_Product__Type_OPair @ SY3096 @ SY3096 @ SY3095 @ SV1085 ) @ ( c_Relation_OId__on @ SY3096 @ SV940 ) ) )
| ~ ~ ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) )
| ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(3728,plain,
! [SV941: $i,SV1086: $i] :
( ( ! [SY3101: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3101 @ SY3101 ) @ ( c_Product__Type_OPair @ SY3101 @ SY3101 @ ( sK57_B_y @ SY3101 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 )
| ~ ~ ( c_member @ SY3101 @ ( sK57_B_y @ SY3101 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SY3101 @ SV941 ) ) )
| ( c_member @ SY3101 @ SV1086 @ ( c_Wellfounded_Oacc @ SY3101 @ SV941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(3729,plain,
! [SV942: $i,SV1087: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ~ ( c_member @ ( tc_prod @ SY3103 @ SY3103 ) @ ( c_Product__Type_OPair @ SY3103 @ SY3103 @ SY3102 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SY3103 @ SV942 ) )
| ( c_member @ ( tc_prod @ SY3103 @ SY3103 ) @ ( c_Product__Type_OPair @ SY3103 @ SY3103 @ SY3102 @ SV1087 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3103 @ SY3103 ) @ ( c_Product__Type_OPair @ SY3103 @ SY3103 @ SY3102 @ ( sK38_B_y @ SY3103 @ SY3102 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SY3103 @ SY3103 ) @ ( c_Product__Type_OPair @ SY3103 @ SY3103 @ ( sK38_B_y @ SY3103 @ SY3102 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SY3103 @ SV942 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(3730,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) )
| ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) )
| ~ ~ ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) )
| ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(3731,plain,
! [SV944: $i,SV1089: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ~ ( c_member @ ( tc_prod @ SY3113 @ SY3113 ) @ ( c_Product__Type_OPair @ SY3113 @ SY3113 @ SY3112 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SY3113 @ SV944 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3113 @ SY3113 ) @ ( c_Product__Type_OPair @ SY3113 @ SY3113 @ SY3112 @ ( sK42_B_z @ SY3113 @ SY3112 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3113 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SY3113 @ SY3113 ) @ ( c_Product__Type_OPair @ SY3113 @ SY3113 @ ( sK42_B_z @ SY3113 @ SY3112 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(3732,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3733,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3734,plain,
! [SV945: $i,SV1090: $i] :
( ( ! [SY3114: $i,SY3115: $i,SY3116: $i,SY3117: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3117 @ SY3117 ) @ ( c_Product__Type_OPair @ SY3117 @ SY3117 @ ( sK56_B_z @ SY3117 @ SY3116 @ SY3115 @ SY3114 @ SV1090 @ SV945 ) @ SY3116 ) @ SY3115 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3117 @ SY3114 @ SY3115 @ SV1090 @ ( sK56_B_z @ SY3117 @ SY3116 @ SY3115 @ SY3114 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SY3117 @ SY3116 @ SY3115 @ SY3114 @ SV1090 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY3117 @ SY3114 @ SY3115 @ SV1090 @ SY3116 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SY3116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3735,plain,
! [SV946: $i] :
( ( ~ ! [SY2733: $i,SY2734: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2734 @ SY2733 @ SV946 )
| ~ ( c_Relation_Oantisym @ SY2734 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SY2734 @ SY2733 @ SV946 ) )
| ~ ~ ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) )
| ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3736,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3737,plain,
( ( ~ ~ ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3738,plain,
! [SV947: $i] :
( ( ~ ! [SY2739: $i,SY2740: $i] :
( ~ ( c_Relation_Oirrefl @ SY2740 @ SV947 )
| ~ ( c_Relation_Otrans @ SY2740 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SY2740 @ SY2739 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY2740 @ SY2739 @ SV947 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
| ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3739,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ( ~ ! [SY3118: $i,SY3119: $i] :
( ~ ( c_member @ SY3119 @ SY3118 @ ( c_Set_Oinsert @ SY3119 @ SV1091 @ SV948 ) )
| ( SY3118 = SV1091 )
| ( c_member @ SY3119 @ SY3118 @ SV948 ) )
| ~ ~ ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) )
| ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(3740,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3567]) ).
thf(3741,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3567]) ).
thf(3742,plain,
! [SV949: $i,SV1092: $i] :
( ( ! [SY3124: $i,SY3125: $i] :
~ ( ~ ! [SY3126: $i,SY3127: $i] :
( ! [SY3128: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3127 @ SY3127 ) @ ( c_Product__Type_OPair @ SY3127 @ SY3127 @ ( sK55_B_z @ SY3128 @ SY3127 @ SY3126 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) @ SV1092 ) @ SY3125 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3127 @ SY3126 @ SY3125 @ SY3124 @ ( sK55_B_z @ SY3128 @ SY3127 @ SY3126 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) @ ( hAPP @ SY3128 @ ( sK55_B_z @ SY3128 @ SY3127 @ SY3126 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SY3124 @ SY3128 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3127 @ SY3126 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) )
| ~ ! [SY3129: $i,SY3130: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3130 @ SY3129 @ SY3125 @ SY3124 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3131: $i] :
( ~ ( c_member @ ( tc_prod @ SY3130 @ SY3130 ) @ ( c_Product__Type_OPair @ SY3130 @ SY3130 @ SY3131 @ SV1092 ) @ SY3125 )
| ( c_Recdef_Owfrec__rel @ SY3130 @ SY3129 @ SY3125 @ SY3124 @ SY3131 @ ( hAPP @ ( sK54_B_g @ SY3130 @ SY3129 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) @ SY3131 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SY3124 @ ( sK54_B_g @ SY3130 @ SY3129 @ SY3125 @ SY3124 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(3743,plain,
! [SV950: $i,SV1093: $i] :
( ( ~ ( ~ ! [SY3132: $i,SY3133: $i] :
( ~ ( c_member @ SY3133 @ SY3132 @ SV1093 )
| ( c_member @ SY3133 @ SY3132 @ ( c_Set_Oinsert @ SY3133 @ SV950 @ SV1093 ) ) )
| ~ ! [SY3134: $i] :
( ( SY3134 != SV950 )
| ! [SY3135: $i] : ( c_member @ SY3135 @ SY3134 @ ( c_Set_Oinsert @ SY3135 @ SV950 @ SV1093 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3744,plain,
! [SV951: $i,SV1094: $i] :
( ( ! [SY3136: $i,SY3137: $i,SY3138: $i] :
( ~ ( c_member @ ( tc_prod @ SY3138 @ SY3138 ) @ ( c_Product__Type_OPair @ SY3138 @ SY3138 @ SY3137 @ SY3136 ) @ ( c_Transitive__Closure_Ortrancl @ SY3138 @ SV1094 ) )
| ~ ( hBOOL @ ( hAPP @ SV951 @ SY3137 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3138 @ SY3138 ) @ ( c_Product__Type_OPair @ SY3138 @ SY3138 @ SY3137 @ ( sK10_B_y @ SY3138 @ SY3137 @ SY3136 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3138 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3138 @ SY3138 ) @ ( c_Product__Type_OPair @ SY3138 @ SY3138 @ ( sK10_B_y @ SY3138 @ SY3137 @ SY3136 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SY3138 @ SY3137 @ SY3136 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SY3138 @ SY3137 @ SY3136 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SY3138 @ SY3137 @ SY3136 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SY3136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(3745,plain,
! [SV952: $i,SV1095: $i] :
( ( ~ ( ~ ! [SY3139: $i] :
( ! [SY3140: $i] :
~ ( c_member @ ( tc_prod @ SY3140 @ SY3140 ) @ ( c_Product__Type_OPair @ SY3140 @ SY3140 @ SY3139 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3140 @ SV952 ) )
| ( SY3139 != SV1095 )
| ( SY3139 = SV1095 ) )
| ~ ! [SY3141: $i,SY3142: $i] :
( ~ ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3142 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SY3142 @ SV952 ) )
| ( SY3141 = SV1095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(3746,plain,
! [SV953: $i,SV1096: $i] :
( ( ! [SY3143: $i,SY3144: $i,SY3145: $i] :
( ~ ( c_member @ SY3145 @ SY3144 @ ( c_Relation_OImage @ SY3143 @ SY3145 @ SV1096 @ SV953 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3143 @ SY3145 ) @ ( c_Product__Type_OPair @ SY3143 @ SY3145 @ ( sK23_B_x @ SY3145 @ SY3144 @ SY3143 @ SV1096 @ SV953 ) @ SY3144 ) @ SV1096 )
| ~ ( c_member @ SY3143 @ ( sK23_B_x @ SY3145 @ SY3144 @ SY3143 @ SV1096 @ SV953 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(3747,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3748,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3749,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3750,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3751,plain,
! [SV954: $i,SV1097: $i] :
( ( ! [SY3146: $i] :
( ( c_member @ SY3146 @ SV1097 @ ( c_Wellfounded_Oacc @ SY3146 @ SV954 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3146 @ SY3146 ) @ ( c_Product__Type_OPair @ SY3146 @ SY3146 @ ( sK58_B_z @ SY3146 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 )
| ~ ~ ( c_member @ SY3146 @ ( sK58_B_z @ SY3146 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SY3146 @ SV954 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(3752,plain,
! [SV1098: $i,SV955: $i] :
( ( ~ ( ~ ! [SY3147: $i,SY3148: $i] :
( ~ ( c_Wellfounded_Owf @ SY3148 @ SV955 )
| ( c_member @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SV1098 @ SY3147 ) @ ( c_Transitive__Closure_Ortrancl @ SY3148 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3148 @ ( c_Set_Oinsert @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SY3147 @ SV1098 ) @ SV955 ) ) )
| ~ ~ ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) )
| ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(3753,plain,
! [SV795: $i,SV956: $i,SV1099: $i] :
( ( ! [SY3153: $i,SY3154: $i] :
( ~ ( c_Relation_Otrans @ SY3154 @ SY3153 )
| ~ ( c_member @ ( tc_prod @ SY3154 @ SY3154 ) @ ( c_Product__Type_OPair @ SY3154 @ SY3154 @ SV1099 @ SV956 ) @ SY3153 )
| ~ ( c_member @ ( tc_prod @ SY3154 @ SY3154 ) @ ( c_Product__Type_OPair @ SY3154 @ SY3154 @ SV956 @ SV795 ) @ SY3153 )
| ( c_member @ ( tc_prod @ SY3154 @ SY3154 ) @ ( c_Product__Type_OPair @ SY3154 @ SY3154 @ SV1099 @ SV795 ) @ SY3153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(3754,plain,
! [SV796: $i,SV957: $i,SV1100: $i] :
( ( ! [SY3155: $i] :
( ( SY3155 != SV1100 )
| ~ ( c_member @ SV957 @ SV1100 @ SV796 )
| ( c_member @ SV957 @ SY3155 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(3755,plain,
! [SV797: $i,SV958: $i,SV1101: $i] :
( ( ! [SY3156: $i,SY3157: $i,SY3158: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY3158 @ SY3157 @ SY3156 @ SV1101 @ ( c_Product__Type_OPair @ SY3158 @ SY3157 @ SV958 @ SV797 ) )
= ( hAPP @ ( hAPP @ SV1101 @ SV958 ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(3756,plain,
! [SV798: $i,SV959: $i,SV1102: $i] :
( ( ! [SY3159: $i,SY3160: $i,SY3161: $i] :
( ( c_Product__Type_Ointernal__split @ SY3161 @ SY3160 @ SY3159 @ SV1102 @ ( c_Product__Type_OPair @ SY3161 @ SY3160 @ SV959 @ SV798 ) )
= ( hAPP @ ( hAPP @ SV1102 @ SV959 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(3757,plain,
! [SV799: $i,SV960: $i,SV1103: $i] :
( ( ! [SY3162: $i,SY3163: $i] :
( ~ ( c_member @ ( tc_prod @ SY3163 @ SY3162 ) @ ( c_Product__Type_OPair @ SY3163 @ SY3162 @ SV1103 @ SV960 ) @ SV799 )
| ( c_member @ SY3162 @ SV960 @ ( c_Relation_ORange @ SY3163 @ SY3162 @ SV799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(3758,plain,
! [SV800: $i,SV961: $i,SV1104: $i] :
( ( ! [SY3164: $i] :
( ( SY3164 != SV1104 )
| ~ ( c_member @ SV961 @ SY3164 @ SV800 )
| ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SY3164 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(3759,plain,
! [SV801: $i,SV962: $i,SV1105: $i] :
( ( ! [SY3165: $i,SY3166: $i] :
( ~ ( c_member @ ( tc_prod @ SY3166 @ SY3165 ) @ ( c_Product__Type_OPair @ SY3166 @ SY3165 @ SV1105 @ SV962 ) @ SV801 )
| ( c_member @ SY3166 @ SV1105 @ ( c_Relation_ODomain @ SY3166 @ SY3165 @ SV801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(3760,plain,
! [SV802: $i,SV963: $i,SV1106: $i] :
( ( ! [SY3167: $i] :
( ~ ( c_Relation_Otrans @ SY3167 @ SV1106 )
| ~ ( c_Relation_Otrans @ SV963 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SY3167 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SY3167 @ SV963 @ SV1106 @ SV802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(3761,plain,
! [SV804: $i,SV965: $i,SV1107: $i] :
( ( ! [SY3168: $i] :
( ~ ( c_Relation_Otrans @ SY3168 @ SV1107 )
| ( c_Relation_Otrans @ SV965 @ ( hAPP @ ( c_Relation_Oinv__image @ SY3168 @ SV965 @ SV1107 ) @ SV804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3762,plain,
! [SV805: $i,SV966: $i,SV1108: $i] :
( ( ! [SY3169: $i] :
( ~ ( c_member @ SY3169 @ SV1108 @ ( c_Relation_ORange @ SV966 @ SY3169 @ SV805 ) )
| ( c_member @ ( tc_prod @ SV966 @ SY3169 ) @ ( c_Product__Type_OPair @ SV966 @ SY3169 @ ( sK63_B_x @ SY3169 @ SV1108 @ SV966 @ SV805 ) @ SV1108 ) @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(3763,plain,
! [SV806: $i,SV967: $i,SV1109: $i] :
( ( ! [SY3170: $i] :
( ~ ( c_member @ SY3170 @ SV1109 @ ( c_Relation_ODomain @ SY3170 @ SV967 @ SV806 ) )
| ( c_member @ ( tc_prod @ SY3170 @ SV967 ) @ ( c_Product__Type_OPair @ SY3170 @ SV967 @ SV1109 @ ( sK62_B_y @ SY3170 @ SV1109 @ SV967 @ SV806 ) ) @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(3764,plain,
! [SV807: $i,SV968: $i,SV1110: $i] :
( ( ! [SY3171: $i] :
( ~ ( c_member @ SY3171 @ SV1110 @ ( c_Wellfounded_Oacc @ SY3171 @ SV968 ) )
| ~ ( c_member @ ( tc_prod @ SY3171 @ SY3171 ) @ ( c_Product__Type_OPair @ SY3171 @ SY3171 @ SV807 @ SV1110 ) @ SV968 )
| ( c_member @ SY3171 @ SV807 @ ( c_Wellfounded_Oacc @ SY3171 @ SV968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(3765,plain,
! [SV808: $i,SV969: $i,SV1111: $i] :
( ( ! [SY3172: $i] :
( ~ ( c_Relation_Orefl__on @ SY3172 @ SV1111 @ SV969 )
| ~ ( c_member @ SY3172 @ SV808 @ SV1111 )
| ( c_member @ ( tc_prod @ SY3172 @ SY3172 ) @ ( c_Product__Type_OPair @ SY3172 @ SY3172 @ SV808 @ SV808 ) @ SV969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(3766,plain,
! [SV809: $i,SV970: $i,SV1112: $i] :
( ( ! [SY3173: $i,SY3174: $i] :
( ~ ( c_Relation_Orefl__on @ SY3174 @ SY3173 @ SV1112 )
| ~ ( c_member @ ( tc_prod @ SY3174 @ SY3174 ) @ ( c_Product__Type_OPair @ SY3174 @ SY3174 @ SV970 @ SV809 ) @ SV1112 )
| ( c_member @ SY3174 @ SV970 @ SY3173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(3767,plain,
! [SV810: $i,SV971: $i,SV1113: $i] :
( ( ! [SY3175: $i,SY3176: $i] :
( ~ ( c_Relation_Orefl__on @ SY3176 @ SY3175 @ SV1113 )
| ~ ( c_member @ ( tc_prod @ SY3176 @ SY3176 ) @ ( c_Product__Type_OPair @ SY3176 @ SY3176 @ SV971 @ SV810 ) @ SV1113 )
| ( c_member @ SY3176 @ SV810 @ SY3175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(3768,plain,
! [SV811: $i,SV972: $i,SV1114: $i] :
( ( ! [SY3177: $i] :
( ~ ( c_member @ ( tc_prod @ SY3177 @ SY3177 ) @ ( c_Product__Type_OPair @ SY3177 @ SY3177 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SY3177 @ SV811 ) )
| ~ ( c_member @ SY3177 @ SV972 @ ( c_Wellfounded_Oacc @ SY3177 @ SV811 ) )
| ( c_member @ SY3177 @ SV1114 @ ( c_Wellfounded_Oacc @ SY3177 @ SV811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(3769,plain,
! [SV812: $i,SV973: $i,SV1115: $i] :
( ( ! [SY3178: $i] :
( ~ ( c_member @ SY3178 @ SV1115 @ ( c_Wellfounded_Oacc @ SY3178 @ SV973 ) )
| ~ ( c_member @ ( tc_prod @ SY3178 @ SY3178 ) @ ( c_Product__Type_OPair @ SY3178 @ SY3178 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SY3178 @ SV973 ) )
| ( c_member @ SY3178 @ SV812 @ ( c_Wellfounded_Oacc @ SY3178 @ SV973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(3770,plain,
! [SV813: $i,SV974: $i,SV1116: $i] :
( ( ! [SY3179: $i,SY3180: $i,SY3181: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3181 @ SY3180 @ SY3179 )
| ~ ( c_member @ ( tc_prod @ SY3181 @ SY3180 ) @ ( c_Product__Type_OPair @ SY3181 @ SY3180 @ SV1116 @ SV974 ) @ SY3179 )
| ~ ( c_member @ ( tc_prod @ SY3181 @ SY3180 ) @ ( c_Product__Type_OPair @ SY3181 @ SY3180 @ SV1116 @ SV813 ) @ SY3179 )
| ( SV974 = SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(3771,plain,
! [SV814: $i,SV975: $i,SV1117: $i] :
( ( ! [SY3182: $i,SY3183: $i,SY3184: $i] :
( ( c_Product__Type_Ocurry @ SY3184 @ SY3183 @ SY3182 @ SV1117 @ SV975 @ SV814 )
= ( hAPP @ SV1117 @ ( c_Product__Type_OPair @ SY3184 @ SY3183 @ SV975 @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(3772,plain,
! [SV815: $i,SV976: $i,SV1118: $i] :
( ( c_member @ ( tc_prod @ SV1118 @ SV1118 ) @ ( c_Product__Type_OPair @ SV1118 @ SV1118 @ SV976 @ SV976 ) @ ( c_Transitive__Closure_Ortrancl @ SV1118 @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(3773,plain,
! [SV816: $i,SV977: $i,SV1119: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ SV816 )
| ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ ( c_Transitive__Closure_Ortrancl @ SV1119 @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(3774,plain,
! [SV817: $i,SV978: $i,SV1120: $i] :
( ( ! [SY3185: $i,SY3186: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3186 @ SY3186 @ SY3185 )
| ~ ( c_member @ ( tc_prod @ SY3186 @ SY3186 ) @ ( c_Product__Type_OPair @ SY3186 @ SY3186 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY3186 @ SY3185 ) )
| ~ ( c_member @ ( tc_prod @ SY3186 @ SY3186 ) @ ( c_Product__Type_OPair @ SY3186 @ SY3186 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY3186 @ SY3185 ) )
| ( c_member @ ( tc_prod @ SY3186 @ SY3186 ) @ ( c_Product__Type_OPair @ SY3186 @ SY3186 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY3186 @ SY3185 ) )
| ( c_member @ ( tc_prod @ SY3186 @ SY3186 ) @ ( c_Product__Type_OPair @ SY3186 @ SY3186 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY3186 @ SY3185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(3775,plain,
! [SV818: $i,SV979: $i,SV1121: $i] :
( ( ! [SY3187: $i,SY3188: $i] :
( ~ ( c_member @ ( tc_prod @ SY3188 @ SY3188 ) @ ( c_Product__Type_OPair @ SY3188 @ SY3188 @ SY3187 @ SV1121 ) @ SV979 )
| ~ ( c_member @ ( tc_prod @ SY3188 @ SY3188 ) @ ( c_Product__Type_OPair @ SY3188 @ SY3188 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY3188 @ SV979 ) )
| ( c_member @ ( tc_prod @ SY3188 @ SY3188 ) @ ( c_Product__Type_OPair @ SY3188 @ SY3188 @ SY3187 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY3188 @ SV979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(3776,plain,
! [SV819: $i,SV980: $i,SV1122: $i] :
( ( ! [SY3189: $i,SY3190: $i] :
( ~ ( c_member @ ( tc_prod @ SY3190 @ SY3190 ) @ ( c_Product__Type_OPair @ SY3190 @ SY3190 @ SY3189 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SY3190 @ SV980 ) )
| ~ ( c_member @ ( tc_prod @ SY3190 @ SY3190 ) @ ( c_Product__Type_OPair @ SY3190 @ SY3190 @ SV1122 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SY3190 @ SY3190 ) @ ( c_Product__Type_OPair @ SY3190 @ SY3190 @ SY3189 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SY3190 @ SV980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(3777,plain,
! [SV820: $i,SV981: $i,SV1123: $i] :
( ( ! [SY3191: $i,SY3192: $i] :
( ~ ( c_member @ ( tc_prod @ SY3192 @ SY3192 ) @ ( c_Product__Type_OPair @ SY3192 @ SY3192 @ SY3191 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SY3192 @ SV981 ) )
| ~ ( c_member @ ( tc_prod @ SY3192 @ SY3192 ) @ ( c_Product__Type_OPair @ SY3192 @ SY3192 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY3192 @ SV981 ) )
| ( c_member @ ( tc_prod @ SY3192 @ SY3192 ) @ ( c_Product__Type_OPair @ SY3192 @ SY3192 @ SY3191 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY3192 @ SV981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(3778,plain,
! [SV822: $i,SV983: $i,SV1124: $i] :
( ( ! [SY3193: $i] :
( ~ ( c_member @ ( tc_prod @ SY3193 @ SY3193 ) @ ( c_Product__Type_OPair @ SY3193 @ SY3193 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Otrancl @ SY3193 @ SV822 ) )
| ( c_member @ ( tc_prod @ SY3193 @ SY3193 ) @ ( c_Product__Type_OPair @ SY3193 @ SY3193 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Ortrancl @ SY3193 @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(3779,plain,
! [SV823: $i,SV984: $i,SV1125: $i] :
( ( ! [SY3194: $i,SY3195: $i,SY3196: $i] :
( ~ ( c_member @ ( tc_prod @ SY3196 @ SY3196 ) @ ( c_Product__Type_OPair @ SY3196 @ SY3196 @ SY3195 @ SY3194 ) @ SV1125 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY3196 @ SV984 @ SV823 @ SV1125 @ SY3194 ) @ SY3195 )
= ( hAPP @ SV823 @ SY3195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(3780,plain,
! [SV824: $i,SV985: $i,SV1126: $i] :
( ( ! [SY3197: $i] :
( ~ ( c_member @ ( tc_prod @ SY3197 @ SY3197 ) @ ( c_Product__Type_OPair @ SY3197 @ SY3197 @ SV1126 @ SV985 ) @ SV824 )
| ( c_member @ ( tc_prod @ SY3197 @ SY3197 ) @ ( c_Product__Type_OPair @ SY3197 @ SY3197 @ SV1126 @ SV985 ) @ ( c_Transitive__Closure_Otrancl @ SY3197 @ SV824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(3781,plain,
! [SV825: $i,SV986: $i,SV1127: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ SV825 )
| ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ ( c_Transitive__Closure_Otrancl @ SV1127 @ SV825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(3782,plain,
! [SV827: $i,SV988: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV988 @ SV827 ) )
= $true )
| ( ( ( c_Transitive__Closure_Otrancl @ SV988 @ SV827 )
= SV827 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3609]) ).
thf(3783,plain,
! [SV828: $i,SV989: $i,SV1128: $i] :
( ( ! [SY3198: $i,SY3199: $i] :
( ~ ( c_member @ ( tc_prod @ SY3199 @ SY3199 ) @ ( c_Product__Type_OPair @ SY3199 @ SY3199 @ SY3198 @ SV1128 ) @ SV989 )
| ~ ( c_member @ ( tc_prod @ SY3199 @ SY3199 ) @ ( c_Product__Type_OPair @ SY3199 @ SY3199 @ SV1128 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SY3199 @ SY3199 ) @ ( c_Product__Type_OPair @ SY3199 @ SY3199 @ SY3198 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SY3199 @ SV989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(3784,plain,
! [SV829: $i,SV990: $i,SV1129: $i] :
( ( ! [SY3200: $i,SY3201: $i] :
( ~ ( c_member @ ( tc_prod @ SY3201 @ SY3201 ) @ ( c_Product__Type_OPair @ SY3201 @ SY3201 @ SY3200 @ SV1129 ) @ SV990 )
| ~ ( c_member @ ( tc_prod @ SY3201 @ SY3201 ) @ ( c_Product__Type_OPair @ SY3201 @ SY3201 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY3201 @ SV990 ) )
| ( c_member @ ( tc_prod @ SY3201 @ SY3201 ) @ ( c_Product__Type_OPair @ SY3201 @ SY3201 @ SY3200 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY3201 @ SV990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(3785,plain,
! [SV830: $i,SV991: $i,SV1130: $i] :
( ( ! [SY3202: $i,SY3203: $i] :
( ~ ( c_member @ ( tc_prod @ SY3203 @ SY3203 ) @ ( c_Product__Type_OPair @ SY3203 @ SY3203 @ SY3202 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SY3203 @ SV991 ) )
| ~ ( c_member @ ( tc_prod @ SY3203 @ SY3203 ) @ ( c_Product__Type_OPair @ SY3203 @ SY3203 @ SV1130 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SY3203 @ SY3203 ) @ ( c_Product__Type_OPair @ SY3203 @ SY3203 @ SY3202 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SY3203 @ SV991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(3786,plain,
! [SV831: $i,SV992: $i,SV1131: $i] :
( ( ! [SY3204: $i,SY3205: $i] :
( ~ ( c_member @ ( tc_prod @ SY3205 @ SY3205 ) @ ( c_Product__Type_OPair @ SY3205 @ SY3205 @ SY3204 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SY3205 @ SV992 ) )
| ~ ( c_member @ ( tc_prod @ SY3205 @ SY3205 ) @ ( c_Product__Type_OPair @ SY3205 @ SY3205 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY3205 @ SV992 ) )
| ( c_member @ ( tc_prod @ SY3205 @ SY3205 ) @ ( c_Product__Type_OPair @ SY3205 @ SY3205 @ SY3204 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY3205 @ SV992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(3787,plain,
! [SV832: $i,SV993: $i,SV1132: $i] :
( ( ! [SY3206: $i,SY3207: $i] :
( ~ ( c_member @ ( tc_prod @ SY3207 @ SY3207 ) @ ( c_Product__Type_OPair @ SY3207 @ SY3207 @ SY3206 @ SV1132 ) @ SV993 )
| ~ ( c_member @ ( tc_prod @ SY3207 @ SY3207 ) @ ( c_Product__Type_OPair @ SY3207 @ SY3207 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SY3207 @ SV993 ) )
| ( c_member @ ( tc_prod @ SY3207 @ SY3207 ) @ ( c_Product__Type_OPair @ SY3207 @ SY3207 @ SY3206 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SY3207 @ SV993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(3788,plain,
! [SV833: $i,SV994: $i,SV1133: $i] :
( ( ! [SY3208: $i,SY3209: $i] :
( ~ ( c_member @ ( tc_prod @ SY3209 @ SY3209 ) @ ( c_Product__Type_OPair @ SY3209 @ SY3209 @ SY3208 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SY3209 @ SV994 ) )
| ~ ( c_member @ ( tc_prod @ SY3209 @ SY3209 ) @ ( c_Product__Type_OPair @ SY3209 @ SY3209 @ SV1133 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SY3209 @ SY3209 ) @ ( c_Product__Type_OPair @ SY3209 @ SY3209 @ SY3208 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SY3209 @ SV994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(3789,plain,
! [SV834: $i,SV995: $i,SV1134: $i] :
( ( ! [SY3210: $i,SY3211: $i] :
( ~ ( c_member @ ( tc_prod @ SY3211 @ SY3211 ) @ ( c_Product__Type_OPair @ SY3211 @ SY3211 @ SY3210 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SY3211 @ SV995 ) )
| ~ ( c_member @ ( tc_prod @ SY3211 @ SY3211 ) @ ( c_Product__Type_OPair @ SY3211 @ SY3211 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SY3211 @ SV995 ) )
| ( c_member @ ( tc_prod @ SY3211 @ SY3211 ) @ ( c_Product__Type_OPair @ SY3211 @ SY3211 @ SY3210 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SY3211 @ SV995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(3790,plain,
! [SV835: $i,SV996: $i,SV1135: $i] :
( ( ! [SY3212: $i,SY3213: $i] :
( ~ ( c_member @ ( tc_prod @ SY3213 @ SY3213 ) @ ( c_Product__Type_OPair @ SY3213 @ SY3213 @ SY3212 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SY3213 @ SV996 ) )
| ~ ( c_member @ ( tc_prod @ SY3213 @ SY3213 ) @ ( c_Product__Type_OPair @ SY3213 @ SY3213 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY3213 @ SV996 ) )
| ( c_member @ ( tc_prod @ SY3213 @ SY3213 ) @ ( c_Product__Type_OPair @ SY3213 @ SY3213 @ SY3212 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY3213 @ SV996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(3791,plain,
! [SV836: $i,SV997: $i,SV1136: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i] :
( ~ ( c_member @ ( tc_prod @ SY3214 @ SY3214 ) @ ( c_Product__Type_OPair @ SY3214 @ SY3214 @ SV1136 @ SV997 ) @ SY3216 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY3214 @ SV836 @ SY3215 @ SY3216 @ SV997 ) @ SV1136 )
= ( hAPP @ SY3215 @ SV1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(3792,plain,
! [SV837: $i,SV998: $i,SV1137: $i] :
( ( ! [SY3217: $i] :
( ( c_member @ ( tc_prod @ SY3217 @ SY3217 ) @ ( c_Product__Type_OPair @ SY3217 @ SY3217 @ ( sK39_B_x @ SY3217 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SY3217 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SY3217 @ SV1137 ) )
| ~ ( c_member @ ( tc_prod @ SY3217 @ SY3217 ) @ ( c_Product__Type_OPair @ SY3217 @ SY3217 @ SV998 @ SV837 ) @ SV1137 )
| ( SV998 != SV837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(3793,plain,
! [SV840: $i,SV1000: $i] :
( ( ( c_member @ ( tc_prod @ SV1000 @ SV1000 ) @ ( c_Product__Type_OPair @ SV1000 @ SV1000 @ ( sK36_B_x @ SV1000 @ SV840 ) @ ( sK36_B_x @ SV1000 @ SV840 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1000 @ SV840 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1000 @ SV840 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3621]) ).
thf(3794,plain,
! [SV841: $i,SV1001: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1001 @ SV1001 ) @ SV841 @ ( c_Relation_OId @ SV1001 ) ) )
= $true )
| ( ( SV841
= ( c_Product__Type_OPair @ SV1001 @ SV1001 @ ( sK35_B_x @ SV1001 @ SV841 ) @ ( sK35_B_x @ SV1001 @ SV841 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(3795,plain,
! [SV842: $i,SV1002: $i,SV1138: $i] :
( ( ! [SY3218: $i] :
( ~ ( c_Relation_Oantisym @ SY3218 @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SY3218 @ SY3218 ) @ ( c_Product__Type_OPair @ SY3218 @ SY3218 @ SV1002 @ SV842 ) @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SY3218 @ SY3218 ) @ ( c_Product__Type_OPair @ SY3218 @ SY3218 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(3796,plain,
! [SV843: $i,SV1003: $i,SV1139: $i] :
( ( ! [SY3219: $i] :
( ~ ( c_member @ SY3219 @ SV1139 @ ( c_Set_Oinsert @ SY3219 @ SV1003 @ SV843 ) )
| ( SV1139 = SV1003 )
| ( c_member @ SY3219 @ SV1139 @ SV843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(3797,plain,
! [SV844: $i,SV1004: $i,SV1140: $i] :
( ( ! [SY3220: $i,SY3221: $i] :
( ( c_Relation_ODomain @ SY3221 @ SY3220 @ ( c_Set_Oinsert @ ( tc_prod @ SY3221 @ SY3220 ) @ ( c_Product__Type_OPair @ SY3221 @ SY3220 @ SV1140 @ SV1004 ) @ SV844 ) )
= ( c_Set_Oinsert @ SY3221 @ SV1140 @ ( c_Relation_ODomain @ SY3221 @ SY3220 @ SV844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(3798,plain,
! [SV845: $i,SV1005: $i,SV1141: $i] :
( ( ! [SY3222: $i,SY3223: $i] :
( ( c_Relation_ORange @ SY3223 @ SY3222 @ ( c_Set_Oinsert @ ( tc_prod @ SY3223 @ SY3222 ) @ ( c_Product__Type_OPair @ SY3223 @ SY3222 @ SV1141 @ SV1005 ) @ SV845 ) )
= ( c_Set_Oinsert @ SY3222 @ SV1005 @ ( c_Relation_ORange @ SY3223 @ SY3222 @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3799,plain,
! [SV846: $i,SV1006: $i,SV1142: $i] :
( ( c_member @ SV1142 @ SV1006 @ ( c_Set_Oinsert @ SV1142 @ SV1006 @ SV846 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(3800,plain,
! [SV847: $i,SV1007: $i,SV1143: $i] :
( ( ! [SY3224: $i] :
( ~ ( c_member @ SY3224 @ SV1143 @ SV1007 )
| ( c_member @ SY3224 @ SV1143 @ ( c_Set_Oinsert @ SY3224 @ SV847 @ SV1007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(3801,plain,
! [SV848: $i,SV1008: $i,SV1144: $i] :
( ( ~ ( c_member @ SV1144 @ SV1008 @ SV848 )
| ( ( c_Set_Oinsert @ SV1144 @ SV1008 @ SV848 )
= SV848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(3802,plain,
! [SV849: $i,SV1009: $i,SV1145: $i] :
( ( ! [SY3225: $i] :
( ~ ( c_Wellfounded_Owf @ SY3225 @ SV1145 )
| ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SY3225 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SY3225 @ SV1009 @ SV1145 @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3803,plain,
! [SV850: $i,SV1010: $i,SV1146: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1146 @ SV1010 )
| ~ ( c_member @ ( tc_prod @ SV1146 @ SV1146 ) @ ( c_Product__Type_OPair @ SV1146 @ SV1146 @ SV850 @ SV850 ) @ SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(3804,plain,
! [SV851: $i,SV1011: $i,SV1147: $i] :
( ( ! [SY3226: $i] :
( ~ ( c_Wellfounded_Owf @ SY3226 @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SY3226 @ SY3226 ) @ ( c_Product__Type_OPair @ SY3226 @ SY3226 @ SV1011 @ SV851 ) @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SY3226 @ SY3226 ) @ ( c_Product__Type_OPair @ SY3226 @ SY3226 @ SV851 @ SV1011 ) @ SV1147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(3805,plain,
! [SV852: $i,SV1012: $i,SV1148: $i] :
( ( ! [SY3227: $i] :
( ~ ( c_Wellfounded_Owf @ SY3227 @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SY3227 @ SY3227 ) @ ( c_Product__Type_OPair @ SY3227 @ SY3227 @ SV1012 @ SV852 ) @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SY3227 @ SY3227 ) @ ( c_Product__Type_OPair @ SY3227 @ SY3227 @ SV852 @ SV1012 ) @ SV1148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(3806,plain,
! [SV853: $i,SV1013: $i,SV1149: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1149 @ SV1013 )
| ~ ( c_member @ ( tc_prod @ SV1149 @ SV1149 ) @ ( c_Product__Type_OPair @ SV1149 @ SV1149 @ SV853 @ SV853 ) @ SV1013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(3807,plain,
! [SV854: $i,SV1014: $i,SV1150: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1150 @ SV1014 )
| ( c_member @ SV1150 @ SV854 @ ( c_Wellfounded_Oacc @ SV1150 @ SV1014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(3808,plain,
! [SV855: $i,SV1015: $i] :
( ( ( ~ ( c_member @ SV1015 @ ( sK25_B_x @ SV1015 @ SV855 ) @ ( c_Wellfounded_Oacc @ SV1015 @ SV855 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1015 @ SV855 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3809,plain,
! [SV856: $i,SV1016: $i,SV1151: $i] :
( ( ! [SY3228: $i,SY3229: $i,SY3230: $i] :
( ~ ( c_member @ SY3230 @ SY3229 @ SY3228 )
| ~ ( c_member @ ( tc_prod @ SY3230 @ SV1151 ) @ ( c_Product__Type_OPair @ SY3230 @ SV1151 @ SY3229 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SY3230 @ SV1151 @ SV856 @ SY3228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(3810,plain,
! [SV857: $i,SV1017: $i,SV1152: $i] :
( ( ! [SY3231: $i,SY3232: $i,SY3233: $i,SY3234: $i,SY3235: $i] :
( ~ ( c_member @ ( tc_prod @ SY3235 @ SY3234 ) @ ( c_Product__Type_OPair @ SY3235 @ SY3234 @ SY3233 @ SY3232 ) @ SY3231 )
| ~ ( c_member @ ( tc_prod @ SY3234 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3234 @ SV1152 @ SY3232 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY3235 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3235 @ SV1152 @ SY3233 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY3235 @ SY3234 @ SV1152 @ SY3231 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(3811,plain,
! [SV858: $i,SV1018: $i] :
( ( ( ( ( hAPP @ SV1018 @ ( sK22_B_x @ SV1018 @ SV858 ) )
!= ( hAPP @ SV858 @ ( sK22_B_x @ SV1018 @ SV858 ) ) ) )
= $true )
| ( ( SV1018 = SV858 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(3812,plain,
! [SV859: $i,SV1019: $i,SV1153: $i] :
( ( ! [SY3236: $i,SY3237: $i,SY3238: $i,SY3239: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3239 @ SY3238 ) )
| ~ ( c_member @ ( tc_prod @ SY3237 @ SY3237 ) @ ( c_Product__Type_OPair @ SY3237 @ SY3237 @ SY3236 @ SV1153 ) @ ( hAPP @ SV1019 @ SY3238 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SY3237 ) @ ( tc_prod @ SV859 @ SY3237 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SY3237 ) @ ( tc_prod @ SV859 @ SY3237 ) @ ( c_Product__Type_OPair @ SV859 @ SY3237 @ SY3238 @ SY3236 ) @ ( c_Product__Type_OPair @ SV859 @ SY3237 @ SY3238 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SY3237 @ SY3239 @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(3813,plain,
! [SV863: $i,SV1023: $i,SV1154: $i] :
( ( ! [SY3240: $i,SY3241: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3241 @ ( c_Product__Type_OPair @ SY3240 @ SV1154 @ SV1023 @ SV863 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SY3240 @ SV1154 @ tc_HOL_Obool @ SY3241 @ SV1023 @ SV863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(3814,plain,
! [SV864: $i,SV1024: $i,SV1155: $i] :
( ( ! [SY3242: $i,SY3243: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY3243 @ SY3242 @ tc_HOL_Obool @ SV1155 @ SV1024 @ SV864 ) )
| ( hBOOL @ ( hAPP @ SV1155 @ ( c_Product__Type_OPair @ SY3243 @ SY3242 @ SV1024 @ SV864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(3815,plain,
! [SV865: $i,SV1025: $i,SV1156: $i] :
( ( ! [SY3244: $i,SY3245: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY3245 @ SY3244 @ tc_HOL_Obool @ SV1156 @ SV1025 @ SV865 ) )
| ( hBOOL @ ( hAPP @ SV1156 @ ( c_Product__Type_OPair @ SY3245 @ SY3244 @ SV1025 @ SV865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(3816,plain,
! [SV873: $i,SV1032: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1032 @ SV873 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1032 @ ( c_Transitive__Closure_Ortrancl @ SV1032 @ SV873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3653]) ).
thf(3817,plain,
! [SV874: $i,SV1033: $i,SV1157: $i] :
( ( ( c_Set_Oinsert @ SV1157 @ SV1033 @ ( c_Set_Oinsert @ SV1157 @ SV1033 @ SV874 ) )
= ( c_Set_Oinsert @ SV1157 @ SV1033 @ SV874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(3818,plain,
! [SV875: $i,SV1034: $i,SV1158: $i] :
( ( ! [SY3246: $i] :
( ( c_Set_Oinsert @ SY3246 @ SV1158 @ ( c_Set_Oinsert @ SY3246 @ SV1034 @ SV875 ) )
= ( c_Set_Oinsert @ SY3246 @ SV1034 @ ( c_Set_Oinsert @ SY3246 @ SV1158 @ SV875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(3819,plain,
! [SV878: $i,SV1036: $i,SV1159: $i] :
( ( ! [SY3247: $i] :
( ~ ( c_Wellfounded_Owf @ SY3247 @ SV1159 )
| ( c_Wellfounded_Owf @ SV1036 @ ( hAPP @ ( c_Relation_Oinv__image @ SY3247 @ SV1036 @ SV1159 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(3820,plain,
! [SV879: $i,SV1037: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1037 @ SV879 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1037 @ ( c_Transitive__Closure_Otrancl @ SV1037 @ SV879 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3658]) ).
thf(3821,plain,
! [SV880: $i,SV1038: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1038 @ SV880 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1038 @ SV880 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3659]) ).
thf(3822,plain,
! [SV882: $i,SV1040: $i,SV1160: $i] :
( ( ! [SY3248: $i,SY3249: $i,SY3250: $i] :
( ( SY3250
!= ( c_Recdef_Owfrec @ SY3249 @ SY3248 @ SV1160 @ SV1040 ) )
| ~ ( c_Wellfounded_Owf @ SY3249 @ SV1160 )
| ( ( hAPP @ SY3250 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SY3249 @ SY3248 @ SY3250 @ SV1160 @ SV882 ) ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(3823,plain,
! [SV883: $i,SV1041: $i,SV1161: $i] :
( ( ! [SY3251: $i,SY3252: $i] :
( ~ ( c_Wellfounded_Owf @ SY3252 @ SY3251 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY3252 @ SV1161 @ SY3251 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SY3252 @ SV1161 @ ( c_Recdef_Owfrec @ SY3252 @ SV1161 @ SY3251 @ SV1041 ) @ SY3251 @ SV883 ) ) @ SV883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3824,plain,
! [SV1162: $i,SV884: $i,SV1042: $i] :
( ( ! [SY3253: $i] :
( ~ ( c_Wellfounded_Owf @ SV1042 @ SY3253 )
| ! [SY3254: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SY3253 @ SV1162 ) @ SY3254 )
= ( hAPP @ ( hAPP @ SV1162 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SY3253 @ SV1162 ) @ SY3253 @ SY3254 ) ) @ SY3254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(3825,plain,
! [SV886: $i,SV1043: $i,SV1163: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1163 @ SV1043 )
| ( c_Wellfounded_Owf @ SV1163 @ ( c_Wellfounded_Omlex__prod @ SV1163 @ SV886 @ SV1043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(3826,plain,
! [SV888: $i,SV1044: $i] :
( ( ( SV1044 = SV888 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1044 @ SV888 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV888 @ SV1044 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3827,plain,
! [SV890: $i,SV1045: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1045 @ SV890 ) )
= $true )
| ( ( ( SV890 != SV1045 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3828,plain,
! [SV891: $i,SV1046: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1046 @ SV891 ) )
= $true )
| ( ( ( SV1046 != SV891 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(3829,plain,
! [SV893: $i,SV1047: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1047 @ SV893 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV893 @ SV1047 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3670]) ).
thf(3830,plain,
! [SV894: $i,SV1048: $i] :
( ( ( ( SV1048 != SV894 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1048 @ SV894 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(3831,plain,
! [SV895: $i,SV1049: $i,SV1164: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV1049 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV895 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(3832,plain,
! [SV896: $i,SV1050: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1050 @ SV896 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SV1050 )
| ( SV1050 = SV896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3673]) ).
thf(3833,plain,
! [SV897: $i,SV1051: $i,SV1165: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV1165 @ SV1051 ) @ SV897 )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ SV1165 @ SV897 ) @ SV1051 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(3834,plain,
! [SV899: $i,SV1053: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ SV1053 ) @ SV899 ) ) )
= $true )
| ( ( SV1053 = SV899 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(3835,plain,
! [SV900: $i,SV1054: $i] :
( ( ( ( SV1054 != SV900 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV1054 ) @ SV900 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3836,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK70_SY736 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(3837,plain,
! [SV902: $i,SV1056: $i,SV1166: $i] :
( ( ! [SY3255: $i,SY3256: $i] :
( ~ ( c_member @ ( tc_prod @ SY3256 @ SY3256 ) @ ( c_Product__Type_OPair @ SY3256 @ SY3256 @ SY3255 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SY3256 @ SV1056 ) )
| ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3256 @ SY3256 ) @ ( c_Product__Type_OPair @ SY3256 @ SY3256 @ ( sK12_B_y @ SY3256 @ SY3255 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SY3256 @ SY3255 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3256 @ SY3256 ) @ ( c_Product__Type_OPair @ SY3256 @ SY3256 @ ( sK13_SY707 @ SY3256 @ SY3255 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SY3256 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SY3256 @ SY3255 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SY3256 @ SY3255 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SY3255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(3838,plain,
! [SV903: $i,SV1057: $i] :
( ( ~ ! [SY2962: $i,SY2963: $i] :
( ( c_member @ SY2963 @ SY2962 @ SV1057 )
| ( c_member @ SY2963 @ SY2962 @ SV903 )
| ( ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV1057 )
!= ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV903 ) )
| ( SV1057 = SV903 ) )
| ~ ! [SY2964: $i,SY2965: $i] :
( ( c_member @ SY2965 @ SY2964 @ SV1057 )
| ( c_member @ SY2965 @ SY2964 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV1057 )
= ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV903 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(3839,plain,
! [SV904: $i,SV1058: $i,SV1167: $i] :
( ( ! [SY3257: $i,SY3258: $i,SY3259: $i,SY3260: $i,SY3261: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ SY3259 @ SY3258 ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ SY3257 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3261 @ SY3260 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY3259 ) @ SY3258 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ SY3259 @ SY3258 ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ ( sK18_B_a @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3261 @ SY3260 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3261 @ SY3260 ) @ ( tc_prod @ SY3261 @ SY3260 ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ ( sK18_B_a @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY3261 @ SY3260 @ ( sK20_SY717 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY3261 @ SY3260 @ SY3259 @ SY3258 @ SY3257 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY3257 ) @ SV1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(3840,plain,
! [SV905: $i] :
( ( ~ ! [SY2496: $i,SY2497: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2497 @ SY2497 ) @ ( c_Product__Type_OPair @ SY2497 @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ SY2496 ) @ SV905 )
| ~ ~ ( c_member @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ( c_member @ SY2497 @ SY2496 @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3682]) ).
thf(3841,plain,
! [SV905: $i] :
( ( ~ ! [SY2498: $i,SY2499: $i] :
( ~ ( c_member @ SY2499 @ SY2498 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) )
| ! [SY2500: $i] :
( ~ ( c_member @ ( tc_prod @ SY2499 @ SY2499 ) @ ( c_Product__Type_OPair @ SY2499 @ SY2499 @ SY2500 @ SY2498 ) @ SV905 )
| ( c_member @ SY2499 @ SY2500 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3682]) ).
thf(3842,plain,
! [SV906: $i] :
( ( ~ ! [SY2501: $i,SY2502: $i] :
( ~ ( ~ ( c_member @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( c_member @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY2502 @ SY2501 @ SV906 )
!= ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY2502 @ SY2501 @ SV906 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3843,plain,
! [SV906: $i] :
( ( ~ ! [SY2503: $i,SY2504: $i] :
( ~ ( c_Relation_Ototal__on @ SY2504 @ SY2503 @ SV906 )
| ! [SY2505: $i] :
( ~ ( c_member @ SY2504 @ SY2505 @ SY2503 )
| ! [SY2506: $i] :
( ~ ( c_member @ SY2504 @ SY2506 @ SY2503 )
| ( SY2505 = SY2506 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2505 @ SY2506 ) @ SV906 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2506 @ SY2505 ) @ SV906 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3844,plain,
! [SV907: $i,SV1059: $i,SV1168: $i] :
( ( ! [SY3262: $i] :
~ ( ~ ( ! [SY3263: $i,SY3264: $i] :
( ( c_Product__Type_OPair @ SY3264 @ SY3263 @ SY3262 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3264 @ SY3263 @ SV1059 @ SV907 ) )
| ( SY3262 = SV1059 ) )
| ~ ( ! [SY3265: $i,SY3266: $i] :
( ( c_Product__Type_OPair @ SY3266 @ SY3265 @ SY3262 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3266 @ SY3265 @ SV1059 @ SV907 ) )
| ( SV1168 = SV907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(3845,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK26_B_x @ SV1060 @ SV908 ) @ ( sK27_SY720 @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3846,plain,
! [SV909: $i] :
( ( ~ ! [SY2515: $i,SY2516: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2516 @ ( sK75_B_x1 @ SY2516 @ SY2515 @ SV909 ) ) )
| ! [SY2517: $i,SY2518: $i] : ( hBOOL @ ( hAPP @ SY2516 @ ( c_Product__Type_OPair @ SY2515 @ SV909 @ SY2517 @ SY2518 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3847,plain,
! [SV909: $i] :
( ( ~ ! [SY2519: $i,SY2520: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2520 @ ( c_Product__Type_OPair @ SY2519 @ SV909 @ ( sK73_B_a @ SY2520 @ SY2519 @ SV909 ) @ ( sK74_SY739 @ SY2520 @ SY2519 @ SV909 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2520 @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3848,plain,
! [SV910: $i] :
( ( ~ ! [SY2522: $i,SY2523: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 )
!= ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2523 @ SY2522 @ SV910 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3687]) ).
thf(3849,plain,
! [SV910: $i] :
( ( ~ ! [SY2524: $i,SY2525: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2525 @ SY2524 @ SV910 )
| ! [SY2526: $i,SY2527: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2527 ) @ SV910 )
| ! [SY2528: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2528 ) @ SV910 )
| ( SY2527 = SY2528 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3687]) ).
thf(3850,plain,
! [SV911: $i,SV1061: $i,SV1169: $i] :
( ( ! [SY3267: $i,SY3268: $i,SY3269: $i] :
~ ( ~ ~ ( ~ ! [SY3270: $i,SY3271: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3271 @ SY3270 ) @ ( tc_prod @ SY3271 @ SY3270 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3271 @ SY3270 ) @ ( tc_prod @ SY3271 @ SY3270 ) @ ( c_Product__Type_OPair @ SY3271 @ SY3270 @ SY3269 @ SY3268 ) @ ( c_Product__Type_OPair @ SY3271 @ SY3270 @ SY3267 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3271 @ SY3270 @ SV1061 @ SV911 ) )
| ( SY3269 = SY3267 )
| ( c_member @ ( tc_prod @ SY3271 @ SY3271 ) @ ( c_Product__Type_OPair @ SY3271 @ SY3271 @ SY3269 @ SY3267 ) @ SV1061 ) )
| ~ ! [SY3272: $i,SY3273: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3273 @ SY3272 ) @ ( tc_prod @ SY3273 @ SY3272 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3273 @ SY3272 ) @ ( tc_prod @ SY3273 @ SY3272 ) @ ( c_Product__Type_OPair @ SY3273 @ SY3272 @ SY3269 @ SY3268 ) @ ( c_Product__Type_OPair @ SY3273 @ SY3272 @ SY3267 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3273 @ SY3272 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3272 @ SY3272 ) @ ( c_Product__Type_OPair @ SY3272 @ SY3272 @ SY3268 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3273 @ SY3273 ) @ ( c_Product__Type_OPair @ SY3273 @ SY3273 @ SY3269 @ SY3267 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY3274: $i] :
( ( SY3269 != SY3267 )
| ~ ( c_member @ ( tc_prod @ SY3274 @ SY3274 ) @ ( c_Product__Type_OPair @ SY3274 @ SY3274 @ SY3268 @ SV1169 ) @ SV911 )
| ! [SY3275: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3275 @ SY3274 ) @ ( tc_prod @ SY3275 @ SY3274 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3275 @ SY3274 ) @ ( tc_prod @ SY3275 @ SY3274 ) @ ( c_Product__Type_OPair @ SY3275 @ SY3274 @ SY3269 @ SY3268 ) @ ( c_Product__Type_OPair @ SY3275 @ SY3274 @ SY3267 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3275 @ SY3274 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3276: $i,SY3277: $i] :
( ~ ( c_member @ ( tc_prod @ SY3277 @ SY3277 ) @ ( c_Product__Type_OPair @ SY3277 @ SY3277 @ SY3269 @ SY3267 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3277 @ SY3276 ) @ ( tc_prod @ SY3277 @ SY3276 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3277 @ SY3276 ) @ ( tc_prod @ SY3277 @ SY3276 ) @ ( c_Product__Type_OPair @ SY3277 @ SY3276 @ SY3269 @ SY3268 ) @ ( c_Product__Type_OPair @ SY3277 @ SY3276 @ SY3267 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3277 @ SY3276 @ SV1061 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(3851,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(3852,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK78_SY740 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK78_SY740 @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK77_B_x @ SX1 @ SX0 ) @ ( sK79_SY742 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3690]) ).
thf(3853,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX4 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3691]) ).
thf(3854,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK33_B_x @ SX1 @ SX0 ) @ ( sK34_SY725 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK34_SY725 @ SX1 @ SX0 ) @ ( sK33_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( ( ( sK33_B_x @ SX1 @ SX0 )
!= ( sK34_SY725 @ SX1 @ SX0 ) ) ) ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3692]) ).
thf(3855,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oantisym @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX3 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3693]) ).
thf(3856,plain,
! [SV913: $i] :
( ( ~ ! [SY2544: $i,SY2545: $i] :
( ~ ( c_Relation_Orefl__on @ SY2545 @ SY2544 @ SV913 )
| ~ ( c_Relation_Otrans @ SY2545 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SY2545 @ SY2544 @ SV913 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3694]) ).
thf(3857,plain,
! [SV913: $i] :
( ( ~ ~ ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) )
| ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3694]) ).
thf(3858,plain,
! [SV1063: $i,SV914: $i,SV1171: $i] :
( ( ~ ( ~ ! [SY3278: $i,SY3279: $i] :
( ! [SY3280: $i] :
( ~ ( c_member @ SV1171 @ SY3280 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3279 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3279 @ SY3280 @ SY3278 ) @ SV1063 ) )
| ( c_member @ SY3279 @ SY3278 @ ( c_Relation_OImage @ SV1171 @ SY3279 @ SV1063 @ SV914 ) ) )
| ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( c_member @ SY3282 @ SY3281 @ ( c_Relation_OImage @ SV1171 @ SY3282 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3282 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3282 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SY3281 ) @ SV1063 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(3859,plain,
! [SV915: $i,SV1064: $i,SV1172: $i] :
( ( ! [SY3283: $i] :
( ~ ( c_member @ ( tc_prod @ SY3283 @ SY3283 ) @ ( c_Product__Type_OPair @ SY3283 @ SY3283 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SY3283 @ SV915 ) )
| ( SV1172 = SV1064 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3283 @ SY3283 ) @ ( c_Product__Type_OPair @ SY3283 @ SY3283 @ SV1172 @ ( sK45_B_y @ SY3283 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3283 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SY3283 @ SY3283 ) @ ( c_Product__Type_OPair @ SY3283 @ SY3283 @ ( sK45_B_y @ SY3283 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(3860,plain,
! [SV916: $i] :
( ( ~ ! [SY2560: $i] :
( ( SY2560 != SV916 )
| ! [SY2561: $i] : ( c_member @ ( tc_prod @ SY2561 @ SY2561 ) @ ( c_Product__Type_OPair @ SY2561 @ SY2561 @ SY2560 @ SV916 ) @ ( c_Relation_OId @ SY2561 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3697]) ).
thf(3861,plain,
! [SV916: $i] :
( ( ~ ! [SY2562: $i] :
( ! [SY2563: $i] :
~ ( c_member @ ( tc_prod @ SY2563 @ SY2563 ) @ ( c_Product__Type_OPair @ SY2563 @ SY2563 @ SY2562 @ SV916 ) @ ( c_Relation_OId @ SY2563 ) )
| ( SY2562 = SV916 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3697]) ).
thf(3862,plain,
! [SV917: $i,SV1065: $i] :
( ( ~ ! [SY2999: $i,SY3000: $i] :
( ( SY3000 != SY2999 )
| ~ ( c_member @ SV1065 @ SY3000 @ SV917 )
| ( c_member @ SV1065 @ SY2999 @ SV917 ) )
| ~ ! [SY3001: $i,SY3002: $i] :
( ( SY3002 != SY3001 )
| ~ ( c_member @ SV1065 @ SY3001 @ SV917 )
| ( c_member @ SV1065 @ SY3002 @ SV917 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3863,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK40_B_x @ SX1 @ SX0 ) @ ( sK40_B_x @ SX1 @ SX0 ) ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) )
| ( c_Wellfounded_Oacyclic @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3699]) ).
thf(3864,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3700]) ).
thf(3865,plain,
! [SV1173: $i,SV918: $i,SV1066: $i] :
( ( ~ ( ~ ! [SY3284: $i,SY3285: $i] :
( ~ ( c_member @ ( tc_prod @ SY3285 @ SY3284 ) @ ( c_Product__Type_OPair @ SY3285 @ SY3284 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3285 @ SY3284 @ SV1173 ) @ SV1066 ) @ SV918 ) ) )
| ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3287 @ SY3286 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3287 @ SY3286 ) @ ( c_Product__Type_OPair @ SY3287 @ SY3286 @ SV1066 @ SV918 ) @ SV1173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(3866,plain,
! [SV919: $i,SV1067: $i,SV1174: $i] :
( ( ! [SY3288: $i] :
~ ( ~ ! [SY3289: $i,SY3290: $i] :
( ! [SY3291: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3290 @ SY3290 ) @ ( c_Product__Type_OPair @ SY3290 @ SY3290 @ ( sK60_B_z @ SY3291 @ SY3290 @ SY3289 @ SY3288 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SY3288 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3290 @ SY3289 @ SY3288 @ SV1174 @ ( sK60_B_z @ SY3291 @ SY3290 @ SY3289 @ SY3288 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3291 @ ( sK60_B_z @ SY3291 @ SY3290 @ SY3289 @ SY3288 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3291 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3290 @ SY3289 @ SY3288 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) )
| ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3293 @ SY3292 @ SY3288 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3294: $i] :
( ~ ( c_member @ ( tc_prod @ SY3293 @ SY3293 ) @ ( c_Product__Type_OPair @ SY3293 @ SY3293 @ SY3294 @ SV1067 ) @ SY3288 )
| ( c_Recdef_Owfrec__rel @ SY3293 @ SY3292 @ SY3288 @ SV1174 @ SY3294 @ ( hAPP @ ( sK59_B_g @ SY3293 @ SY3292 @ SY3288 @ SV1174 @ SV1067 @ SV919 ) @ SY3294 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3293 @ SY3292 @ SY3288 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(3867,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
| ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3868,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
| ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3869,plain,
! [SV921: $i,SV1068: $i,SV1175: $i] :
( ( ! [SY3295: $i] :
~ ( ~ ! [SY3296: $i] :
( ! [SY3297: $i] :
~ ( c_member @ ( tc_prod @ SY3297 @ SY3297 ) @ ( c_Product__Type_OPair @ SY3297 @ SY3297 @ SY3296 @ SY3295 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3297 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3296 ) @ ( hAPP @ SV921 @ SY3295 ) ) @ SV1068 ) )
| ~ ! [SY3298: $i] :
( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3298 ) @ ( hAPP @ SV921 @ SY3295 ) ) @ SV1068 )
| ! [SY3299: $i] : ( c_member @ ( tc_prod @ SY3299 @ SY3299 ) @ ( c_Product__Type_OPair @ SY3299 @ SY3299 @ SY3298 @ SY3295 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3299 @ SV1068 ) @ SV921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(3870,plain,
! [SV922: $i] :
( ( ~ ! [SY2607: $i] :
( ( SY2607 != SV922 )
| ! [SY2608: $i] : ( c_member @ SY2608 @ SY2607 @ ( c_fequal @ SV922 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3871,plain,
! [SV922: $i] :
( ( ~ ! [SY2609: $i] :
( ! [SY2610: $i] :
~ ( c_member @ SY2610 @ SY2609 @ ( c_fequal @ SV922 ) )
| ( SY2609 = SV922 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3872,plain,
! [SV923: $i,SV1069: $i,SV1176: $i] :
( ( ! [SY3300: $i] :
( ~ ( c_member @ ( tc_prod @ SY3300 @ SY3300 ) @ ( c_Product__Type_OPair @ SY3300 @ SY3300 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SY3300 @ SV923 ) )
| ( SV1176 = SV1069 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3300 @ SY3300 ) @ ( c_Product__Type_OPair @ SY3300 @ SY3300 @ SV1176 @ ( sK44_B_y @ SY3300 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SY3300 @ SY3300 ) @ ( c_Product__Type_OPair @ SY3300 @ SY3300 @ ( sK44_B_y @ SY3300 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SY3300 @ SV923 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3873,plain,
! [SV924: $i,SV1070: $i,SV1177: $i] :
( ( ! [SY3301: $i] :
( ~ ( c_member @ ( tc_prod @ SY3301 @ SY3301 ) @ ( c_Product__Type_OPair @ SY3301 @ SY3301 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SY3301 @ SV924 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3301 @ SY3301 ) @ ( c_Product__Type_OPair @ SY3301 @ SY3301 @ SV1177 @ ( sK41_B_z @ SY3301 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SY3301 @ SY3301 ) @ ( c_Product__Type_OPair @ SY3301 @ SY3301 @ ( sK41_B_z @ SY3301 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SY3301 @ SV924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(3874,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
| ~ ( ~ ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 )
| ( SV1071
!= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(3875,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3876,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SX1 @ SX0 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3877,plain,
! [SV926: $i,SV1072: $i] :
( ( ~ ! [SY3027: $i,SY3028: $i] :
( ! [SY3029: $i] :
~ ( c_member @ ( tc_prod @ SY3028 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3028 @ SV1072 @ SY3027 @ SY3029 ) @ SV926 )
| ( c_member @ SY3028 @ SY3027 @ ( c_Relation_ODomain @ SY3028 @ SV1072 @ SV926 ) ) )
| ~ ! [SY3030: $i,SY3031: $i] :
( ~ ( c_member @ SY3031 @ SY3030 @ ( c_Relation_ODomain @ SY3031 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY3031 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3031 @ SV1072 @ SY3030 @ ( sK66_B_y @ SY3031 @ SY3030 @ SV1072 @ SV926 ) ) @ SV926 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3878,plain,
! [SV927: $i,SV1073: $i] :
( ( ~ ! [SY3032: $i,SY3033: $i] :
( ( c_member @ SY3033 @ SY3032 @ ( c_Relation_ODomain @ SY3033 @ SY3033 @ SV1073 ) )
| ( SY3032 != SV927 )
| ( c_member @ ( tc_prod @ SY3033 @ SY3033 ) @ ( c_Product__Type_OPair @ SY3033 @ SY3033 @ SY3032 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3033 @ SV1073 ) ) )
| ~ ! [SY3034: $i,SY3035: $i] :
( ( c_member @ SY3035 @ SY3034 @ ( c_Relation_ODomain @ SY3035 @ SY3035 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SY3035 @ SY3035 ) @ ( c_Product__Type_OPair @ SY3035 @ SY3035 @ SY3034 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3035 @ SV1073 ) )
| ( SY3034 = SV927 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3879,plain,
! [SV928: $i,SV1074: $i] :
( ( ~ ! [SY3036: $i] :
( ! [SY3037: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3037 @ SY3036 @ SV1074 ) @ SV928 ) )
| ( SY3036 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
| ~ ~ ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3880,plain,
! [SV929: $i,SV1075: $i,SV1179: $i] :
( ( ! [SY3302: $i,SY3303: $i,SY3304: $i,SY3305: $i,SY3306: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ SY3304 @ SY3303 ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ SY3302 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3306 @ SY3305 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3302 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ ( sK14_B_a @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ ( sK16_SY711 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3306 @ SY3305 ) @ ( tc_prod @ SY3306 @ SY3305 ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ ( sK16_SY711 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3306 @ SY3305 @ SY3302 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3306 @ SY3305 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3306 @ SY3305 @ SY3304 @ SY3303 @ SY3302 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3304 ) @ SY3303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(3881,plain,
! [SV1076: $i,SV930: $i] :
( ( ~ ! [SY3048: $i,SY3049: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3049 @ SV930 )
| ( c_member @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SV1076 @ SY3048 ) @ ( c_Transitive__Closure_Ortrancl @ SY3049 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3049 @ ( c_Set_Oinsert @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SY3048 @ SV1076 ) @ SV930 ) ) )
| ~ ~ ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) )
| ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3715]) ).
thf(3882,plain,
! [SV931: $i,SV1077: $i] :
( ( ~ ! [SY3054: $i,SY3055: $i] :
( ! [SY3056: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SY3055 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3055 @ SY3056 @ SY3054 ) @ SV931 )
| ( c_member @ SY3055 @ SY3054 @ ( c_Relation_ORange @ SV1077 @ SY3055 @ SV931 ) ) )
| ~ ! [SY3057: $i,SY3058: $i] :
( ~ ( c_member @ SY3058 @ SY3057 @ ( c_Relation_ORange @ SV1077 @ SY3058 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SY3058 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3058 @ ( sK65_B_y @ SY3058 @ SY3057 @ SV1077 @ SV931 ) @ SY3057 ) @ SV931 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(3883,plain,
! [SV932: $i,SV1078: $i,SV1180: $i] :
( ( ! [SY3307: $i,SY3308: $i,SY3309: $i,SY3310: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SY3308 @ SY3307 ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3310 @ SY3309 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SY3308 @ SY3307 )
= ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SY3308 @ SY3307 ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ ( sK46_B_a @ SY3310 @ SY3309 @ SY3308 @ SY3307 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3310 @ SY3309 @ SY3308 @ SY3307 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3310 @ SY3309 ) @ ( tc_prod @ SY3310 @ SY3309 ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ ( sK46_B_a @ SY3310 @ SY3309 @ SY3308 @ SY3307 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3310 @ SY3309 @ SY3308 @ SY3307 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY3310 @ SY3309 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3310 @ SY3309 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(3884,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( c_member @ SX1 @ ( sK31_SY722 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( c_member @ SX1 @ ( sK30_SY724 @ SX2 @ SX1 @ SX0 ) @ ( sK29_B_Q @ SX1 @ SX0 ) ) )
| ~ ( c_member @ SX1 @ SX2 @ ( sK29_B_Q @ SX1 @ SX0 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( c_member @ SX1 @ SX3 @ SX2 ) )
| ~ ( c_member @ SX1 @ ( sK28_B_x @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3886,plain,
! [SV933: $i,SV1079: $i,SV1181: $i] :
( ( ! [SY3311: $i] :
~ ( ~ ! [SY3312: $i,SY3313: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3313 @ SY3313 ) @ ( c_Product__Type_OPair @ SY3313 @ SY3313 @ ( sK43_B_y @ SY3313 @ SY3312 @ SY3311 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SY3311 @ ( sK43_B_y @ SY3313 @ SY3312 @ SY3311 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3313 @ SY3312 @ SY3311 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3313 @ SY3312 @ SY3311 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3313 @ SY3312 @ SV933 @ SV1181 @ SV1079 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ( ( c_Recdef_Ocut @ SY3315 @ SY3314 @ SY3311 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3315 @ SY3314 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3316: $i] :
( ~ ( c_member @ ( tc_prod @ SY3315 @ SY3315 ) @ ( c_Product__Type_OPair @ SY3315 @ SY3315 @ SY3316 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SY3311 @ SY3316 )
= ( hAPP @ SV933 @ SY3316 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(3887,plain,
! [SV934: $i,SV1080: $i] :
( ( ~ ! [SY3071: $i,SY3072: $i] :
( ( SY3072 != SY3071 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3072 )
| ( c_member @ SV1080 @ SV934 @ SY3071 ) )
| ~ ! [SY3073: $i,SY3074: $i] :
( ( SY3074 != SY3073 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3073 )
| ( c_member @ SV1080 @ SV934 @ SY3074 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3888,plain,
! [SV935: $i,SV1081: $i,SV1182: $i] :
( ( ! [SY3317: $i] :
( ~ ( c_member @ ( tc_prod @ SY3317 @ SY3317 ) @ ( c_Product__Type_OPair @ SY3317 @ SY3317 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SY3317 @ SV935 ) )
| ( c_member @ ( tc_prod @ SY3317 @ SY3317 ) @ ( c_Product__Type_OPair @ SY3317 @ SY3317 @ SV1182 @ SV1081 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3317 @ SY3317 ) @ ( c_Product__Type_OPair @ SY3317 @ SY3317 @ SV1182 @ ( sK37_B_c @ SY3317 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SY3317 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SY3317 @ SY3317 ) @ ( c_Product__Type_OPair @ SY3317 @ SY3317 @ ( sK37_B_c @ SY3317 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(3889,plain,
! [SV936: $i,SV1183: $i,SV1082: $i] :
( ( ! [SY3318: $i] :
~ ( ~ ( ( SY3318 != SV1082 )
| ( SV1183 != SV936 )
| ! [SY3319: $i,SY3320: $i] :
( ( c_Product__Type_OPair @ SY3320 @ SY3319 @ SY3318 @ SV1183 )
= ( c_Product__Type_OPair @ SY3320 @ SY3319 @ SV1082 @ SV936 ) ) )
| ~ ~ ( ~ ( ! [SY3321: $i,SY3322: $i] :
( ( c_Product__Type_OPair @ SY3322 @ SY3321 @ SY3318 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3322 @ SY3321 @ SV1082 @ SV936 ) )
| ( SY3318 = SV1082 ) )
| ~ ( ! [SY3323: $i,SY3324: $i] :
( ( c_Product__Type_OPair @ SY3324 @ SY3323 @ SY3318 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3324 @ SY3323 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(3890,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ~ ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) )
| ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) )
| ~ ~ ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) )
| ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(3891,plain,
! [SV938: $i,SV1084: $i,SV1184: $i] :
( ( ! [SY3325: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ SY3325 @ ( sK9_B_x @ SY3325 @ SV1184 @ SV1084 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SY3325 @ SV1184 @ SV1084 @ SV938 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SY3325 @ SV1084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(3892,plain,
! [SV939: $i] :
( ( ~ ! [SY2700: $i] :
( ! [SY2701: $i] :
~ ( c_member @ SY2701 @ SY2700 @ SV939 )
| ( hBOOL @ ( hAPP @ SV939 @ SY2700 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3893,plain,
! [SV939: $i] :
( ( ~ ! [SY2702: $i] :
( ~ ( hBOOL @ ( hAPP @ SV939 @ SY2702 ) )
| ! [SY2703: $i] : ( c_member @ SY2703 @ SY2702 @ SV939 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3894,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ! [SY3095: $i,SY3096: $i] :
( ( SY3095 != SV1085 )
| ~ ( c_member @ SY3096 @ SY3095 @ SV940 )
| ( c_member @ ( tc_prod @ SY3096 @ SY3096 ) @ ( c_Product__Type_OPair @ SY3096 @ SY3096 @ SY3095 @ SV1085 ) @ ( c_Relation_OId__on @ SY3096 @ SV940 ) ) )
| ~ ~ ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) )
| ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(3895,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1185 @ SV1185 ) @ ( c_Product__Type_OPair @ SV1185 @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 )
| ~ ~ ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) )
| ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(3896,plain,
! [SV942: $i,SV1087: $i,SV1186: $i] :
( ( ! [SY3326: $i] :
( ~ ( c_member @ ( tc_prod @ SY3326 @ SY3326 ) @ ( c_Product__Type_OPair @ SY3326 @ SY3326 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SY3326 @ SV942 ) )
| ( c_member @ ( tc_prod @ SY3326 @ SY3326 ) @ ( c_Product__Type_OPair @ SY3326 @ SY3326 @ SV1186 @ SV1087 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3326 @ SY3326 ) @ ( c_Product__Type_OPair @ SY3326 @ SY3326 @ SV1186 @ ( sK38_B_y @ SY3326 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SY3326 @ SY3326 ) @ ( c_Product__Type_OPair @ SY3326 @ SY3326 @ ( sK38_B_y @ SY3326 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SY3326 @ SV942 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3897,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ~ ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) )
| ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) )
| ~ ~ ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) )
| ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(3898,plain,
! [SV944: $i,SV1089: $i,SV1187: $i] :
( ( ! [SY3327: $i] :
( ~ ( c_member @ ( tc_prod @ SY3327 @ SY3327 ) @ ( c_Product__Type_OPair @ SY3327 @ SY3327 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SY3327 @ SV944 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3327 @ SY3327 ) @ ( c_Product__Type_OPair @ SY3327 @ SY3327 @ SV1187 @ ( sK42_B_z @ SY3327 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3327 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SY3327 @ SY3327 ) @ ( c_Product__Type_OPair @ SY3327 @ SY3327 @ ( sK42_B_z @ SY3327 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(3899,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK76_B_x @ SX1 @ SX0 ) @ ( sK76_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(3900,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Nitpick_Orefl_H @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3733]) ).
thf(3901,plain,
! [SV945: $i,SV1090: $i,SV1188: $i] :
( ( ! [SY3328: $i,SY3329: $i,SY3330: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3330 @ SY3330 ) @ ( c_Product__Type_OPair @ SY3330 @ SY3330 @ ( sK56_B_z @ SY3330 @ SY3329 @ SY3328 @ SV1188 @ SV1090 @ SV945 ) @ SY3329 ) @ SY3328 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3330 @ SV1188 @ SY3328 @ SV1090 @ ( sK56_B_z @ SY3330 @ SY3329 @ SY3328 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SY3330 @ SY3329 @ SY3328 @ SV1188 @ SV1090 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY3330 @ SV1188 @ SY3328 @ SV1090 @ SY3329 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SY3329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(3902,plain,
! [SV946: $i] :
( ( ~ ! [SY2733: $i,SY2734: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2734 @ SY2733 @ SV946 )
| ~ ( c_Relation_Oantisym @ SY2734 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SY2734 @ SY2733 @ SV946 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3903,plain,
! [SV946: $i] :
( ( ~ ~ ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) )
| ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3904,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3736]) ).
thf(3905,plain,
( ( ~ ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(3906,plain,
! [SV947: $i] :
( ( ~ ! [SY2739: $i,SY2740: $i] :
( ~ ( c_Relation_Oirrefl @ SY2740 @ SV947 )
| ~ ( c_Relation_Otrans @ SY2740 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SY2740 @ SY2739 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY2740 @ SY2739 @ SV947 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3907,plain,
! [SV947: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
| ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3908,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ! [SY3118: $i,SY3119: $i] :
( ~ ( c_member @ SY3119 @ SY3118 @ ( c_Set_Oinsert @ SY3119 @ SV1091 @ SV948 ) )
| ( SY3118 = SV1091 )
| ( c_member @ SY3119 @ SY3118 @ SV948 ) )
| ~ ~ ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) )
| ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3909,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ ( sK72_B_x @ SX1 @ SX0 ) @ ( sK72_B_x @ SX1 @ SX0 ) ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(3910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Oirrefl @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3741]) ).
thf(3911,plain,
! [SV949: $i,SV1092: $i,SV1189: $i] :
( ( ! [SY3331: $i] :
~ ( ~ ! [SY3332: $i,SY3333: $i] :
( ! [SY3334: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3333 @ SY3333 ) @ ( c_Product__Type_OPair @ SY3333 @ SY3333 @ ( sK55_B_z @ SY3334 @ SY3333 @ SY3332 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SY3331 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3333 @ SY3332 @ SY3331 @ SV1189 @ ( sK55_B_z @ SY3334 @ SY3333 @ SY3332 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3334 @ ( sK55_B_z @ SY3334 @ SY3333 @ SY3332 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3334 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3333 @ SY3332 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) )
| ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3336 @ SY3335 @ SY3331 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3337: $i] :
( ~ ( c_member @ ( tc_prod @ SY3336 @ SY3336 ) @ ( c_Product__Type_OPair @ SY3336 @ SY3336 @ SY3337 @ SV1092 ) @ SY3331 )
| ( c_Recdef_Owfrec__rel @ SY3336 @ SY3335 @ SY3331 @ SV1189 @ SY3337 @ ( hAPP @ ( sK54_B_g @ SY3336 @ SY3335 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) @ SY3337 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3336 @ SY3335 @ SY3331 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(3912,plain,
! [SV950: $i,SV1093: $i] :
( ( ~ ! [SY3132: $i,SY3133: $i] :
( ~ ( c_member @ SY3133 @ SY3132 @ SV1093 )
| ( c_member @ SY3133 @ SY3132 @ ( c_Set_Oinsert @ SY3133 @ SV950 @ SV1093 ) ) )
| ~ ! [SY3134: $i] :
( ( SY3134 != SV950 )
| ! [SY3135: $i] : ( c_member @ SY3135 @ SY3134 @ ( c_Set_Oinsert @ SY3135 @ SV950 @ SV1093 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3913,plain,
! [SV951: $i,SV1094: $i,SV1190: $i] :
( ( ! [SY3338: $i,SY3339: $i] :
( ~ ( c_member @ ( tc_prod @ SY3339 @ SY3339 ) @ ( c_Product__Type_OPair @ SY3339 @ SY3339 @ SY3338 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SY3339 @ SV1094 ) )
| ~ ( hBOOL @ ( hAPP @ SV951 @ SY3338 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3339 @ SY3339 ) @ ( c_Product__Type_OPair @ SY3339 @ SY3339 @ SY3338 @ ( sK10_B_y @ SY3339 @ SY3338 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3339 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3339 @ SY3339 ) @ ( c_Product__Type_OPair @ SY3339 @ SY3339 @ ( sK10_B_y @ SY3339 @ SY3338 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SY3339 @ SY3338 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SY3339 @ SY3338 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SY3339 @ SY3338 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(3914,plain,
! [SV952: $i,SV1095: $i] :
( ( ~ ! [SY3139: $i] :
( ! [SY3140: $i] :
~ ( c_member @ ( tc_prod @ SY3140 @ SY3140 ) @ ( c_Product__Type_OPair @ SY3140 @ SY3140 @ SY3139 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3140 @ SV952 ) )
| ( SY3139 != SV1095 )
| ( SY3139 = SV1095 ) )
| ~ ! [SY3141: $i,SY3142: $i] :
( ~ ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3142 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SY3142 @ SV952 ) )
| ( SY3141 = SV1095 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3915,plain,
! [SV953: $i,SV1096: $i,SV1191: $i] :
( ( ! [SY3340: $i,SY3341: $i] :
( ~ ( c_member @ SY3341 @ SY3340 @ ( c_Relation_OImage @ SV1191 @ SY3341 @ SV1096 @ SV953 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1191 @ SY3341 ) @ ( c_Product__Type_OPair @ SV1191 @ SY3341 @ ( sK23_B_x @ SY3341 @ SY3340 @ SV1191 @ SV1096 @ SV953 ) @ SY3340 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SY3341 @ SY3340 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(3916,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 = SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(3917,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3748]) ).
thf(3918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ SX1 @ ( sK32_B_x @ SX1 @ SX0 ) @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3919,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] : ( c_member @ SX1 @ SX2 @ ( c_Wellfounded_Oacc @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3920,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1192 @ SV1192 ) @ ( c_Product__Type_OPair @ SV1192 @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 )
| ~ ~ ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(3921,plain,
! [SV1098: $i,SV955: $i] :
( ( ~ ! [SY3147: $i,SY3148: $i] :
( ~ ( c_Wellfounded_Owf @ SY3148 @ SV955 )
| ( c_member @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SV1098 @ SY3147 ) @ ( c_Transitive__Closure_Ortrancl @ SY3148 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3148 @ ( c_Set_Oinsert @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SY3147 @ SV1098 ) @ SV955 ) ) )
| ~ ~ ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) )
| ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3922,plain,
! [SV795: $i,SV956: $i,SV1099: $i,SV1193: $i] :
( ( ! [SY3342: $i] :
( ~ ( c_Relation_Otrans @ SY3342 @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SY3342 @ SY3342 ) @ ( c_Product__Type_OPair @ SY3342 @ SY3342 @ SV1099 @ SV956 ) @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SY3342 @ SY3342 ) @ ( c_Product__Type_OPair @ SY3342 @ SY3342 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SY3342 @ SY3342 ) @ ( c_Product__Type_OPair @ SY3342 @ SY3342 @ SV1099 @ SV795 ) @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(3923,plain,
! [SV796: $i,SV957: $i,SV1100: $i,SV1194: $i] :
( ( ( SV1194 != SV1100 )
| ~ ( c_member @ SV957 @ SV1100 @ SV796 )
| ( c_member @ SV957 @ SV1194 @ SV796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(3924,plain,
! [SV797: $i,SV958: $i,SV1101: $i,SV1195: $i] :
( ( ! [SY3343: $i,SY3344: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY3344 @ SY3343 @ SV1195 @ SV1101 @ ( c_Product__Type_OPair @ SY3344 @ SY3343 @ SV958 @ SV797 ) )
= ( hAPP @ ( hAPP @ SV1101 @ SV958 ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(3925,plain,
! [SV798: $i,SV959: $i,SV1102: $i,SV1196: $i] :
( ( ! [SY3345: $i,SY3346: $i] :
( ( c_Product__Type_Ointernal__split @ SY3346 @ SY3345 @ SV1196 @ SV1102 @ ( c_Product__Type_OPair @ SY3346 @ SY3345 @ SV959 @ SV798 ) )
= ( hAPP @ ( hAPP @ SV1102 @ SV959 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(3926,plain,
! [SV799: $i,SV960: $i,SV1103: $i,SV1197: $i] :
( ( ! [SY3347: $i] :
( ~ ( c_member @ ( tc_prod @ SY3347 @ SV1197 ) @ ( c_Product__Type_OPair @ SY3347 @ SV1197 @ SV1103 @ SV960 ) @ SV799 )
| ( c_member @ SV1197 @ SV960 @ ( c_Relation_ORange @ SY3347 @ SV1197 @ SV799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(3927,plain,
! [SV800: $i,SV961: $i,SV1104: $i,SV1198: $i] :
( ( ( SV1198 != SV1104 )
| ~ ( c_member @ SV961 @ SV1198 @ SV800 )
| ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SV1198 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(3928,plain,
! [SV801: $i,SV962: $i,SV1105: $i,SV1199: $i] :
( ( ! [SY3348: $i] :
( ~ ( c_member @ ( tc_prod @ SY3348 @ SV1199 ) @ ( c_Product__Type_OPair @ SY3348 @ SV1199 @ SV1105 @ SV962 ) @ SV801 )
| ( c_member @ SY3348 @ SV1105 @ ( c_Relation_ODomain @ SY3348 @ SV1199 @ SV801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(3929,plain,
! [SV802: $i,SV963: $i,SV1106: $i,SV1200: $i] :
( ( ~ ( c_Relation_Otrans @ SV1200 @ SV1106 )
| ~ ( c_Relation_Otrans @ SV963 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SV1200 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SV1200 @ SV963 @ SV1106 @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3930,plain,
! [SV804: $i,SV965: $i,SV1107: $i,SV1201: $i] :
( ( ~ ( c_Relation_Otrans @ SV1201 @ SV1107 )
| ( c_Relation_Otrans @ SV965 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1201 @ SV965 @ SV1107 ) @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(3931,plain,
! [SV805: $i,SV966: $i,SV1108: $i,SV1202: $i] :
( ( ~ ( c_member @ SV1202 @ SV1108 @ ( c_Relation_ORange @ SV966 @ SV1202 @ SV805 ) )
| ( c_member @ ( tc_prod @ SV966 @ SV1202 ) @ ( c_Product__Type_OPair @ SV966 @ SV1202 @ ( sK63_B_x @ SV1202 @ SV1108 @ SV966 @ SV805 ) @ SV1108 ) @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3932,plain,
! [SV806: $i,SV967: $i,SV1109: $i,SV1203: $i] :
( ( ~ ( c_member @ SV1203 @ SV1109 @ ( c_Relation_ODomain @ SV1203 @ SV967 @ SV806 ) )
| ( c_member @ ( tc_prod @ SV1203 @ SV967 ) @ ( c_Product__Type_OPair @ SV1203 @ SV967 @ SV1109 @ ( sK62_B_y @ SV1203 @ SV1109 @ SV967 @ SV806 ) ) @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(3933,plain,
! [SV807: $i,SV968: $i,SV1110: $i,SV1204: $i] :
( ( ~ ( c_member @ SV1204 @ SV1110 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
| ~ ( c_member @ ( tc_prod @ SV1204 @ SV1204 ) @ ( c_Product__Type_OPair @ SV1204 @ SV1204 @ SV807 @ SV1110 ) @ SV968 )
| ( c_member @ SV1204 @ SV807 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(3934,plain,
! [SV808: $i,SV969: $i,SV1111: $i,SV1205: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV1205 @ SV1111 @ SV969 )
| ~ ( c_member @ SV1205 @ SV808 @ SV1111 )
| ( c_member @ ( tc_prod @ SV1205 @ SV1205 ) @ ( c_Product__Type_OPair @ SV1205 @ SV1205 @ SV808 @ SV808 ) @ SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(3935,plain,
! [SV809: $i,SV970: $i,SV1112: $i,SV1206: $i] :
( ( ! [SY3349: $i] :
( ~ ( c_Relation_Orefl__on @ SY3349 @ SV1206 @ SV1112 )
| ~ ( c_member @ ( tc_prod @ SY3349 @ SY3349 ) @ ( c_Product__Type_OPair @ SY3349 @ SY3349 @ SV970 @ SV809 ) @ SV1112 )
| ( c_member @ SY3349 @ SV970 @ SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(3936,plain,
! [SV810: $i,SV971: $i,SV1113: $i,SV1207: $i] :
( ( ! [SY3350: $i] :
( ~ ( c_Relation_Orefl__on @ SY3350 @ SV1207 @ SV1113 )
| ~ ( c_member @ ( tc_prod @ SY3350 @ SY3350 ) @ ( c_Product__Type_OPair @ SY3350 @ SY3350 @ SV971 @ SV810 ) @ SV1113 )
| ( c_member @ SY3350 @ SV810 @ SV1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(3937,plain,
! [SV811: $i,SV972: $i,SV1114: $i,SV1208: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1208 @ SV1208 ) @ ( c_Product__Type_OPair @ SV1208 @ SV1208 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SV1208 @ SV811 ) )
| ~ ( c_member @ SV1208 @ SV972 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
| ( c_member @ SV1208 @ SV1114 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(3938,plain,
! [SV812: $i,SV973: $i,SV1115: $i,SV1209: $i] :
( ( ~ ( c_member @ SV1209 @ SV1115 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
| ~ ( c_member @ ( tc_prod @ SV1209 @ SV1209 ) @ ( c_Product__Type_OPair @ SV1209 @ SV1209 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SV1209 @ SV973 ) )
| ( c_member @ SV1209 @ SV812 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(3939,plain,
! [SV813: $i,SV974: $i,SV1116: $i,SV1210: $i] :
( ( ! [SY3351: $i,SY3352: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3352 @ SY3351 @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SY3352 @ SY3351 ) @ ( c_Product__Type_OPair @ SY3352 @ SY3351 @ SV1116 @ SV974 ) @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SY3352 @ SY3351 ) @ ( c_Product__Type_OPair @ SY3352 @ SY3351 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(3940,plain,
! [SV814: $i,SV975: $i,SV1117: $i,SV1211: $i] :
( ( ! [SY3353: $i,SY3354: $i] :
( ( c_Product__Type_Ocurry @ SY3354 @ SY3353 @ SV1211 @ SV1117 @ SV975 @ SV814 )
= ( hAPP @ SV1117 @ ( c_Product__Type_OPair @ SY3354 @ SY3353 @ SV975 @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3771]) ).
thf(3941,plain,
! [SV816: $i,SV977: $i,SV1119: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ SV816 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ ( c_Transitive__Closure_Ortrancl @ SV1119 @ SV816 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3942,plain,
! [SV817: $i,SV978: $i,SV1120: $i,SV1212: $i] :
( ( ! [SY3355: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3355 @ SY3355 @ SV1212 )
| ~ ( c_member @ ( tc_prod @ SY3355 @ SY3355 ) @ ( c_Product__Type_OPair @ SY3355 @ SY3355 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY3355 @ SV1212 ) )
| ~ ( c_member @ ( tc_prod @ SY3355 @ SY3355 ) @ ( c_Product__Type_OPair @ SY3355 @ SY3355 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY3355 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SY3355 @ SY3355 ) @ ( c_Product__Type_OPair @ SY3355 @ SY3355 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SY3355 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SY3355 @ SY3355 ) @ ( c_Product__Type_OPair @ SY3355 @ SY3355 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SY3355 @ SV1212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(3943,plain,
! [SV818: $i,SV979: $i,SV1121: $i,SV1213: $i] :
( ( ! [SY3356: $i] :
( ~ ( c_member @ ( tc_prod @ SY3356 @ SY3356 ) @ ( c_Product__Type_OPair @ SY3356 @ SY3356 @ SV1213 @ SV1121 ) @ SV979 )
| ~ ( c_member @ ( tc_prod @ SY3356 @ SY3356 ) @ ( c_Product__Type_OPair @ SY3356 @ SY3356 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY3356 @ SV979 ) )
| ( c_member @ ( tc_prod @ SY3356 @ SY3356 ) @ ( c_Product__Type_OPair @ SY3356 @ SY3356 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SY3356 @ SV979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(3944,plain,
! [SV819: $i,SV980: $i,SV1122: $i,SV1214: $i] :
( ( ! [SY3357: $i] :
( ~ ( c_member @ ( tc_prod @ SY3357 @ SY3357 ) @ ( c_Product__Type_OPair @ SY3357 @ SY3357 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SY3357 @ SV980 ) )
| ~ ( c_member @ ( tc_prod @ SY3357 @ SY3357 ) @ ( c_Product__Type_OPair @ SY3357 @ SY3357 @ SV1122 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SY3357 @ SY3357 ) @ ( c_Product__Type_OPair @ SY3357 @ SY3357 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SY3357 @ SV980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(3945,plain,
! [SV820: $i,SV981: $i,SV1123: $i,SV1215: $i] :
( ( ! [SY3358: $i] :
( ~ ( c_member @ ( tc_prod @ SY3358 @ SY3358 ) @ ( c_Product__Type_OPair @ SY3358 @ SY3358 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SY3358 @ SV981 ) )
| ~ ( c_member @ ( tc_prod @ SY3358 @ SY3358 ) @ ( c_Product__Type_OPair @ SY3358 @ SY3358 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY3358 @ SV981 ) )
| ( c_member @ ( tc_prod @ SY3358 @ SY3358 ) @ ( c_Product__Type_OPair @ SY3358 @ SY3358 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SY3358 @ SV981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(3946,plain,
! [SV822: $i,SV983: $i,SV1124: $i,SV1216: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Otrancl @ SV1216 @ SV822 ) )
| ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Ortrancl @ SV1216 @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(3947,plain,
! [SV823: $i,SV984: $i,SV1125: $i,SV1217: $i] :
( ( ! [SY3359: $i,SY3360: $i] :
( ~ ( c_member @ ( tc_prod @ SY3360 @ SY3360 ) @ ( c_Product__Type_OPair @ SY3360 @ SY3360 @ SY3359 @ SV1217 ) @ SV1125 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY3360 @ SV984 @ SV823 @ SV1125 @ SV1217 ) @ SY3359 )
= ( hAPP @ SV823 @ SY3359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(3948,plain,
! [SV824: $i,SV985: $i,SV1126: $i,SV1218: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ SV824 )
| ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ ( c_Transitive__Closure_Otrancl @ SV1218 @ SV824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(3949,plain,
! [SV825: $i,SV986: $i,SV1127: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ SV825 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ ( c_Transitive__Closure_Otrancl @ SV1127 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(3950,plain,
! [SV827: $i,SV988: $i] :
( ( ( c_Relation_Otrans @ SV988 @ SV827 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV988 @ SV827 )
= SV827 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3951,plain,
! [SV828: $i,SV989: $i,SV1128: $i,SV1219: $i] :
( ( ! [SY3361: $i] :
( ~ ( c_member @ ( tc_prod @ SY3361 @ SY3361 ) @ ( c_Product__Type_OPair @ SY3361 @ SY3361 @ SV1219 @ SV1128 ) @ SV989 )
| ~ ( c_member @ ( tc_prod @ SY3361 @ SY3361 ) @ ( c_Product__Type_OPair @ SY3361 @ SY3361 @ SV1128 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SY3361 @ SY3361 ) @ ( c_Product__Type_OPair @ SY3361 @ SY3361 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SY3361 @ SV989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(3952,plain,
! [SV829: $i,SV990: $i,SV1129: $i,SV1220: $i] :
( ( ! [SY3362: $i] :
( ~ ( c_member @ ( tc_prod @ SY3362 @ SY3362 ) @ ( c_Product__Type_OPair @ SY3362 @ SY3362 @ SV1220 @ SV1129 ) @ SV990 )
| ~ ( c_member @ ( tc_prod @ SY3362 @ SY3362 ) @ ( c_Product__Type_OPair @ SY3362 @ SY3362 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY3362 @ SV990 ) )
| ( c_member @ ( tc_prod @ SY3362 @ SY3362 ) @ ( c_Product__Type_OPair @ SY3362 @ SY3362 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SY3362 @ SV990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(3953,plain,
! [SV830: $i,SV991: $i,SV1130: $i,SV1221: $i] :
( ( ! [SY3363: $i] :
( ~ ( c_member @ ( tc_prod @ SY3363 @ SY3363 ) @ ( c_Product__Type_OPair @ SY3363 @ SY3363 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SY3363 @ SV991 ) )
| ~ ( c_member @ ( tc_prod @ SY3363 @ SY3363 ) @ ( c_Product__Type_OPair @ SY3363 @ SY3363 @ SV1130 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SY3363 @ SY3363 ) @ ( c_Product__Type_OPair @ SY3363 @ SY3363 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SY3363 @ SV991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(3954,plain,
! [SV831: $i,SV992: $i,SV1131: $i,SV1222: $i] :
( ( ! [SY3364: $i] :
( ~ ( c_member @ ( tc_prod @ SY3364 @ SY3364 ) @ ( c_Product__Type_OPair @ SY3364 @ SY3364 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SY3364 @ SV992 ) )
| ~ ( c_member @ ( tc_prod @ SY3364 @ SY3364 ) @ ( c_Product__Type_OPair @ SY3364 @ SY3364 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY3364 @ SV992 ) )
| ( c_member @ ( tc_prod @ SY3364 @ SY3364 ) @ ( c_Product__Type_OPair @ SY3364 @ SY3364 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SY3364 @ SV992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(3955,plain,
! [SV832: $i,SV993: $i,SV1132: $i,SV1223: $i] :
( ( ! [SY3365: $i] :
( ~ ( c_member @ ( tc_prod @ SY3365 @ SY3365 ) @ ( c_Product__Type_OPair @ SY3365 @ SY3365 @ SV1223 @ SV1132 ) @ SV993 )
| ~ ( c_member @ ( tc_prod @ SY3365 @ SY3365 ) @ ( c_Product__Type_OPair @ SY3365 @ SY3365 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SY3365 @ SV993 ) )
| ( c_member @ ( tc_prod @ SY3365 @ SY3365 ) @ ( c_Product__Type_OPair @ SY3365 @ SY3365 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SY3365 @ SV993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(3956,plain,
! [SV833: $i,SV994: $i,SV1133: $i,SV1224: $i] :
( ( ! [SY3366: $i] :
( ~ ( c_member @ ( tc_prod @ SY3366 @ SY3366 ) @ ( c_Product__Type_OPair @ SY3366 @ SY3366 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SY3366 @ SV994 ) )
| ~ ( c_member @ ( tc_prod @ SY3366 @ SY3366 ) @ ( c_Product__Type_OPair @ SY3366 @ SY3366 @ SV1133 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SY3366 @ SY3366 ) @ ( c_Product__Type_OPair @ SY3366 @ SY3366 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SY3366 @ SV994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(3957,plain,
! [SV834: $i,SV995: $i,SV1134: $i,SV1225: $i] :
( ( ! [SY3367: $i] :
( ~ ( c_member @ ( tc_prod @ SY3367 @ SY3367 ) @ ( c_Product__Type_OPair @ SY3367 @ SY3367 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SY3367 @ SV995 ) )
| ~ ( c_member @ ( tc_prod @ SY3367 @ SY3367 ) @ ( c_Product__Type_OPair @ SY3367 @ SY3367 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SY3367 @ SV995 ) )
| ( c_member @ ( tc_prod @ SY3367 @ SY3367 ) @ ( c_Product__Type_OPair @ SY3367 @ SY3367 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SY3367 @ SV995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(3958,plain,
! [SV835: $i,SV996: $i,SV1135: $i,SV1226: $i] :
( ( ! [SY3368: $i] :
( ~ ( c_member @ ( tc_prod @ SY3368 @ SY3368 ) @ ( c_Product__Type_OPair @ SY3368 @ SY3368 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SY3368 @ SV996 ) )
| ~ ( c_member @ ( tc_prod @ SY3368 @ SY3368 ) @ ( c_Product__Type_OPair @ SY3368 @ SY3368 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY3368 @ SV996 ) )
| ( c_member @ ( tc_prod @ SY3368 @ SY3368 ) @ ( c_Product__Type_OPair @ SY3368 @ SY3368 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SY3368 @ SV996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(3959,plain,
! [SV836: $i,SV997: $i,SV1136: $i,SV1227: $i] :
( ( ! [SY3369: $i,SY3370: $i] :
( ~ ( c_member @ ( tc_prod @ SV1227 @ SV1227 ) @ ( c_Product__Type_OPair @ SV1227 @ SV1227 @ SV1136 @ SV997 ) @ SY3370 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV1227 @ SV836 @ SY3369 @ SY3370 @ SV997 ) @ SV1136 )
= ( hAPP @ SY3369 @ SV1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(3960,plain,
! [SV837: $i,SV998: $i,SV1137: $i,SV1228: $i] :
( ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1228 @ SV1137 ) )
| ~ ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ SV998 @ SV837 ) @ SV1137 )
| ( SV998 != SV837 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(3961,plain,
! [SV841: $i,SV1001: $i] :
( ( ( c_member @ ( tc_prod @ SV1001 @ SV1001 ) @ SV841 @ ( c_Relation_OId @ SV1001 ) )
= $false )
| ( ( SV841
= ( c_Product__Type_OPair @ SV1001 @ SV1001 @ ( sK35_B_x @ SV1001 @ SV841 ) @ ( sK35_B_x @ SV1001 @ SV841 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3794]) ).
thf(3962,plain,
! [SV842: $i,SV1002: $i,SV1138: $i,SV1229: $i] :
( ( ~ ( c_Relation_Oantisym @ SV1229 @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(3963,plain,
! [SV843: $i,SV1003: $i,SV1139: $i,SV1230: $i] :
( ( ~ ( c_member @ SV1230 @ SV1139 @ ( c_Set_Oinsert @ SV1230 @ SV1003 @ SV843 ) )
| ( SV1139 = SV1003 )
| ( c_member @ SV1230 @ SV1139 @ SV843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(3964,plain,
! [SV844: $i,SV1004: $i,SV1140: $i,SV1231: $i] :
( ( ! [SY3371: $i] :
( ( c_Relation_ODomain @ SY3371 @ SV1231 @ ( c_Set_Oinsert @ ( tc_prod @ SY3371 @ SV1231 ) @ ( c_Product__Type_OPair @ SY3371 @ SV1231 @ SV1140 @ SV1004 ) @ SV844 ) )
= ( c_Set_Oinsert @ SY3371 @ SV1140 @ ( c_Relation_ODomain @ SY3371 @ SV1231 @ SV844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(3965,plain,
! [SV845: $i,SV1005: $i,SV1141: $i,SV1232: $i] :
( ( ! [SY3372: $i] :
( ( c_Relation_ORange @ SY3372 @ SV1232 @ ( c_Set_Oinsert @ ( tc_prod @ SY3372 @ SV1232 ) @ ( c_Product__Type_OPair @ SY3372 @ SV1232 @ SV1141 @ SV1005 ) @ SV845 ) )
= ( c_Set_Oinsert @ SV1232 @ SV1005 @ ( c_Relation_ORange @ SY3372 @ SV1232 @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(3966,plain,
! [SV847: $i,SV1007: $i,SV1143: $i,SV1233: $i] :
( ( ~ ( c_member @ SV1233 @ SV1143 @ SV1007 )
| ( c_member @ SV1233 @ SV1143 @ ( c_Set_Oinsert @ SV1233 @ SV847 @ SV1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(3967,plain,
! [SV848: $i,SV1008: $i,SV1144: $i] :
( ( ( ~ ( c_member @ SV1144 @ SV1008 @ SV848 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV1144 @ SV1008 @ SV848 )
= SV848 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(3968,plain,
! [SV849: $i,SV1009: $i,SV1145: $i,SV1234: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1234 @ SV1145 )
| ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV1234 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SV1234 @ SV1009 @ SV1145 @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(3969,plain,
! [SV850: $i,SV1010: $i,SV1146: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1146 @ SV1010 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1146 @ SV1146 ) @ ( c_Product__Type_OPair @ SV1146 @ SV1146 @ SV850 @ SV850 ) @ SV1010 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(3970,plain,
! [SV851: $i,SV1011: $i,SV1147: $i,SV1235: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1235 @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(3971,plain,
! [SV852: $i,SV1012: $i,SV1148: $i,SV1236: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1236 @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(3972,plain,
! [SV853: $i,SV1013: $i,SV1149: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1149 @ SV1013 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1149 @ SV1149 ) @ ( c_Product__Type_OPair @ SV1149 @ SV1149 @ SV853 @ SV853 ) @ SV1013 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(3973,plain,
! [SV854: $i,SV1014: $i,SV1150: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1150 @ SV1014 ) )
= $true )
| ( ( c_member @ SV1150 @ SV854 @ ( c_Wellfounded_Oacc @ SV1150 @ SV1014 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(3974,plain,
! [SV855: $i,SV1015: $i] :
( ( ( c_member @ SV1015 @ ( sK25_B_x @ SV1015 @ SV855 ) @ ( c_Wellfounded_Oacc @ SV1015 @ SV855 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1015 @ SV855 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3808]) ).
thf(3975,plain,
! [SV856: $i,SV1016: $i,SV1151: $i,SV1237: $i] :
( ( ! [SY3373: $i,SY3374: $i] :
( ~ ( c_member @ SY3374 @ SY3373 @ SV1237 )
| ~ ( c_member @ ( tc_prod @ SY3374 @ SV1151 ) @ ( c_Product__Type_OPair @ SY3374 @ SV1151 @ SY3373 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SY3374 @ SV1151 @ SV856 @ SV1237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(3976,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i] :
( ( ! [SY3375: $i,SY3376: $i,SY3377: $i,SY3378: $i] :
( ~ ( c_member @ ( tc_prod @ SY3378 @ SY3377 ) @ ( c_Product__Type_OPair @ SY3378 @ SY3377 @ SY3376 @ SY3375 ) @ SV1238 )
| ~ ( c_member @ ( tc_prod @ SY3377 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3377 @ SV1152 @ SY3375 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY3378 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3378 @ SV1152 @ SY3376 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY3378 @ SY3377 @ SV1152 @ SV1238 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(3977,plain,
! [SV858: $i,SV1018: $i] :
( ( ( ( hAPP @ SV1018 @ ( sK22_B_x @ SV1018 @ SV858 ) )
= ( hAPP @ SV858 @ ( sK22_B_x @ SV1018 @ SV858 ) ) )
= $false )
| ( ( SV1018 = SV858 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(3978,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i] :
( ( ! [SY3379: $i,SY3380: $i,SY3381: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3381 @ SY3380 ) )
| ~ ( c_member @ ( tc_prod @ SY3379 @ SY3379 ) @ ( c_Product__Type_OPair @ SY3379 @ SY3379 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SY3380 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SY3379 ) @ ( tc_prod @ SV859 @ SY3379 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SY3379 ) @ ( tc_prod @ SV859 @ SY3379 ) @ ( c_Product__Type_OPair @ SV859 @ SY3379 @ SY3380 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SY3379 @ SY3380 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SY3379 @ SY3381 @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(3979,plain,
! [SV863: $i,SV1023: $i,SV1154: $i,SV1240: $i] :
( ( ! [SY3382: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3382 @ ( c_Product__Type_OPair @ SV1240 @ SV1154 @ SV1023 @ SV863 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SV1240 @ SV1154 @ tc_HOL_Obool @ SY3382 @ SV1023 @ SV863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(3980,plain,
! [SV864: $i,SV1024: $i,SV1155: $i,SV1241: $i] :
( ( ! [SY3383: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY3383 @ SV1241 @ tc_HOL_Obool @ SV1155 @ SV1024 @ SV864 ) )
| ( hBOOL @ ( hAPP @ SV1155 @ ( c_Product__Type_OPair @ SY3383 @ SV1241 @ SV1024 @ SV864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(3981,plain,
! [SV865: $i,SV1025: $i,SV1156: $i,SV1242: $i] :
( ( ! [SY3384: $i] :
( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SY3384 @ SV1242 @ tc_HOL_Obool @ SV1156 @ SV1025 @ SV865 ) )
| ( hBOOL @ ( hAPP @ SV1156 @ ( c_Product__Type_OPair @ SY3384 @ SV1242 @ SV1025 @ SV865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(3982,plain,
! [SV873: $i,SV1032: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1032 @ SV873 )
= $false )
| ( ( c_Relation_Oantisym @ SV1032 @ ( c_Transitive__Closure_Ortrancl @ SV1032 @ SV873 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(3983,plain,
! [SV875: $i,SV1034: $i,SV1158: $i,SV1243: $i] :
( ( ( c_Set_Oinsert @ SV1243 @ SV1158 @ ( c_Set_Oinsert @ SV1243 @ SV1034 @ SV875 ) )
= ( c_Set_Oinsert @ SV1243 @ SV1034 @ ( c_Set_Oinsert @ SV1243 @ SV1158 @ SV875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(3984,plain,
! [SV878: $i,SV1036: $i,SV1159: $i,SV1244: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1244 @ SV1159 )
| ( c_Wellfounded_Owf @ SV1036 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1244 @ SV1036 @ SV1159 ) @ SV878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(3985,plain,
! [SV879: $i,SV1037: $i] :
( ( ( c_Wellfounded_Owf @ SV1037 @ SV879 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1037 @ ( c_Transitive__Closure_Otrancl @ SV1037 @ SV879 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(3986,plain,
! [SV880: $i,SV1038: $i] :
( ( ( c_Wellfounded_Owf @ SV1038 @ SV880 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV1038 @ SV880 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3987,plain,
! [SV882: $i,SV1040: $i,SV1160: $i,SV1245: $i] :
( ( ! [SY3385: $i,SY3386: $i] :
( ( SY3386
!= ( c_Recdef_Owfrec @ SY3385 @ SV1245 @ SV1160 @ SV1040 ) )
| ~ ( c_Wellfounded_Owf @ SY3385 @ SV1160 )
| ( ( hAPP @ SY3386 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SY3385 @ SV1245 @ SY3386 @ SV1160 @ SV882 ) ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(3988,plain,
! [SV883: $i,SV1041: $i,SV1161: $i,SV1246: $i] :
( ( ! [SY3387: $i] :
( ~ ( c_Wellfounded_Owf @ SY3387 @ SV1246 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SY3387 @ SV1161 @ SV1246 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SY3387 @ SV1161 @ ( c_Recdef_Owfrec @ SY3387 @ SV1161 @ SV1246 @ SV1041 ) @ SV1246 @ SV883 ) ) @ SV883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(3989,plain,
! [SV1162: $i,SV884: $i,SV1247: $i,SV1042: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1042 @ SV1247 )
| ! [SY3388: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SY3388 )
= ( hAPP @ ( hAPP @ SV1162 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SV1247 @ SY3388 ) ) @ SY3388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(3990,plain,
! [SV886: $i,SV1043: $i,SV1163: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1163 @ SV1043 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1163 @ ( c_Wellfounded_Omlex__prod @ SV1163 @ SV886 @ SV1043 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(3991,plain,
! [SV888: $i,SV1044: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1044 @ SV888 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV888 @ SV1044 )
= $true )
| ( ( SV1044 = SV888 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(3992,plain,
! [SV890: $i,SV1045: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1045 @ SV890 )
= $false )
| ( ( ( SV890 != SV1045 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(3993,plain,
! [SV891: $i,SV1046: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1046 @ SV891 )
= $false )
| ( ( ( SV1046 != SV891 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(3994,plain,
! [SV894: $i,SV1048: $i] :
( ( ( SV1048 = SV894 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1048 @ SV894 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(3995,plain,
! [SV895: $i,SV1049: $i,SV1164: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV1049 ) )
= $true )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV895 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(3996,plain,
! [SV896: $i,SV1050: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1050 @ SV896 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SV1050 )
| ( SV1050 = SV896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(3997,plain,
! [SV899: $i,SV1053: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV1053 ) @ SV899 ) )
= $false )
| ( ( SV1053 = SV899 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(3998,plain,
! [SV900: $i,SV1054: $i] :
( ( ( SV1054 = SV900 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_fequal @ SV1054 ) @ SV900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3835]) ).
thf(3999,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK70_SY736 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(4000,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i] :
( ( ! [SY3389: $i] :
( ~ ( c_member @ ( tc_prod @ SY3389 @ SY3389 ) @ ( c_Product__Type_OPair @ SY3389 @ SY3389 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SY3389 @ SV1056 ) )
| ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3389 @ SY3389 ) @ ( c_Product__Type_OPair @ SY3389 @ SY3389 @ ( sK12_B_y @ SY3389 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SY3389 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3389 @ SY3389 ) @ ( c_Product__Type_OPair @ SY3389 @ SY3389 @ ( sK13_SY707 @ SY3389 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SY3389 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SY3389 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SY3389 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4001,plain,
! [SV903: $i,SV1057: $i] :
( ( ~ ! [SY2962: $i,SY2963: $i] :
( ( c_member @ SY2963 @ SY2962 @ SV1057 )
| ( c_member @ SY2963 @ SY2962 @ SV903 )
| ( ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV1057 )
!= ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV903 ) )
| ( SV1057 = SV903 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3838]) ).
thf(4002,plain,
! [SV903: $i,SV1057: $i] :
( ( ~ ! [SY2964: $i,SY2965: $i] :
( ( c_member @ SY2965 @ SY2964 @ SV1057 )
| ( c_member @ SY2965 @ SY2964 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV1057 )
= ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV903 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3838]) ).
thf(4003,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i] :
( ( ! [SY3390: $i,SY3391: $i,SY3392: $i,SY3393: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ SY3391 @ SY3390 ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3393 @ SY3392 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY3391 ) @ SY3390 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ SY3391 @ SY3390 ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ ( sK18_B_a @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3393 @ SY3392 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3393 @ SY3392 ) @ ( tc_prod @ SY3393 @ SY3392 ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ ( sK18_B_a @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY3393 @ SY3392 @ ( sK20_SY717 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY3393 @ SY3392 @ SY3391 @ SY3390 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4004,plain,
! [SV905: $i] :
( ( ! [SY2496: $i,SY2497: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2497 @ SY2497 ) @ ( c_Product__Type_OPair @ SY2497 @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ SY2496 ) @ SV905 )
| ~ ~ ( c_member @ SY2497 @ ( sK61_B_x @ SY2497 @ SY2496 @ SV905 ) @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) )
| ( c_member @ SY2497 @ SY2496 @ ( c_Wellfounded_Oacc @ SY2497 @ SV905 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3840]) ).
thf(4005,plain,
! [SV905: $i] :
( ( ! [SY2498: $i,SY2499: $i] :
( ~ ( c_member @ SY2499 @ SY2498 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) )
| ! [SY2500: $i] :
( ~ ( c_member @ ( tc_prod @ SY2499 @ SY2499 ) @ ( c_Product__Type_OPair @ SY2499 @ SY2499 @ SY2500 @ SY2498 ) @ SV905 )
| ( c_member @ SY2499 @ SY2500 @ ( c_Wellfounded_Oacc @ SY2499 @ SV905 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3841]) ).
thf(4006,plain,
! [SV906: $i] :
( ( ! [SY2501: $i,SY2502: $i] :
( ~ ( ~ ( c_member @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( c_member @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ SY2501 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY2502 @ SY2501 @ SV906 )
!= ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SY2502 @ SY2502 ) @ ( c_Product__Type_OPair @ SY2502 @ SY2502 @ ( sK68_SY735 @ SY2502 @ SY2501 @ SV906 ) @ ( sK67_B_x @ SY2502 @ SY2501 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY2502 @ SY2501 @ SV906 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3842]) ).
thf(4007,plain,
! [SV906: $i] :
( ( ! [SY2503: $i,SY2504: $i] :
( ~ ( c_Relation_Ototal__on @ SY2504 @ SY2503 @ SV906 )
| ! [SY2505: $i] :
( ~ ( c_member @ SY2504 @ SY2505 @ SY2503 )
| ! [SY2506: $i] :
( ~ ( c_member @ SY2504 @ SY2506 @ SY2503 )
| ( SY2505 = SY2506 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2505 @ SY2506 ) @ SV906 )
| ( c_member @ ( tc_prod @ SY2504 @ SY2504 ) @ ( c_Product__Type_OPair @ SY2504 @ SY2504 @ SY2506 @ SY2505 ) @ SV906 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3843]) ).
thf(4008,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ~ ( ~ ( ! [SY3394: $i,SY3395: $i] :
( ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1059 @ SV907 ) )
| ( SV1250 = SV1059 ) )
| ~ ( ! [SY3396: $i,SY3397: $i] :
( ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1059 @ SV907 ) )
| ( SV1168 = SV907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4009,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK26_B_x @ SV1060 @ SV908 ) @ ( sK27_SY720 @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4010,plain,
! [SV909: $i] :
( ( ! [SY2515: $i,SY2516: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2516 @ ( sK75_B_x1 @ SY2516 @ SY2515 @ SV909 ) ) )
| ! [SY2517: $i,SY2518: $i] : ( hBOOL @ ( hAPP @ SY2516 @ ( c_Product__Type_OPair @ SY2515 @ SV909 @ SY2517 @ SY2518 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3846]) ).
thf(4011,plain,
! [SV909: $i] :
( ( ! [SY2519: $i,SY2520: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2520 @ ( c_Product__Type_OPair @ SY2519 @ SV909 @ ( sK73_B_a @ SY2520 @ SY2519 @ SV909 ) @ ( sK74_SY739 @ SY2520 @ SY2519 @ SV909 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2520 @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3847]) ).
thf(4012,plain,
! [SV910: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY2523 @ SY2522 ) @ ( c_Product__Type_OPair @ SY2523 @ SY2522 @ ( sK51_B_x @ SY2523 @ SY2522 @ SV910 ) @ ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SY2523 @ SY2522 @ SV910 )
!= ( sK53_SY732 @ SY2523 @ SY2522 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY2523 @ SY2522 @ SV910 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(4013,plain,
! [SV910: $i] :
( ( ! [SY2524: $i,SY2525: $i] :
( ~ ( c_Relation_Osingle__valued @ SY2525 @ SY2524 @ SV910 )
| ! [SY2526: $i,SY2527: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2527 ) @ SV910 )
| ! [SY2528: $i] :
( ~ ( c_member @ ( tc_prod @ SY2525 @ SY2524 ) @ ( c_Product__Type_OPair @ SY2525 @ SY2524 @ SY2526 @ SY2528 ) @ SV910 )
| ( SY2527 = SY2528 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3849]) ).
thf(4014,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i] :
( ( ! [SY3398: $i,SY3399: $i] :
~ ( ~ ~ ( ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3401 @ SY3400 ) @ ( tc_prod @ SY3401 @ SY3400 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3401 @ SY3400 ) @ ( tc_prod @ SY3401 @ SY3400 ) @ ( c_Product__Type_OPair @ SY3401 @ SY3400 @ SY3399 @ SY3398 ) @ ( c_Product__Type_OPair @ SY3401 @ SY3400 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3401 @ SY3400 @ SV1061 @ SV911 ) )
| ( SY3399 = SV1251 )
| ( c_member @ ( tc_prod @ SY3401 @ SY3401 ) @ ( c_Product__Type_OPair @ SY3401 @ SY3401 @ SY3399 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3403 @ SY3402 ) @ ( tc_prod @ SY3403 @ SY3402 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3403 @ SY3402 ) @ ( tc_prod @ SY3403 @ SY3402 ) @ ( c_Product__Type_OPair @ SY3403 @ SY3402 @ SY3399 @ SY3398 ) @ ( c_Product__Type_OPair @ SY3403 @ SY3402 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3403 @ SY3402 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3402 @ SY3402 ) @ ( c_Product__Type_OPair @ SY3402 @ SY3402 @ SY3398 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3403 @ SY3403 ) @ ( c_Product__Type_OPair @ SY3403 @ SY3403 @ SY3399 @ SV1251 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY3404: $i] :
( ( SY3399 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3404 @ SY3404 ) @ ( c_Product__Type_OPair @ SY3404 @ SY3404 @ SY3398 @ SV1169 ) @ SV911 )
| ! [SY3405: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3405 @ SY3404 ) @ ( tc_prod @ SY3405 @ SY3404 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3405 @ SY3404 ) @ ( tc_prod @ SY3405 @ SY3404 ) @ ( c_Product__Type_OPair @ SY3405 @ SY3404 @ SY3399 @ SY3398 ) @ ( c_Product__Type_OPair @ SY3405 @ SY3404 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3405 @ SY3404 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ( c_member @ ( tc_prod @ SY3407 @ SY3407 ) @ ( c_Product__Type_OPair @ SY3407 @ SY3407 @ SY3399 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3407 @ SY3406 ) @ ( tc_prod @ SY3407 @ SY3406 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3407 @ SY3406 ) @ ( tc_prod @ SY3407 @ SY3406 ) @ ( c_Product__Type_OPair @ SY3407 @ SY3406 @ SY3399 @ SY3398 ) @ ( c_Product__Type_OPair @ SY3407 @ SY3406 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3407 @ SY3406 @ SV1061 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4015,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4016,plain,
! [SV1252: $i] :
( ( ! [SY3408: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3408 @ SY3408 ) @ ( c_Product__Type_OPair @ SY3408 @ SY3408 @ ( sK77_B_x @ SY3408 @ SV1252 ) @ ( sK78_SY740 @ SY3408 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3408 @ SY3408 ) @ ( c_Product__Type_OPair @ SY3408 @ SY3408 @ ( sK78_SY740 @ SY3408 @ SV1252 ) @ ( sK79_SY742 @ SY3408 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SY3408 @ SY3408 ) @ ( c_Product__Type_OPair @ SY3408 @ SY3408 @ ( sK77_B_x @ SY3408 @ SV1252 ) @ ( sK79_SY742 @ SY3408 @ SV1252 ) ) @ SV1252 ) ) )
| ( c_Relation_Otrans @ SY3408 @ SV1252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4017,plain,
! [SV1253: $i] :
( ( ! [SY3409: $i] :
( ~ ( c_Relation_Otrans @ SY3409 @ SV1253 )
| ! [SY3410: $i,SY3411: $i] :
( ~ ( c_member @ ( tc_prod @ SY3409 @ SY3409 ) @ ( c_Product__Type_OPair @ SY3409 @ SY3409 @ SY3410 @ SY3411 ) @ SV1253 )
| ! [SY3412: $i] :
( ~ ( c_member @ ( tc_prod @ SY3409 @ SY3409 ) @ ( c_Product__Type_OPair @ SY3409 @ SY3409 @ SY3411 @ SY3412 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SY3409 @ SY3409 ) @ ( c_Product__Type_OPair @ SY3409 @ SY3409 @ SY3410 @ SY3412 ) @ SV1253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4018,plain,
! [SV1254: $i] :
( ( ! [SY3413: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3413 @ SY3413 ) @ ( c_Product__Type_OPair @ SY3413 @ SY3413 @ ( sK33_B_x @ SY3413 @ SV1254 ) @ ( sK34_SY725 @ SY3413 @ SV1254 ) ) @ SV1254 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3413 @ SY3413 ) @ ( c_Product__Type_OPair @ SY3413 @ SY3413 @ ( sK34_SY725 @ SY3413 @ SV1254 ) @ ( sK33_B_x @ SY3413 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SY3413 @ SV1254 )
!= ( sK34_SY725 @ SY3413 @ SV1254 ) ) ) ) )
| ( c_Relation_Oantisym @ SY3413 @ SV1254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4019,plain,
! [SV1255: $i] :
( ( ! [SY3414: $i] :
( ~ ( c_Relation_Oantisym @ SY3414 @ SV1255 )
| ! [SY3415: $i,SY3416: $i] :
( ~ ( c_member @ ( tc_prod @ SY3414 @ SY3414 ) @ ( c_Product__Type_OPair @ SY3414 @ SY3414 @ SY3415 @ SY3416 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SY3414 @ SY3414 ) @ ( c_Product__Type_OPair @ SY3414 @ SY3414 @ SY3416 @ SY3415 ) @ SV1255 )
| ( SY3415 = SY3416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4020,plain,
! [SV913: $i] :
( ( ! [SY2544: $i,SY2545: $i] :
( ~ ( c_Relation_Orefl__on @ SY2545 @ SY2544 @ SV913 )
| ~ ( c_Relation_Otrans @ SY2545 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SY2545 @ SY2544 @ SV913 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3856]) ).
thf(4021,plain,
! [SV913: $i] :
( ( ~ ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) )
| ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3857]) ).
thf(4022,plain,
! [SV1063: $i,SV914: $i,SV1171: $i] :
( ( ~ ! [SY3278: $i,SY3279: $i] :
( ! [SY3280: $i] :
( ~ ( c_member @ SV1171 @ SY3280 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3279 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3279 @ SY3280 @ SY3278 ) @ SV1063 ) )
| ( c_member @ SY3279 @ SY3278 @ ( c_Relation_OImage @ SV1171 @ SY3279 @ SV1063 @ SV914 ) ) )
| ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( c_member @ SY3282 @ SY3281 @ ( c_Relation_OImage @ SV1171 @ SY3282 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3282 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3282 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SY3281 ) @ SV1063 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4023,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ( SV1172 = SV1064 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(4024,plain,
! [SV916: $i] :
( ( ! [SY2560: $i] :
( ( SY2560 != SV916 )
| ! [SY2561: $i] : ( c_member @ ( tc_prod @ SY2561 @ SY2561 ) @ ( c_Product__Type_OPair @ SY2561 @ SY2561 @ SY2560 @ SV916 ) @ ( c_Relation_OId @ SY2561 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3860]) ).
thf(4025,plain,
! [SV916: $i] :
( ( ! [SY2562: $i] :
( ! [SY2563: $i] :
~ ( c_member @ ( tc_prod @ SY2563 @ SY2563 ) @ ( c_Product__Type_OPair @ SY2563 @ SY2563 @ SY2562 @ SV916 ) @ ( c_Relation_OId @ SY2563 ) )
| ( SY2562 = SV916 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3861]) ).
thf(4026,plain,
! [SV917: $i,SV1065: $i] :
( ( ~ ! [SY2999: $i,SY3000: $i] :
( ( SY3000 != SY2999 )
| ~ ( c_member @ SV1065 @ SY3000 @ SV917 )
| ( c_member @ SV1065 @ SY2999 @ SV917 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3862]) ).
thf(4027,plain,
! [SV917: $i,SV1065: $i] :
( ( ~ ! [SY3001: $i,SY3002: $i] :
( ( SY3002 != SY3001 )
| ~ ( c_member @ SV1065 @ SY3001 @ SV917 )
| ( c_member @ SV1065 @ SY3002 @ SV917 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3862]) ).
thf(4028,plain,
! [SV1257: $i] :
( ( ! [SY3417: $i] :
( ( c_member @ ( tc_prod @ SY3417 @ SY3417 ) @ ( c_Product__Type_OPair @ SY3417 @ SY3417 @ ( sK40_B_x @ SY3417 @ SV1257 ) @ ( sK40_B_x @ SY3417 @ SV1257 ) ) @ ( c_Transitive__Closure_Otrancl @ SY3417 @ SV1257 ) )
| ( c_Wellfounded_Oacyclic @ SY3417 @ SV1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4029,plain,
! [SV1258: $i] :
( ( ! [SY3418: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3418 @ SV1258 )
| ! [SY3419: $i] :
~ ( c_member @ ( tc_prod @ SY3418 @ SY3418 ) @ ( c_Product__Type_OPair @ SY3418 @ SY3418 @ SY3419 @ SY3419 ) @ ( c_Transitive__Closure_Otrancl @ SY3418 @ SV1258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4030,plain,
! [SV1173: $i,SV918: $i,SV1066: $i] :
( ( ~ ! [SY3284: $i,SY3285: $i] :
( ~ ( c_member @ ( tc_prod @ SY3285 @ SY3284 ) @ ( c_Product__Type_OPair @ SY3285 @ SY3284 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3285 @ SY3284 @ SV1173 ) @ SV1066 ) @ SV918 ) ) )
| ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3287 @ SY3286 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3287 @ SY3286 ) @ ( c_Product__Type_OPair @ SY3287 @ SY3286 @ SV1066 @ SV918 ) @ SV1173 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(4031,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ~ ( ~ ! [SY3420: $i,SY3421: $i] :
( ! [SY3422: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3421 @ SY3421 ) @ ( c_Product__Type_OPair @ SY3421 @ SY3421 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3422 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3422 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) )
| ~ ! [SY3423: $i,SY3424: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3425: $i] :
( ~ ( c_member @ ( tc_prod @ SY3424 @ SY3424 ) @ ( c_Product__Type_OPair @ SY3424 @ SY3424 @ SY3425 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SY3425 @ ( hAPP @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3425 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4032,plain,
! [SV920: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
| ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3867]) ).
thf(4033,plain,
! [SV920: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
| ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3868]) ).
thf(4034,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i] :
( ( ~ ( ~ ! [SY3426: $i] :
( ! [SY3427: $i] :
~ ( c_member @ ( tc_prod @ SY3427 @ SY3427 ) @ ( c_Product__Type_OPair @ SY3427 @ SY3427 @ SY3426 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3427 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3426 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) )
| ~ ! [SY3428: $i] :
( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3428 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
| ! [SY3429: $i] : ( c_member @ ( tc_prod @ SY3429 @ SY3429 ) @ ( c_Product__Type_OPair @ SY3429 @ SY3429 @ SY3428 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3429 @ SV1068 ) @ SV921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4035,plain,
! [SV922: $i] :
( ( ! [SY2607: $i] :
( ( SY2607 != SV922 )
| ! [SY2608: $i] : ( c_member @ SY2608 @ SY2607 @ ( c_fequal @ SV922 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(4036,plain,
! [SV922: $i] :
( ( ! [SY2609: $i] :
( ! [SY2610: $i] :
~ ( c_member @ SY2610 @ SY2609 @ ( c_fequal @ SV922 ) )
| ( SY2609 = SV922 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3871]) ).
thf(4037,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
| ( SV1176 = SV1069 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3872]) ).
thf(4038,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4039,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 )
| ( SV1071
!= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4040,plain,
! [SV1263: $i] :
( ( ! [SY3430: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3430 @ SV1263 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SY3430 @ SV1263 ) @ c_Wellfounded_Oless__than ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4041,plain,
! [SV1264: $i] :
( ( ! [SY3431: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SY3431 @ SV1264 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3431 @ SV1264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4042,plain,
! [SV926: $i,SV1072: $i] :
( ( ~ ! [SY3027: $i,SY3028: $i] :
( ! [SY3029: $i] :
~ ( c_member @ ( tc_prod @ SY3028 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3028 @ SV1072 @ SY3027 @ SY3029 ) @ SV926 )
| ( c_member @ SY3028 @ SY3027 @ ( c_Relation_ODomain @ SY3028 @ SV1072 @ SV926 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(4043,plain,
! [SV926: $i,SV1072: $i] :
( ( ~ ! [SY3030: $i,SY3031: $i] :
( ~ ( c_member @ SY3031 @ SY3030 @ ( c_Relation_ODomain @ SY3031 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY3031 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3031 @ SV1072 @ SY3030 @ ( sK66_B_y @ SY3031 @ SY3030 @ SV1072 @ SV926 ) ) @ SV926 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(4044,plain,
! [SV927: $i,SV1073: $i] :
( ( ~ ! [SY3032: $i,SY3033: $i] :
( ( c_member @ SY3033 @ SY3032 @ ( c_Relation_ODomain @ SY3033 @ SY3033 @ SV1073 ) )
| ( SY3032 != SV927 )
| ( c_member @ ( tc_prod @ SY3033 @ SY3033 ) @ ( c_Product__Type_OPair @ SY3033 @ SY3033 @ SY3032 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3033 @ SV1073 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3878]) ).
thf(4045,plain,
! [SV927: $i,SV1073: $i] :
( ( ~ ! [SY3034: $i,SY3035: $i] :
( ( c_member @ SY3035 @ SY3034 @ ( c_Relation_ODomain @ SY3035 @ SY3035 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SY3035 @ SY3035 ) @ ( c_Product__Type_OPair @ SY3035 @ SY3035 @ SY3034 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3035 @ SV1073 ) )
| ( SY3034 = SV927 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3878]) ).
thf(4046,plain,
! [SV928: $i,SV1074: $i] :
( ( ~ ! [SY3036: $i] :
( ! [SY3037: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3037 @ SY3036 @ SV1074 ) @ SV928 ) )
| ( SY3036 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3879]) ).
thf(4047,plain,
! [SV1074: $i,SV928: $i] :
( ( ~ ~ ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3879]) ).
thf(4048,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i] :
( ( ! [SY3432: $i,SY3433: $i,SY3434: $i,SY3435: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ SY3433 @ SY3432 ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3435 @ SY3434 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ ( sK14_B_a @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ ( sK16_SY711 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3435 @ SY3434 ) @ ( tc_prod @ SY3435 @ SY3434 ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ ( sK16_SY711 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3435 @ SY3434 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3435 @ SY3434 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3435 @ SY3434 @ SY3433 @ SY3432 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3433 ) @ SY3432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(4049,plain,
! [SV1076: $i,SV930: $i] :
( ( ~ ! [SY3048: $i,SY3049: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3049 @ SV930 )
| ( c_member @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SV1076 @ SY3048 ) @ ( c_Transitive__Closure_Ortrancl @ SY3049 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3049 @ ( c_Set_Oinsert @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SY3048 @ SV1076 ) @ SV930 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3881]) ).
thf(4050,plain,
! [SV930: $i,SV1076: $i] :
( ( ~ ~ ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) )
| ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3881]) ).
thf(4051,plain,
! [SV931: $i,SV1077: $i] :
( ( ~ ! [SY3054: $i,SY3055: $i] :
( ! [SY3056: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SY3055 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3055 @ SY3056 @ SY3054 ) @ SV931 )
| ( c_member @ SY3055 @ SY3054 @ ( c_Relation_ORange @ SV1077 @ SY3055 @ SV931 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3882]) ).
thf(4052,plain,
! [SV931: $i,SV1077: $i] :
( ( ~ ! [SY3057: $i,SY3058: $i] :
( ~ ( c_member @ SY3058 @ SY3057 @ ( c_Relation_ORange @ SV1077 @ SY3058 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SY3058 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3058 @ ( sK65_B_y @ SY3058 @ SY3057 @ SV1077 @ SV931 ) @ SY3057 ) @ SV931 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3882]) ).
thf(4053,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i] :
( ( ! [SY3436: $i,SY3437: $i,SY3438: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SY3436 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3438 @ SY3437 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SY3436 @ SV1266 )
= ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SY3436 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ ( sK46_B_a @ SY3438 @ SY3437 @ SY3436 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3438 @ SY3437 @ SY3436 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3438 @ SY3437 ) @ ( tc_prod @ SY3438 @ SY3437 ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ ( sK46_B_a @ SY3438 @ SY3437 @ SY3436 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3438 @ SY3437 @ SY3436 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY3438 @ SY3437 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3438 @ SY3437 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4054,plain,
! [SV1267: $i] :
( ( ! [SY3439: $i] :
( ~ ( ~ ( c_member @ SY3439 @ ( sK31_SY722 @ SY3439 @ SV1267 ) @ ( sK29_B_Q @ SY3439 @ SV1267 ) )
| ~ ! [SY3440: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3439 @ SY3439 ) @ ( c_Product__Type_OPair @ SY3439 @ SY3439 @ ( sK30_SY724 @ SY3440 @ SY3439 @ SV1267 ) @ SY3440 ) @ SV1267 )
| ~ ( c_member @ SY3439 @ ( sK30_SY724 @ SY3440 @ SY3439 @ SV1267 ) @ ( sK29_B_Q @ SY3439 @ SV1267 ) ) )
| ~ ( c_member @ SY3439 @ SY3440 @ ( sK29_B_Q @ SY3439 @ SV1267 ) ) ) )
| ( c_Wellfounded_Owf @ SY3439 @ SV1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4055,plain,
! [SV1268: $i] :
( ( ! [SY3441: $i] :
( ~ ( c_Wellfounded_Owf @ SY3441 @ SV1268 )
| ! [SY3442: $i] :
( ! [SX3: $i] :
~ ( c_member @ SY3441 @ SX3 @ SY3442 )
| ~ ( ~ ! [SY3444: $i] :
( ~ ( c_member @ ( tc_prod @ SY3441 @ SY3441 ) @ ( c_Product__Type_OPair @ SY3441 @ SY3441 @ SY3444 @ ( sK28_B_x @ SY3442 @ SY3441 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SY3441 @ SY3444 @ SY3442 ) )
| ~ ( c_member @ SY3441 @ ( sK28_B_x @ SY3442 @ SY3441 @ SV1268 ) @ SY3442 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4056,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ~ ( ~ ! [SY3445: $i,SY3446: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3446 @ SY3446 ) @ ( c_Product__Type_OPair @ SY3446 @ SY3446 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV933 @ SV1181 @ SV1079 ) ) )
| ~ ! [SY3447: $i,SY3448: $i] :
( ( ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3449: $i] :
( ~ ( c_member @ ( tc_prod @ SY3448 @ SY3448 ) @ ( c_Product__Type_OPair @ SY3448 @ SY3448 @ SY3449 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3449 )
= ( hAPP @ SV933 @ SY3449 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4057,plain,
! [SV934: $i,SV1080: $i] :
( ( ~ ! [SY3071: $i,SY3072: $i] :
( ( SY3072 != SY3071 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3072 )
| ( c_member @ SV1080 @ SV934 @ SY3071 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3887]) ).
thf(4058,plain,
! [SV934: $i,SV1080: $i] :
( ( ~ ! [SY3073: $i,SY3074: $i] :
( ( SY3074 != SY3073 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3073 )
| ( c_member @ SV1080 @ SV934 @ SY3074 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3887]) ).
thf(4059,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4060,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ~ ( ~ ( ( SV1271 != SV1082 )
| ( SV1183 != SV936 )
| ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
| ~ ~ ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
| ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4061,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ~ ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) )
| ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(4062,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ~ ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) )
| ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(4063,plain,
! [SV938: $i,SV1084: $i,SV1184: $i,SV1272: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV1272 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4064,plain,
! [SV939: $i] :
( ( ! [SY2700: $i] :
( ! [SY2701: $i] :
~ ( c_member @ SY2701 @ SY2700 @ SV939 )
| ( hBOOL @ ( hAPP @ SV939 @ SY2700 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3892]) ).
thf(4065,plain,
! [SV939: $i] :
( ( ! [SY2702: $i] :
( ~ ( hBOOL @ ( hAPP @ SV939 @ SY2702 ) )
| ! [SY2703: $i] : ( c_member @ SY2703 @ SY2702 @ SV939 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3893]) ).
thf(4066,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ! [SY3095: $i,SY3096: $i] :
( ( SY3095 != SV1085 )
| ~ ( c_member @ SY3096 @ SY3095 @ SV940 )
| ( c_member @ ( tc_prod @ SY3096 @ SY3096 ) @ ( c_Product__Type_OPair @ SY3096 @ SY3096 @ SY3095 @ SV1085 ) @ ( c_Relation_OId__on @ SY3096 @ SV940 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3894]) ).
thf(4067,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ~ ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) )
| ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3894]) ).
thf(4068,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1185 @ SV1185 ) @ ( c_Product__Type_OPair @ SV1185 @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 )
| ~ ~ ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) ) )
= $true )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3895]) ).
thf(4069,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
| ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4070,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ~ ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) )
| ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3897]) ).
thf(4071,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ~ ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) )
| ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3897]) ).
thf(4072,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4073,plain,
! [SV1275: $i] :
( ( ! [SY3456: $i] :
( ~ ( c_member @ ( tc_prod @ SY3456 @ SY3456 ) @ ( c_Product__Type_OPair @ SY3456 @ SY3456 @ ( sK76_B_x @ SY3456 @ SV1275 ) @ ( sK76_B_x @ SY3456 @ SV1275 ) ) @ SV1275 )
| ( c_Nitpick_Orefl_H @ SY3456 @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4074,plain,
! [SV1276: $i] :
( ( ! [SY3457: $i] :
( ~ ( c_Nitpick_Orefl_H @ SY3457 @ SV1276 )
| ! [SY3458: $i] : ( c_member @ ( tc_prod @ SY3457 @ SY3457 ) @ ( c_Product__Type_OPair @ SY3457 @ SY3457 @ SY3458 @ SY3458 ) @ SV1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4075,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i] :
( ( ! [SY3459: $i,SY3460: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3460 @ SY3460 ) @ ( c_Product__Type_OPair @ SY3460 @ SY3460 @ ( sK56_B_z @ SY3460 @ SY3459 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SY3459 ) @ SV1277 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3460 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SY3460 @ SY3459 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SY3460 @ SY3459 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY3460 @ SV1188 @ SV1277 @ SV1090 @ SY3459 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SY3459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4076,plain,
! [SV946: $i] :
( ( ! [SY2733: $i,SY2734: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2734 @ SY2733 @ SV946 )
| ~ ( c_Relation_Oantisym @ SY2734 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SY2734 @ SY2733 @ SV946 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3902]) ).
thf(4077,plain,
! [SV946: $i] :
( ( ~ ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) )
| ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3903]) ).
thf(4078,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) )
| ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3904]) ).
thf(4079,plain,
( ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4080,plain,
! [SV947: $i] :
( ( ! [SY2739: $i,SY2740: $i] :
( ~ ( c_Relation_Oirrefl @ SY2740 @ SV947 )
| ~ ( c_Relation_Otrans @ SY2740 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SY2740 @ SY2739 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY2740 @ SY2739 @ SV947 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3906]) ).
thf(4081,plain,
! [SV947: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
| ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3907]) ).
thf(4082,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ! [SY3118: $i,SY3119: $i] :
( ~ ( c_member @ SY3119 @ SY3118 @ ( c_Set_Oinsert @ SY3119 @ SV1091 @ SV948 ) )
| ( SY3118 = SV1091 )
| ( c_member @ SY3119 @ SY3118 @ SV948 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3908]) ).
thf(4083,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ~ ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) )
| ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3908]) ).
thf(4084,plain,
! [SV1278: $i] :
( ( ! [SY3461: $i] :
( ( c_member @ ( tc_prod @ SY3461 @ SY3461 ) @ ( c_Product__Type_OPair @ SY3461 @ SY3461 @ ( sK72_B_x @ SY3461 @ SV1278 ) @ ( sK72_B_x @ SY3461 @ SV1278 ) ) @ SV1278 )
| ( c_Relation_Oirrefl @ SY3461 @ SV1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4085,plain,
! [SV1279: $i] :
( ( ! [SY3462: $i] :
( ~ ( c_Relation_Oirrefl @ SY3462 @ SV1279 )
| ! [SY3463: $i] :
~ ( c_member @ ( tc_prod @ SY3462 @ SY3462 ) @ ( c_Product__Type_OPair @ SY3462 @ SY3462 @ SY3463 @ SY3463 ) @ SV1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4086,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ~ ( ~ ! [SY3464: $i,SY3465: $i] :
( ! [SY3466: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3465 @ SY3465 ) @ ( c_Product__Type_OPair @ SY3465 @ SY3465 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3466 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3466 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) )
| ~ ! [SY3467: $i,SY3468: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3469: $i] :
( ~ ( c_member @ ( tc_prod @ SY3468 @ SY3468 ) @ ( c_Product__Type_OPair @ SY3468 @ SY3468 @ SY3469 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SY3469 @ ( hAPP @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3469 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4087,plain,
! [SV950: $i,SV1093: $i] :
( ( ~ ! [SY3132: $i,SY3133: $i] :
( ~ ( c_member @ SY3133 @ SY3132 @ SV1093 )
| ( c_member @ SY3133 @ SY3132 @ ( c_Set_Oinsert @ SY3133 @ SV950 @ SV1093 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4088,plain,
! [SV1093: $i,SV950: $i] :
( ( ~ ! [SY3134: $i] :
( ( SY3134 != SV950 )
| ! [SY3135: $i] : ( c_member @ SY3135 @ SY3134 @ ( c_Set_Oinsert @ SY3135 @ SV950 @ SV1093 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4089,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i] :
( ( ! [SY3470: $i] :
( ~ ( c_member @ ( tc_prod @ SY3470 @ SY3470 ) @ ( c_Product__Type_OPair @ SY3470 @ SY3470 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SY3470 @ SV1094 ) )
| ~ ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SY3470 @ SY3470 ) @ ( c_Product__Type_OPair @ SY3470 @ SY3470 @ SV1281 @ ( sK10_B_y @ SY3470 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SY3470 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3470 @ SY3470 ) @ ( c_Product__Type_OPair @ SY3470 @ SY3470 @ ( sK10_B_y @ SY3470 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SY3470 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SY3470 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SY3470 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4090,plain,
! [SV952: $i,SV1095: $i] :
( ( ~ ! [SY3139: $i] :
( ! [SY3140: $i] :
~ ( c_member @ ( tc_prod @ SY3140 @ SY3140 ) @ ( c_Product__Type_OPair @ SY3140 @ SY3140 @ SY3139 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3140 @ SV952 ) )
| ( SY3139 != SV1095 )
| ( SY3139 = SV1095 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4091,plain,
! [SV952: $i,SV1095: $i] :
( ( ~ ! [SY3141: $i,SY3142: $i] :
( ~ ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3142 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SY3142 @ SV952 ) )
| ( SY3141 = SV1095 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4092,plain,
! [SV953: $i,SV1096: $i,SV1191: $i,SV1282: $i] :
( ( ! [SY3471: $i] :
( ~ ( c_member @ SY3471 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SY3471 @ SV1096 @ SV953 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1191 @ SY3471 ) @ ( c_Product__Type_OPair @ SV1191 @ SY3471 @ ( sK23_B_x @ SY3471 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SY3471 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4093,plain,
! [SV1283: $i] :
( ( ! [SY3472: $i] :
( ( SY3472 = SV1283 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3472 @ SV1283 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1283 @ SY3472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4094,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4095,plain,
! [SV1284: $i] :
( ( ! [SY3473: $i] :
( ~ ( c_member @ SY3473 @ ( sK32_B_x @ SY3473 @ SV1284 ) @ ( c_Wellfounded_Oacc @ SY3473 @ SV1284 ) )
| ( c_Wellfounded_Owf @ SY3473 @ SV1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4096,plain,
! [SV1285: $i] :
( ( ! [SY3474: $i] :
( ~ ( c_Wellfounded_Owf @ SY3474 @ SV1285 )
| ! [SY3475: $i] : ( c_member @ SY3474 @ SY3475 @ ( c_Wellfounded_Oacc @ SY3474 @ SV1285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4097,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1192 @ SV1192 ) @ ( c_Product__Type_OPair @ SV1192 @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 )
| ~ ~ ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4098,plain,
! [SV1098: $i,SV955: $i] :
( ( ~ ! [SY3147: $i,SY3148: $i] :
( ~ ( c_Wellfounded_Owf @ SY3148 @ SV955 )
| ( c_member @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SV1098 @ SY3147 ) @ ( c_Transitive__Closure_Ortrancl @ SY3148 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3148 @ ( c_Set_Oinsert @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SY3147 @ SV1098 ) @ SV955 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3921]) ).
thf(4099,plain,
! [SV955: $i,SV1098: $i] :
( ( ~ ~ ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) )
| ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3921]) ).
thf(4100,plain,
! [SV795: $i,SV956: $i,SV1099: $i,SV1193: $i,SV1286: $i] :
( ( ~ ( c_Relation_Otrans @ SV1286 @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4101,plain,
! [SV796: $i,SV957: $i,SV1100: $i,SV1194: $i] :
( ( ( ( SV1194 != SV1100 ) )
= $true )
| ( ( ~ ( c_member @ SV957 @ SV1100 @ SV796 )
| ( c_member @ SV957 @ SV1194 @ SV796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3923]) ).
thf(4102,plain,
! [SV797: $i,SV958: $i,SV1101: $i,SV1195: $i,SV1287: $i] :
( ( ! [SY3476: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ SY3476 @ SV1287 @ SV1195 @ SV1101 @ ( c_Product__Type_OPair @ SY3476 @ SV1287 @ SV958 @ SV797 ) )
= ( hAPP @ ( hAPP @ SV1101 @ SV958 ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4103,plain,
! [SV798: $i,SV959: $i,SV1102: $i,SV1196: $i,SV1288: $i] :
( ( ! [SY3477: $i] :
( ( c_Product__Type_Ointernal__split @ SY3477 @ SV1288 @ SV1196 @ SV1102 @ ( c_Product__Type_OPair @ SY3477 @ SV1288 @ SV959 @ SV798 ) )
= ( hAPP @ ( hAPP @ SV1102 @ SV959 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4104,plain,
! [SV799: $i,SV960: $i,SV1103: $i,SV1197: $i,SV1289: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1289 @ SV1197 ) @ ( c_Product__Type_OPair @ SV1289 @ SV1197 @ SV1103 @ SV960 ) @ SV799 )
| ( c_member @ SV1197 @ SV960 @ ( c_Relation_ORange @ SV1289 @ SV1197 @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3926]) ).
thf(4105,plain,
! [SV800: $i,SV961: $i,SV1104: $i,SV1198: $i] :
( ( ( ( SV1198 != SV1104 ) )
= $true )
| ( ( ~ ( c_member @ SV961 @ SV1198 @ SV800 )
| ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SV1198 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4106,plain,
! [SV801: $i,SV962: $i,SV1105: $i,SV1199: $i,SV1290: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1290 @ SV1199 ) @ ( c_Product__Type_OPair @ SV1290 @ SV1199 @ SV1105 @ SV962 ) @ SV801 )
| ( c_member @ SV1290 @ SV1105 @ ( c_Relation_ODomain @ SV1290 @ SV1199 @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3928]) ).
thf(4107,plain,
! [SV802: $i,SV963: $i,SV1106: $i,SV1200: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV1200 @ SV1106 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV963 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SV1200 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SV1200 @ SV963 @ SV1106 @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4108,plain,
! [SV804: $i,SV965: $i,SV1107: $i,SV1201: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV1201 @ SV1107 ) )
= $true )
| ( ( c_Relation_Otrans @ SV965 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1201 @ SV965 @ SV1107 ) @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4109,plain,
! [SV805: $i,SV966: $i,SV1108: $i,SV1202: $i] :
( ( ( ~ ( c_member @ SV1202 @ SV1108 @ ( c_Relation_ORange @ SV966 @ SV1202 @ SV805 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV966 @ SV1202 ) @ ( c_Product__Type_OPair @ SV966 @ SV1202 @ ( sK63_B_x @ SV1202 @ SV1108 @ SV966 @ SV805 ) @ SV1108 ) @ SV805 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3931]) ).
thf(4110,plain,
! [SV806: $i,SV967: $i,SV1109: $i,SV1203: $i] :
( ( ( ~ ( c_member @ SV1203 @ SV1109 @ ( c_Relation_ODomain @ SV1203 @ SV967 @ SV806 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1203 @ SV967 ) @ ( c_Product__Type_OPair @ SV1203 @ SV967 @ SV1109 @ ( sK62_B_y @ SV1203 @ SV1109 @ SV967 @ SV806 ) ) @ SV806 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3932]) ).
thf(4111,plain,
! [SV807: $i,SV968: $i,SV1110: $i,SV1204: $i] :
( ( ( ~ ( c_member @ SV1204 @ SV1110 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1204 @ SV1204 ) @ ( c_Product__Type_OPair @ SV1204 @ SV1204 @ SV807 @ SV1110 ) @ SV968 )
| ( c_member @ SV1204 @ SV807 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3933]) ).
thf(4112,plain,
! [SV808: $i,SV969: $i,SV1111: $i,SV1205: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1205 @ SV1111 @ SV969 ) )
= $true )
| ( ( ~ ( c_member @ SV1205 @ SV808 @ SV1111 )
| ( c_member @ ( tc_prod @ SV1205 @ SV1205 ) @ ( c_Product__Type_OPair @ SV1205 @ SV1205 @ SV808 @ SV808 ) @ SV969 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4113,plain,
! [SV809: $i,SV970: $i,SV1112: $i,SV1206: $i,SV1291: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV1291 @ SV1206 @ SV1112 )
| ~ ( c_member @ ( tc_prod @ SV1291 @ SV1291 ) @ ( c_Product__Type_OPair @ SV1291 @ SV1291 @ SV970 @ SV809 ) @ SV1112 )
| ( c_member @ SV1291 @ SV970 @ SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4114,plain,
! [SV810: $i,SV971: $i,SV1113: $i,SV1207: $i,SV1292: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV1292 @ SV1207 @ SV1113 )
| ~ ( c_member @ ( tc_prod @ SV1292 @ SV1292 ) @ ( c_Product__Type_OPair @ SV1292 @ SV1292 @ SV971 @ SV810 ) @ SV1113 )
| ( c_member @ SV1292 @ SV810 @ SV1207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4115,plain,
! [SV811: $i,SV972: $i,SV1114: $i,SV1208: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1208 @ SV1208 ) @ ( c_Product__Type_OPair @ SV1208 @ SV1208 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SV1208 @ SV811 ) ) )
= $true )
| ( ( ~ ( c_member @ SV1208 @ SV972 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
| ( c_member @ SV1208 @ SV1114 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4116,plain,
! [SV812: $i,SV973: $i,SV1115: $i,SV1209: $i] :
( ( ( ~ ( c_member @ SV1209 @ SV1115 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1209 @ SV1209 ) @ ( c_Product__Type_OPair @ SV1209 @ SV1209 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SV1209 @ SV973 ) )
| ( c_member @ SV1209 @ SV812 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3938]) ).
thf(4117,plain,
! [SV813: $i,SV974: $i,SV1116: $i,SV1210: $i,SV1293: $i] :
( ( ! [SY3478: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3478 @ SV1293 @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SY3478 @ SV1293 ) @ ( c_Product__Type_OPair @ SY3478 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SY3478 @ SV1293 ) @ ( c_Product__Type_OPair @ SY3478 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4118,plain,
! [SV814: $i,SV975: $i,SV1117: $i,SV1211: $i,SV1294: $i] :
( ( ! [SY3479: $i] :
( ( c_Product__Type_Ocurry @ SY3479 @ SV1294 @ SV1211 @ SV1117 @ SV975 @ SV814 )
= ( hAPP @ SV1117 @ ( c_Product__Type_OPair @ SY3479 @ SV1294 @ SV975 @ SV814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4119,plain,
! [SV816: $i,SV977: $i,SV1119: $i] :
( ( ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ SV816 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1119 @ SV1119 ) @ SV977 @ ( c_Transitive__Closure_Ortrancl @ SV1119 @ SV816 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4120,plain,
! [SV817: $i,SV978: $i,SV1120: $i,SV1212: $i,SV1295: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
| ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4121,plain,
! [SV818: $i,SV979: $i,SV1121: $i,SV1213: $i,SV1296: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV1121 ) @ SV979 )
| ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
| ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4122,plain,
! [SV819: $i,SV980: $i,SV1122: $i,SV1214: $i,SV1297: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
| ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1122 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4123,plain,
! [SV820: $i,SV981: $i,SV1123: $i,SV1215: $i,SV1298: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
| ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
| ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4124,plain,
! [SV822: $i,SV983: $i,SV1124: $i,SV1216: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Otrancl @ SV1216 @ SV822 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Ortrancl @ SV1216 @ SV822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3946]) ).
thf(4125,plain,
! [SV823: $i,SV984: $i,SV1125: $i,SV1217: $i,SV1299: $i] :
( ( ! [SY3480: $i] :
( ~ ( c_member @ ( tc_prod @ SY3480 @ SY3480 ) @ ( c_Product__Type_OPair @ SY3480 @ SY3480 @ SV1299 @ SV1217 ) @ SV1125 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SY3480 @ SV984 @ SV823 @ SV1125 @ SV1217 ) @ SV1299 )
= ( hAPP @ SV823 @ SV1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4126,plain,
! [SV824: $i,SV985: $i,SV1126: $i,SV1218: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ SV824 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ ( c_Transitive__Closure_Otrancl @ SV1218 @ SV824 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4127,plain,
! [SV825: $i,SV986: $i,SV1127: $i] :
( ( ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ SV825 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1127 @ SV1127 ) @ SV986 @ ( c_Transitive__Closure_Otrancl @ SV1127 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3949]) ).
thf(4128,plain,
! [SV828: $i,SV989: $i,SV1128: $i,SV1219: $i,SV1300: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV1128 ) @ SV989 )
| ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1128 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(4129,plain,
! [SV829: $i,SV990: $i,SV1129: $i,SV1220: $i,SV1301: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV1129 ) @ SV990 )
| ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
| ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4130,plain,
! [SV830: $i,SV991: $i,SV1130: $i,SV1221: $i,SV1302: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
| ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1130 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4131,plain,
! [SV831: $i,SV992: $i,SV1131: $i,SV1222: $i,SV1303: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
| ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
| ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4132,plain,
! [SV832: $i,SV993: $i,SV1132: $i,SV1223: $i,SV1304: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV1132 ) @ SV993 )
| ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SV1304 @ SV993 ) )
| ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SV1304 @ SV993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4133,plain,
! [SV833: $i,SV994: $i,SV1133: $i,SV1224: $i,SV1305: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV994 ) )
| ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1133 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SV1305 @ SV994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4134,plain,
! [SV834: $i,SV995: $i,SV1134: $i,SV1225: $i,SV1306: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
| ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV995 ) )
| ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4135,plain,
! [SV835: $i,SV996: $i,SV1135: $i,SV1226: $i,SV1307: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SV1307 @ SV996 ) )
| ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
| ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4136,plain,
! [SV1308: $i,SV836: $i,SV997: $i,SV1136: $i,SV1227: $i] :
( ( ! [SY3481: $i] :
( ~ ( c_member @ ( tc_prod @ SV1227 @ SV1227 ) @ ( c_Product__Type_OPair @ SV1227 @ SV1227 @ SV1136 @ SV997 ) @ SY3481 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV1227 @ SV836 @ SV1308 @ SY3481 @ SV997 ) @ SV1136 )
= ( hAPP @ SV1308 @ SV1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4137,plain,
! [SV837: $i,SV998: $i,SV1137: $i,SV1228: $i] :
( ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1228 @ SV1137 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ SV998 @ SV837 ) @ SV1137 )
| ( SV998 != SV837 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4138,plain,
! [SV842: $i,SV1002: $i,SV1138: $i,SV1229: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1229 @ SV1138 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4139,plain,
! [SV843: $i,SV1003: $i,SV1139: $i,SV1230: $i] :
( ( ( ~ ( c_member @ SV1230 @ SV1139 @ ( c_Set_Oinsert @ SV1230 @ SV1003 @ SV843 ) ) )
= $true )
| ( ( ( SV1139 = SV1003 )
| ( c_member @ SV1230 @ SV1139 @ SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3963]) ).
thf(4140,plain,
! [SV844: $i,SV1004: $i,SV1140: $i,SV1231: $i,SV1309: $i] :
( ( ( c_Relation_ODomain @ SV1309 @ SV1231 @ ( c_Set_Oinsert @ ( tc_prod @ SV1309 @ SV1231 ) @ ( c_Product__Type_OPair @ SV1309 @ SV1231 @ SV1140 @ SV1004 ) @ SV844 ) )
= ( c_Set_Oinsert @ SV1309 @ SV1140 @ ( c_Relation_ODomain @ SV1309 @ SV1231 @ SV844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4141,plain,
! [SV845: $i,SV1005: $i,SV1141: $i,SV1232: $i,SV1310: $i] :
( ( ( c_Relation_ORange @ SV1310 @ SV1232 @ ( c_Set_Oinsert @ ( tc_prod @ SV1310 @ SV1232 ) @ ( c_Product__Type_OPair @ SV1310 @ SV1232 @ SV1141 @ SV1005 ) @ SV845 ) )
= ( c_Set_Oinsert @ SV1232 @ SV1005 @ ( c_Relation_ORange @ SV1310 @ SV1232 @ SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4142,plain,
! [SV847: $i,SV1007: $i,SV1143: $i,SV1233: $i] :
( ( ( ~ ( c_member @ SV1233 @ SV1143 @ SV1007 ) )
= $true )
| ( ( c_member @ SV1233 @ SV1143 @ ( c_Set_Oinsert @ SV1233 @ SV847 @ SV1007 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4143,plain,
! [SV848: $i,SV1008: $i,SV1144: $i] :
( ( ( c_member @ SV1144 @ SV1008 @ SV848 )
= $false )
| ( ( ( c_Set_Oinsert @ SV1144 @ SV1008 @ SV848 )
= SV848 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4144,plain,
! [SV849: $i,SV1009: $i,SV1145: $i,SV1234: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1234 @ SV1145 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV1234 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SV1234 @ SV1009 @ SV1145 @ SV849 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4145,plain,
! [SV850: $i,SV1010: $i,SV1146: $i] :
( ( ( c_Wellfounded_Owf @ SV1146 @ SV1010 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1146 @ SV1146 ) @ ( c_Product__Type_OPair @ SV1146 @ SV1146 @ SV850 @ SV850 ) @ SV1010 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(4146,plain,
! [SV851: $i,SV1011: $i,SV1147: $i,SV1235: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1235 @ SV1147 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4147,plain,
! [SV852: $i,SV1012: $i,SV1148: $i,SV1236: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1236 @ SV1148 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4148,plain,
! [SV853: $i,SV1013: $i,SV1149: $i] :
( ( ( c_Wellfounded_Owf @ SV1149 @ SV1013 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1149 @ SV1149 ) @ ( c_Product__Type_OPair @ SV1149 @ SV1149 @ SV853 @ SV853 ) @ SV1013 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4149,plain,
! [SV854: $i,SV1014: $i,SV1150: $i] :
( ( ( c_Wellfounded_Owf @ SV1150 @ SV1014 )
= $false )
| ( ( c_member @ SV1150 @ SV854 @ ( c_Wellfounded_Oacc @ SV1150 @ SV1014 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4150,plain,
! [SV856: $i,SV1016: $i,SV1151: $i,SV1237: $i,SV1311: $i] :
( ( ! [SY3482: $i] :
( ~ ( c_member @ SY3482 @ SV1311 @ SV1237 )
| ~ ( c_member @ ( tc_prod @ SY3482 @ SV1151 ) @ ( c_Product__Type_OPair @ SY3482 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SY3482 @ SV1151 @ SV856 @ SV1237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4151,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i] :
( ( ! [SY3483: $i,SY3484: $i,SY3485: $i] :
( ~ ( c_member @ ( tc_prod @ SY3485 @ SY3484 ) @ ( c_Product__Type_OPair @ SY3485 @ SY3484 @ SY3483 @ SV1312 ) @ SV1238 )
| ~ ( c_member @ ( tc_prod @ SY3484 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3484 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY3485 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3485 @ SV1152 @ SY3483 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY3485 @ SY3484 @ SV1152 @ SV1238 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4152,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i] :
( ( ! [SY3486: $i,SY3487: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3487 @ SY3486 ) )
| ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SY3486 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SY3486 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SY3486 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SY3487 @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4153,plain,
! [SV863: $i,SV1023: $i,SV1154: $i,SV1240: $i,SV1314: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1314 @ ( c_Product__Type_OPair @ SV1240 @ SV1154 @ SV1023 @ SV863 ) ) )
| ( hBOOL @ ( c_Product__Type_Ocurry @ SV1240 @ SV1154 @ tc_HOL_Obool @ SV1314 @ SV1023 @ SV863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4154,plain,
! [SV864: $i,SV1024: $i,SV1155: $i,SV1241: $i,SV1315: $i] :
( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV1315 @ SV1241 @ tc_HOL_Obool @ SV1155 @ SV1024 @ SV864 ) )
| ( hBOOL @ ( hAPP @ SV1155 @ ( c_Product__Type_OPair @ SV1315 @ SV1241 @ SV1024 @ SV864 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4155,plain,
! [SV865: $i,SV1025: $i,SV1156: $i,SV1242: $i,SV1316: $i] :
( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV1316 @ SV1242 @ tc_HOL_Obool @ SV1156 @ SV1025 @ SV865 ) )
| ( hBOOL @ ( hAPP @ SV1156 @ ( c_Product__Type_OPair @ SV1316 @ SV1242 @ SV1025 @ SV865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4156,plain,
! [SV878: $i,SV1036: $i,SV1159: $i,SV1244: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1244 @ SV1159 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1036 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1244 @ SV1036 @ SV1159 ) @ SV878 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4157,plain,
! [SV882: $i,SV1040: $i,SV1160: $i,SV1245: $i,SV1317: $i] :
( ( ! [SY3488: $i] :
( ( SY3488
!= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) )
| ~ ( c_Wellfounded_Owf @ SV1317 @ SV1160 )
| ( ( hAPP @ SY3488 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SY3488 @ SV1160 @ SV882 ) ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4158,plain,
! [SV883: $i,SV1041: $i,SV1161: $i,SV1246: $i,SV1318: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1318 @ SV1246 )
| ( ( hAPP @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SV1318 @ SV1161 @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV1246 @ SV883 ) ) @ SV883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4159,plain,
! [SV1162: $i,SV884: $i,SV1247: $i,SV1042: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1042 @ SV1247 ) )
= $true )
| ( ( ! [SY3388: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SY3388 )
= ( hAPP @ ( hAPP @ SV1162 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SV1247 @ SY3388 ) ) @ SY3388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4160,plain,
! [SV886: $i,SV1043: $i,SV1163: $i] :
( ( ( c_Wellfounded_Owf @ SV1163 @ SV1043 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1163 @ ( c_Wellfounded_Omlex__prod @ SV1163 @ SV886 @ SV1043 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4161,plain,
! [SV1045: $i,SV890: $i] :
( ( ( SV890 = SV1045 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1045 @ SV890 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4162,plain,
! [SV891: $i,SV1046: $i] :
( ( ( SV1046 = SV891 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1046 @ SV891 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4163,plain,
! [SV895: $i,SV1049: $i,SV1164: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV1049 )
= $false )
| ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4164,plain,
! [SV1050: $i,SV896: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SV1050 ) )
= $true )
| ( ( SV1050 = SV896 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1050 @ SV896 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4165,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK70_SY736 @ SV1055 @ SV901 ) ) @ SV901 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4166,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4167,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4168,plain,
! [SV903: $i,SV1057: $i] :
( ( ! [SY2962: $i,SY2963: $i] :
( ( c_member @ SY2963 @ SY2962 @ SV1057 )
| ( c_member @ SY2963 @ SY2962 @ SV903 )
| ( ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV1057 )
!= ( c_Set_Oinsert @ SY2963 @ SY2962 @ SV903 ) )
| ( SV1057 = SV903 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4001]) ).
thf(4169,plain,
! [SV903: $i,SV1057: $i] :
( ( ! [SY2964: $i,SY2965: $i] :
( ( c_member @ SY2965 @ SY2964 @ SV1057 )
| ( c_member @ SY2965 @ SY2964 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV1057 )
= ( c_Set_Oinsert @ SY2965 @ SY2964 @ SV903 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4002]) ).
thf(4170,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i] :
( ( ! [SY3489: $i,SY3490: $i,SY3491: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ SY3489 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3491 @ SY3490 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SY3489 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ SY3489 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ ( sK18_B_a @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3491 @ SY3490 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3491 @ SY3490 ) @ ( tc_prod @ SY3491 @ SY3490 ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ ( sK18_B_a @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY3491 @ SY3490 @ ( sK20_SY717 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY3491 @ SY3490 @ SY3489 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4171,plain,
! [SV905: $i,SV1321: $i] :
( ( ! [SY3492: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3492 @ SY3492 ) @ ( c_Product__Type_OPair @ SY3492 @ SY3492 @ ( sK61_B_x @ SY3492 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 )
| ~ ~ ( c_member @ SY3492 @ ( sK61_B_x @ SY3492 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SY3492 @ SV905 ) ) )
| ( c_member @ SY3492 @ SV1321 @ ( c_Wellfounded_Oacc @ SY3492 @ SV905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4172,plain,
! [SV905: $i,SV1322: $i] :
( ( ! [SY3493: $i] :
( ~ ( c_member @ SY3493 @ SV1322 @ ( c_Wellfounded_Oacc @ SY3493 @ SV905 ) )
| ! [SY3494: $i] :
( ~ ( c_member @ ( tc_prod @ SY3493 @ SY3493 ) @ ( c_Product__Type_OPair @ SY3493 @ SY3493 @ SY3494 @ SV1322 ) @ SV905 )
| ( c_member @ SY3493 @ SY3494 @ ( c_Wellfounded_Oacc @ SY3493 @ SV905 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4173,plain,
! [SV906: $i,SV1323: $i] :
( ( ! [SY3495: $i] :
( ~ ( ~ ( c_member @ SY3495 @ ( sK67_B_x @ SY3495 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( c_member @ SY3495 @ ( sK68_SY735 @ SY3495 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SY3495 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SY3495 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SY3495 @ SY3495 ) @ ( c_Product__Type_OPair @ SY3495 @ SY3495 @ ( sK67_B_x @ SY3495 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SY3495 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SY3495 @ SY3495 ) @ ( c_Product__Type_OPair @ SY3495 @ SY3495 @ ( sK68_SY735 @ SY3495 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SY3495 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SY3495 @ SV1323 @ SV906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4174,plain,
! [SV906: $i,SV1324: $i] :
( ( ! [SY3496: $i] :
( ~ ( c_Relation_Ototal__on @ SY3496 @ SV1324 @ SV906 )
| ! [SY3497: $i] :
( ~ ( c_member @ SY3496 @ SY3497 @ SV1324 )
| ! [SY3498: $i] :
( ~ ( c_member @ SY3496 @ SY3498 @ SV1324 )
| ( SY3497 = SY3498 )
| ( c_member @ ( tc_prod @ SY3496 @ SY3496 ) @ ( c_Product__Type_OPair @ SY3496 @ SY3496 @ SY3497 @ SY3498 ) @ SV906 )
| ( c_member @ ( tc_prod @ SY3496 @ SY3496 ) @ ( c_Product__Type_OPair @ SY3496 @ SY3496 @ SY3498 @ SY3497 ) @ SV906 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4175,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ~ ( ! [SY3394: $i,SY3395: $i] :
( ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1059 @ SV907 ) )
| ( SV1250 = SV1059 ) )
| ~ ( ! [SY3396: $i,SY3397: $i] :
( ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1059 @ SV907 ) )
| ( SV1168 = SV907 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4176,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK26_B_x @ SV1060 @ SV908 ) @ ( sK27_SY720 @ SV1060 @ SV908 ) ) @ SV908 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4009]) ).
thf(4177,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4009]) ).
thf(4178,plain,
! [SV909: $i,SV1325: $i] :
( ( ! [SY3499: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3499 @ ( sK75_B_x1 @ SY3499 @ SV1325 @ SV909 ) ) )
| ! [SY3500: $i,SY3501: $i] : ( hBOOL @ ( hAPP @ SY3499 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SY3500 @ SY3501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4010]) ).
thf(4179,plain,
! [SV909: $i,SV1326: $i] :
( ( ! [SY3502: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3502 @ ( c_Product__Type_OPair @ SV1326 @ SV909 @ ( sK73_B_a @ SY3502 @ SV1326 @ SV909 ) @ ( sK74_SY739 @ SY3502 @ SV1326 @ SV909 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY3502 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4180,plain,
! [SV910: $i,SV1327: $i] :
( ( ! [SY3504: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3504 @ SV1327 ) @ ( c_Product__Type_OPair @ SY3504 @ SV1327 @ ( sK51_B_x @ SY3504 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SY3504 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SY3504 @ SV1327 ) @ ( c_Product__Type_OPair @ SY3504 @ SV1327 @ ( sK51_B_x @ SY3504 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SY3504 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SY3504 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SY3504 @ SV1327 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SY3504 @ SV1327 @ SV910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4181,plain,
! [SV910: $i,SV1328: $i] :
( ( ! [SY3505: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3505 @ SV1328 @ SV910 )
| ! [SY3506: $i,SY3507: $i] :
( ~ ( c_member @ ( tc_prod @ SY3505 @ SV1328 ) @ ( c_Product__Type_OPair @ SY3505 @ SV1328 @ SY3506 @ SY3507 ) @ SV910 )
| ! [SY3508: $i] :
( ~ ( c_member @ ( tc_prod @ SY3505 @ SV1328 ) @ ( c_Product__Type_OPair @ SY3505 @ SV1328 @ SY3506 @ SY3508 ) @ SV910 )
| ( SY3507 = SY3508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4182,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i] :
( ( ! [SY3509: $i] :
~ ( ~ ~ ( ~ ! [SY3510: $i,SY3511: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3511 @ SY3510 ) @ ( tc_prod @ SY3511 @ SY3510 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3511 @ SY3510 ) @ ( tc_prod @ SY3511 @ SY3510 ) @ ( c_Product__Type_OPair @ SY3511 @ SY3510 @ SY3509 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3511 @ SY3510 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3511 @ SY3510 @ SV1061 @ SV911 ) )
| ( SY3509 = SV1251 )
| ( c_member @ ( tc_prod @ SY3511 @ SY3511 ) @ ( c_Product__Type_OPair @ SY3511 @ SY3511 @ SY3509 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3512: $i,SY3513: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3513 @ SY3512 ) @ ( tc_prod @ SY3513 @ SY3512 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3513 @ SY3512 ) @ ( tc_prod @ SY3513 @ SY3512 ) @ ( c_Product__Type_OPair @ SY3513 @ SY3512 @ SY3509 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3513 @ SY3512 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3513 @ SY3512 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3512 @ SY3512 ) @ ( c_Product__Type_OPair @ SY3512 @ SY3512 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3513 @ SY3513 ) @ ( c_Product__Type_OPair @ SY3513 @ SY3513 @ SY3509 @ SV1251 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY3514: $i] :
( ( SY3509 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3514 @ SY3514 ) @ ( c_Product__Type_OPair @ SY3514 @ SY3514 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3515: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3515 @ SY3514 ) @ ( tc_prod @ SY3515 @ SY3514 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3515 @ SY3514 ) @ ( tc_prod @ SY3515 @ SY3514 ) @ ( c_Product__Type_OPair @ SY3515 @ SY3514 @ SY3509 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3515 @ SY3514 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3515 @ SY3514 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3516: $i,SY3517: $i] :
( ~ ( c_member @ ( tc_prod @ SY3517 @ SY3517 ) @ ( c_Product__Type_OPair @ SY3517 @ SY3517 @ SY3509 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3517 @ SY3516 ) @ ( tc_prod @ SY3517 @ SY3516 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3517 @ SY3516 ) @ ( tc_prod @ SY3517 @ SY3516 ) @ ( c_Product__Type_OPair @ SY3517 @ SY3516 @ SY3509 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3517 @ SY3516 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3517 @ SY3516 @ SV1061 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4183,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4184,plain,
! [SV1252: $i,SV1330: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK78_SY740 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) ) )
| ( c_Relation_Otrans @ SV1330 @ SV1252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4185,plain,
! [SV1253: $i,SV1331: $i] :
( ( ~ ( c_Relation_Otrans @ SV1331 @ SV1253 )
| ! [SY3518: $i,SY3519: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3519 ) @ SV1253 )
| ! [SY3520: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3519 @ SY3520 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3520 ) @ SV1253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4186,plain,
! [SV1254: $i,SV1332: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK33_B_x @ SV1332 @ SV1254 ) @ ( sK34_SY725 @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) ) )
| ( c_Relation_Oantisym @ SV1332 @ SV1254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4187,plain,
! [SV1255: $i,SV1333: $i] :
( ( ~ ( c_Relation_Oantisym @ SV1333 @ SV1255 )
| ! [SY3521: $i,SY3522: $i] :
( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3521 @ SY3522 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3522 @ SY3521 ) @ SV1255 )
| ( SY3521 = SY3522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4019]) ).
thf(4188,plain,
! [SV913: $i,SV1334: $i] :
( ( ! [SY3523: $i] :
( ~ ( c_Relation_Orefl__on @ SY3523 @ SV1334 @ SV913 )
| ~ ( c_Relation_Otrans @ SY3523 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SY3523 @ SV1334 @ SV913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4189,plain,
! [SV913: $i] :
( ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) )
| ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4190,plain,
! [SV1063: $i,SV914: $i,SV1171: $i] :
( ( ~ ! [SY3278: $i,SY3279: $i] :
( ! [SY3280: $i] :
( ~ ( c_member @ SV1171 @ SY3280 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3279 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3279 @ SY3280 @ SY3278 ) @ SV1063 ) )
| ( c_member @ SY3279 @ SY3278 @ ( c_Relation_OImage @ SV1171 @ SY3279 @ SV1063 @ SV914 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4022]) ).
thf(4191,plain,
! [SV914: $i,SV1063: $i,SV1171: $i] :
( ( ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( c_member @ SY3282 @ SY3281 @ ( c_Relation_OImage @ SV1171 @ SY3282 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3282 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3282 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SY3281 ) @ SV1063 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4022]) ).
thf(4192,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) ) )
= $true )
| ( ( ( SV1172 = SV1064 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4193,plain,
! [SV916: $i,SV1335: $i] :
( ( ( SV1335 != SV916 )
| ! [SY3524: $i] : ( c_member @ ( tc_prod @ SY3524 @ SY3524 ) @ ( c_Product__Type_OPair @ SY3524 @ SY3524 @ SV1335 @ SV916 ) @ ( c_Relation_OId @ SY3524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4194,plain,
! [SV916: $i,SV1336: $i] :
( ( ! [SY3525: $i] :
~ ( c_member @ ( tc_prod @ SY3525 @ SY3525 ) @ ( c_Product__Type_OPair @ SY3525 @ SY3525 @ SV1336 @ SV916 ) @ ( c_Relation_OId @ SY3525 ) )
| ( SV1336 = SV916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4195,plain,
! [SV917: $i,SV1065: $i] :
( ( ! [SY2999: $i,SY3000: $i] :
( ( SY3000 != SY2999 )
| ~ ( c_member @ SV1065 @ SY3000 @ SV917 )
| ( c_member @ SV1065 @ SY2999 @ SV917 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4026]) ).
thf(4196,plain,
! [SV917: $i,SV1065: $i] :
( ( ! [SY3001: $i,SY3002: $i] :
( ( SY3002 != SY3001 )
| ~ ( c_member @ SV1065 @ SY3001 @ SV917 )
| ( c_member @ SV1065 @ SY3002 @ SV917 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4027]) ).
thf(4197,plain,
! [SV1257: $i,SV1337: $i] :
( ( ( c_member @ ( tc_prod @ SV1337 @ SV1337 ) @ ( c_Product__Type_OPair @ SV1337 @ SV1337 @ ( sK40_B_x @ SV1337 @ SV1257 ) @ ( sK40_B_x @ SV1337 @ SV1257 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1337 @ SV1257 ) )
| ( c_Wellfounded_Oacyclic @ SV1337 @ SV1257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4028]) ).
thf(4198,plain,
! [SV1258: $i,SV1338: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV1338 @ SV1258 )
| ! [SY3526: $i] :
~ ( c_member @ ( tc_prod @ SV1338 @ SV1338 ) @ ( c_Product__Type_OPair @ SV1338 @ SV1338 @ SY3526 @ SY3526 ) @ ( c_Transitive__Closure_Otrancl @ SV1338 @ SV1258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4029]) ).
thf(4199,plain,
! [SV1173: $i,SV918: $i,SV1066: $i] :
( ( ~ ! [SY3284: $i,SY3285: $i] :
( ~ ( c_member @ ( tc_prod @ SY3285 @ SY3284 ) @ ( c_Product__Type_OPair @ SY3285 @ SY3284 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3285 @ SY3284 @ SV1173 ) @ SV1066 ) @ SV918 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4200,plain,
! [SV918: $i,SV1066: $i,SV1173: $i] :
( ( ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3287 @ SY3286 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3287 @ SY3286 ) @ ( c_Product__Type_OPair @ SY3287 @ SY3286 @ SV1066 @ SV918 ) @ SV1173 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4201,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ~ ! [SY3420: $i,SY3421: $i] :
( ! [SY3422: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3421 @ SY3421 ) @ ( c_Product__Type_OPair @ SY3421 @ SY3421 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3422 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3422 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) )
| ~ ! [SY3423: $i,SY3424: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3425: $i] :
( ~ ( c_member @ ( tc_prod @ SY3424 @ SY3424 ) @ ( c_Product__Type_OPair @ SY3424 @ SY3424 @ SY3425 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SY3425 @ ( hAPP @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3425 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4202,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
| ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4203,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
| ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4204,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i] :
( ( ~ ! [SY3426: $i] :
( ! [SY3427: $i] :
~ ( c_member @ ( tc_prod @ SY3427 @ SY3427 ) @ ( c_Product__Type_OPair @ SY3427 @ SY3427 @ SY3426 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3427 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3426 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) )
| ~ ! [SY3428: $i] :
( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3428 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
| ! [SY3429: $i] : ( c_member @ ( tc_prod @ SY3429 @ SY3429 ) @ ( c_Product__Type_OPair @ SY3429 @ SY3429 @ SY3428 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3429 @ SV1068 ) @ SV921 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4205,plain,
! [SV922: $i,SV1339: $i] :
( ( ( SV1339 != SV922 )
| ! [SY3527: $i] : ( c_member @ SY3527 @ SV1339 @ ( c_fequal @ SV922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4206,plain,
! [SV922: $i,SV1340: $i] :
( ( ! [SY3528: $i] :
~ ( c_member @ SY3528 @ SV1340 @ ( c_fequal @ SV922 ) )
| ( SV1340 = SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4207,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) )
= $true )
| ( ( ( SV1176 = SV1069 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4037]) ).
thf(4208,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4209,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 )
| ( SV1071
!= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4210,plain,
! [SV1263: $i,SV1341: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1341 @ SV1263 )
| ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1341 @ SV1263 ) @ c_Wellfounded_Oless__than ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4211,plain,
! [SV1264: $i,SV1342: $i] :
( ( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1342 @ SV1264 ) @ c_Wellfounded_Oless__than )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1342 @ SV1264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4212,plain,
! [SV926: $i,SV1072: $i] :
( ( ! [SY3027: $i,SY3028: $i] :
( ! [SY3029: $i] :
~ ( c_member @ ( tc_prod @ SY3028 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3028 @ SV1072 @ SY3027 @ SY3029 ) @ SV926 )
| ( c_member @ SY3028 @ SY3027 @ ( c_Relation_ODomain @ SY3028 @ SV1072 @ SV926 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4042]) ).
thf(4213,plain,
! [SV926: $i,SV1072: $i] :
( ( ! [SY3030: $i,SY3031: $i] :
( ~ ( c_member @ SY3031 @ SY3030 @ ( c_Relation_ODomain @ SY3031 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY3031 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3031 @ SV1072 @ SY3030 @ ( sK66_B_y @ SY3031 @ SY3030 @ SV1072 @ SV926 ) ) @ SV926 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4043]) ).
thf(4214,plain,
! [SV927: $i,SV1073: $i] :
( ( ! [SY3032: $i,SY3033: $i] :
( ( c_member @ SY3033 @ SY3032 @ ( c_Relation_ODomain @ SY3033 @ SY3033 @ SV1073 ) )
| ( SY3032 != SV927 )
| ( c_member @ ( tc_prod @ SY3033 @ SY3033 ) @ ( c_Product__Type_OPair @ SY3033 @ SY3033 @ SY3032 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3033 @ SV1073 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4044]) ).
thf(4215,plain,
! [SV927: $i,SV1073: $i] :
( ( ! [SY3034: $i,SY3035: $i] :
( ( c_member @ SY3035 @ SY3034 @ ( c_Relation_ODomain @ SY3035 @ SY3035 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SY3035 @ SY3035 ) @ ( c_Product__Type_OPair @ SY3035 @ SY3035 @ SY3034 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3035 @ SV1073 ) )
| ( SY3034 = SV927 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4045]) ).
thf(4216,plain,
! [SV928: $i,SV1074: $i] :
( ( ! [SY3036: $i] :
( ! [SY3037: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3037 @ SY3036 @ SV1074 ) @ SV928 ) )
| ( SY3036 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4046]) ).
thf(4217,plain,
! [SV1074: $i,SV928: $i] :
( ( ~ ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4047]) ).
thf(4218,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i] :
( ( ! [SY3529: $i,SY3530: $i,SY3531: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ SY3529 @ SV1343 ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3531 @ SY3530 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ ( sK14_B_a @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ ( sK16_SY711 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3531 @ SY3530 ) @ ( tc_prod @ SY3531 @ SY3530 ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ ( sK16_SY711 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3531 @ SY3530 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3531 @ SY3530 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3531 @ SY3530 @ SY3529 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SY3529 ) @ SV1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4048]) ).
thf(4219,plain,
! [SV1076: $i,SV930: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3049 @ SV930 )
| ( c_member @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SV1076 @ SY3048 ) @ ( c_Transitive__Closure_Ortrancl @ SY3049 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3049 @ ( c_Set_Oinsert @ ( tc_prod @ SY3049 @ SY3049 ) @ ( c_Product__Type_OPair @ SY3049 @ SY3049 @ SY3048 @ SV1076 ) @ SV930 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4049]) ).
thf(4220,plain,
! [SV930: $i,SV1076: $i] :
( ( ~ ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) )
| ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4050]) ).
thf(4221,plain,
! [SV931: $i,SV1077: $i] :
( ( ! [SY3054: $i,SY3055: $i] :
( ! [SY3056: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SY3055 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3055 @ SY3056 @ SY3054 ) @ SV931 )
| ( c_member @ SY3055 @ SY3054 @ ( c_Relation_ORange @ SV1077 @ SY3055 @ SV931 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4051]) ).
thf(4222,plain,
! [SV931: $i,SV1077: $i] :
( ( ! [SY3057: $i,SY3058: $i] :
( ~ ( c_member @ SY3058 @ SY3057 @ ( c_Relation_ORange @ SV1077 @ SY3058 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SY3058 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3058 @ ( sK65_B_y @ SY3058 @ SY3057 @ SV1077 @ SV931 ) @ SY3057 ) @ SV931 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4052]) ).
thf(4223,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i] :
( ( ! [SY3532: $i,SY3533: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3533 @ SY3532 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ ( sK46_B_a @ SY3533 @ SY3532 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3533 @ SY3532 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3533 @ SY3532 ) @ ( tc_prod @ SY3533 @ SY3532 ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ ( sK46_B_a @ SY3533 @ SY3532 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3533 @ SY3532 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY3533 @ SY3532 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3533 @ SY3532 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4224,plain,
! [SV1267: $i,SV1345: $i] :
( ( ~ ( ~ ( c_member @ SV1345 @ ( sK31_SY722 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
| ~ ! [SY3534: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ SY3534 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SY3534 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) )
| ( c_Wellfounded_Owf @ SV1345 @ SV1267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4225,plain,
! [SV1268: $i,SV1346: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
| ! [SY3535: $i] :
( ! [SY3536: $i] :
~ ( c_member @ SV1346 @ SY3536 @ SY3535 )
| ~ ( ~ ! [SY3537: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3537 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3537 @ SY3535 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) @ SY3535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4055]) ).
thf(4226,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ~ ! [SY3445: $i,SY3446: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3446 @ SY3446 ) @ ( c_Product__Type_OPair @ SY3446 @ SY3446 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV933 @ SV1181 @ SV1079 ) ) )
| ~ ! [SY3447: $i,SY3448: $i] :
( ( ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3449: $i] :
( ~ ( c_member @ ( tc_prod @ SY3448 @ SY3448 ) @ ( c_Product__Type_OPair @ SY3448 @ SY3448 @ SY3449 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3449 )
= ( hAPP @ SV933 @ SY3449 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4227,plain,
! [SV934: $i,SV1080: $i] :
( ( ! [SY3071: $i,SY3072: $i] :
( ( SY3072 != SY3071 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3072 )
| ( c_member @ SV1080 @ SV934 @ SY3071 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4057]) ).
thf(4228,plain,
! [SV934: $i,SV1080: $i] :
( ( ! [SY3073: $i,SY3074: $i] :
( ( SY3074 != SY3073 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3073 )
| ( c_member @ SV1080 @ SV934 @ SY3074 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4058]) ).
thf(4229,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4230,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ~ ( ( SV1271 != SV1082 )
| ( SV1183 != SV936 )
| ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
| ~ ~ ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
| ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4231,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) )
| ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4061]) ).
thf(4232,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) )
| ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4062]) ).
thf(4233,plain,
! [SV938: $i,SV1084: $i,SV1184: $i,SV1272: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV1272 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4234,plain,
! [SV939: $i,SV1347: $i] :
( ( ! [SY3538: $i] :
~ ( c_member @ SY3538 @ SV1347 @ SV939 )
| ( hBOOL @ ( hAPP @ SV939 @ SV1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4235,plain,
! [SV1348: $i,SV939: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV939 @ SV1348 ) )
| ! [SY3539: $i] : ( c_member @ SY3539 @ SV1348 @ SV939 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4236,plain,
! [SV940: $i,SV1085: $i] :
( ( ! [SY3095: $i,SY3096: $i] :
( ( SY3095 != SV1085 )
| ~ ( c_member @ SY3096 @ SY3095 @ SV940 )
| ( c_member @ ( tc_prod @ SY3096 @ SY3096 ) @ ( c_Product__Type_OPair @ SY3096 @ SY3096 @ SY3095 @ SV1085 ) @ ( c_Relation_OId__on @ SY3096 @ SV940 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4066]) ).
thf(4237,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) )
| ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4067]) ).
thf(4238,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1185 @ SV1185 ) @ ( c_Product__Type_OPair @ SV1185 @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 )
| ~ ~ ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) )
= $false )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4239,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4240,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) )
| ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4070]) ).
thf(4241,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) )
| ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4071]) ).
thf(4242,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4243,plain,
! [SV1275: $i,SV1349: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1349 @ SV1349 ) @ ( c_Product__Type_OPair @ SV1349 @ SV1349 @ ( sK76_B_x @ SV1349 @ SV1275 ) @ ( sK76_B_x @ SV1349 @ SV1275 ) ) @ SV1275 )
| ( c_Nitpick_Orefl_H @ SV1349 @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(4244,plain,
! [SV1276: $i,SV1350: $i] :
( ( ~ ( c_Nitpick_Orefl_H @ SV1350 @ SV1276 )
| ! [SY3540: $i] : ( c_member @ ( tc_prod @ SV1350 @ SV1350 ) @ ( c_Product__Type_OPair @ SV1350 @ SV1350 @ SY3540 @ SY3540 ) @ SV1276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4074]) ).
thf(4245,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i] :
( ( ! [SY3541: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3541 @ SY3541 ) @ ( c_Product__Type_OPair @ SY3541 @ SY3541 @ ( sK56_B_z @ SY3541 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3541 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SY3541 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SY3541 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SY3541 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4246,plain,
! [SV946: $i,SV1352: $i] :
( ( ! [SY3542: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY3542 @ SV1352 @ SV946 )
| ~ ( c_Relation_Oantisym @ SY3542 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SY3542 @ SV1352 @ SV946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4247,plain,
! [SV946: $i] :
( ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) )
| ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4078]) ).
thf(4249,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4078]) ).
thf(4250,plain,
( ( ~ ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4079]) ).
thf(4251,plain,
( ( ~ ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4079]) ).
thf(4252,plain,
! [SV1353: $i,SV947: $i] :
( ( ! [SY3543: $i] :
( ~ ( c_Relation_Oirrefl @ SY3543 @ SV947 )
| ~ ( c_Relation_Otrans @ SY3543 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SY3543 @ SV1353 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SY3543 @ SV1353 @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4253,plain,
! [SV947: $i] :
( ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
| ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4254,plain,
! [SV948: $i,SV1091: $i] :
( ( ! [SY3118: $i,SY3119: $i] :
( ~ ( c_member @ SY3119 @ SY3118 @ ( c_Set_Oinsert @ SY3119 @ SV1091 @ SV948 ) )
| ( SY3118 = SV1091 )
| ( c_member @ SY3119 @ SY3118 @ SV948 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4082]) ).
thf(4255,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) )
| ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4083]) ).
thf(4256,plain,
! [SV1278: $i,SV1354: $i] :
( ( ( c_member @ ( tc_prod @ SV1354 @ SV1354 ) @ ( c_Product__Type_OPair @ SV1354 @ SV1354 @ ( sK72_B_x @ SV1354 @ SV1278 ) @ ( sK72_B_x @ SV1354 @ SV1278 ) ) @ SV1278 )
| ( c_Relation_Oirrefl @ SV1354 @ SV1278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(4257,plain,
! [SV1279: $i,SV1355: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV1355 @ SV1279 )
| ! [SY3544: $i] :
~ ( c_member @ ( tc_prod @ SV1355 @ SV1355 ) @ ( c_Product__Type_OPair @ SV1355 @ SV1355 @ SY3544 @ SY3544 ) @ SV1279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4258,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ~ ! [SY3464: $i,SY3465: $i] :
( ! [SY3466: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3465 @ SY3465 ) @ ( c_Product__Type_OPair @ SY3465 @ SY3465 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3466 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3466 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) )
| ~ ! [SY3467: $i,SY3468: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3469: $i] :
( ~ ( c_member @ ( tc_prod @ SY3468 @ SY3468 ) @ ( c_Product__Type_OPair @ SY3468 @ SY3468 @ SY3469 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SY3469 @ ( hAPP @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3469 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4259,plain,
! [SV950: $i,SV1093: $i] :
( ( ! [SY3132: $i,SY3133: $i] :
( ~ ( c_member @ SY3133 @ SY3132 @ SV1093 )
| ( c_member @ SY3133 @ SY3132 @ ( c_Set_Oinsert @ SY3133 @ SV950 @ SV1093 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4087]) ).
thf(4260,plain,
! [SV1093: $i,SV950: $i] :
( ( ! [SY3134: $i] :
( ( SY3134 != SV950 )
| ! [SY3135: $i] : ( c_member @ SY3135 @ SY3134 @ ( c_Set_Oinsert @ SY3135 @ SV950 @ SV1093 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4088]) ).
thf(4261,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4262,plain,
! [SV952: $i,SV1095: $i] :
( ( ! [SY3139: $i] :
( ! [SY3140: $i] :
~ ( c_member @ ( tc_prod @ SY3140 @ SY3140 ) @ ( c_Product__Type_OPair @ SY3140 @ SY3140 @ SY3139 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3140 @ SV952 ) )
| ( SY3139 != SV1095 )
| ( SY3139 = SV1095 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4090]) ).
thf(4263,plain,
! [SV952: $i,SV1095: $i] :
( ( ! [SY3141: $i,SY3142: $i] :
( ~ ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3142 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY3142 @ SY3142 ) @ ( c_Product__Type_OPair @ SY3142 @ SY3142 @ SY3141 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SY3142 @ SV952 ) )
| ( SY3141 = SV1095 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4091]) ).
thf(4264,plain,
! [SV953: $i,SV1096: $i,SV1191: $i,SV1282: $i,SV1357: $i] :
( ( ~ ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4265,plain,
! [SV1283: $i,SV1358: $i] :
( ( ( SV1358 = SV1283 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1358 @ SV1283 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1283 @ SV1358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4266,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4094]) ).
thf(4267,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4094]) ).
thf(4268,plain,
! [SV1284: $i,SV1359: $i] :
( ( ~ ( c_member @ SV1359 @ ( sK32_B_x @ SV1359 @ SV1284 ) @ ( c_Wellfounded_Oacc @ SV1359 @ SV1284 ) )
| ( c_Wellfounded_Owf @ SV1359 @ SV1284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4269,plain,
! [SV1285: $i,SV1360: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1360 @ SV1285 )
| ! [SY3545: $i] : ( c_member @ SV1360 @ SY3545 @ ( c_Wellfounded_Oacc @ SV1360 @ SV1285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4270,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1192 @ SV1192 ) @ ( c_Product__Type_OPair @ SV1192 @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 )
| ~ ~ ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) ) )
= $false )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4271,plain,
! [SV1098: $i,SV955: $i] :
( ( ! [SY3147: $i,SY3148: $i] :
( ~ ( c_Wellfounded_Owf @ SY3148 @ SV955 )
| ( c_member @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SV1098 @ SY3147 ) @ ( c_Transitive__Closure_Ortrancl @ SY3148 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3148 @ ( c_Set_Oinsert @ ( tc_prod @ SY3148 @ SY3148 ) @ ( c_Product__Type_OPair @ SY3148 @ SY3148 @ SY3147 @ SV1098 ) @ SV955 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4098]) ).
thf(4272,plain,
! [SV955: $i,SV1098: $i] :
( ( ~ ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) )
| ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4099]) ).
thf(4273,plain,
! [SV795: $i,SV956: $i,SV1099: $i,SV1193: $i,SV1286: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV1286 @ SV1193 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4100]) ).
thf(4274,plain,
! [SV796: $i,SV957: $i,SV1100: $i,SV1194: $i] :
( ( ( SV1194 = SV1100 )
= $false )
| ( ( ~ ( c_member @ SV957 @ SV1100 @ SV796 )
| ( c_member @ SV957 @ SV1194 @ SV796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4275,plain,
! [SV797: $i,SV958: $i,SV1101: $i,SV1195: $i,SV1287: $i,SV1361: $i] :
( ( ( c_Product__Type_Oprod_Oprod__rec @ SV1361 @ SV1287 @ SV1195 @ SV1101 @ ( c_Product__Type_OPair @ SV1361 @ SV1287 @ SV958 @ SV797 ) )
= ( hAPP @ ( hAPP @ SV1101 @ SV958 ) @ SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4276,plain,
! [SV798: $i,SV959: $i,SV1102: $i,SV1196: $i,SV1288: $i,SV1362: $i] :
( ( ( c_Product__Type_Ointernal__split @ SV1362 @ SV1288 @ SV1196 @ SV1102 @ ( c_Product__Type_OPair @ SV1362 @ SV1288 @ SV959 @ SV798 ) )
= ( hAPP @ ( hAPP @ SV1102 @ SV959 ) @ SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4277,plain,
! [SV799: $i,SV960: $i,SV1103: $i,SV1197: $i,SV1289: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1289 @ SV1197 ) @ ( c_Product__Type_OPair @ SV1289 @ SV1197 @ SV1103 @ SV960 ) @ SV799 ) )
= $true )
| ( ( c_member @ SV1197 @ SV960 @ ( c_Relation_ORange @ SV1289 @ SV1197 @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4278,plain,
! [SV800: $i,SV961: $i,SV1104: $i,SV1198: $i] :
( ( ( SV1198 = SV1104 )
= $false )
| ( ( ~ ( c_member @ SV961 @ SV1198 @ SV800 )
| ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SV1198 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4279,plain,
! [SV801: $i,SV962: $i,SV1105: $i,SV1199: $i,SV1290: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1290 @ SV1199 ) @ ( c_Product__Type_OPair @ SV1290 @ SV1199 @ SV1105 @ SV962 ) @ SV801 ) )
= $true )
| ( ( c_member @ SV1290 @ SV1105 @ ( c_Relation_ODomain @ SV1290 @ SV1199 @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4106]) ).
thf(4280,plain,
! [SV802: $i,SV963: $i,SV1106: $i,SV1200: $i] :
( ( ( c_Relation_Otrans @ SV1200 @ SV1106 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV963 @ SV802 )
| ( c_Relation_Otrans @ ( tc_prod @ SV1200 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SV1200 @ SV963 @ SV1106 @ SV802 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4281,plain,
! [SV804: $i,SV965: $i,SV1107: $i,SV1201: $i] :
( ( ( c_Relation_Otrans @ SV1201 @ SV1107 )
= $false )
| ( ( c_Relation_Otrans @ SV965 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1201 @ SV965 @ SV1107 ) @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4108]) ).
thf(4282,plain,
! [SV805: $i,SV966: $i,SV1108: $i,SV1202: $i] :
( ( ( c_member @ SV1202 @ SV1108 @ ( c_Relation_ORange @ SV966 @ SV1202 @ SV805 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV966 @ SV1202 ) @ ( c_Product__Type_OPair @ SV966 @ SV1202 @ ( sK63_B_x @ SV1202 @ SV1108 @ SV966 @ SV805 ) @ SV1108 ) @ SV805 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4109]) ).
thf(4283,plain,
! [SV806: $i,SV967: $i,SV1109: $i,SV1203: $i] :
( ( ( c_member @ SV1203 @ SV1109 @ ( c_Relation_ODomain @ SV1203 @ SV967 @ SV806 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1203 @ SV967 ) @ ( c_Product__Type_OPair @ SV1203 @ SV967 @ SV1109 @ ( sK62_B_y @ SV1203 @ SV1109 @ SV967 @ SV806 ) ) @ SV806 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4284,plain,
! [SV807: $i,SV968: $i,SV1110: $i,SV1204: $i] :
( ( ( c_member @ SV1204 @ SV1110 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1204 @ SV1204 ) @ ( c_Product__Type_OPair @ SV1204 @ SV1204 @ SV807 @ SV1110 ) @ SV968 )
| ( c_member @ SV1204 @ SV807 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4111]) ).
thf(4285,plain,
! [SV808: $i,SV969: $i,SV1111: $i,SV1205: $i] :
( ( ( c_Relation_Orefl__on @ SV1205 @ SV1111 @ SV969 )
= $false )
| ( ( ~ ( c_member @ SV1205 @ SV808 @ SV1111 )
| ( c_member @ ( tc_prod @ SV1205 @ SV1205 ) @ ( c_Product__Type_OPair @ SV1205 @ SV1205 @ SV808 @ SV808 ) @ SV969 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4286,plain,
! [SV809: $i,SV970: $i,SV1112: $i,SV1206: $i,SV1291: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1291 @ SV1206 @ SV1112 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1291 @ SV1291 ) @ ( c_Product__Type_OPair @ SV1291 @ SV1291 @ SV970 @ SV809 ) @ SV1112 )
| ( c_member @ SV1291 @ SV970 @ SV1206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4287,plain,
! [SV810: $i,SV971: $i,SV1113: $i,SV1207: $i,SV1292: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1292 @ SV1207 @ SV1113 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1292 @ SV1292 ) @ ( c_Product__Type_OPair @ SV1292 @ SV1292 @ SV971 @ SV810 ) @ SV1113 )
| ( c_member @ SV1292 @ SV810 @ SV1207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4288,plain,
! [SV811: $i,SV972: $i,SV1114: $i,SV1208: $i] :
( ( ( c_member @ ( tc_prod @ SV1208 @ SV1208 ) @ ( c_Product__Type_OPair @ SV1208 @ SV1208 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SV1208 @ SV811 ) )
= $false )
| ( ( ~ ( c_member @ SV1208 @ SV972 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
| ( c_member @ SV1208 @ SV1114 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4115]) ).
thf(4289,plain,
! [SV812: $i,SV973: $i,SV1115: $i,SV1209: $i] :
( ( ( c_member @ SV1209 @ SV1115 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1209 @ SV1209 ) @ ( c_Product__Type_OPair @ SV1209 @ SV1209 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SV1209 @ SV973 ) )
| ( c_member @ SV1209 @ SV812 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4290,plain,
! [SV813: $i,SV974: $i,SV1116: $i,SV1210: $i,SV1293: $i,SV1363: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4291,plain,
! [SV814: $i,SV975: $i,SV1117: $i,SV1211: $i,SV1294: $i,SV1364: $i] :
( ( ( c_Product__Type_Ocurry @ SV1364 @ SV1294 @ SV1211 @ SV1117 @ SV975 @ SV814 )
= ( hAPP @ SV1117 @ ( c_Product__Type_OPair @ SV1364 @ SV1294 @ SV975 @ SV814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4292,plain,
! [SV817: $i,SV978: $i,SV1120: $i,SV1212: $i,SV1295: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4293,plain,
! [SV818: $i,SV979: $i,SV1121: $i,SV1213: $i,SV1296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV1121 ) @ SV979 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
| ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4294,plain,
! [SV819: $i,SV980: $i,SV1122: $i,SV1214: $i,SV1297: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1122 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4295,plain,
! [SV820: $i,SV981: $i,SV1123: $i,SV1215: $i,SV1298: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
| ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4296,plain,
! [SV822: $i,SV983: $i,SV1124: $i,SV1216: $i] :
( ( ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Otrancl @ SV1216 @ SV822 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1216 @ SV1216 ) @ ( c_Product__Type_OPair @ SV1216 @ SV1216 @ SV1124 @ SV983 ) @ ( c_Transitive__Closure_Ortrancl @ SV1216 @ SV822 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4124]) ).
thf(4297,plain,
! [SV823: $i,SV984: $i,SV1125: $i,SV1217: $i,SV1299: $i,SV1365: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1365 @ SV1365 ) @ ( c_Product__Type_OPair @ SV1365 @ SV1365 @ SV1299 @ SV1217 ) @ SV1125 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV1365 @ SV984 @ SV823 @ SV1125 @ SV1217 ) @ SV1299 )
= ( hAPP @ SV823 @ SV1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4298,plain,
! [SV824: $i,SV985: $i,SV1126: $i,SV1218: $i] :
( ( ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ SV824 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1218 @ SV1218 ) @ ( c_Product__Type_OPair @ SV1218 @ SV1218 @ SV1126 @ SV985 ) @ ( c_Transitive__Closure_Otrancl @ SV1218 @ SV824 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4126]) ).
thf(4299,plain,
! [SV828: $i,SV989: $i,SV1128: $i,SV1219: $i,SV1300: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV1128 ) @ SV989 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1128 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV989 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4300,plain,
! [SV829: $i,SV990: $i,SV1129: $i,SV1220: $i,SV1301: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV1129 ) @ SV990 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
| ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4129]) ).
thf(4301,plain,
! [SV830: $i,SV991: $i,SV1130: $i,SV1221: $i,SV1302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1130 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4130]) ).
thf(4302,plain,
! [SV831: $i,SV992: $i,SV1131: $i,SV1222: $i,SV1303: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
| ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4131]) ).
thf(4303,plain,
! [SV832: $i,SV993: $i,SV1132: $i,SV1223: $i,SV1304: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV1132 ) @ SV993 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SV1304 @ SV993 ) )
| ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SV1304 @ SV993 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4132]) ).
thf(4304,plain,
! [SV833: $i,SV994: $i,SV1133: $i,SV1224: $i,SV1305: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV994 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1133 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SV1305 @ SV994 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4305,plain,
! [SV834: $i,SV995: $i,SV1134: $i,SV1225: $i,SV1306: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV995 ) )
| ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4306,plain,
! [SV835: $i,SV996: $i,SV1135: $i,SV1226: $i,SV1307: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SV1307 @ SV996 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
| ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4135]) ).
thf(4307,plain,
! [SV1308: $i,SV836: $i,SV1366: $i,SV997: $i,SV1136: $i,SV1227: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1227 @ SV1227 ) @ ( c_Product__Type_OPair @ SV1227 @ SV1227 @ SV1136 @ SV997 ) @ SV1366 )
| ( ( hAPP @ ( c_Recdef_Ocut @ SV1227 @ SV836 @ SV1308 @ SV1366 @ SV997 ) @ SV1136 )
= ( hAPP @ SV1308 @ SV1136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4308,plain,
! [SV1137: $i,SV837: $i,SV998: $i,SV1228: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ SV998 @ SV837 ) @ SV1137 ) )
= $true )
| ( ( ( SV998 != SV837 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1228 @ SV1137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4137]) ).
thf(4309,plain,
! [SV842: $i,SV1002: $i,SV1138: $i,SV1229: $i] :
( ( ( c_Relation_Oantisym @ SV1229 @ SV1138 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
| ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4310,plain,
! [SV843: $i,SV1003: $i,SV1139: $i,SV1230: $i] :
( ( ( c_member @ SV1230 @ SV1139 @ ( c_Set_Oinsert @ SV1230 @ SV1003 @ SV843 ) )
= $false )
| ( ( ( SV1139 = SV1003 )
| ( c_member @ SV1230 @ SV1139 @ SV843 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4139]) ).
thf(4311,plain,
! [SV847: $i,SV1007: $i,SV1143: $i,SV1233: $i] :
( ( ( c_member @ SV1233 @ SV1143 @ SV1007 )
= $false )
| ( ( c_member @ SV1233 @ SV1143 @ ( c_Set_Oinsert @ SV1233 @ SV847 @ SV1007 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4312,plain,
! [SV849: $i,SV1009: $i,SV1145: $i,SV1234: $i] :
( ( ( c_Wellfounded_Owf @ SV1234 @ SV1145 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 )
| ( c_Wellfounded_Owf @ ( tc_prod @ SV1234 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SV1234 @ SV1009 @ SV1145 @ SV849 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4313,plain,
! [SV1010: $i,SV850: $i,SV1146: $i] :
( ( ( c_member @ ( tc_prod @ SV1146 @ SV1146 ) @ ( c_Product__Type_OPair @ SV1146 @ SV1146 @ SV850 @ SV850 ) @ SV1010 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1146 @ SV1010 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4314,plain,
! [SV851: $i,SV1011: $i,SV1147: $i,SV1235: $i] :
( ( ( c_Wellfounded_Owf @ SV1235 @ SV1147 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 )
| ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4315,plain,
! [SV852: $i,SV1012: $i,SV1148: $i,SV1236: $i] :
( ( ( c_Wellfounded_Owf @ SV1236 @ SV1148 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 )
| ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4316,plain,
! [SV1013: $i,SV853: $i,SV1149: $i] :
( ( ( c_member @ ( tc_prod @ SV1149 @ SV1149 ) @ ( c_Product__Type_OPair @ SV1149 @ SV1149 @ SV853 @ SV853 ) @ SV1013 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1149 @ SV1013 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4317,plain,
! [SV856: $i,SV1016: $i,SV1151: $i,SV1237: $i,SV1311: $i,SV1367: $i] :
( ( ~ ( c_member @ SV1367 @ SV1311 @ SV1237 )
| ~ ( c_member @ ( tc_prod @ SV1367 @ SV1151 ) @ ( c_Product__Type_OPair @ SV1367 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SV1367 @ SV1151 @ SV856 @ SV1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(4318,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i,SV1368: $i] :
( ( ! [SY3546: $i,SY3547: $i] :
( ~ ( c_member @ ( tc_prod @ SY3547 @ SY3546 ) @ ( c_Product__Type_OPair @ SY3547 @ SY3546 @ SV1368 @ SV1312 ) @ SV1238 )
| ~ ( c_member @ ( tc_prod @ SY3546 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3546 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY3547 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3547 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY3547 @ SY3546 @ SV1152 @ SV1238 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4319,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i,SV1369: $i] :
( ( ! [SY3548: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3548 @ SV1369 ) )
| ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SY3548 @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4320,plain,
! [SV863: $i,SV1023: $i,SV1154: $i,SV1240: $i,SV1314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1314 @ ( c_Product__Type_OPair @ SV1240 @ SV1154 @ SV1023 @ SV863 ) ) ) )
= $true )
| ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV1240 @ SV1154 @ tc_HOL_Obool @ SV1314 @ SV1023 @ SV863 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4321,plain,
! [SV864: $i,SV1024: $i,SV1155: $i,SV1241: $i,SV1315: $i] :
( ( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV1315 @ SV1241 @ tc_HOL_Obool @ SV1155 @ SV1024 @ SV864 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1155 @ ( c_Product__Type_OPair @ SV1315 @ SV1241 @ SV1024 @ SV864 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4322,plain,
! [SV865: $i,SV1025: $i,SV1156: $i,SV1242: $i,SV1316: $i] :
( ( ( ~ ( hBOOL @ ( c_Product__Type_Ocurry @ SV1316 @ SV1242 @ tc_HOL_Obool @ SV1156 @ SV1025 @ SV865 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1156 @ ( c_Product__Type_OPair @ SV1316 @ SV1242 @ SV1025 @ SV865 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4323,plain,
! [SV878: $i,SV1036: $i,SV1159: $i,SV1244: $i] :
( ( ( c_Wellfounded_Owf @ SV1244 @ SV1159 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1036 @ ( hAPP @ ( c_Relation_Oinv__image @ SV1244 @ SV1036 @ SV1159 ) @ SV878 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4324,plain,
! [SV882: $i,SV1040: $i,SV1160: $i,SV1245: $i,SV1317: $i,SV1370: $i] :
( ( ( SV1370
!= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) )
| ~ ( c_Wellfounded_Owf @ SV1317 @ SV1160 )
| ( ( hAPP @ SV1370 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SV1370 @ SV1160 @ SV882 ) ) @ SV882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4325,plain,
! [SV883: $i,SV1041: $i,SV1161: $i,SV1246: $i,SV1318: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1318 @ SV1246 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SV1318 @ SV1161 @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV1246 @ SV883 ) ) @ SV883 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4326,plain,
! [SV1162: $i,SV884: $i,SV1247: $i,SV1042: $i] :
( ( ( c_Wellfounded_Owf @ SV1042 @ SV1247 )
= $false )
| ( ( ! [SY3388: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SY3388 )
= ( hAPP @ ( hAPP @ SV1162 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SV1247 @ SY3388 ) ) @ SY3388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4327,plain,
! [SV1164: $i,SV895: $i,SV1049: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV895 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV1049 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4163]) ).
thf(4328,plain,
! [SV1050: $i,SV896: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV896 @ SV1050 )
= $false )
| ( ( SV1050 = SV896 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1050 @ SV896 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4164]) ).
thf(4329,plain,
! [SV901: $i,SV1055: $i] :
( ( ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK70_SY736 @ SV1055 @ SV901 ) ) @ SV901 )
= $true )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4165]) ).
thf(4330,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4331,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4332,plain,
! [SV903: $i,SV1057: $i,SV1371: $i] :
( ( ! [SY3549: $i] :
( ( c_member @ SY3549 @ SV1371 @ SV1057 )
| ( c_member @ SY3549 @ SV1371 @ SV903 )
| ( ( c_Set_Oinsert @ SY3549 @ SV1371 @ SV1057 )
!= ( c_Set_Oinsert @ SY3549 @ SV1371 @ SV903 ) )
| ( SV1057 = SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4333,plain,
! [SV903: $i,SV1057: $i,SV1372: $i] :
( ( ! [SY3550: $i] :
( ( c_member @ SY3550 @ SV1372 @ SV1057 )
| ( c_member @ SY3550 @ SV1372 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SY3550 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SY3550 @ SV1372 @ SV903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4334,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i] :
( ( ! [SY3551: $i,SY3552: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3552 @ SY3551 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ ( sK18_B_a @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3552 @ SY3551 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3552 @ SY3551 ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ ( sK18_B_a @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY3552 @ SY3551 @ ( sK20_SY717 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY3552 @ SY3551 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4335,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1374 @ SV1374 ) @ ( c_Product__Type_OPair @ SV1374 @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 )
| ~ ~ ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) )
| ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4336,plain,
! [SV905: $i,SV1322: $i,SV1375: $i] :
( ( ~ ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
| ! [SY3553: $i] :
( ~ ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SY3553 @ SV1322 ) @ SV905 )
| ( c_member @ SV1375 @ SY3553 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4337,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ~ ( ~ ( c_member @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) )
| ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4338,plain,
! [SV906: $i,SV1324: $i,SV1377: $i] :
( ( ~ ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
| ! [SY3554: $i] :
( ~ ( c_member @ SV1377 @ SY3554 @ SV1324 )
| ! [SY3555: $i] :
( ~ ( c_member @ SV1377 @ SY3555 @ SV1324 )
| ( SY3554 = SY3555 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3554 @ SY3555 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3555 @ SY3554 ) @ SV906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4339,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ~ ( ! [SY3394: $i,SY3395: $i] :
( ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1059 @ SV907 ) )
| ( SV1250 = SV1059 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4175]) ).
thf(4340,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ~ ( ! [SY3396: $i,SY3397: $i] :
( ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1059 @ SV907 ) )
| ( SV1168 = SV907 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4175]) ).
thf(4341,plain,
! [SV908: $i,SV1060: $i] :
( ( ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK26_B_x @ SV1060 @ SV908 ) @ ( sK27_SY720 @ SV1060 @ SV908 ) ) @ SV908 )
= $true )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4176]) ).
thf(4342,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4177]) ).
thf(4343,plain,
! [SV909: $i,SV1325: $i,SV1378: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1378 @ ( sK75_B_x1 @ SV1378 @ SV1325 @ SV909 ) ) )
| ! [SY3556: $i,SY3557: $i] : ( hBOOL @ ( hAPP @ SV1378 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SY3556 @ SY3557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4344,plain,
! [SV909: $i,SV1326: $i,SV1379: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1379 @ ( c_Product__Type_OPair @ SV1326 @ SV909 @ ( sK73_B_a @ SV1379 @ SV1326 @ SV909 ) @ ( sK74_SY739 @ SV1379 @ SV1326 @ SV909 ) ) ) )
| ! [SY3558: $i] : ( hBOOL @ ( hAPP @ SV1379 @ SY3558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4345,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) ) )
| ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4346,plain,
! [SV910: $i,SV1328: $i,SV1381: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
| ! [SY3559: $i,SY3560: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3560 ) @ SV910 )
| ! [SY3561: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3561 ) @ SV910 )
| ( SY3560 = SY3561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4347,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4348,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4183]) ).
thf(4349,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4183]) ).
thf(4350,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK78_SY740 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4351,plain,
! [SV1253: $i,SV1331: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV1331 @ SV1253 ) )
= $true )
| ( ( ! [SY3518: $i,SY3519: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3519 ) @ SV1253 )
| ! [SY3520: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3519 @ SY3520 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3520 ) @ SV1253 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4185]) ).
thf(4352,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK33_B_x @ SV1332 @ SV1254 ) @ ( sK34_SY725 @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4353,plain,
! [SV1255: $i,SV1333: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1333 @ SV1255 ) )
= $true )
| ( ( ! [SY3521: $i,SY3522: $i] :
( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3521 @ SY3522 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3522 @ SY3521 ) @ SV1255 )
| ( SY3521 = SY3522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4354,plain,
! [SV913: $i,SV1334: $i,SV1383: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV1383 @ SV1334 @ SV913 )
| ~ ( c_Relation_Otrans @ SV1383 @ SV913 )
| ( c_Order__Relation_Opreorder__on @ SV1383 @ SV1334 @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4188]) ).
thf(4355,plain,
! [SV913: $i] :
( ( ~ ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4356,plain,
! [SV913: $i] :
( ( ~ ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4357,plain,
! [SV1063: $i,SV914: $i,SV1171: $i] :
( ( ! [SY3278: $i,SY3279: $i] :
( ! [SY3280: $i] :
( ~ ( c_member @ SV1171 @ SY3280 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3279 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3279 @ SY3280 @ SY3278 ) @ SV1063 ) )
| ( c_member @ SY3279 @ SY3278 @ ( c_Relation_OImage @ SV1171 @ SY3279 @ SV1063 @ SV914 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4190]) ).
thf(4358,plain,
! [SV914: $i,SV1063: $i,SV1171: $i] :
( ( ! [SY3281: $i,SY3282: $i] :
( ~ ( c_member @ SY3282 @ SY3281 @ ( c_Relation_OImage @ SV1171 @ SY3282 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3282 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3282 @ ( sK24_B_x @ SY3282 @ SY3281 @ SV1171 @ SV1063 @ SV914 ) @ SY3281 ) @ SV1063 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4191]) ).
thf(4359,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false )
| ( ( ( SV1172 = SV1064 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4360,plain,
! [SV916: $i,SV1335: $i] :
( ( ( ( SV1335 != SV916 ) )
= $true )
| ( ( ! [SY3524: $i] : ( c_member @ ( tc_prod @ SY3524 @ SY3524 ) @ ( c_Product__Type_OPair @ SY3524 @ SY3524 @ SV1335 @ SV916 ) @ ( c_Relation_OId @ SY3524 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4193]) ).
thf(4361,plain,
! [SV916: $i,SV1336: $i] :
( ( ( ! [SY3525: $i] :
~ ( c_member @ ( tc_prod @ SY3525 @ SY3525 ) @ ( c_Product__Type_OPair @ SY3525 @ SY3525 @ SV1336 @ SV916 ) @ ( c_Relation_OId @ SY3525 ) ) )
= $true )
| ( ( SV1336 = SV916 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4194]) ).
thf(4362,plain,
! [SV917: $i,SV1065: $i,SV1384: $i] :
( ( ! [SY3570: $i] :
( ( SY3570 != SV1384 )
| ~ ( c_member @ SV1065 @ SY3570 @ SV917 )
| ( c_member @ SV1065 @ SV1384 @ SV917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4363,plain,
! [SV917: $i,SV1065: $i,SV1385: $i] :
( ( ! [SY3571: $i] :
( ( SY3571 != SV1385 )
| ~ ( c_member @ SV1065 @ SV1385 @ SV917 )
| ( c_member @ SV1065 @ SY3571 @ SV917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4364,plain,
! [SV1257: $i,SV1337: $i] :
( ( ( c_member @ ( tc_prod @ SV1337 @ SV1337 ) @ ( c_Product__Type_OPair @ SV1337 @ SV1337 @ ( sK40_B_x @ SV1337 @ SV1257 ) @ ( sK40_B_x @ SV1337 @ SV1257 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1337 @ SV1257 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1337 @ SV1257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4365,plain,
! [SV1258: $i,SV1338: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1338 @ SV1258 ) )
= $true )
| ( ( ! [SY3526: $i] :
~ ( c_member @ ( tc_prod @ SV1338 @ SV1338 ) @ ( c_Product__Type_OPair @ SV1338 @ SV1338 @ SY3526 @ SY3526 ) @ ( c_Transitive__Closure_Otrancl @ SV1338 @ SV1258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(4366,plain,
! [SV1173: $i,SV918: $i,SV1066: $i] :
( ( ! [SY3284: $i,SY3285: $i] :
( ~ ( c_member @ ( tc_prod @ SY3285 @ SY3284 ) @ ( c_Product__Type_OPair @ SY3285 @ SY3284 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3285 @ SY3284 @ SV1173 ) @ SV1066 ) @ SV918 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4199]) ).
thf(4367,plain,
! [SV918: $i,SV1066: $i,SV1173: $i] :
( ( ! [SY3286: $i,SY3287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3287 @ SY3286 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3287 @ SY3286 ) @ ( c_Product__Type_OPair @ SY3287 @ SY3286 @ SV1066 @ SV918 ) @ SV1173 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4200]) ).
thf(4368,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ~ ! [SY3420: $i,SY3421: $i] :
( ! [SY3422: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3421 @ SY3421 ) @ ( c_Product__Type_OPair @ SY3421 @ SY3421 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3422 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3422 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4201]) ).
thf(4369,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ~ ! [SY3423: $i,SY3424: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3425: $i] :
( ~ ( c_member @ ( tc_prod @ SY3424 @ SY3424 ) @ ( c_Product__Type_OPair @ SY3424 @ SY3424 @ SY3425 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SY3425 @ ( hAPP @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3425 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4201]) ).
thf(4370,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4202]) ).
thf(4371,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4202]) ).
thf(4372,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4203]) ).
thf(4373,plain,
! [SV920: $i] :
( ( ~ ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4203]) ).
thf(4374,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i] :
( ( ~ ! [SY3426: $i] :
( ! [SY3427: $i] :
~ ( c_member @ ( tc_prod @ SY3427 @ SY3427 ) @ ( c_Product__Type_OPair @ SY3427 @ SY3427 @ SY3426 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3427 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3426 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4204]) ).
thf(4375,plain,
! [SV1068: $i,SV1260: $i,SV921: $i,SV1175: $i] :
( ( ~ ! [SY3428: $i] :
( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3428 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
| ! [SY3429: $i] : ( c_member @ ( tc_prod @ SY3429 @ SY3429 ) @ ( c_Product__Type_OPair @ SY3429 @ SY3429 @ SY3428 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3429 @ SV1068 ) @ SV921 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4204]) ).
thf(4376,plain,
! [SV922: $i,SV1339: $i] :
( ( ( ( SV1339 != SV922 ) )
= $true )
| ( ( ! [SY3527: $i] : ( c_member @ SY3527 @ SV1339 @ ( c_fequal @ SV922 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4205]) ).
thf(4377,plain,
! [SV922: $i,SV1340: $i] :
( ( ( ! [SY3528: $i] :
~ ( c_member @ SY3528 @ SV1340 @ ( c_fequal @ SV922 ) ) )
= $true )
| ( ( SV1340 = SV922 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4378,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false )
| ( ( ( SV1176 = SV1069 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4379,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4380,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ( ~ ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 )
| ( SV1071
!= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4209]) ).
thf(4381,plain,
! [SV1263: $i,SV1341: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1341 @ SV1263 ) )
= $true )
| ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1341 @ SV1263 ) @ c_Wellfounded_Oless__than )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4382,plain,
! [SV1264: $i,SV1342: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1342 @ SV1264 ) @ c_Wellfounded_Oless__than ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1342 @ SV1264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4383,plain,
! [SV926: $i,SV1386: $i,SV1072: $i] :
( ( ! [SY3572: $i] :
( ! [SY3573: $i] :
~ ( c_member @ ( tc_prod @ SY3572 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3572 @ SV1072 @ SV1386 @ SY3573 ) @ SV926 )
| ( c_member @ SY3572 @ SV1386 @ ( c_Relation_ODomain @ SY3572 @ SV1072 @ SV926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4384,plain,
! [SV926: $i,SV1072: $i,SV1387: $i] :
( ( ! [SY3574: $i] :
( ~ ( c_member @ SY3574 @ SV1387 @ ( c_Relation_ODomain @ SY3574 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SY3574 @ SV1072 ) @ ( c_Product__Type_OPair @ SY3574 @ SV1072 @ SV1387 @ ( sK66_B_y @ SY3574 @ SV1387 @ SV1072 @ SV926 ) ) @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4385,plain,
! [SV927: $i,SV1073: $i,SV1388: $i] :
( ( ! [SY3575: $i] :
( ( c_member @ SY3575 @ SV1388 @ ( c_Relation_ODomain @ SY3575 @ SY3575 @ SV1073 ) )
| ( SV1388 != SV927 )
| ( c_member @ ( tc_prod @ SY3575 @ SY3575 ) @ ( c_Product__Type_OPair @ SY3575 @ SY3575 @ SV1388 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3575 @ SV1073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(4386,plain,
! [SV927: $i,SV1073: $i,SV1389: $i] :
( ( ! [SY3576: $i] :
( ( c_member @ SY3576 @ SV1389 @ ( c_Relation_ODomain @ SY3576 @ SY3576 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SY3576 @ SY3576 ) @ ( c_Product__Type_OPair @ SY3576 @ SY3576 @ SV1389 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SY3576 @ SV1073 ) )
| ( SV1389 = SV927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4215]) ).
thf(4387,plain,
! [SV928: $i,SV1074: $i,SV1390: $i] :
( ( ! [SY3577: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3577 @ SV1390 @ SV1074 ) @ SV928 ) )
| ( SV1390 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(4388,plain,
! [SV1074: $i,SV928: $i] :
( ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4389,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i] :
( ( ! [SY3578: $i,SY3579: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3579 @ SY3578 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ ( sK14_B_a @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ ( sK16_SY711 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3579 @ SY3578 ) @ ( tc_prod @ SY3579 @ SY3578 ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ ( sK16_SY711 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3579 @ SY3578 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3579 @ SY3578 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3579 @ SY3578 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4390,plain,
! [SV1392: $i,SV1076: $i,SV930: $i] :
( ( ! [SY3580: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3580 @ SV930 )
| ( c_member @ ( tc_prod @ SY3580 @ SY3580 ) @ ( c_Product__Type_OPair @ SY3580 @ SY3580 @ SV1076 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SY3580 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3580 @ ( c_Set_Oinsert @ ( tc_prod @ SY3580 @ SY3580 ) @ ( c_Product__Type_OPair @ SY3580 @ SY3580 @ SV1392 @ SV1076 ) @ SV930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4391,plain,
! [SV930: $i,SV1076: $i] :
( ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) )
| ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4220]) ).
thf(4392,plain,
! [SV931: $i,SV1393: $i,SV1077: $i] :
( ( ! [SY3581: $i] :
( ! [SY3582: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SY3581 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3581 @ SY3582 @ SV1393 ) @ SV931 )
| ( c_member @ SY3581 @ SV1393 @ ( c_Relation_ORange @ SV1077 @ SY3581 @ SV931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4221]) ).
thf(4393,plain,
! [SV931: $i,SV1077: $i,SV1394: $i] :
( ( ! [SY3583: $i] :
( ~ ( c_member @ SY3583 @ SV1394 @ ( c_Relation_ORange @ SV1077 @ SY3583 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SY3583 ) @ ( c_Product__Type_OPair @ SV1077 @ SY3583 @ ( sK65_B_y @ SY3583 @ SV1394 @ SV1077 @ SV931 ) @ SV1394 ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4394,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i] :
( ( ! [SY3584: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3584 @ SV1395 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ ( sK46_B_a @ SY3584 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3584 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3584 @ SV1395 ) @ ( tc_prod @ SY3584 @ SV1395 ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ ( sK46_B_a @ SY3584 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SY3584 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SY3584 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3584 @ SV1395 ) @ SV932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4223]) ).
thf(4395,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( ~ ( ~ ( c_member @ SV1345 @ ( sK31_SY722 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
| ~ ! [SY3534: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ SY3534 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SY3534 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4396,plain,
! [SV1268: $i,SV1346: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1346 @ SV1268 ) )
= $true )
| ( ( ! [SY3535: $i] :
( ! [SY3536: $i] :
~ ( c_member @ SV1346 @ SY3536 @ SY3535 )
| ~ ( ~ ! [SY3537: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3537 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3537 @ SY3535 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) @ SY3535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4397,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ~ ! [SY3445: $i,SY3446: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3446 @ SY3446 ) @ ( c_Product__Type_OPair @ SY3446 @ SY3446 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV933 @ SV1181 @ SV1079 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4226]) ).
thf(4398,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ~ ! [SY3447: $i,SY3448: $i] :
( ( ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3449: $i] :
( ~ ( c_member @ ( tc_prod @ SY3448 @ SY3448 ) @ ( c_Product__Type_OPair @ SY3448 @ SY3448 @ SY3449 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3449 )
= ( hAPP @ SV933 @ SY3449 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4226]) ).
thf(4399,plain,
! [SV934: $i,SV1080: $i,SV1396: $i] :
( ( ! [SY3585: $i] :
( ( SY3585 != SV1396 )
| ~ ( c_member @ SV1080 @ SV934 @ SY3585 )
| ( c_member @ SV1080 @ SV934 @ SV1396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(4400,plain,
! [SV934: $i,SV1080: $i,SV1397: $i] :
( ( ! [SY3586: $i] :
( ( SY3586 != SV1397 )
| ~ ( c_member @ SV1080 @ SV934 @ SV1397 )
| ( c_member @ SV1080 @ SV934 @ SY3586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4401,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4402,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ~ ( ( SV1271 != SV1082 )
| ( SV1183 != SV936 )
| ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4230]) ).
thf(4403,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ~ ~ ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
| ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4230]) ).
thf(4404,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) )
| ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4405,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) )
| ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4406,plain,
! [SV938: $i,SV1084: $i,SV1184: $i,SV1272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1272 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) )
| ~ ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4407,plain,
! [SV939: $i,SV1347: $i] :
( ( ( ! [SY3538: $i] :
~ ( c_member @ SY3538 @ SV1347 @ SV939 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV939 @ SV1347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4234]) ).
thf(4408,plain,
! [SV1348: $i,SV939: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV939 @ SV1348 ) ) )
= $true )
| ( ( ! [SY3539: $i] : ( c_member @ SY3539 @ SV1348 @ SV939 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4409,plain,
! [SV940: $i,SV1085: $i,SV1398: $i] :
( ( ! [SY3587: $i] :
( ( SV1398 != SV1085 )
| ~ ( c_member @ SY3587 @ SV1398 @ SV940 )
| ( c_member @ ( tc_prod @ SY3587 @ SY3587 ) @ ( c_Product__Type_OPair @ SY3587 @ SY3587 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SY3587 @ SV940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4410,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) )
| ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4411,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1185 @ SV1185 ) @ ( c_Product__Type_OPair @ SV1185 @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 ) )
= $false )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4412,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( ~ ~ ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) )
= $false )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4413,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4414,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) )
| ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4415,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) )
| ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4241]) ).
thf(4416,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4417,plain,
! [SV1275: $i,SV1349: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1349 @ SV1349 ) @ ( c_Product__Type_OPair @ SV1349 @ SV1349 @ ( sK76_B_x @ SV1349 @ SV1275 ) @ ( sK76_B_x @ SV1349 @ SV1275 ) ) @ SV1275 ) )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV1349 @ SV1275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4418,plain,
! [SV1276: $i,SV1350: $i] :
( ( ( ~ ( c_Nitpick_Orefl_H @ SV1350 @ SV1276 ) )
= $true )
| ( ( ! [SY3540: $i] : ( c_member @ ( tc_prod @ SV1350 @ SV1350 ) @ ( c_Product__Type_OPair @ SV1350 @ SV1350 @ SY3540 @ SY3540 ) @ SV1276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4419,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i,SV1399: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1399 @ SV1399 ) @ ( c_Product__Type_OPair @ SV1399 @ SV1399 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
| ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(4420,plain,
! [SV946: $i,SV1352: $i,SV1400: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV1400 @ SV1352 @ SV946 )
| ~ ( c_Relation_Oantisym @ SV1400 @ SV946 )
| ( c_Order__Relation_Opartial__order__on @ SV1400 @ SV1352 @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(4421,plain,
! [SV946: $i] :
( ( ~ ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4247]) ).
thf(4422,plain,
! [SV946: $i] :
( ( ~ ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4247]) ).
thf(4423,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX1 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX1 @ SX0 ) @ v_L ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4248]) ).
thf(4424,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4249]) ).
thf(4425,plain,
( ( sK8_REN
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4250]) ).
thf(4426,plain,
( ( ~ sK8_REN
| ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4251]) ).
thf(4427,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV1401 @ SV947 )
| ~ ( c_Relation_Otrans @ SV1401 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 )
| ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4252]) ).
thf(4428,plain,
! [SV947: $i] :
( ( ~ ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4429,plain,
! [SV947: $i] :
( ( ~ ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4430,plain,
! [SV948: $i,SV1091: $i,SV1402: $i] :
( ( ! [SY3588: $i] :
( ~ ( c_member @ SY3588 @ SV1402 @ ( c_Set_Oinsert @ SY3588 @ SV1091 @ SV948 ) )
| ( SV1402 = SV1091 )
| ( c_member @ SY3588 @ SV1402 @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4254]) ).
thf(4431,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) )
| ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4432,plain,
! [SV1278: $i,SV1354: $i] :
( ( ( c_member @ ( tc_prod @ SV1354 @ SV1354 ) @ ( c_Product__Type_OPair @ SV1354 @ SV1354 @ ( sK72_B_x @ SV1354 @ SV1278 ) @ ( sK72_B_x @ SV1354 @ SV1278 ) ) @ SV1278 )
= $true )
| ( ( c_Relation_Oirrefl @ SV1354 @ SV1278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4256]) ).
thf(4433,plain,
! [SV1279: $i,SV1355: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV1355 @ SV1279 ) )
= $true )
| ( ( ! [SY3544: $i] :
~ ( c_member @ ( tc_prod @ SV1355 @ SV1355 ) @ ( c_Product__Type_OPair @ SV1355 @ SV1355 @ SY3544 @ SY3544 ) @ SV1279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4257]) ).
thf(4434,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ~ ! [SY3464: $i,SY3465: $i] :
( ! [SY3466: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3465 @ SY3465 ) @ ( c_Product__Type_OPair @ SY3465 @ SY3465 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3466 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3466 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4258]) ).
thf(4435,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ~ ! [SY3467: $i,SY3468: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3469: $i] :
( ~ ( c_member @ ( tc_prod @ SY3468 @ SY3468 ) @ ( c_Product__Type_OPair @ SY3468 @ SY3468 @ SY3469 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SY3469 @ ( hAPP @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3469 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4258]) ).
thf(4436,plain,
! [SV950: $i,SV1093: $i,SV1403: $i] :
( ( ! [SY3589: $i] :
( ~ ( c_member @ SY3589 @ SV1403 @ SV1093 )
| ( c_member @ SY3589 @ SV1403 @ ( c_Set_Oinsert @ SY3589 @ SV950 @ SV1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(4437,plain,
! [SV1093: $i,SV950: $i,SV1404: $i] :
( ( ( SV1404 != SV950 )
| ! [SY3590: $i] : ( c_member @ SY3590 @ SV1404 @ ( c_Set_Oinsert @ SY3590 @ SV950 @ SV1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(4438,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4439,plain,
! [SV952: $i,SV1095: $i,SV1405: $i] :
( ( ! [SY3591: $i] :
~ ( c_member @ ( tc_prod @ SY3591 @ SY3591 ) @ ( c_Product__Type_OPair @ SY3591 @ SY3591 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3591 @ SV952 ) )
| ( SV1405 != SV1095 )
| ( SV1405 = SV1095 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(4440,plain,
! [SV952: $i,SV1095: $i,SV1406: $i] :
( ( ! [SY3592: $i] :
( ~ ( c_member @ ( tc_prod @ SY3592 @ SY3592 ) @ ( c_Product__Type_OPair @ SY3592 @ SY3592 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3592 @ SV952 ) )
| ( c_member @ ( tc_prod @ SY3592 @ SY3592 ) @ ( c_Product__Type_OPair @ SY3592 @ SY3592 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SY3592 @ SV952 ) )
| ( SV1406 = SV1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4441,plain,
! [SV953: $i,SV1096: $i,SV1191: $i,SV1282: $i,SV1357: $i] :
( ( ( ~ ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4442,plain,
! [SV1283: $i,SV1358: $i] :
( ( ( SV1358 = SV1283 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1358 @ SV1283 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1283 @ SV1358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4443,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX1 @ SX0 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4266]) ).
thf(4444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4267]) ).
thf(4445,plain,
! [SV1284: $i,SV1359: $i] :
( ( ( ~ ( c_member @ SV1359 @ ( sK32_B_x @ SV1359 @ SV1284 ) @ ( c_Wellfounded_Oacc @ SV1359 @ SV1284 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1359 @ SV1284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4268]) ).
thf(4446,plain,
! [SV1285: $i,SV1360: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1360 @ SV1285 ) )
= $true )
| ( ( ! [SY3545: $i] : ( c_member @ SV1360 @ SY3545 @ ( c_Wellfounded_Oacc @ SV1360 @ SV1285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4447,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1192 @ SV1192 ) @ ( c_Product__Type_OPair @ SV1192 @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 ) )
= $false )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4270]) ).
thf(4448,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( ~ ~ ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) ) )
= $false )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4270]) ).
thf(4449,plain,
! [SV1407: $i,SV1098: $i,SV955: $i] :
( ( ! [SY3593: $i] :
( ~ ( c_Wellfounded_Owf @ SY3593 @ SV955 )
| ( c_member @ ( tc_prod @ SY3593 @ SY3593 ) @ ( c_Product__Type_OPair @ SY3593 @ SY3593 @ SV1098 @ SV1407 ) @ ( c_Transitive__Closure_Ortrancl @ SY3593 @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3593 @ ( c_Set_Oinsert @ ( tc_prod @ SY3593 @ SY3593 ) @ ( c_Product__Type_OPair @ SY3593 @ SY3593 @ SV1407 @ SV1098 ) @ SV955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4271]) ).
thf(4450,plain,
! [SV955: $i,SV1098: $i] :
( ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) )
| ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4451,plain,
! [SV795: $i,SV956: $i,SV1099: $i,SV1193: $i,SV1286: $i] :
( ( ( c_Relation_Otrans @ SV1286 @ SV1193 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
| ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4452,plain,
! [SV1194: $i,SV796: $i,SV1100: $i,SV957: $i] :
( ( ( ~ ( c_member @ SV957 @ SV1100 @ SV796 ) )
= $true )
| ( ( c_member @ SV957 @ SV1194 @ SV796 )
= $true )
| ( ( SV1194 = SV1100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4453,plain,
! [SV799: $i,SV960: $i,SV1103: $i,SV1197: $i,SV1289: $i] :
( ( ( c_member @ ( tc_prod @ SV1289 @ SV1197 ) @ ( c_Product__Type_OPair @ SV1289 @ SV1197 @ SV1103 @ SV960 ) @ SV799 )
= $false )
| ( ( c_member @ SV1197 @ SV960 @ ( c_Relation_ORange @ SV1289 @ SV1197 @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4454,plain,
! [SV1104: $i,SV800: $i,SV1198: $i,SV961: $i] :
( ( ( ~ ( c_member @ SV961 @ SV1198 @ SV800 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SV1198 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) )
= $true )
| ( ( SV1198 = SV1104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4278]) ).
thf(4455,plain,
! [SV801: $i,SV962: $i,SV1105: $i,SV1199: $i,SV1290: $i] :
( ( ( c_member @ ( tc_prod @ SV1290 @ SV1199 ) @ ( c_Product__Type_OPair @ SV1290 @ SV1199 @ SV1105 @ SV962 ) @ SV801 )
= $false )
| ( ( c_member @ SV1290 @ SV1105 @ ( c_Relation_ODomain @ SV1290 @ SV1199 @ SV801 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4279]) ).
thf(4456,plain,
! [SV1106: $i,SV1200: $i,SV802: $i,SV963: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV963 @ SV802 ) )
= $true )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV1200 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SV1200 @ SV963 @ SV1106 @ SV802 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1200 @ SV1106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4457,plain,
! [SV968: $i,SV1110: $i,SV807: $i,SV1204: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1204 @ SV1204 ) @ ( c_Product__Type_OPair @ SV1204 @ SV1204 @ SV807 @ SV1110 ) @ SV968 ) )
= $true )
| ( ( c_member @ SV1204 @ SV807 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
= $true )
| ( ( c_member @ SV1204 @ SV1110 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(4458,plain,
! [SV969: $i,SV1111: $i,SV808: $i,SV1205: $i] :
( ( ( ~ ( c_member @ SV1205 @ SV808 @ SV1111 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1205 @ SV1205 ) @ ( c_Product__Type_OPair @ SV1205 @ SV1205 @ SV808 @ SV808 ) @ SV969 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1205 @ SV1111 @ SV969 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4285]) ).
thf(4459,plain,
! [SV809: $i,SV970: $i,SV1112: $i,SV1206: $i,SV1291: $i] :
( ( ( c_Relation_Orefl__on @ SV1291 @ SV1206 @ SV1112 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1291 @ SV1291 ) @ ( c_Product__Type_OPair @ SV1291 @ SV1291 @ SV970 @ SV809 ) @ SV1112 )
| ( c_member @ SV1291 @ SV970 @ SV1206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4460,plain,
! [SV810: $i,SV971: $i,SV1113: $i,SV1207: $i,SV1292: $i] :
( ( ( c_Relation_Orefl__on @ SV1292 @ SV1207 @ SV1113 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1292 @ SV1292 ) @ ( c_Product__Type_OPair @ SV1292 @ SV1292 @ SV971 @ SV810 ) @ SV1113 )
| ( c_member @ SV1292 @ SV810 @ SV1207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4461,plain,
! [SV1114: $i,SV811: $i,SV972: $i,SV1208: $i] :
( ( ( ~ ( c_member @ SV1208 @ SV972 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) ) )
= $true )
| ( ( c_member @ SV1208 @ SV1114 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1208 @ SV1208 ) @ ( c_Product__Type_OPair @ SV1208 @ SV1208 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SV1208 @ SV811 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4462,plain,
! [SV973: $i,SV1115: $i,SV812: $i,SV1209: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1209 @ SV1209 ) @ ( c_Product__Type_OPair @ SV1209 @ SV1209 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SV1209 @ SV973 ) ) )
= $true )
| ( ( c_member @ SV1209 @ SV812 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
= $true )
| ( ( c_member @ SV1209 @ SV1115 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4289]) ).
thf(4463,plain,
! [SV813: $i,SV974: $i,SV1116: $i,SV1210: $i,SV1293: $i,SV1363: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4464,plain,
! [SV817: $i,SV978: $i,SV1120: $i,SV1212: $i,SV1295: $i] :
( ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4465,plain,
! [SV818: $i,SV979: $i,SV1121: $i,SV1213: $i,SV1296: $i] :
( ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV1121 ) @ SV979 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
| ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4466,plain,
! [SV819: $i,SV980: $i,SV1122: $i,SV1214: $i,SV1297: $i] :
( ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1122 @ SV819 ) @ SV980 )
| ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4294]) ).
thf(4467,plain,
! [SV820: $i,SV981: $i,SV1123: $i,SV1215: $i,SV1298: $i] :
( ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
| ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4295]) ).
thf(4468,plain,
! [SV823: $i,SV984: $i,SV1125: $i,SV1217: $i,SV1299: $i,SV1365: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1365 @ SV1365 ) @ ( c_Product__Type_OPair @ SV1365 @ SV1365 @ SV1299 @ SV1217 ) @ SV1125 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV1365 @ SV984 @ SV823 @ SV1125 @ SV1217 ) @ SV1299 )
= ( hAPP @ SV823 @ SV1299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4297]) ).
thf(4469,plain,
! [SV828: $i,SV989: $i,SV1128: $i,SV1219: $i,SV1300: $i] :
( ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV1128 ) @ SV989 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1128 @ SV828 ) @ SV989 )
| ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV989 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4470,plain,
! [SV829: $i,SV990: $i,SV1129: $i,SV1220: $i,SV1301: $i] :
( ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV1129 ) @ SV990 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
| ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4471,plain,
! [SV830: $i,SV991: $i,SV1130: $i,SV1221: $i,SV1302: $i] :
( ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1130 @ SV830 ) @ SV991 )
| ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4472,plain,
! [SV831: $i,SV992: $i,SV1131: $i,SV1222: $i,SV1303: $i] :
( ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
| ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4473,plain,
! [SV832: $i,SV993: $i,SV1132: $i,SV1223: $i,SV1304: $i] :
( ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV1132 ) @ SV993 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SV1304 @ SV993 ) )
| ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SV1304 @ SV993 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4303]) ).
thf(4474,plain,
! [SV833: $i,SV994: $i,SV1133: $i,SV1224: $i,SV1305: $i] :
( ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV994 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1133 @ SV833 ) @ SV994 )
| ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SV1305 @ SV994 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4475,plain,
! [SV834: $i,SV995: $i,SV1134: $i,SV1225: $i,SV1306: $i] :
( ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV995 ) )
| ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4476,plain,
! [SV835: $i,SV996: $i,SV1135: $i,SV1226: $i,SV1307: $i] :
( ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SV1307 @ SV996 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
| ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4306]) ).
thf(4477,plain,
! [SV1308: $i,SV836: $i,SV1366: $i,SV997: $i,SV1136: $i,SV1227: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1227 @ SV1227 ) @ ( c_Product__Type_OPair @ SV1227 @ SV1227 @ SV1136 @ SV997 ) @ SV1366 ) )
= $true )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV1227 @ SV836 @ SV1308 @ SV1366 @ SV997 ) @ SV1136 )
= ( hAPP @ SV1308 @ SV1136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4307]) ).
thf(4478,plain,
! [SV1137: $i,SV837: $i,SV998: $i,SV1228: $i] :
( ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ SV998 @ SV837 ) @ SV1137 )
= $false )
| ( ( ( SV998 != SV837 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1228 @ SV1137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4308]) ).
thf(4479,plain,
! [SV1138: $i,SV842: $i,SV1002: $i,SV1229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1229 @ SV1138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4480,plain,
! [SV843: $i,SV1230: $i,SV1003: $i,SV1139: $i] :
( ( ( SV1139 = SV1003 )
= $true )
| ( ( c_member @ SV1230 @ SV1139 @ SV843 )
= $true )
| ( ( c_member @ SV1230 @ SV1139 @ ( c_Set_Oinsert @ SV1230 @ SV1003 @ SV843 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4481,plain,
! [SV1145: $i,SV1234: $i,SV849: $i,SV1009: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1009 @ SV849 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV1234 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SV1234 @ SV1009 @ SV1145 @ SV849 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1234 @ SV1145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4482,plain,
! [SV1147: $i,SV851: $i,SV1011: $i,SV1235: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1235 @ SV1147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4483,plain,
! [SV1148: $i,SV852: $i,SV1012: $i,SV1236: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1236 @ SV1148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4484,plain,
! [SV856: $i,SV1016: $i,SV1151: $i,SV1237: $i,SV1311: $i,SV1367: $i] :
( ( ( ~ ( c_member @ SV1367 @ SV1311 @ SV1237 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1367 @ SV1151 ) @ ( c_Product__Type_OPair @ SV1367 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SV1367 @ SV1151 @ SV856 @ SV1237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4485,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i,SV1368: $i,SV1408: $i] :
( ( ! [SY3594: $i] :
( ~ ( c_member @ ( tc_prod @ SY3594 @ SV1408 ) @ ( c_Product__Type_OPair @ SY3594 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 )
| ~ ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SY3594 @ SV1152 ) @ ( c_Product__Type_OPair @ SY3594 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SY3594 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4486,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i,SV1369: $i,SV1409: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1409 @ SV1369 ) )
| ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SV1409 @ SV1019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(4487,plain,
! [SV863: $i,SV1023: $i,SV1154: $i,SV1240: $i,SV1314: $i] :
( ( ( hBOOL @ ( hAPP @ SV1314 @ ( c_Product__Type_OPair @ SV1240 @ SV1154 @ SV1023 @ SV863 ) ) )
= $false )
| ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV1240 @ SV1154 @ tc_HOL_Obool @ SV1314 @ SV1023 @ SV863 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4488,plain,
! [SV864: $i,SV1024: $i,SV1155: $i,SV1241: $i,SV1315: $i] :
( ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV1315 @ SV1241 @ tc_HOL_Obool @ SV1155 @ SV1024 @ SV864 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1155 @ ( c_Product__Type_OPair @ SV1315 @ SV1241 @ SV1024 @ SV864 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4489,plain,
! [SV865: $i,SV1025: $i,SV1156: $i,SV1242: $i,SV1316: $i] :
( ( ( hBOOL @ ( c_Product__Type_Ocurry @ SV1316 @ SV1242 @ tc_HOL_Obool @ SV1156 @ SV1025 @ SV865 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1156 @ ( c_Product__Type_OPair @ SV1316 @ SV1242 @ SV1025 @ SV865 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4490,plain,
! [SV882: $i,SV1040: $i,SV1160: $i,SV1245: $i,SV1317: $i,SV1370: $i] :
( ( ( ( SV1370
!= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1317 @ SV1160 )
| ( ( hAPP @ SV1370 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SV1370 @ SV1160 @ SV882 ) ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4491,plain,
! [SV883: $i,SV1041: $i,SV1161: $i,SV1246: $i,SV1318: $i] :
( ( ( c_Wellfounded_Owf @ SV1318 @ SV1246 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV883 )
= ( hAPP @ ( hAPP @ SV1041 @ ( c_Recdef_Ocut @ SV1318 @ SV1161 @ ( c_Recdef_Owfrec @ SV1318 @ SV1161 @ SV1246 @ SV1041 ) @ SV1246 @ SV883 ) ) @ SV883 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4325]) ).
thf(4492,plain,
! [SV1410: $i,SV1162: $i,SV1247: $i,SV884: $i,SV1042: $i] :
( ( ( ( hAPP @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SV1410 )
= ( hAPP @ ( hAPP @ SV1162 @ ( c_Recdef_Ocut @ SV1042 @ SV884 @ ( c_Recdef_Owfrec @ SV1042 @ SV884 @ SV1247 @ SV1162 ) @ SV1247 @ SV1410 ) ) @ SV1410 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1042 @ SV1247 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4493,plain,
! [SV1164: $i,SV895: $i,SV1049: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1049 @ SV895 )
= $false )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV895 )
= $true )
| ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ SV1164 @ SV1049 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4494,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
| ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4330]) ).
thf(4495,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4496,plain,
! [SV903: $i,SV1057: $i,SV1371: $i,SV1411: $i] :
( ( ( c_member @ SV1411 @ SV1371 @ SV1057 )
| ( c_member @ SV1411 @ SV1371 @ SV903 )
| ( ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV1057 )
!= ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV903 ) )
| ( SV1057 = SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4497,plain,
! [SV903: $i,SV1057: $i,SV1372: $i,SV1412: $i] :
( ( ( c_member @ SV1412 @ SV1372 @ SV1057 )
| ( c_member @ SV1412 @ SV1372 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4498,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i] :
( ( ! [SY3595: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3595 @ SV1413 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ ( sK18_B_a @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3595 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3595 @ SV1413 ) @ ( tc_prod @ SY3595 @ SV1413 ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ ( sK18_B_a @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SY3595 @ SV1413 @ ( sK20_SY717 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SY3595 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4499,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1374 @ SV1374 ) @ ( c_Product__Type_OPair @ SV1374 @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 )
| ~ ~ ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) ) )
= $true )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4500,plain,
! [SV905: $i,SV1322: $i,SV1375: $i] :
( ( ( ~ ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) ) )
= $true )
| ( ( ! [SY3553: $i] :
( ~ ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SY3553 @ SV1322 ) @ SV905 )
| ( c_member @ SV1375 @ SY3553 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4501,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ~ ( c_member @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4337]) ).
thf(4502,plain,
! [SV906: $i,SV1324: $i,SV1377: $i] :
( ( ( ~ ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 ) )
= $true )
| ( ( ! [SY3554: $i] :
( ~ ( c_member @ SV1377 @ SY3554 @ SV1324 )
| ! [SY3555: $i] :
( ~ ( c_member @ SV1377 @ SY3555 @ SV1324 )
| ( SY3554 = SY3555 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3554 @ SY3555 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3555 @ SY3554 ) @ SV906 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4338]) ).
thf(4503,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ! [SY3394: $i,SY3395: $i] :
( ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1059 @ SV907 ) )
| ( SV1250 = SV1059 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4339]) ).
thf(4504,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ! [SY3396: $i,SY3397: $i] :
( ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1059 @ SV907 ) )
| ( SV1168 = SV907 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4340]) ).
thf(4505,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
| ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4506,plain,
! [SV909: $i,SV1325: $i,SV1378: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1378 @ ( sK75_B_x1 @ SV1378 @ SV1325 @ SV909 ) ) ) )
= $true )
| ( ( ! [SY3556: $i,SY3557: $i] : ( hBOOL @ ( hAPP @ SV1378 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SY3556 @ SY3557 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(4507,plain,
! [SV909: $i,SV1326: $i,SV1379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1379 @ ( c_Product__Type_OPair @ SV1326 @ SV909 @ ( sK73_B_a @ SV1379 @ SV1326 @ SV909 ) @ ( sK74_SY739 @ SV1379 @ SV1326 @ SV909 ) ) ) ) )
= $true )
| ( ( ! [SY3558: $i] : ( hBOOL @ ( hAPP @ SV1379 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4344]) ).
thf(4508,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4509,plain,
! [SV910: $i,SV1328: $i,SV1381: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 ) )
= $true )
| ( ( ! [SY3559: $i,SY3560: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3560 ) @ SV910 )
| ! [SY3561: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3561 ) @ SV910 )
| ( SY3560 = SY3561 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4510,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ~ ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
| ~ ~ ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4511,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4348]) ).
thf(4512,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4349]) ).
thf(4513,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK78_SY740 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4350]) ).
thf(4514,plain,
! [SV1253: $i,SV1331: $i] :
( ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false )
| ( ( ! [SY3518: $i,SY3519: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3519 ) @ SV1253 )
| ! [SY3520: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3519 @ SY3520 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3518 @ SY3520 ) @ SV1253 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4351]) ).
thf(4515,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK33_B_x @ SV1332 @ SV1254 ) @ ( sK34_SY725 @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4352]) ).
thf(4516,plain,
! [SV1255: $i,SV1333: $i] :
( ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false )
| ( ( ! [SY3521: $i,SY3522: $i] :
( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3521 @ SY3522 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3522 @ SY3521 ) @ SV1255 )
| ( SY3521 = SY3522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4517,plain,
! [SV913: $i,SV1334: $i,SV1383: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1383 @ SV1334 @ SV913 )
| ~ ( c_Relation_Otrans @ SV1383 @ SV913 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV1383 @ SV1334 @ SV913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4354]) ).
thf(4518,plain,
! [SV913: $i] :
( ( ! [SY2546: $i,SY2547: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2547 @ SY2546 @ SV913 )
| ( c_Relation_Orefl__on @ SY2547 @ SY2546 @ SV913 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4355]) ).
thf(4519,plain,
! [SV913: $i] :
( ( ! [SY2548: $i,SY2549: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY2549 @ SY2548 @ SV913 )
| ( c_Relation_Otrans @ SY2549 @ SV913 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4356]) ).
thf(4520,plain,
! [SV1063: $i,SV1414: $i,SV914: $i,SV1171: $i] :
( ( ! [SY3596: $i] :
( ! [SY3597: $i] :
( ~ ( c_member @ SV1171 @ SY3597 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3596 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3596 @ SY3597 @ SV1414 ) @ SV1063 ) )
| ( c_member @ SY3596 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SY3596 @ SV1063 @ SV914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4521,plain,
! [SV914: $i,SV1063: $i,SV1171: $i,SV1415: $i] :
( ( ! [SY3598: $i] :
( ~ ( c_member @ SY3598 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SY3598 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SY3598 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SY3598 ) @ ( c_Product__Type_OPair @ SV1171 @ SY3598 @ ( sK24_B_x @ SY3598 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4522,plain,
! [SV915: $i,SV1256: $i,SV1064: $i,SV1172: $i] :
( ( ( SV1172 = SV1064 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4359]) ).
thf(4523,plain,
! [SV916: $i,SV1335: $i] :
( ( ( SV1335 = SV916 )
= $false )
| ( ( ! [SY3524: $i] : ( c_member @ ( tc_prod @ SY3524 @ SY3524 ) @ ( c_Product__Type_OPair @ SY3524 @ SY3524 @ SV1335 @ SV916 ) @ ( c_Relation_OId @ SY3524 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4524,plain,
! [SV916: $i,SV1336: $i,SV1416: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1416 @ SV1416 ) @ ( c_Product__Type_OPair @ SV1416 @ SV1416 @ SV1336 @ SV916 ) @ ( c_Relation_OId @ SV1416 ) ) )
= $true )
| ( ( SV1336 = SV916 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4525,plain,
! [SV917: $i,SV1065: $i,SV1384: $i,SV1417: $i] :
( ( ( SV1417 != SV1384 )
| ~ ( c_member @ SV1065 @ SV1417 @ SV917 )
| ( c_member @ SV1065 @ SV1384 @ SV917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4526,plain,
! [SV917: $i,SV1065: $i,SV1385: $i,SV1418: $i] :
( ( ( SV1418 != SV1385 )
| ~ ( c_member @ SV1065 @ SV1385 @ SV917 )
| ( c_member @ SV1065 @ SV1418 @ SV917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(4527,plain,
! [SV1258: $i,SV1338: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1338 @ SV1258 )
= $false )
| ( ( ! [SY3526: $i] :
~ ( c_member @ ( tc_prod @ SV1338 @ SV1338 ) @ ( c_Product__Type_OPair @ SV1338 @ SV1338 @ SY3526 @ SY3526 ) @ ( c_Transitive__Closure_Otrancl @ SV1338 @ SV1258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4365]) ).
thf(4528,plain,
! [SV1173: $i,SV918: $i,SV1066: $i,SV1419: $i] :
( ( ! [SY3599: $i] :
( ~ ( c_member @ ( tc_prod @ SY3599 @ SV1419 ) @ ( c_Product__Type_OPair @ SY3599 @ SV1419 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3599 @ SV1419 @ SV1173 ) @ SV1066 ) @ SV918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(4529,plain,
! [SV918: $i,SV1066: $i,SV1173: $i,SV1420: $i] :
( ( ! [SY3600: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3600 @ SV1420 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SY3600 @ SV1420 ) @ ( c_Product__Type_OPair @ SY3600 @ SV1420 @ SV1066 @ SV918 ) @ SV1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4530,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ! [SY3420: $i,SY3421: $i] :
( ! [SY3422: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3421 @ SY3421 ) @ ( c_Product__Type_OPair @ SY3421 @ SY3421 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3422 @ ( sK60_B_z @ SY3422 @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3422 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3421 @ SY3420 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4368]) ).
thf(4531,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i] :
( ( ! [SY3423: $i,SY3424: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3425: $i] :
( ~ ( c_member @ ( tc_prod @ SY3424 @ SY3424 ) @ ( c_Product__Type_OPair @ SY3424 @ SY3424 @ SY3425 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SY3425 @ ( hAPP @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3425 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3424 @ SY3423 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4369]) ).
thf(4532,plain,
! [SV920: $i] :
( ( ~ ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4370]) ).
thf(4533,plain,
! [SV920: $i] :
( ( ~ ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4371]) ).
thf(4534,plain,
! [SV920: $i] :
( ( ~ ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4535,plain,
! [SV920: $i] :
( ( ~ ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4373]) ).
thf(4536,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i] :
( ( ! [SY3426: $i] :
( ! [SY3427: $i] :
~ ( c_member @ ( tc_prod @ SY3427 @ SY3427 ) @ ( c_Product__Type_OPair @ SY3427 @ SY3427 @ SY3426 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3427 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3426 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4374]) ).
thf(4537,plain,
! [SV1068: $i,SV1260: $i,SV921: $i,SV1175: $i] :
( ( ! [SY3428: $i] :
( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SY3428 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
| ! [SY3429: $i] : ( c_member @ ( tc_prod @ SY3429 @ SY3429 ) @ ( c_Product__Type_OPair @ SY3429 @ SY3429 @ SY3428 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3429 @ SV1068 ) @ SV921 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4375]) ).
thf(4538,plain,
! [SV922: $i,SV1339: $i] :
( ( ( SV1339 = SV922 )
= $false )
| ( ( ! [SY3527: $i] : ( c_member @ SY3527 @ SV1339 @ ( c_fequal @ SV922 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4539,plain,
! [SV922: $i,SV1340: $i,SV1421: $i] :
( ( ( ~ ( c_member @ SV1421 @ SV1340 @ ( c_fequal @ SV922 ) ) )
= $true )
| ( ( SV1340 = SV922 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4540,plain,
! [SV923: $i,SV1261: $i,SV1069: $i,SV1176: $i] :
( ( ( SV1176 = SV1069 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4378]) ).
thf(4541,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
| ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4542,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ( ~ ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4380]) ).
thf(4543,plain,
! [SV925: $i,SV1178: $i,SV1071: $i] :
( ( ( ( SV1071
!= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4380]) ).
thf(4544,plain,
! [SV1263: $i,SV1341: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1341 @ SV1263 )
= $false )
| ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1341 @ SV1263 ) @ c_Wellfounded_Oless__than )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4545,plain,
! [SV1264: $i,SV1342: $i] :
( ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ SV1342 @ SV1264 ) @ c_Wellfounded_Oless__than )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1342 @ SV1264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4382]) ).
thf(4546,plain,
! [SV926: $i,SV1386: $i,SV1072: $i,SV1422: $i] :
( ( ! [SY3601: $i] :
~ ( c_member @ ( tc_prod @ SV1422 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1422 @ SV1072 @ SV1386 @ SY3601 ) @ SV926 )
| ( c_member @ SV1422 @ SV1386 @ ( c_Relation_ODomain @ SV1422 @ SV1072 @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(4547,plain,
! [SV926: $i,SV1072: $i,SV1387: $i,SV1423: $i] :
( ( ~ ( c_member @ SV1423 @ SV1387 @ ( c_Relation_ODomain @ SV1423 @ SV1072 @ SV926 ) )
| ( c_member @ ( tc_prod @ SV1423 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1423 @ SV1072 @ SV1387 @ ( sK66_B_y @ SV1423 @ SV1387 @ SV1072 @ SV926 ) ) @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(4548,plain,
! [SV927: $i,SV1073: $i,SV1388: $i,SV1424: $i] :
( ( ( c_member @ SV1424 @ SV1388 @ ( c_Relation_ODomain @ SV1424 @ SV1424 @ SV1073 ) )
| ( SV1388 != SV927 )
| ( c_member @ ( tc_prod @ SV1424 @ SV1424 ) @ ( c_Product__Type_OPair @ SV1424 @ SV1424 @ SV1388 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1424 @ SV1073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4549,plain,
! [SV927: $i,SV1073: $i,SV1389: $i,SV1425: $i] :
( ( ( c_member @ SV1425 @ SV1389 @ ( c_Relation_ODomain @ SV1425 @ SV1425 @ SV1073 ) )
| ~ ( c_member @ ( tc_prod @ SV1425 @ SV1425 ) @ ( c_Product__Type_OPair @ SV1425 @ SV1425 @ SV1389 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1425 @ SV1073 ) )
| ( SV1389 = SV927 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(4550,plain,
! [SV928: $i,SV1074: $i,SV1390: $i] :
( ( ( ! [SY3577: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3577 @ SV1390 @ SV1074 ) @ SV928 ) ) )
= $true )
| ( ( ( SV1390 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4387]) ).
thf(4551,plain,
! [SV1074: $i,SV928: $i] :
( ( ~ ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4388]) ).
thf(4552,plain,
! [SV928: $i,SV1074: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4388]) ).
thf(4553,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i] :
( ( ! [SY3602: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3602 @ SV1426 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ ( sK14_B_a @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ ( sK16_SY711 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3602 @ SV1426 ) @ ( tc_prod @ SY3602 @ SV1426 ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ ( sK16_SY711 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SY3602 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY3602 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SY3602 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(4554,plain,
! [SV1392: $i,SV1076: $i,SV930: $i,SV1427: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV1427 @ SV930 )
| ( c_member @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1076 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1427 @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SV1427 @ ( c_Set_Oinsert @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1392 @ SV1076 ) @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4390]) ).
thf(4555,plain,
! [SV930: $i,SV1076: $i] :
( ( ~ ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4391]) ).
thf(4556,plain,
! [SV930: $i,SV1076: $i] :
( ( ~ ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4391]) ).
thf(4557,plain,
! [SV931: $i,SV1393: $i,SV1428: $i,SV1077: $i] :
( ( ! [SY3603: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SV1428 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1428 @ SY3603 @ SV1393 ) @ SV931 )
| ( c_member @ SV1428 @ SV1393 @ ( c_Relation_ORange @ SV1077 @ SV1428 @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(4558,plain,
! [SV931: $i,SV1077: $i,SV1394: $i,SV1429: $i] :
( ( ~ ( c_member @ SV1429 @ SV1394 @ ( c_Relation_ORange @ SV1077 @ SV1429 @ SV931 ) )
| ( c_member @ ( tc_prod @ SV1077 @ SV1429 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1429 @ ( sK65_B_y @ SV1429 @ SV1394 @ SV1077 @ SV931 ) @ SV1394 ) @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(4559,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
| ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(4560,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( ~ ( c_member @ SV1345 @ ( sK31_SY722 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
| ~ ! [SY3534: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ SY3534 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SY3534 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4395]) ).
thf(4561,plain,
! [SV1268: $i,SV1346: $i] :
( ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false )
| ( ( ! [SY3535: $i] :
( ! [SY3536: $i] :
~ ( c_member @ SV1346 @ SY3536 @ SY3535 )
| ~ ( ~ ! [SY3537: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3537 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3537 @ SY3535 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SY3535 @ SV1346 @ SV1268 ) @ SY3535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4562,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ! [SY3445: $i,SY3446: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3446 @ SY3446 ) @ ( c_Product__Type_OPair @ SY3446 @ SY3446 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3446 @ SY3445 @ SV933 @ SV1181 @ SV1079 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4397]) ).
thf(4563,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i] :
( ( ! [SY3447: $i,SY3448: $i] :
( ( ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3448 @ SY3447 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3449: $i] :
( ~ ( c_member @ ( tc_prod @ SY3448 @ SY3448 ) @ ( c_Product__Type_OPair @ SY3448 @ SY3448 @ SY3449 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3449 )
= ( hAPP @ SV933 @ SY3449 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4398]) ).
thf(4564,plain,
! [SV934: $i,SV1080: $i,SV1396: $i,SV1431: $i] :
( ( ( SV1431 != SV1396 )
| ~ ( c_member @ SV1080 @ SV934 @ SV1431 )
| ( c_member @ SV1080 @ SV934 @ SV1396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(4565,plain,
! [SV934: $i,SV1080: $i,SV1397: $i,SV1432: $i] :
( ( ( SV1432 != SV1397 )
| ~ ( c_member @ SV1080 @ SV934 @ SV1397 )
| ( c_member @ SV1080 @ SV934 @ SV1432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(4566,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4567,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ( SV1271 != SV1082 )
| ( SV1183 != SV936 )
| ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4402]) ).
thf(4568,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ~ ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
| ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4403]) ).
thf(4569,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4570,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4571,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4405]) ).
thf(4572,plain,
! [SV937: $i,SV1083: $i] :
( ( ~ ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4405]) ).
thf(4573,plain,
! [SV938: $i,SV1084: $i,SV1184: $i,SV1272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1272 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4406]) ).
thf(4574,plain,
! [SV938: $i,SV1272: $i,SV1084: $i,SV1184: $i] :
( ( ( ~ ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4406]) ).
thf(4575,plain,
! [SV939: $i,SV1347: $i,SV1433: $i] :
( ( ( ~ ( c_member @ SV1433 @ SV1347 @ SV939 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV939 @ SV1347 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(4576,plain,
! [SV1348: $i,SV939: $i] :
( ( ( hBOOL @ ( hAPP @ SV939 @ SV1348 ) )
= $false )
| ( ( ! [SY3539: $i] : ( c_member @ SY3539 @ SV1348 @ SV939 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4577,plain,
! [SV940: $i,SV1434: $i,SV1085: $i,SV1398: $i] :
( ( ( SV1398 != SV1085 )
| ~ ( c_member @ SV1434 @ SV1398 @ SV940 )
| ( c_member @ ( tc_prod @ SV1434 @ SV1434 ) @ ( c_Product__Type_OPair @ SV1434 @ SV1434 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SV1434 @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4409]) ).
thf(4578,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4410]) ).
thf(4579,plain,
! [SV940: $i,SV1085: $i] :
( ( ~ ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4410]) ).
thf(4580,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( c_member @ ( tc_prod @ SV1185 @ SV1185 ) @ ( c_Product__Type_OPair @ SV1185 @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ SV1086 ) @ SV941 )
= $true )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4411]) ).
thf(4581,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( ~ ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) ) )
= $true )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4582,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(4583,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4414]) ).
thf(4584,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4414]) ).
thf(4585,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4415]) ).
thf(4586,plain,
! [SV943: $i,SV1088: $i] :
( ( ~ ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4415]) ).
thf(4587,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) )
| ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4416]) ).
thf(4588,plain,
! [SV1275: $i,SV1349: $i] :
( ( ( c_member @ ( tc_prod @ SV1349 @ SV1349 ) @ ( c_Product__Type_OPair @ SV1349 @ SV1349 @ ( sK76_B_x @ SV1349 @ SV1275 ) @ ( sK76_B_x @ SV1349 @ SV1275 ) ) @ SV1275 )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV1349 @ SV1275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(4589,plain,
! [SV1276: $i,SV1350: $i] :
( ( ( c_Nitpick_Orefl_H @ SV1350 @ SV1276 )
= $false )
| ( ( ! [SY3540: $i] : ( c_member @ ( tc_prod @ SV1350 @ SV1350 ) @ ( c_Product__Type_OPair @ SV1350 @ SV1350 @ SY3540 @ SY3540 ) @ SV1276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4590,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i,SV1399: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1399 @ SV1399 ) @ ( c_Product__Type_OPair @ SV1399 @ SV1399 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(4591,plain,
! [SV946: $i,SV1352: $i,SV1400: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV1400 @ SV1352 @ SV946 )
| ~ ( c_Relation_Oantisym @ SV1400 @ SV946 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV1400 @ SV1352 @ SV946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4592,plain,
! [SV946: $i] :
( ( ! [SY2735: $i,SY2736: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2736 @ SY2735 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY2736 @ SY2735 @ SV946 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4421]) ).
thf(4593,plain,
! [SV946: $i] :
( ( ! [SY2737: $i,SY2738: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY2738 @ SY2737 @ SV946 )
| ( c_Relation_Oantisym @ SY2738 @ SV946 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4422]) ).
thf(4594,plain,
! [SV1435: $i] :
( ( ! [SY3604: $i] :
( ( SV1435 = SY3604 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1435 @ SY3604 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SY3604 @ SV1435 ) @ v_L ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4423]) ).
thf(4595,plain,
( ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(4596,plain,
( ( sK8_REN = $true )
| ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
| ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(4597,plain,
( ( ( ~ sK8_REN )
= $true )
| ( ( ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4426]) ).
thf(4598,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV1401 @ SV947 )
| ~ ( c_Relation_Otrans @ SV1401 @ SV947 )
| ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4427]) ).
thf(4599,plain,
! [SV947: $i] :
( ( ~ ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4428]) ).
thf(4600,plain,
! [SV947: $i] :
( ( ! [SY2745: $i,SY2746: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2746 @ SY2745 @ SV947 )
| ( c_Relation_Ototal__on @ SY2746 @ SY2745 @ SV947 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4429]) ).
thf(4601,plain,
! [SV948: $i,SV1091: $i,SV1402: $i,SV1436: $i] :
( ( ~ ( c_member @ SV1436 @ SV1402 @ ( c_Set_Oinsert @ SV1436 @ SV1091 @ SV948 ) )
| ( SV1402 = SV1091 )
| ( c_member @ SV1436 @ SV1402 @ SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4430]) ).
thf(4602,plain,
! [SV948: $i,SV1091: $i] :
( ( ~ ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4603,plain,
! [SV1091: $i,SV948: $i] :
( ( ~ ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4604,plain,
! [SV1279: $i,SV1355: $i] :
( ( ( c_Relation_Oirrefl @ SV1355 @ SV1279 )
= $false )
| ( ( ! [SY3544: $i] :
~ ( c_member @ ( tc_prod @ SV1355 @ SV1355 ) @ ( c_Product__Type_OPair @ SV1355 @ SV1355 @ SY3544 @ SY3544 ) @ SV1279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4433]) ).
thf(4605,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ! [SY3464: $i,SY3465: $i] :
( ! [SY3466: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3465 @ SY3465 ) @ ( c_Product__Type_OPair @ SY3465 @ SY3465 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3466 @ ( sK55_B_z @ SY3466 @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3466 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3465 @ SY3464 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4434]) ).
thf(4606,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i] :
( ( ! [SY3467: $i,SY3468: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3469: $i] :
( ~ ( c_member @ ( tc_prod @ SY3468 @ SY3468 ) @ ( c_Product__Type_OPair @ SY3468 @ SY3468 @ SY3469 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SY3469 @ ( hAPP @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3469 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3468 @ SY3467 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4435]) ).
thf(4607,plain,
! [SV950: $i,SV1093: $i,SV1403: $i,SV1437: $i] :
( ( ~ ( c_member @ SV1437 @ SV1403 @ SV1093 )
| ( c_member @ SV1437 @ SV1403 @ ( c_Set_Oinsert @ SV1437 @ SV950 @ SV1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4436]) ).
thf(4608,plain,
! [SV1093: $i,SV950: $i,SV1404: $i] :
( ( ( ( SV1404 != SV950 ) )
= $true )
| ( ( ! [SY3590: $i] : ( c_member @ SY3590 @ SV1404 @ ( c_Set_Oinsert @ SY3590 @ SV950 @ SV1093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4609,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4438]) ).
thf(4610,plain,
! [SV952: $i,SV1095: $i,SV1405: $i] :
( ( ( ! [SY3591: $i] :
~ ( c_member @ ( tc_prod @ SY3591 @ SY3591 ) @ ( c_Product__Type_OPair @ SY3591 @ SY3591 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SY3591 @ SV952 ) ) )
= $true )
| ( ( ( SV1405 != SV1095 )
| ( SV1405 = SV1095 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(4611,plain,
! [SV952: $i,SV1095: $i,SV1406: $i,SV1438: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1438 @ SV952 ) )
| ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SV1438 @ SV952 ) )
| ( SV1406 = SV1095 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(4612,plain,
! [SV953: $i,SV1096: $i,SV1191: $i,SV1282: $i,SV1357: $i] :
( ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4441]) ).
thf(4613,plain,
! [SV1283: $i,SV1358: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1358 @ SV1283 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1283 @ SV1358 )
= $true )
| ( ( SV1358 = SV1283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4442]) ).
thf(4614,plain,
! [SV1439: $i] :
( ( ! [SY3605: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3605 @ SV1439 )
| ( SY3605 != SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4615,plain,
! [SV1440: $i] :
( ( ! [SY3606: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1440 @ SY3606 )
| ( SY3606 != SV1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(4616,plain,
! [SV1284: $i,SV1359: $i] :
( ( ( c_member @ SV1359 @ ( sK32_B_x @ SV1359 @ SV1284 ) @ ( c_Wellfounded_Oacc @ SV1359 @ SV1284 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1359 @ SV1284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4617,plain,
! [SV1285: $i,SV1360: $i] :
( ( ( c_Wellfounded_Owf @ SV1360 @ SV1285 )
= $false )
| ( ( ! [SY3545: $i] : ( c_member @ SV1360 @ SY3545 @ ( c_Wellfounded_Oacc @ SV1360 @ SV1285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4446]) ).
thf(4618,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( c_member @ ( tc_prod @ SV1192 @ SV1192 ) @ ( c_Product__Type_OPair @ SV1192 @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ SV1097 ) @ SV954 )
= $true )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4447]) ).
thf(4619,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( ~ ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) ) )
= $true )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4448]) ).
thf(4620,plain,
! [SV1407: $i,SV1098: $i,SV955: $i,SV1441: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1441 @ SV955 )
| ( c_member @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1098 @ SV1407 ) @ ( c_Transitive__Closure_Ortrancl @ SV1441 @ SV955 ) )
| ( c_Wellfounded_Owf @ SV1441 @ ( c_Set_Oinsert @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1407 @ SV1098 ) @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(4621,plain,
! [SV955: $i,SV1098: $i] :
( ( ~ ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4622,plain,
! [SV955: $i,SV1098: $i] :
( ( ~ ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4623,plain,
! [SV795: $i,SV1193: $i,SV956: $i,SV1099: $i,SV1286: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1286 @ SV1193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(4624,plain,
! [SV1194: $i,SV796: $i,SV1100: $i,SV957: $i] :
( ( ( c_member @ SV957 @ SV1100 @ SV796 )
= $false )
| ( ( c_member @ SV957 @ SV1194 @ SV796 )
= $true )
| ( ( SV1194 = SV1100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4452]) ).
thf(4625,plain,
! [SV1104: $i,SV800: $i,SV1198: $i,SV961: $i] :
( ( ( c_member @ SV961 @ SV1198 @ SV800 )
= $false )
| ( ( c_member @ ( tc_prod @ SV961 @ SV961 ) @ ( c_Product__Type_OPair @ SV961 @ SV961 @ SV1198 @ SV1104 ) @ ( c_Relation_OId__on @ SV961 @ SV800 ) )
= $true )
| ( ( SV1198 = SV1104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4454]) ).
thf(4626,plain,
! [SV1106: $i,SV1200: $i,SV802: $i,SV963: $i] :
( ( ( c_Relation_Otrans @ SV963 @ SV802 )
= $false )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV1200 @ SV963 ) @ ( c_Wellfounded_Olex__prod @ SV1200 @ SV963 @ SV1106 @ SV802 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1200 @ SV1106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4627,plain,
! [SV968: $i,SV1110: $i,SV807: $i,SV1204: $i] :
( ( ( c_member @ ( tc_prod @ SV1204 @ SV1204 ) @ ( c_Product__Type_OPair @ SV1204 @ SV1204 @ SV807 @ SV1110 ) @ SV968 )
= $false )
| ( ( c_member @ SV1204 @ SV807 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
= $true )
| ( ( c_member @ SV1204 @ SV1110 @ ( c_Wellfounded_Oacc @ SV1204 @ SV968 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(4628,plain,
! [SV969: $i,SV1111: $i,SV808: $i,SV1205: $i] :
( ( ( c_member @ SV1205 @ SV808 @ SV1111 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1205 @ SV1205 ) @ ( c_Product__Type_OPair @ SV1205 @ SV1205 @ SV808 @ SV808 ) @ SV969 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1205 @ SV1111 @ SV969 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4458]) ).
thf(4629,plain,
! [SV1206: $i,SV1112: $i,SV809: $i,SV970: $i,SV1291: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1291 @ SV1291 ) @ ( c_Product__Type_OPair @ SV1291 @ SV1291 @ SV970 @ SV809 ) @ SV1112 ) )
= $true )
| ( ( c_member @ SV1291 @ SV970 @ SV1206 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1291 @ SV1206 @ SV1112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4630,plain,
! [SV1207: $i,SV1113: $i,SV810: $i,SV971: $i,SV1292: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1292 @ SV1292 ) @ ( c_Product__Type_OPair @ SV1292 @ SV1292 @ SV971 @ SV810 ) @ SV1113 ) )
= $true )
| ( ( c_member @ SV1292 @ SV810 @ SV1207 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1292 @ SV1207 @ SV1113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(4631,plain,
! [SV1114: $i,SV811: $i,SV972: $i,SV1208: $i] :
( ( ( c_member @ SV1208 @ SV972 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
= $false )
| ( ( c_member @ SV1208 @ SV1114 @ ( c_Wellfounded_Oacc @ SV1208 @ SV811 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1208 @ SV1208 ) @ ( c_Product__Type_OPair @ SV1208 @ SV1208 @ SV1114 @ SV972 ) @ ( c_Transitive__Closure_Ortrancl @ SV1208 @ SV811 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(4632,plain,
! [SV973: $i,SV1115: $i,SV812: $i,SV1209: $i] :
( ( ( c_member @ ( tc_prod @ SV1209 @ SV1209 ) @ ( c_Product__Type_OPair @ SV1209 @ SV1209 @ SV812 @ SV1115 ) @ ( c_Transitive__Closure_Ortrancl @ SV1209 @ SV973 ) )
= $false )
| ( ( c_member @ SV1209 @ SV812 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
= $true )
| ( ( c_member @ SV1209 @ SV1115 @ ( c_Wellfounded_Oacc @ SV1209 @ SV973 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4633,plain,
! [SV813: $i,SV974: $i,SV1116: $i,SV1210: $i,SV1293: $i,SV1363: $i] :
( ( ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
| ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4634,plain,
! [SV817: $i,SV1212: $i,SV978: $i,SV1120: $i,SV1295: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(4635,plain,
! [SV1213: $i,SV979: $i,SV818: $i,SV1121: $i,SV1296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV1121 ) @ SV979 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4636,plain,
! [SV1214: $i,SV980: $i,SV819: $i,SV1122: $i,SV1297: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1122 @ SV819 ) @ SV980 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4637,plain,
! [SV1215: $i,SV981: $i,SV820: $i,SV1123: $i,SV1298: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4638,plain,
! [SV823: $i,SV984: $i,SV1125: $i,SV1217: $i,SV1299: $i,SV1365: $i] :
( ( ( c_member @ ( tc_prod @ SV1365 @ SV1365 ) @ ( c_Product__Type_OPair @ SV1365 @ SV1365 @ SV1299 @ SV1217 ) @ SV1125 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV1365 @ SV984 @ SV823 @ SV1125 @ SV1217 ) @ SV1299 )
= ( hAPP @ SV823 @ SV1299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4639,plain,
! [SV1219: $i,SV989: $i,SV828: $i,SV1128: $i,SV1300: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1128 @ SV828 ) @ SV989 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV989 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV1128 ) @ SV989 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(4640,plain,
! [SV1220: $i,SV990: $i,SV829: $i,SV1129: $i,SV1301: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV1129 ) @ SV990 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4470]) ).
thf(4641,plain,
! [SV1221: $i,SV991: $i,SV830: $i,SV1130: $i,SV1302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1130 @ SV830 ) @ SV991 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(4642,plain,
! [SV1222: $i,SV992: $i,SV831: $i,SV1131: $i,SV1303: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4472]) ).
thf(4643,plain,
! [SV1223: $i,SV993: $i,SV832: $i,SV1132: $i,SV1304: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SV1304 @ SV993 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SV1304 @ SV993 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV1132 ) @ SV993 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(4644,plain,
! [SV1224: $i,SV994: $i,SV833: $i,SV1133: $i,SV1305: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1133 @ SV833 ) @ SV994 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SV1305 @ SV994 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV994 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(4645,plain,
! [SV1225: $i,SV995: $i,SV834: $i,SV1134: $i,SV1306: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV995 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4646,plain,
! [SV1226: $i,SV996: $i,SV835: $i,SV1135: $i,SV1307: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SV1307 @ SV996 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(4647,plain,
! [SV1308: $i,SV836: $i,SV1366: $i,SV997: $i,SV1136: $i,SV1227: $i] :
( ( ( c_member @ ( tc_prod @ SV1227 @ SV1227 ) @ ( c_Product__Type_OPair @ SV1227 @ SV1227 @ SV1136 @ SV997 ) @ SV1366 )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV1227 @ SV836 @ SV1308 @ SV1366 @ SV997 ) @ SV1136 )
= ( hAPP @ SV1308 @ SV1136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4648,plain,
! [SV1137: $i,SV1228: $i,SV837: $i,SV998: $i] :
( ( ( SV998 = SV837 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ SV998 @ SV837 ) @ SV1137 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1228 @ SV1228 ) @ ( c_Product__Type_OPair @ SV1228 @ SV1228 @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) @ ( sK39_B_x @ SV1228 @ SV1137 @ SV998 @ SV837 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1228 @ SV1137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4478]) ).
thf(4649,plain,
! [SV1138: $i,SV842: $i,SV1002: $i,SV1229: $i] :
( ( ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
| ( SV1002 = SV842 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1229 @ SV1138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4650,plain,
! [SV1145: $i,SV1234: $i,SV849: $i,SV1009: $i] :
( ( ( c_Wellfounded_Owf @ SV1009 @ SV849 )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV1234 @ SV1009 ) @ ( c_Wellfounded_Olex__prod @ SV1234 @ SV1009 @ SV1145 @ SV849 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1234 @ SV1145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4481]) ).
thf(4651,plain,
! [SV1147: $i,SV851: $i,SV1011: $i,SV1235: $i] :
( ( ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1235 @ SV1147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4652,plain,
! [SV1148: $i,SV852: $i,SV1012: $i,SV1236: $i] :
( ( ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1236 @ SV1148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4653,plain,
! [SV856: $i,SV1016: $i,SV1151: $i,SV1237: $i,SV1311: $i,SV1367: $i] :
( ( ( c_member @ SV1367 @ SV1311 @ SV1237 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1367 @ SV1151 ) @ ( c_Product__Type_OPair @ SV1367 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 )
| ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SV1367 @ SV1151 @ SV856 @ SV1237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4654,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i,SV1368: $i,SV1408: $i,SV1442: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1442 @ SV1408 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 )
| ~ ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SV1442 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SV1442 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4485]) ).
thf(4655,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i,SV1369: $i,SV1409: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1409 @ SV1369 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SV1409 @ SV1019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(4656,plain,
! [SV882: $i,SV1040: $i,SV1160: $i,SV1245: $i,SV1317: $i,SV1370: $i] :
( ( ( SV1370
= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1317 @ SV1160 )
| ( ( hAPP @ SV1370 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SV1370 @ SV1160 @ SV882 ) ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(4657,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4494]) ).
thf(4658,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4494]) ).
thf(4659,plain,
! [SV1056: $i,SV1248: $i,SV1319: $i,SV1166: $i,SV902: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(4660,plain,
! [SV903: $i,SV1057: $i,SV1371: $i,SV1411: $i] :
( ( ( c_member @ SV1411 @ SV1371 @ SV1057 )
= $true )
| ( ( ( c_member @ SV1411 @ SV1371 @ SV903 )
| ( ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV1057 )
!= ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV903 ) )
| ( SV1057 = SV903 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(4661,plain,
! [SV903: $i,SV1057: $i,SV1372: $i,SV1412: $i] :
( ( ( c_member @ SV1412 @ SV1372 @ SV1057 )
= $true )
| ( ( ( c_member @ SV1412 @ SV1372 @ SV903 )
| ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(4662,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4498]) ).
thf(4663,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1374 @ SV1374 ) @ ( c_Product__Type_OPair @ SV1374 @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 )
| ~ ~ ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) )
= $false )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4664,plain,
! [SV905: $i,SV1322: $i,SV1375: $i] :
( ( ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $false )
| ( ( ! [SY3553: $i] :
( ~ ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SY3553 @ SV1322 ) @ SV905 )
| ( c_member @ SV1375 @ SY3553 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4665,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4666,plain,
! [SV906: $i,SV1324: $i,SV1377: $i] :
( ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false )
| ( ( ! [SY3554: $i] :
( ~ ( c_member @ SV1377 @ SY3554 @ SV1324 )
| ! [SY3555: $i] :
( ~ ( c_member @ SV1377 @ SY3555 @ SV1324 )
| ( SY3554 = SY3555 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3554 @ SY3555 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3555 @ SY3554 ) @ SV906 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4667,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ( ! [SY3394: $i,SY3395: $i] :
( ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3395 @ SY3394 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1250 = SV1059 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(4668,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i] :
( ( ( ! [SY3396: $i,SY3397: $i] :
( ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3397 @ SY3396 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1168 = SV907 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4669,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4670,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ~ ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4671,plain,
! [SV909: $i,SV1325: $i,SV1378: $i] :
( ( ( hBOOL @ ( hAPP @ SV1378 @ ( sK75_B_x1 @ SV1378 @ SV1325 @ SV909 ) ) )
= $false )
| ( ( ! [SY3556: $i,SY3557: $i] : ( hBOOL @ ( hAPP @ SV1378 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SY3556 @ SY3557 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4506]) ).
thf(4672,plain,
! [SV909: $i,SV1326: $i,SV1379: $i] :
( ( ( hBOOL @ ( hAPP @ SV1379 @ ( c_Product__Type_OPair @ SV1326 @ SV909 @ ( sK73_B_a @ SV1379 @ SV1326 @ SV909 ) @ ( sK74_SY739 @ SV1379 @ SV1326 @ SV909 ) ) ) )
= $false )
| ( ( ! [SY3558: $i] : ( hBOOL @ ( hAPP @ SV1379 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(4673,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4674,plain,
! [SV910: $i,SV1328: $i,SV1381: $i] :
( ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false )
| ( ( ! [SY3559: $i,SY3560: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3560 ) @ SV910 )
| ! [SY3561: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SY3559 @ SY3561 ) @ SV910 )
| ( SY3560 = SY3561 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4509]) ).
thf(4675,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ~ ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4676,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1251: $i,SV1382: $i] :
( ( ~ ~ ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4677,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
| ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(4678,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK78_SY740 @ SV1330 @ SV1252 ) ) @ SV1252 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4513]) ).
thf(4679,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4513]) ).
thf(4680,plain,
! [SV1253: $i,SV1444: $i,SV1331: $i] :
( ( ( ! [SY3607: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SY3607 ) @ SV1253 )
| ! [SY3608: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SY3607 @ SY3608 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SY3608 ) @ SV1253 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4514]) ).
thf(4681,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK33_B_x @ SV1332 @ SV1254 ) @ ( sK34_SY725 @ SV1332 @ SV1254 ) ) @ SV1254 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4515]) ).
thf(4682,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4515]) ).
thf(4683,plain,
! [SV1255: $i,SV1445: $i,SV1333: $i] :
( ( ( ! [SY3609: $i] :
( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SY3609 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SY3609 @ SV1445 ) @ SV1255 )
| ( SV1445 = SY3609 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4516]) ).
thf(4684,plain,
! [SV913: $i,SV1334: $i,SV1383: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1383 @ SV1334 @ SV913 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1383 @ SV913 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV1383 @ SV1334 @ SV913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(4685,plain,
! [SV913: $i,SV1446: $i] :
( ( ! [SY3610: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY3610 @ SV1446 @ SV913 )
| ( c_Relation_Orefl__on @ SY3610 @ SV1446 @ SV913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(4686,plain,
! [SV913: $i,SV1447: $i] :
( ( ! [SY3611: $i] :
( ~ ( c_Order__Relation_Opreorder__on @ SY3611 @ SV1447 @ SV913 )
| ( c_Relation_Otrans @ SY3611 @ SV913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4519]) ).
thf(4687,plain,
! [SV1063: $i,SV1414: $i,SV1448: $i,SV914: $i,SV1171: $i] :
( ( ! [SY3612: $i] :
( ~ ( c_member @ SV1171 @ SY3612 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SY3612 @ SV1414 ) @ SV1063 ) )
| ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4520]) ).
thf(4688,plain,
! [SV914: $i,SV1063: $i,SV1171: $i,SV1415: $i,SV1449: $i] :
( ( ~ ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
| ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4521]) ).
thf(4689,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
| ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) )
= $false )
| ( ( SV1172 = SV1064 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(4690,plain,
! [SV916: $i,SV1335: $i,SV1450: $i] :
( ( ( c_member @ ( tc_prod @ SV1450 @ SV1450 ) @ ( c_Product__Type_OPair @ SV1450 @ SV1450 @ SV1335 @ SV916 ) @ ( c_Relation_OId @ SV1450 ) )
= $true )
| ( ( SV1335 = SV916 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4523]) ).
thf(4691,plain,
! [SV916: $i,SV1336: $i,SV1416: $i] :
( ( ( c_member @ ( tc_prod @ SV1416 @ SV1416 ) @ ( c_Product__Type_OPair @ SV1416 @ SV1416 @ SV1336 @ SV916 ) @ ( c_Relation_OId @ SV1416 ) )
= $false )
| ( ( SV1336 = SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4524]) ).
thf(4692,plain,
! [SV917: $i,SV1065: $i,SV1384: $i,SV1417: $i] :
( ( ( ( SV1417 != SV1384 ) )
= $true )
| ( ( ~ ( c_member @ SV1065 @ SV1417 @ SV917 )
| ( c_member @ SV1065 @ SV1384 @ SV917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4693,plain,
! [SV917: $i,SV1065: $i,SV1385: $i,SV1418: $i] :
( ( ( ( SV1418 != SV1385 ) )
= $true )
| ( ( ~ ( c_member @ SV1065 @ SV1385 @ SV917 )
| ( c_member @ SV1065 @ SV1418 @ SV917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4526]) ).
thf(4694,plain,
! [SV1258: $i,SV1451: $i,SV1338: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1338 @ SV1338 ) @ ( c_Product__Type_OPair @ SV1338 @ SV1338 @ SV1451 @ SV1451 ) @ ( c_Transitive__Closure_Otrancl @ SV1338 @ SV1258 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1338 @ SV1258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(4695,plain,
! [SV1173: $i,SV918: $i,SV1066: $i,SV1419: $i,SV1452: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1452 @ SV1419 ) @ ( c_Product__Type_OPair @ SV1452 @ SV1419 @ SV1066 @ SV918 ) @ SV1173 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1452 @ SV1419 @ SV1173 ) @ SV1066 ) @ SV918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4528]) ).
thf(4696,plain,
! [SV918: $i,SV1066: $i,SV1173: $i,SV1420: $i,SV1453: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1453 @ SV1420 @ SV1173 ) @ SV1066 ) @ SV918 ) )
| ( c_member @ ( tc_prod @ SV1453 @ SV1420 ) @ ( c_Product__Type_OPair @ SV1453 @ SV1420 @ SV1066 @ SV918 ) @ SV1173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4529]) ).
thf(4697,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i] :
( ( ! [SY3613: $i] :
( ! [SY3614: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3613 @ SY3613 ) @ ( c_Product__Type_OPair @ SY3613 @ SY3613 @ ( sK60_B_z @ SY3614 @ SY3613 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3613 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3614 @ SY3613 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3614 @ ( sK60_B_z @ SY3614 @ SY3613 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3614 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3613 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4530]) ).
thf(4698,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1455: $i] :
( ( ! [SY3615: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3615 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3616: $i] :
( ~ ( c_member @ ( tc_prod @ SY3615 @ SY3615 ) @ ( c_Product__Type_OPair @ SY3615 @ SY3615 @ SY3616 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SY3615 @ SV1455 @ SV1259 @ SV1174 @ SY3616 @ ( hAPP @ ( sK59_B_g @ SY3615 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3616 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SY3615 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(4699,plain,
! [SV920: $i] :
( ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) )
| ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4700,plain,
! [SV920: $i] :
( ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) )
| ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4701,plain,
! [SV920: $i] :
( ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) )
| ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4702,plain,
! [SV920: $i] :
( ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) )
| ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4703,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i,SV1456: $i] :
( ( ! [SY3617: $i] :
~ ( c_member @ ( tc_prod @ SY3617 @ SY3617 ) @ ( c_Product__Type_OPair @ SY3617 @ SY3617 @ SV1456 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3617 @ SV1068 ) @ SV921 ) )
| ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1456 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4536]) ).
thf(4704,plain,
! [SV1068: $i,SV1260: $i,SV1457: $i,SV921: $i,SV1175: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1457 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
| ! [SY3618: $i] : ( c_member @ ( tc_prod @ SY3618 @ SY3618 ) @ ( c_Product__Type_OPair @ SY3618 @ SY3618 @ SV1457 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3618 @ SV1068 ) @ SV921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4537]) ).
thf(4705,plain,
! [SV922: $i,SV1339: $i,SV1458: $i] :
( ( ( c_member @ SV1458 @ SV1339 @ ( c_fequal @ SV922 ) )
= $true )
| ( ( SV1339 = SV922 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4538]) ).
thf(4706,plain,
! [SV922: $i,SV1340: $i,SV1421: $i] :
( ( ( c_member @ SV1421 @ SV1340 @ ( c_fequal @ SV922 ) )
= $false )
| ( ( SV1340 = SV922 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4707,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
| ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) )
= $false )
| ( ( SV1176 = SV1069 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4708,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4709,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4710,plain,
! [SV925: $i,SV1071: $i,SV1178: $i] :
( ( ( c_member @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ SV925 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4542]) ).
thf(4711,plain,
! [SV925: $i,SV1178: $i,SV1071: $i] :
( ( ( SV1071
= ( c_Product__Type_OPair @ SV1178 @ SV1178 @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) @ ( sK64_B_x @ SV1178 @ SV1071 @ SV925 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1178 @ SV1178 ) @ SV1071 @ ( c_Relation_OId__on @ SV1178 @ SV925 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4543]) ).
thf(4712,plain,
! [SV926: $i,SV1386: $i,SV1072: $i,SV1422: $i] :
( ( ( ! [SY3601: $i] :
~ ( c_member @ ( tc_prod @ SV1422 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1422 @ SV1072 @ SV1386 @ SY3601 ) @ SV926 ) )
= $true )
| ( ( c_member @ SV1422 @ SV1386 @ ( c_Relation_ODomain @ SV1422 @ SV1072 @ SV926 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4713,plain,
! [SV926: $i,SV1072: $i,SV1387: $i,SV1423: $i] :
( ( ( ~ ( c_member @ SV1423 @ SV1387 @ ( c_Relation_ODomain @ SV1423 @ SV1072 @ SV926 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1423 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1423 @ SV1072 @ SV1387 @ ( sK66_B_y @ SV1423 @ SV1387 @ SV1072 @ SV926 ) ) @ SV926 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4714,plain,
! [SV927: $i,SV1073: $i,SV1388: $i,SV1424: $i] :
( ( ( c_member @ SV1424 @ SV1388 @ ( c_Relation_ODomain @ SV1424 @ SV1424 @ SV1073 ) )
= $true )
| ( ( ( SV1388 != SV927 )
| ( c_member @ ( tc_prod @ SV1424 @ SV1424 ) @ ( c_Product__Type_OPair @ SV1424 @ SV1424 @ SV1388 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1424 @ SV1073 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(4715,plain,
! [SV927: $i,SV1073: $i,SV1389: $i,SV1425: $i] :
( ( ( c_member @ SV1425 @ SV1389 @ ( c_Relation_ODomain @ SV1425 @ SV1425 @ SV1073 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1425 @ SV1425 ) @ ( c_Product__Type_OPair @ SV1425 @ SV1425 @ SV1389 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1425 @ SV1073 ) )
| ( SV1389 = SV927 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(4716,plain,
! [SV928: $i,SV1074: $i,SV1390: $i,SV1459: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1459 @ SV1390 @ SV1074 ) @ SV928 ) ) )
= $true )
| ( ( ( SV1390 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4550]) ).
thf(4717,plain,
! [SV1074: $i,SV928: $i] :
( ( ! [SY3038: $i] :
( ( SY3038 != SV928 )
| ! [SY3039: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3039 @ SY3038 @ SV1074 ) @ SV928 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4551]) ).
thf(4718,plain,
! [SV928: $i,SV1074: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
| ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4552]) ).
thf(4719,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4553]) ).
thf(4720,plain,
! [SV1392: $i,SV1076: $i,SV930: $i,SV1427: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1427 @ SV930 )
| ( c_member @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1076 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1427 @ SV930 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1427 @ ( c_Set_Oinsert @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1392 @ SV1076 ) @ SV930 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4554]) ).
thf(4721,plain,
! [SV930: $i,SV1076: $i] :
( ( ! [SY3050: $i,SY3051: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3051 @ ( c_Set_Oinsert @ ( tc_prod @ SY3051 @ SY3051 ) @ ( c_Product__Type_OPair @ SY3051 @ SY3051 @ SY3050 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3051 @ SV930 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4555]) ).
thf(4722,plain,
! [SV930: $i,SV1076: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3053 @ ( c_Set_Oinsert @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SY3052 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3053 @ SY3053 ) @ ( c_Product__Type_OPair @ SY3053 @ SY3053 @ SV1076 @ SY3052 ) @ ( c_Transitive__Closure_Ortrancl @ SY3053 @ SV930 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4556]) ).
thf(4723,plain,
! [SV931: $i,SV1393: $i,SV1428: $i,SV1077: $i] :
( ( ( ! [SY3603: $i] :
~ ( c_member @ ( tc_prod @ SV1077 @ SV1428 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1428 @ SY3603 @ SV1393 ) @ SV931 ) )
= $true )
| ( ( c_member @ SV1428 @ SV1393 @ ( c_Relation_ORange @ SV1077 @ SV1428 @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4557]) ).
thf(4724,plain,
! [SV931: $i,SV1077: $i,SV1394: $i,SV1429: $i] :
( ( ( ~ ( c_member @ SV1429 @ SV1394 @ ( c_Relation_ORange @ SV1077 @ SV1429 @ SV931 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1077 @ SV1429 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1429 @ ( sK65_B_y @ SV1429 @ SV1394 @ SV1077 @ SV931 ) @ SV1394 ) @ SV931 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(4725,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) )
= $true )
| ( ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4726,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( ~ ( c_member @ SV1345 @ ( sK31_SY722 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4560]) ).
thf(4727,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( ~ ! [SY3534: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ SY3534 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SY3534 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4560]) ).
thf(4728,plain,
! [SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ! [SY3619: $i] :
~ ( c_member @ SV1346 @ SY3619 @ SV1461 )
| ~ ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4561]) ).
thf(4729,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i] :
( ( ! [SY3621: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3621 @ SY3621 ) @ ( c_Product__Type_OPair @ SY3621 @ SY3621 @ ( sK43_B_y @ SY3621 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SY3621 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SY3621 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SY3621 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SY3621 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4562]) ).
thf(4730,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1463: $i] :
( ( ! [SY3622: $i] :
( ( ( c_Recdef_Ocut @ SY3622 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SY3622 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3449: $i] :
( ~ ( c_member @ ( tc_prod @ SY3622 @ SY3622 ) @ ( c_Product__Type_OPair @ SY3622 @ SY3622 @ SY3449 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3449 )
= ( hAPP @ SV933 @ SY3449 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4563]) ).
thf(4731,plain,
! [SV934: $i,SV1080: $i,SV1396: $i,SV1431: $i] :
( ( ( ( SV1431 != SV1396 ) )
= $true )
| ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1431 )
| ( c_member @ SV1080 @ SV934 @ SV1396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(4732,plain,
! [SV934: $i,SV1080: $i,SV1397: $i,SV1432: $i] :
( ( ( ( SV1432 != SV1397 ) )
= $true )
| ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1397 )
| ( c_member @ SV1080 @ SV934 @ SV1432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(4733,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
| ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4734,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ( ( SV1271 != SV1082 )
| ( SV1183 != SV936 ) )
= $true )
| ( ( ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(4735,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
| ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4736,plain,
! [SV937: $i,SV1083: $i] :
( ( ! [SY3085: $i,SY3086: $i] :
( ( SY3086 != SY3085 )
| ( c_member @ SV1083 @ SV937 @ SY3086 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3086 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4569]) ).
thf(4737,plain,
! [SV937: $i,SV1083: $i] :
( ( ! [SY3087: $i,SY3088: $i] :
( ( SY3088 != SY3087 )
| ( c_member @ SV1083 @ SV937 @ SY3088 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3087 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4570]) ).
thf(4738,plain,
! [SV937: $i,SV1083: $i] :
( ( ! [SY3089: $i,SY3090: $i] :
( ( SY3090 != SY3089 )
| ( c_member @ SV1083 @ SV937 @ SY3089 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3090 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4571]) ).
thf(4739,plain,
! [SV937: $i,SV1083: $i] :
( ( ! [SY3091: $i] :
( ! [SX3: $i] : ( SX3 != SY3091 )
| ( c_member @ SV1083 @ SV937 @ SY3091 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3091 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4572]) ).
thf(4740,plain,
! [SV938: $i,SV1084: $i,SV1184: $i,SV1272: $i] :
( ( ( hBOOL @ ( hAPP @ SV1272 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4573]) ).
thf(4741,plain,
! [SV938: $i,SV1272: $i,SV1084: $i,SV1184: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4574]) ).
thf(4742,plain,
! [SV939: $i,SV1347: $i,SV1433: $i] :
( ( ( c_member @ SV1433 @ SV1347 @ SV939 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV939 @ SV1347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4743,plain,
! [SV939: $i,SV1348: $i,SV1464: $i] :
( ( ( c_member @ SV1464 @ SV1348 @ SV939 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV939 @ SV1348 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4576]) ).
thf(4744,plain,
! [SV940: $i,SV1434: $i,SV1085: $i,SV1398: $i] :
( ( ( ( SV1398 != SV1085 )
| ~ ( c_member @ SV1434 @ SV1398 @ SV940 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1434 @ SV1434 ) @ ( c_Product__Type_OPair @ SV1434 @ SV1434 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SV1434 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(4745,plain,
! [SV940: $i,SV1085: $i] :
( ( ! [SY3097: $i] :
( ! [SY3098: $i] :
~ ( c_member @ ( tc_prod @ SY3098 @ SY3098 ) @ ( c_Product__Type_OPair @ SY3098 @ SY3098 @ SY3097 @ SV1085 ) @ ( c_Relation_OId__on @ SY3098 @ SV940 ) )
| ( SY3097 = SV1085 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4578]) ).
thf(4746,plain,
! [SV940: $i,SV1085: $i] :
( ( ! [SY3099: $i,SY3100: $i] :
( ~ ( c_member @ ( tc_prod @ SY3100 @ SY3100 ) @ ( c_Product__Type_OPair @ SY3100 @ SY3100 @ SY3099 @ SV1085 ) @ ( c_Relation_OId__on @ SY3100 @ SV940 ) )
| ( c_member @ SY3100 @ SY3099 @ SV940 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4579]) ).
thf(4747,plain,
! [SV941: $i,SV1086: $i,SV1185: $i] :
( ( ( c_member @ SV1185 @ ( sK57_B_y @ SV1185 @ SV1086 @ SV941 ) @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $false )
| ( ( c_member @ SV1185 @ SV1086 @ ( c_Wellfounded_Oacc @ SV1185 @ SV941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4748,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
| ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4749,plain,
! [SV943: $i,SV1088: $i] :
( ( ! [SY3104: $i] :
( ! [SY3105: $i] :
~ ( c_member @ ( tc_prod @ SY3105 @ SY3105 ) @ ( c_Product__Type_OPair @ SY3105 @ SY3105 @ SY3104 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3105 @ SV943 ) )
| ( SY3104 != SV1088 )
| ( SY3104 = SV1088 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4583]) ).
thf(4750,plain,
! [SV943: $i,SV1088: $i] :
( ( ! [SY3106: $i,SY3107: $i] :
( ~ ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3107 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3107 @ SY3107 ) @ ( c_Product__Type_OPair @ SY3107 @ SY3107 @ SY3106 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3107 @ SV943 ) )
| ( SY3106 = SV1088 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4584]) ).
thf(4751,plain,
! [SV943: $i,SV1088: $i] :
( ( ! [SY3108: $i,SY3109: $i] :
( ( SY3108 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3109 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3109 @ SY3109 ) @ ( c_Product__Type_OPair @ SY3109 @ SY3109 @ SY3108 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SV943 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4585]) ).
thf(4752,plain,
! [SV943: $i,SV1088: $i] :
( ( ! [SY3110: $i] :
( ( SY3110 != SV1088 )
| ! [SY3111: $i] : ( c_member @ ( tc_prod @ SY3111 @ SY3111 ) @ ( c_Product__Type_OPair @ SY3111 @ SY3111 @ SY3110 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3111 @ SV943 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4586]) ).
thf(4753,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4587]) ).
thf(4754,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4587]) ).
thf(4755,plain,
! [SV1276: $i,SV1465: $i,SV1350: $i] :
( ( ( c_member @ ( tc_prod @ SV1350 @ SV1350 ) @ ( c_Product__Type_OPair @ SV1350 @ SV1350 @ SV1465 @ SV1465 ) @ SV1276 )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV1350 @ SV1276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(4756,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i,SV1399: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1399 @ SV1399 ) @ ( c_Product__Type_OPair @ SV1399 @ SV1399 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(4757,plain,
! [SV946: $i,SV1352: $i,SV1400: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV1400 @ SV1352 @ SV946 ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV1400 @ SV946 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV1400 @ SV1352 @ SV946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4591]) ).
thf(4758,plain,
! [SV946: $i,SV1466: $i] :
( ( ! [SY3624: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY3624 @ SV1466 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SY3624 @ SV1466 @ SV946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4592]) ).
thf(4759,plain,
! [SV946: $i,SV1467: $i] :
( ( ! [SY3625: $i] :
( ~ ( c_Order__Relation_Opartial__order__on @ SY3625 @ SV1467 @ SV946 )
| ( c_Relation_Oantisym @ SY3625 @ SV946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4593]) ).
thf(4760,plain,
! [SV1468: $i,SV1435: $i] :
( ( ( SV1435 = SV1468 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1435 @ SV1468 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1468 @ SV1435 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(4761,plain,
( ( ~ ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4595]) ).
thf(4762,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4595]) ).
thf(4763,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
= $true )
| ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(4764,plain,
( ( sK8_REN = $false )
| ( ( ~ ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4597]) ).
thf(4765,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV1401 @ SV947 )
| ~ ( c_Relation_Otrans @ SV1401 @ SV947 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(4766,plain,
! [SV947: $i] :
( ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) )
| ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4599]) ).
thf(4767,plain,
! [SV947: $i,SV1469: $i] :
( ( ! [SY3626: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY3626 @ SV1469 @ SV947 )
| ( c_Relation_Ototal__on @ SY3626 @ SV1469 @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(4768,plain,
! [SV948: $i,SV1091: $i,SV1402: $i,SV1436: $i] :
( ( ( ~ ( c_member @ SV1436 @ SV1402 @ ( c_Set_Oinsert @ SV1436 @ SV1091 @ SV948 ) ) )
= $true )
| ( ( ( SV1402 = SV1091 )
| ( c_member @ SV1436 @ SV1402 @ SV948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4601]) ).
thf(4769,plain,
! [SV948: $i,SV1091: $i] :
( ( ! [SY3120: $i] :
( ( SY3120 != SV1091 )
| ! [SY3121: $i] : ( c_member @ SY3121 @ SY3120 @ ( c_Set_Oinsert @ SY3121 @ SV1091 @ SV948 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4602]) ).
thf(4770,plain,
! [SV1091: $i,SV948: $i] :
( ( ! [SY3122: $i,SY3123: $i] :
( ~ ( c_member @ SY3123 @ SY3122 @ SV948 )
| ( c_member @ SY3123 @ SY3122 @ ( c_Set_Oinsert @ SY3123 @ SV1091 @ SV948 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4603]) ).
thf(4771,plain,
! [SV1279: $i,SV1470: $i,SV1355: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1355 @ SV1355 ) @ ( c_Product__Type_OPair @ SV1355 @ SV1355 @ SV1470 @ SV1470 ) @ SV1279 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV1355 @ SV1279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4604]) ).
thf(4772,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i] :
( ( ! [SY3627: $i] :
( ! [SY3628: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SY3627 @ SY3627 ) @ ( c_Product__Type_OPair @ SY3627 @ SY3627 @ ( sK55_B_z @ SY3628 @ SY3627 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SY3627 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3628 @ SY3627 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3628 @ ( sK55_B_z @ SY3628 @ SY3627 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3628 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SY3627 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(4773,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1472: $i] :
( ( ! [SY3629: $i] :
( ~ ( c_Recdef_Owfrec__rel @ SY3629 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3630: $i] :
( ~ ( c_member @ ( tc_prod @ SY3629 @ SY3629 ) @ ( c_Product__Type_OPair @ SY3629 @ SY3629 @ SY3630 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SY3629 @ SV1472 @ SV1280 @ SV1189 @ SY3630 @ ( hAPP @ ( sK54_B_g @ SY3629 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3630 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SY3629 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(4774,plain,
! [SV950: $i,SV1093: $i,SV1403: $i,SV1437: $i] :
( ( ( ~ ( c_member @ SV1437 @ SV1403 @ SV1093 ) )
= $true )
| ( ( c_member @ SV1437 @ SV1403 @ ( c_Set_Oinsert @ SV1437 @ SV950 @ SV1093 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(4775,plain,
! [SV1093: $i,SV950: $i,SV1404: $i] :
( ( ( SV1404 = SV950 )
= $false )
| ( ( ! [SY3590: $i] : ( c_member @ SY3590 @ SV1404 @ ( c_Set_Oinsert @ SY3590 @ SV950 @ SV1093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(4776,plain,
! [SV1094: $i,SV1190: $i,SV1356: $i,SV1281: $i,SV951: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4609]) ).
thf(4777,plain,
! [SV952: $i,SV1095: $i,SV1405: $i,SV1473: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1473 @ SV1473 ) @ ( c_Product__Type_OPair @ SV1473 @ SV1473 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1473 @ SV952 ) ) )
= $true )
| ( ( ( SV1405 != SV1095 )
| ( SV1405 = SV1095 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4610]) ).
thf(4778,plain,
! [SV952: $i,SV1095: $i,SV1406: $i,SV1438: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1438 @ SV952 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SV1438 @ SV952 ) )
| ( SV1406 = SV1095 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(4779,plain,
! [SV953: $i,SV1096: $i,SV1282: $i,SV1357: $i,SV1191: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
| ~ ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) )
= $false )
| ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(4780,plain,
! [SV1439: $i,SV1474: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1474 @ SV1439 )
| ( SV1474 != SV1439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(4781,plain,
! [SV1475: $i,SV1440: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1440 @ SV1475 )
| ( SV1475 != SV1440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4615]) ).
thf(4782,plain,
! [SV1285: $i,SV1476: $i,SV1360: $i] :
( ( ( c_member @ SV1360 @ SV1476 @ ( c_Wellfounded_Oacc @ SV1360 @ SV1285 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1360 @ SV1285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4617]) ).
thf(4783,plain,
! [SV954: $i,SV1097: $i,SV1192: $i] :
( ( ( c_member @ SV1192 @ ( sK58_B_z @ SV1192 @ SV1097 @ SV954 ) @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $false )
| ( ( c_member @ SV1192 @ SV1097 @ ( c_Wellfounded_Oacc @ SV1192 @ SV954 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4619]) ).
thf(4784,plain,
! [SV1407: $i,SV1098: $i,SV955: $i,SV1441: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1441 @ SV955 )
| ( c_member @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1098 @ SV1407 ) @ ( c_Transitive__Closure_Ortrancl @ SV1441 @ SV955 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1441 @ ( c_Set_Oinsert @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1407 @ SV1098 ) @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4620]) ).
thf(4785,plain,
! [SV955: $i,SV1098: $i] :
( ( ! [SY3149: $i,SY3150: $i] :
( ~ ( c_Wellfounded_Owf @ SY3150 @ ( c_Set_Oinsert @ ( tc_prod @ SY3150 @ SY3150 ) @ ( c_Product__Type_OPair @ SY3150 @ SY3150 @ SY3149 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3150 @ SV955 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4621]) ).
thf(4786,plain,
! [SV955: $i,SV1098: $i] :
( ( ! [SY3151: $i,SY3152: $i] :
( ~ ( c_Wellfounded_Owf @ SY3152 @ ( c_Set_Oinsert @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SY3151 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3152 @ SY3152 ) @ ( c_Product__Type_OPair @ SY3152 @ SY3152 @ SV1098 @ SY3151 ) @ ( c_Transitive__Closure_Ortrancl @ SY3152 @ SV955 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4622]) ).
thf(4787,plain,
! [SV795: $i,SV1193: $i,SV956: $i,SV1099: $i,SV1286: $i] :
( ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
| ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1286 @ SV1193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(4788,plain,
! [SV1206: $i,SV1112: $i,SV809: $i,SV970: $i,SV1291: $i] :
( ( ( c_member @ ( tc_prod @ SV1291 @ SV1291 ) @ ( c_Product__Type_OPair @ SV1291 @ SV1291 @ SV970 @ SV809 ) @ SV1112 )
= $false )
| ( ( c_member @ SV1291 @ SV970 @ SV1206 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1291 @ SV1206 @ SV1112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4789,plain,
! [SV1207: $i,SV1113: $i,SV810: $i,SV971: $i,SV1292: $i] :
( ( ( c_member @ ( tc_prod @ SV1292 @ SV1292 ) @ ( c_Product__Type_OPair @ SV1292 @ SV1292 @ SV971 @ SV810 ) @ SV1113 )
= $false )
| ( ( c_member @ SV1292 @ SV810 @ SV1207 )
= $true )
| ( ( c_Relation_Orefl__on @ SV1292 @ SV1207 @ SV1113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4790,plain,
! [SV813: $i,SV1210: $i,SV974: $i,SV1116: $i,SV1293: $i,SV1363: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(4791,plain,
! [SV817: $i,SV1212: $i,SV978: $i,SV1120: $i,SV1295: $i] :
( ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(4792,plain,
! [SV1213: $i,SV979: $i,SV818: $i,SV1121: $i,SV1296: $i] :
( ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1121 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV818 ) @ ( c_Transitive__Closure_Ortrancl @ SV1296 @ SV979 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1296 @ SV1296 ) @ ( c_Product__Type_OPair @ SV1296 @ SV1296 @ SV1213 @ SV1121 ) @ SV979 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4635]) ).
thf(4793,plain,
! [SV1214: $i,SV980: $i,SV819: $i,SV1122: $i,SV1297: $i] :
( ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1122 @ SV819 ) @ SV980 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV819 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1297 @ SV1297 ) @ ( c_Product__Type_OPair @ SV1297 @ SV1297 @ SV1214 @ SV1122 ) @ ( c_Transitive__Closure_Ortrancl @ SV1297 @ SV980 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4636]) ).
thf(4794,plain,
! [SV1215: $i,SV981: $i,SV820: $i,SV1123: $i,SV1298: $i] :
( ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1123 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV820 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1298 @ SV1298 ) @ ( c_Product__Type_OPair @ SV1298 @ SV1298 @ SV1215 @ SV1123 ) @ ( c_Transitive__Closure_Ortrancl @ SV1298 @ SV981 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4795,plain,
! [SV1219: $i,SV989: $i,SV828: $i,SV1128: $i,SV1300: $i] :
( ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1128 @ SV828 ) @ SV989 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV828 ) @ ( c_Transitive__Closure_Otrancl @ SV1300 @ SV989 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1300 @ SV1300 ) @ ( c_Product__Type_OPair @ SV1300 @ SV1300 @ SV1219 @ SV1128 ) @ SV989 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(4796,plain,
! [SV1220: $i,SV990: $i,SV829: $i,SV1129: $i,SV1301: $i] :
( ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1129 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV829 ) @ ( c_Transitive__Closure_Otrancl @ SV1301 @ SV990 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1301 @ SV1301 ) @ ( c_Product__Type_OPair @ SV1301 @ SV1301 @ SV1220 @ SV1129 ) @ SV990 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4640]) ).
thf(4797,plain,
! [SV1221: $i,SV991: $i,SV830: $i,SV1130: $i,SV1302: $i] :
( ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1130 @ SV830 ) @ SV991 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV830 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1302 @ SV1302 ) @ ( c_Product__Type_OPair @ SV1302 @ SV1302 @ SV1221 @ SV1130 ) @ ( c_Transitive__Closure_Otrancl @ SV1302 @ SV991 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4641]) ).
thf(4798,plain,
! [SV1222: $i,SV992: $i,SV831: $i,SV1131: $i,SV1303: $i] :
( ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1131 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV831 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1303 @ SV1303 ) @ ( c_Product__Type_OPair @ SV1303 @ SV1303 @ SV1222 @ SV1131 ) @ ( c_Transitive__Closure_Otrancl @ SV1303 @ SV992 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4642]) ).
thf(4799,plain,
! [SV1223: $i,SV993: $i,SV832: $i,SV1132: $i,SV1304: $i] :
( ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1132 @ SV832 ) @ ( c_Transitive__Closure_Ortrancl @ SV1304 @ SV993 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV832 ) @ ( c_Transitive__Closure_Otrancl @ SV1304 @ SV993 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1304 @ SV1304 ) @ ( c_Product__Type_OPair @ SV1304 @ SV1304 @ SV1223 @ SV1132 ) @ SV993 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4643]) ).
thf(4800,plain,
! [SV1224: $i,SV994: $i,SV833: $i,SV1133: $i,SV1305: $i] :
( ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1133 @ SV833 ) @ SV994 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV833 ) @ ( c_Transitive__Closure_Otrancl @ SV1305 @ SV994 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1305 @ SV1305 ) @ ( c_Product__Type_OPair @ SV1305 @ SV1305 @ SV1224 @ SV1133 ) @ ( c_Transitive__Closure_Ortrancl @ SV1305 @ SV994 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4644]) ).
thf(4801,plain,
! [SV1225: $i,SV995: $i,SV834: $i,SV1134: $i,SV1306: $i] :
( ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1134 @ SV834 ) @ ( c_Transitive__Closure_Ortrancl @ SV1306 @ SV995 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV834 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1306 @ SV1306 ) @ ( c_Product__Type_OPair @ SV1306 @ SV1306 @ SV1225 @ SV1134 ) @ ( c_Transitive__Closure_Otrancl @ SV1306 @ SV995 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(4802,plain,
! [SV1226: $i,SV996: $i,SV835: $i,SV1135: $i,SV1307: $i] :
( ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1135 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV835 ) @ ( c_Transitive__Closure_Otrancl @ SV1307 @ SV996 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1307 @ SV1307 ) @ ( c_Product__Type_OPair @ SV1307 @ SV1307 @ SV1226 @ SV1135 ) @ ( c_Transitive__Closure_Ortrancl @ SV1307 @ SV996 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(4803,plain,
! [SV1138: $i,SV1002: $i,SV842: $i,SV1229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 ) )
= $true )
| ( ( SV1002 = SV842 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
= $false )
| ( ( c_Relation_Oantisym @ SV1229 @ SV1138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(4804,plain,
! [SV1147: $i,SV1011: $i,SV851: $i,SV1235: $i] :
( ( ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV851 @ SV1011 ) @ SV1147 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1235 @ SV1235 ) @ ( c_Product__Type_OPair @ SV1235 @ SV1235 @ SV1011 @ SV851 ) @ SV1147 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1235 @ SV1147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(4805,plain,
! [SV1148: $i,SV1012: $i,SV852: $i,SV1236: $i] :
( ( ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV852 @ SV1012 ) @ SV1148 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1236 @ SV1236 ) @ ( c_Product__Type_OPair @ SV1236 @ SV1236 @ SV1012 @ SV852 ) @ SV1148 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1236 @ SV1148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(4806,plain,
! [SV1237: $i,SV856: $i,SV1016: $i,SV1311: $i,SV1151: $i,SV1367: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1367 @ SV1151 ) @ ( c_Product__Type_OPair @ SV1367 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 ) )
= $true )
| ( ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SV1367 @ SV1151 @ SV856 @ SV1237 ) )
= $true )
| ( ( c_member @ SV1367 @ SV1311 @ SV1237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4653]) ).
thf(4807,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i,SV1368: $i,SV1408: $i,SV1442: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1442 @ SV1408 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SV1442 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SV1442 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4654]) ).
thf(4808,plain,
! [SV859: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i,SV1369: $i,SV1409: $i] :
( ( ( hBOOL @ ( hAPP @ SV1409 @ SV1369 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SV1409 @ SV1019 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4809,plain,
! [SV1245: $i,SV1040: $i,SV882: $i,SV1370: $i,SV1160: $i,SV1317: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1317 @ SV1160 ) )
= $true )
| ( ( ( hAPP @ SV1370 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SV1370 @ SV1160 @ SV882 ) ) @ SV882 ) )
= $true )
| ( ( SV1370
= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4810,plain,
! [SV901: $i,SV1055: $i] :
( ( ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK70_SY736 @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
= $true )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4657]) ).
thf(4811,plain,
! [SV901: $i,SV1055: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4658]) ).
thf(4812,plain,
! [SV1056: $i,SV1248: $i,SV1319: $i,SV1166: $i,SV902: $i] :
( ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4659]) ).
thf(4813,plain,
! [SV1057: $i,SV903: $i,SV1371: $i,SV1411: $i] :
( ( ( c_member @ SV1411 @ SV1371 @ SV903 )
= $true )
| ( ( ( ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV1057 )
!= ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV903 ) )
| ( SV1057 = SV903 ) )
= $true )
| ( ( c_member @ SV1411 @ SV1371 @ SV1057 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(4814,plain,
! [SV1057: $i,SV903: $i,SV1372: $i,SV1412: $i] :
( ( ( c_member @ SV1412 @ SV1372 @ SV903 )
= $true )
| ( ( ( SV1057 != SV903 )
| ( ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV903 ) ) )
= $true )
| ( ( c_member @ SV1412 @ SV1372 @ SV1057 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(4815,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(4816,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1374 @ SV1374 ) @ ( c_Product__Type_OPair @ SV1374 @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 ) )
= $false )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4663]) ).
thf(4817,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( ~ ~ ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) )
= $false )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4663]) ).
thf(4818,plain,
! [SV905: $i,SV1322: $i,SV1477: $i,SV1375: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SV1477 @ SV1322 ) @ SV905 )
| ( c_member @ SV1375 @ SV1477 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) ) )
= $true )
| ( ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(4819,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ SV1323 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4820,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4821,plain,
! [SV906: $i,SV1324: $i,SV1478: $i,SV1377: $i] :
( ( ( ~ ( c_member @ SV1377 @ SV1478 @ SV1324 )
| ! [SY3631: $i] :
( ~ ( c_member @ SV1377 @ SY3631 @ SV1324 )
| ( SV1478 = SY3631 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SY3631 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3631 @ SV1478 ) @ SV906 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4666]) ).
thf(4822,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1479: $i] :
( ( ( ! [SY3632: $i] :
( ( c_Product__Type_OPair @ SY3632 @ SV1479 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3632 @ SV1479 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1250 = SV1059 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(4823,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1480: $i] :
( ( ( ! [SY3633: $i] :
( ( c_Product__Type_OPair @ SY3633 @ SV1480 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SY3633 @ SV1480 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1168 = SV907 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4668]) ).
thf(4824,plain,
! [SV908: $i,SV1060: $i] :
( ( ( c_member @ ( tc_prod @ SV1060 @ SV1060 ) @ ( c_Product__Type_OPair @ SV1060 @ SV1060 @ ( sK27_SY720 @ SV1060 @ SV908 ) @ ( sK26_B_x @ SV1060 @ SV908 ) ) @ SV908 )
= $true )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4669]) ).
thf(4825,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ( ( sK26_B_x @ SV1060 @ SV908 )
!= ( sK27_SY720 @ SV1060 @ SV908 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4670]) ).
thf(4826,plain,
! [SV1481: $i,SV909: $i,SV1325: $i,SV1378: $i] :
( ( ( ! [SY3634: $i] : ( hBOOL @ ( hAPP @ SV1378 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SV1481 @ SY3634 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1378 @ ( sK75_B_x1 @ SV1378 @ SV1325 @ SV909 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4671]) ).
thf(4827,plain,
! [SV909: $i,SV1326: $i,SV1482: $i,SV1379: $i] :
( ( ( hBOOL @ ( hAPP @ SV1379 @ SV1482 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1379 @ ( c_Product__Type_OPair @ SV1326 @ SV909 @ ( sK73_B_a @ SV1379 @ SV1326 @ SV909 ) @ ( sK74_SY739 @ SV1379 @ SV1326 @ SV909 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4672]) ).
thf(4828,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4673]) ).
thf(4829,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4673]) ).
thf(4830,plain,
! [SV910: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( ! [SY3635: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SY3635 ) @ SV910 )
| ! [SY3636: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SY3636 ) @ SV910 )
| ( SY3635 = SY3636 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4674]) ).
thf(4831,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4675]) ).
thf(4832,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1251: $i,SV1382: $i] :
( ( ~ ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4676]) ).
thf(4833,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4834,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ~ ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4835,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK78_SY740 @ SV1330 @ SV1252 ) ) @ SV1252 )
= $true )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4678]) ).
thf(4836,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4679]) ).
thf(4837,plain,
! [SV1253: $i,SV1484: $i,SV1444: $i,SV1331: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 )
| ! [SY3637: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SY3637 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SY3637 ) @ SV1253 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4680]) ).
thf(4838,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK33_B_x @ SV1332 @ SV1254 ) @ ( sK34_SY725 @ SV1332 @ SV1254 ) ) @ SV1254 )
= $true )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4681]) ).
thf(4839,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4682]) ).
thf(4840,plain,
! [SV1255: $i,SV1485: $i,SV1445: $i,SV1333: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SV1485 ) @ SV1255 )
| ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1485 @ SV1445 ) @ SV1255 )
| ( SV1445 = SV1485 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4683]) ).
thf(4841,plain,
! [SV913: $i,SV1334: $i,SV1383: $i] :
( ( ( c_Relation_Orefl__on @ SV1383 @ SV1334 @ SV913 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1383 @ SV913 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV1383 @ SV1334 @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4842,plain,
! [SV913: $i,SV1446: $i,SV1486: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV1486 @ SV1446 @ SV913 )
| ( c_Relation_Orefl__on @ SV1486 @ SV1446 @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4685]) ).
thf(4843,plain,
! [SV913: $i,SV1447: $i,SV1487: $i] :
( ( ~ ( c_Order__Relation_Opreorder__on @ SV1487 @ SV1447 @ SV913 )
| ( c_Relation_Otrans @ SV1487 @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(4844,plain,
! [SV1063: $i,SV1414: $i,SV1448: $i,SV914: $i,SV1171: $i] :
( ( ( ! [SY3612: $i] :
( ~ ( c_member @ SV1171 @ SY3612 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SY3612 @ SV1414 ) @ SV1063 ) ) )
= $true )
| ( ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(4845,plain,
! [SV914: $i,SV1063: $i,SV1171: $i,SV1415: $i,SV1449: $i] :
( ( ( ~ ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4688]) ).
thf(4846,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) ) )
= $false )
| ( ( SV1172 = SV1064 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4689]) ).
thf(4847,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 ) )
= $false )
| ( ( SV1172 = SV1064 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4689]) ).
thf(4848,plain,
! [SV917: $i,SV1065: $i,SV1384: $i,SV1417: $i] :
( ( ( SV1417 = SV1384 )
= $false )
| ( ( ~ ( c_member @ SV1065 @ SV1417 @ SV917 )
| ( c_member @ SV1065 @ SV1384 @ SV917 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4849,plain,
! [SV917: $i,SV1065: $i,SV1385: $i,SV1418: $i] :
( ( ( SV1418 = SV1385 )
= $false )
| ( ( ~ ( c_member @ SV1065 @ SV1385 @ SV917 )
| ( c_member @ SV1065 @ SV1418 @ SV917 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(4850,plain,
! [SV1258: $i,SV1451: $i,SV1338: $i] :
( ( ( c_member @ ( tc_prod @ SV1338 @ SV1338 ) @ ( c_Product__Type_OPair @ SV1338 @ SV1338 @ SV1451 @ SV1451 ) @ ( c_Transitive__Closure_Otrancl @ SV1338 @ SV1258 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV1338 @ SV1258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(4851,plain,
! [SV1173: $i,SV918: $i,SV1066: $i,SV1419: $i,SV1452: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1452 @ SV1419 ) @ ( c_Product__Type_OPair @ SV1452 @ SV1419 @ SV1066 @ SV918 ) @ SV1173 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1452 @ SV1419 @ SV1173 ) @ SV1066 ) @ SV918 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(4852,plain,
! [SV918: $i,SV1066: $i,SV1173: $i,SV1420: $i,SV1453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1453 @ SV1420 @ SV1173 ) @ SV1066 ) @ SV918 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1453 @ SV1420 ) @ ( c_Product__Type_OPair @ SV1453 @ SV1420 @ SV1066 @ SV918 ) @ SV1173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(4853,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1488: $i] :
( ( ! [SY3638: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3638 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3638 ) @ SV1067 ) ) )
| ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4697]) ).
thf(4854,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1455: $i,SV1489: $i] :
( ( ~ ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
| ~ ( ~ ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4698]) ).
thf(4855,plain,
! [SV920: $i] :
( ( ~ ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4699]) ).
thf(4856,plain,
! [SV920: $i] :
( ( ~ ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4699]) ).
thf(4857,plain,
! [SV920: $i] :
( ( ~ ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4858,plain,
! [SV920: $i] :
( ( ~ ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4859,plain,
! [SV920: $i] :
( ( ~ ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4701]) ).
thf(4860,plain,
! [SV920: $i] :
( ( ~ ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4701]) ).
thf(4861,plain,
! [SV920: $i] :
( ( ~ ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4702]) ).
thf(4862,plain,
! [SV920: $i] :
( ( ~ ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4702]) ).
thf(4863,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i,SV1456: $i] :
( ( ( ! [SY3617: $i] :
~ ( c_member @ ( tc_prod @ SY3617 @ SY3617 ) @ ( c_Product__Type_OPair @ SY3617 @ SY3617 @ SV1456 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3617 @ SV1068 ) @ SV921 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1456 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4703]) ).
thf(4864,plain,
! [SV1068: $i,SV1260: $i,SV1457: $i,SV921: $i,SV1175: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1457 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 ) )
= $true )
| ( ( ! [SY3618: $i] : ( c_member @ ( tc_prod @ SY3618 @ SY3618 ) @ ( c_Product__Type_OPair @ SY3618 @ SY3618 @ SV1457 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3618 @ SV1068 ) @ SV921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4704]) ).
thf(4865,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 ) )
= $false )
| ( ( SV1176 = SV1069 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4707]) ).
thf(4866,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) ) )
= $false )
| ( ( SV1176 = SV1069 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4707]) ).
thf(4867,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) ) @ SV924 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4708]) ).
thf(4868,plain,
! [SV924: $i,SV1070: $i,SV1177: $i,SV1262: $i] :
( ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ ( sK41_B_z @ SV1262 @ SV1177 @ SV1070 @ SV924 ) @ SV1070 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV924 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1262 @ SV1262 ) @ ( c_Product__Type_OPair @ SV1262 @ SV1262 @ SV1177 @ SV1070 ) @ ( c_Transitive__Closure_Otrancl @ SV1262 @ SV924 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4709]) ).
thf(4869,plain,
! [SV926: $i,SV1490: $i,SV1386: $i,SV1072: $i,SV1422: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1422 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1422 @ SV1072 @ SV1386 @ SV1490 ) @ SV926 ) )
= $true )
| ( ( c_member @ SV1422 @ SV1386 @ ( c_Relation_ODomain @ SV1422 @ SV1072 @ SV926 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(4870,plain,
! [SV926: $i,SV1072: $i,SV1387: $i,SV1423: $i] :
( ( ( c_member @ SV1423 @ SV1387 @ ( c_Relation_ODomain @ SV1423 @ SV1072 @ SV926 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1423 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1423 @ SV1072 @ SV1387 @ ( sK66_B_y @ SV1423 @ SV1387 @ SV1072 @ SV926 ) ) @ SV926 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4871,plain,
! [SV1073: $i,SV1424: $i,SV927: $i,SV1388: $i] :
( ( ( ( SV1388 != SV927 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1424 @ SV1424 ) @ ( c_Product__Type_OPair @ SV1424 @ SV1424 @ SV1388 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1424 @ SV1073 ) )
= $true )
| ( ( c_member @ SV1424 @ SV1388 @ ( c_Relation_ODomain @ SV1424 @ SV1424 @ SV1073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(4872,plain,
! [SV1073: $i,SV927: $i,SV1389: $i,SV1425: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1425 @ SV1425 ) @ ( c_Product__Type_OPair @ SV1425 @ SV1425 @ SV1389 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1425 @ SV1073 ) ) )
= $true )
| ( ( SV1389 = SV927 )
= $true )
| ( ( c_member @ SV1425 @ SV1389 @ ( c_Relation_ODomain @ SV1425 @ SV1425 @ SV1073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(4873,plain,
! [SV928: $i,SV1074: $i,SV1390: $i,SV1459: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1459 @ SV1390 @ SV1074 ) @ SV928 ) )
= $false )
| ( ( ( SV1390 = SV928 )
| ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4716]) ).
thf(4874,plain,
! [SV1074: $i,SV928: $i,SV1491: $i] :
( ( ( SV1491 != SV928 )
| ! [SY3640: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3640 @ SV1491 @ SV1074 ) @ SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4717]) ).
thf(4875,plain,
! [SV928: $i,SV1074: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) ) )
= $true )
| ( ( ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(4876,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(4877,plain,
! [SV1392: $i,SV1076: $i,SV930: $i,SV1427: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1427 @ SV930 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1076 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1427 @ SV930 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1427 @ ( c_Set_Oinsert @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1392 @ SV1076 ) @ SV930 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(4878,plain,
! [SV930: $i,SV1076: $i,SV1492: $i] :
( ( ! [SY3641: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3641 @ ( c_Set_Oinsert @ ( tc_prod @ SY3641 @ SY3641 ) @ ( c_Product__Type_OPair @ SY3641 @ SY3641 @ SV1492 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SY3641 @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4721]) ).
thf(4879,plain,
! [SV930: $i,SV1076: $i,SV1493: $i] :
( ( ! [SY3642: $i] :
( ~ ( c_Wellfounded_Oacyclic @ SY3642 @ ( c_Set_Oinsert @ ( tc_prod @ SY3642 @ SY3642 ) @ ( c_Product__Type_OPair @ SY3642 @ SY3642 @ SV1493 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SY3642 @ SY3642 ) @ ( c_Product__Type_OPair @ SY3642 @ SY3642 @ SV1076 @ SV1493 ) @ ( c_Transitive__Closure_Ortrancl @ SY3642 @ SV930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4722]) ).
thf(4880,plain,
! [SV931: $i,SV1393: $i,SV1494: $i,SV1428: $i,SV1077: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1077 @ SV1428 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1428 @ SV1494 @ SV1393 ) @ SV931 ) )
= $true )
| ( ( c_member @ SV1428 @ SV1393 @ ( c_Relation_ORange @ SV1077 @ SV1428 @ SV931 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4723]) ).
thf(4881,plain,
! [SV931: $i,SV1077: $i,SV1394: $i,SV1429: $i] :
( ( ( c_member @ SV1429 @ SV1394 @ ( c_Relation_ORange @ SV1077 @ SV1429 @ SV931 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1077 @ SV1429 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1429 @ ( sK65_B_y @ SV1429 @ SV1394 @ SV1077 @ SV931 ) @ SV1394 ) @ SV931 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4724]) ).
thf(4882,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false )
| ( ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(4883,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( c_member @ SV1345 @ ( sK31_SY722 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4726]) ).
thf(4884,plain,
! [SV1267: $i,SV1345: $i] :
( ( ( ! [SY3534: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ SY3534 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SY3534 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SY3534 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4727]) ).
thf(4885,plain,
! [SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ! [SY3619: $i] :
~ ( c_member @ SV1346 @ SY3619 @ SV1461 ) )
= $true )
| ( ( ~ ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(4886,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i,SV1495: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1495 @ SV1495 ) @ ( c_Product__Type_OPair @ SV1495 @ SV1495 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
| ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4729]) ).
thf(4887,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1463: $i,SV1496: $i] :
( ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
| ! [SY3643: $i] :
( ~ ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SY3643 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3643 )
= ( hAPP @ SV933 @ SY3643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4730]) ).
thf(4888,plain,
! [SV934: $i,SV1080: $i,SV1396: $i,SV1431: $i] :
( ( ( SV1431 = SV1396 )
= $false )
| ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1431 )
| ( c_member @ SV1080 @ SV934 @ SV1396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4889,plain,
! [SV934: $i,SV1080: $i,SV1397: $i,SV1432: $i] :
( ( ( SV1432 = SV1397 )
= $false )
| ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1397 )
| ( c_member @ SV1080 @ SV934 @ SV1432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4732]) ).
thf(4890,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4733]) ).
thf(4891,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4733]) ).
thf(4892,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ( ( SV1271 != SV1082 ) )
= $true )
| ( ( ( SV1183 != SV936 ) )
= $true )
| ( ( ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(4893,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ~ ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4735]) ).
thf(4894,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ~ ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4735]) ).
thf(4895,plain,
! [SV937: $i,SV1083: $i,SV1497: $i] :
( ( ! [SY3644: $i] :
( ( SY3644 != SV1497 )
| ( c_member @ SV1083 @ SV937 @ SY3644 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4736]) ).
thf(4896,plain,
! [SV937: $i,SV1083: $i,SV1498: $i] :
( ( ! [SY3645: $i] :
( ( SY3645 != SV1498 )
| ( c_member @ SV1083 @ SV937 @ SY3645 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4737]) ).
thf(4897,plain,
! [SV937: $i,SV1083: $i,SV1499: $i] :
( ( ! [SY3646: $i] :
( ( SY3646 != SV1499 )
| ( c_member @ SV1083 @ SV937 @ SV1499 )
| ~ ( c_member @ SV1083 @ SV937 @ SY3646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4738]) ).
thf(4898,plain,
! [SV937: $i,SV1083: $i,SV1500: $i] :
( ( ! [SY3647: $i] : ( SY3647 != SV1500 )
| ( c_member @ SV1083 @ SV937 @ SV1500 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(4899,plain,
! [SV938: $i,SV1272: $i,SV1084: $i,SV1184: $i] :
( ( ( c_Wellfounded_Owf @ SV1184 @ ( hAPP @ SV1084 @ ( sK9_B_x @ SV1272 @ SV1184 @ SV1084 @ SV938 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( tc_prod @ SV938 @ SV1184 ) @ ( c_Recdef_Osame__fst @ SV938 @ SV1184 @ SV1272 @ SV1084 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(4900,plain,
! [SV940: $i,SV1434: $i,SV1085: $i,SV1398: $i] :
( ( ( ( SV1398 != SV1085 ) )
= $true )
| ( ( ~ ( c_member @ SV1434 @ SV1398 @ SV940 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1434 @ SV1434 ) @ ( c_Product__Type_OPair @ SV1434 @ SV1434 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SV1434 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(4901,plain,
! [SV940: $i,SV1085: $i,SV1501: $i] :
( ( ! [SY3648: $i] :
~ ( c_member @ ( tc_prod @ SY3648 @ SY3648 ) @ ( c_Product__Type_OPair @ SY3648 @ SY3648 @ SV1501 @ SV1085 ) @ ( c_Relation_OId__on @ SY3648 @ SV940 ) )
| ( SV1501 = SV1085 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4745]) ).
thf(4902,plain,
! [SV940: $i,SV1085: $i,SV1502: $i] :
( ( ! [SY3649: $i] :
( ~ ( c_member @ ( tc_prod @ SY3649 @ SY3649 ) @ ( c_Product__Type_OPair @ SY3649 @ SY3649 @ SV1502 @ SV1085 ) @ ( c_Relation_OId__on @ SY3649 @ SV940 ) )
| ( c_member @ SY3649 @ SV1502 @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(4903,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4748]) ).
thf(4904,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4748]) ).
thf(4905,plain,
! [SV943: $i,SV1088: $i,SV1503: $i] :
( ( ! [SY3650: $i] :
~ ( c_member @ ( tc_prod @ SY3650 @ SY3650 ) @ ( c_Product__Type_OPair @ SY3650 @ SY3650 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3650 @ SV943 ) )
| ( SV1503 != SV1088 )
| ( SV1503 = SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(4906,plain,
! [SV943: $i,SV1088: $i,SV1504: $i] :
( ( ! [SY3651: $i] :
( ~ ( c_member @ ( tc_prod @ SY3651 @ SY3651 ) @ ( c_Product__Type_OPair @ SY3651 @ SY3651 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3651 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3651 @ SY3651 ) @ ( c_Product__Type_OPair @ SY3651 @ SY3651 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3651 @ SV943 ) )
| ( SV1504 = SV1088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4750]) ).
thf(4907,plain,
! [SV943: $i,SV1088: $i,SV1505: $i] :
( ( ! [SY3652: $i] :
( ( SV1505 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SY3652 @ SY3652 ) @ ( c_Product__Type_OPair @ SY3652 @ SY3652 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SY3652 @ SV943 ) )
| ( c_member @ ( tc_prod @ SY3652 @ SY3652 ) @ ( c_Product__Type_OPair @ SY3652 @ SY3652 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3652 @ SV943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4751]) ).
thf(4908,plain,
! [SV943: $i,SV1088: $i,SV1506: $i] :
( ( ( SV1506 != SV1088 )
| ! [SY3653: $i] : ( c_member @ ( tc_prod @ SY3653 @ SY3653 ) @ ( c_Product__Type_OPair @ SY3653 @ SY3653 @ SV1506 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3653 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4752]) ).
thf(4909,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1274 @ SV944 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4753]) ).
thf(4910,plain,
! [SV944: $i,SV1089: $i,SV1187: $i,SV1274: $i] :
( ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ ( sK42_B_z @ SV1274 @ SV1187 @ SV1089 @ SV944 ) @ SV1089 ) @ SV944 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1274 @ SV1274 ) @ ( c_Product__Type_OPair @ SV1274 @ SV1274 @ SV1187 @ SV1089 ) @ ( c_Transitive__Closure_Otrancl @ SV1274 @ SV944 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4754]) ).
thf(4911,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i,SV1399: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1399 @ SV1399 ) @ ( c_Product__Type_OPair @ SV1399 @ SV1399 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4756]) ).
thf(4912,plain,
! [SV945: $i,SV1351: $i,SV1090: $i,SV1277: $i,SV1188: $i,SV1399: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4756]) ).
thf(4913,plain,
! [SV946: $i,SV1352: $i,SV1400: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV1400 @ SV1352 @ SV946 )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV1400 @ SV946 ) )
= $true )
| ( ( c_Order__Relation_Opartial__order__on @ SV1400 @ SV1352 @ SV946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4757]) ).
thf(4914,plain,
! [SV946: $i,SV1466: $i,SV1507: $i] :
( ( ~ ( c_Order__Relation_Opartial__order__on @ SV1507 @ SV1466 @ SV946 )
| ( c_Order__Relation_Opreorder__on @ SV1507 @ SV1466 @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4758]) ).
thf(4915,plain,
! [SV946: $i,SV1467: $i,SV1508: $i] :
( ( ~ ( c_Order__Relation_Opartial__order__on @ SV1508 @ SV1467 @ SV946 )
| ( c_Relation_Oantisym @ SV1508 @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4759]) ).
thf(4916,plain,
! [SV1468: $i,SV1435: $i] :
( ( ( SV1435 = SV1468 )
= $true )
| ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1435 @ SV1468 ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1468 @ SV1435 ) @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4760]) ).
thf(4917,plain,
( ( ! [SX0: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SX0 @ SX0 ) @ v_L ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4761]) ).
thf(4918,plain,
( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4762]) ).
thf(4919,plain,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK5_B_x @ sK5_B_x ) @ v_L )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(4920,plain,
( ( ( ~ ( ( sK6_B_x != sK7_SY705 ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(4921,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV1401 @ SV947 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1401 @ SV947 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(4922,plain,
! [SV947: $i] :
( ( ~ ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4766]) ).
thf(4923,plain,
! [SV947: $i] :
( ( ~ ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4766]) ).
thf(4924,plain,
! [SV947: $i,SV1469: $i,SV1509: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1509 @ SV1469 @ SV947 )
| ( c_Relation_Ototal__on @ SV1509 @ SV1469 @ SV947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4767]) ).
thf(4925,plain,
! [SV948: $i,SV1091: $i,SV1402: $i,SV1436: $i] :
( ( ( c_member @ SV1436 @ SV1402 @ ( c_Set_Oinsert @ SV1436 @ SV1091 @ SV948 ) )
= $false )
| ( ( ( SV1402 = SV1091 )
| ( c_member @ SV1436 @ SV1402 @ SV948 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4768]) ).
thf(4926,plain,
! [SV948: $i,SV1091: $i,SV1510: $i] :
( ( ( SV1510 != SV1091 )
| ! [SY3654: $i] : ( c_member @ SY3654 @ SV1510 @ ( c_Set_Oinsert @ SY3654 @ SV1091 @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4769]) ).
thf(4927,plain,
! [SV1091: $i,SV948: $i,SV1511: $i] :
( ( ! [SY3655: $i] :
( ~ ( c_member @ SY3655 @ SV1511 @ SV948 )
| ( c_member @ SY3655 @ SV1511 @ ( c_Set_Oinsert @ SY3655 @ SV1091 @ SV948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4770]) ).
thf(4928,plain,
! [SV1279: $i,SV1470: $i,SV1355: $i] :
( ( ( c_member @ ( tc_prod @ SV1355 @ SV1355 ) @ ( c_Product__Type_OPair @ SV1355 @ SV1355 @ SV1470 @ SV1470 ) @ SV1279 )
= $false )
| ( ( c_Relation_Oirrefl @ SV1355 @ SV1279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(4929,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1512: $i] :
( ( ! [SY3656: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3656 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3656 ) @ SV1092 ) ) )
| ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4772]) ).
thf(4930,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1472: $i,SV1513: $i] :
( ( ~ ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
| ~ ( ~ ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4773]) ).
thf(4931,plain,
! [SV950: $i,SV1093: $i,SV1403: $i,SV1437: $i] :
( ( ( c_member @ SV1437 @ SV1403 @ SV1093 )
= $false )
| ( ( c_member @ SV1437 @ SV1403 @ ( c_Set_Oinsert @ SV1437 @ SV950 @ SV1093 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4932,plain,
! [SV1093: $i,SV950: $i,SV1404: $i,SV1514: $i] :
( ( ( c_member @ SV1514 @ SV1404 @ ( c_Set_Oinsert @ SV1514 @ SV950 @ SV1093 ) )
= $true )
| ( ( SV1404 = SV950 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4775]) ).
thf(4933,plain,
! [SV1094: $i,SV1190: $i,SV1356: $i,SV1281: $i,SV951: $i] :
( ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(4934,plain,
! [SV952: $i,SV1095: $i,SV1405: $i,SV1473: $i] :
( ( ( c_member @ ( tc_prod @ SV1473 @ SV1473 ) @ ( c_Product__Type_OPair @ SV1473 @ SV1473 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1473 @ SV952 ) )
= $false )
| ( ( ( SV1405 != SV1095 )
| ( SV1405 = SV1095 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4935,plain,
! [SV952: $i,SV1095: $i,SV1406: $i,SV1438: $i] :
( ( ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1438 @ SV952 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SV1438 @ SV952 ) )
| ( SV1406 = SV1095 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(4936,plain,
! [SV953: $i,SV1096: $i,SV1282: $i,SV1357: $i,SV1191: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 ) )
= $false )
| ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4779]) ).
thf(4937,plain,
! [SV953: $i,SV1096: $i,SV1282: $i,SV1357: $i,SV1191: $i] :
( ( ( ~ ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 ) )
= $false )
| ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4779]) ).
thf(4938,plain,
! [SV1439: $i,SV1474: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1474 @ SV1439 ) )
= $true )
| ( ( ( SV1474 != SV1439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(4939,plain,
! [SV1475: $i,SV1440: $i] :
( ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1440 @ SV1475 ) )
= $true )
| ( ( ( SV1475 != SV1440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(4940,plain,
! [SV1407: $i,SV1098: $i,SV955: $i,SV1441: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1441 @ SV955 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1098 @ SV1407 ) @ ( c_Transitive__Closure_Ortrancl @ SV1441 @ SV955 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1441 @ ( c_Set_Oinsert @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1407 @ SV1098 ) @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(4941,plain,
! [SV955: $i,SV1098: $i,SV1515: $i] :
( ( ! [SY3658: $i] :
( ~ ( c_Wellfounded_Owf @ SY3658 @ ( c_Set_Oinsert @ ( tc_prod @ SY3658 @ SY3658 ) @ ( c_Product__Type_OPair @ SY3658 @ SY3658 @ SV1515 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SY3658 @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4785]) ).
thf(4942,plain,
! [SV955: $i,SV1098: $i,SV1516: $i] :
( ( ! [SY3659: $i] :
( ~ ( c_Wellfounded_Owf @ SY3659 @ ( c_Set_Oinsert @ ( tc_prod @ SY3659 @ SY3659 ) @ ( c_Product__Type_OPair @ SY3659 @ SY3659 @ SV1516 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SY3659 @ SY3659 ) @ ( c_Product__Type_OPair @ SY3659 @ SY3659 @ SV1098 @ SV1516 ) @ ( c_Transitive__Closure_Ortrancl @ SY3659 @ SV955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4786]) ).
thf(4943,plain,
! [SV1099: $i,SV1193: $i,SV795: $i,SV956: $i,SV1286: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
= $false )
| ( ( c_Relation_Otrans @ SV1286 @ SV1193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(4944,plain,
! [SV813: $i,SV1210: $i,SV974: $i,SV1116: $i,SV1293: $i,SV1363: $i] :
( ( ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
| ( SV974 = SV813 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4945,plain,
! [SV978: $i,SV1212: $i,SV817: $i,SV1120: $i,SV1295: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(4946,plain,
! [SV1138: $i,SV1002: $i,SV842: $i,SV1229: $i] :
( ( ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV842 @ SV1002 ) @ SV1138 )
= $false )
| ( ( SV1002 = SV842 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1229 @ SV1229 ) @ ( c_Product__Type_OPair @ SV1229 @ SV1229 @ SV1002 @ SV842 ) @ SV1138 )
= $false )
| ( ( c_Relation_Oantisym @ SV1229 @ SV1138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(4947,plain,
! [SV1237: $i,SV856: $i,SV1016: $i,SV1311: $i,SV1151: $i,SV1367: $i] :
( ( ( c_member @ ( tc_prod @ SV1367 @ SV1151 ) @ ( c_Product__Type_OPair @ SV1367 @ SV1151 @ SV1311 @ SV1016 ) @ SV856 )
= $false )
| ( ( c_member @ SV1151 @ SV1016 @ ( c_Relation_OImage @ SV1367 @ SV1151 @ SV856 @ SV1237 ) )
= $true )
| ( ( c_member @ SV1367 @ SV1311 @ SV1237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(4948,plain,
! [SV857: $i,SV1017: $i,SV1152: $i,SV1238: $i,SV1312: $i,SV1368: $i,SV1408: $i,SV1442: $i] :
( ( ( c_member @ ( tc_prod @ SV1442 @ SV1408 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
| ( c_member @ ( tc_prod @ SV1442 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SV1442 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4949,plain,
! [SV1409: $i,SV859: $i,SV1369: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SV1409 @ SV1019 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1409 @ SV1369 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(4950,plain,
! [SV1245: $i,SV1040: $i,SV882: $i,SV1370: $i,SV1160: $i,SV1317: $i] :
( ( ( c_Wellfounded_Owf @ SV1317 @ SV1160 )
= $false )
| ( ( ( hAPP @ SV1370 @ SV882 )
= ( hAPP @ ( hAPP @ SV1040 @ ( c_Recdef_Ocut @ SV1317 @ SV1245 @ SV1370 @ SV1160 @ SV882 ) ) @ SV882 ) )
= $true )
| ( ( SV1370
= ( c_Recdef_Owfrec @ SV1317 @ SV1245 @ SV1160 @ SV1040 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4809]) ).
thf(4951,plain,
! [SV901: $i,SV1055: $i] :
( ( ( c_member @ ( tc_prod @ SV1055 @ SV1055 ) @ ( c_Product__Type_OPair @ SV1055 @ SV1055 @ ( sK69_B_x @ SV1055 @ SV901 ) @ ( sK71_SY738 @ SV1055 @ SV901 ) ) @ SV901 )
= $false )
| ( ( c_Relation_Otrans @ SV1055 @ SV901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(4952,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(4953,plain,
! [SV903: $i,SV1057: $i,SV1371: $i,SV1411: $i] :
( ( ( ( ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV1057 )
!= ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV903 ) ) )
= $true )
| ( ( SV1057 = SV903 )
= $true )
| ( ( c_member @ SV1411 @ SV1371 @ SV903 )
= $true )
| ( ( c_member @ SV1411 @ SV1371 @ SV1057 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(4954,plain,
! [SV1372: $i,SV1412: $i,SV903: $i,SV1057: $i] :
( ( ( ( SV1057 != SV903 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV903 ) )
= $true )
| ( ( c_member @ SV1412 @ SV1372 @ SV903 )
= $true )
| ( ( c_member @ SV1412 @ SV1372 @ SV1057 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(4955,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4815]) ).
thf(4956,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( c_member @ ( tc_prod @ SV1374 @ SV1374 ) @ ( c_Product__Type_OPair @ SV1374 @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ SV1321 ) @ SV905 )
= $true )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4816]) ).
thf(4957,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( ~ ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) ) )
= $true )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4817]) ).
thf(4958,plain,
! [SV905: $i,SV1322: $i,SV1477: $i,SV1375: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SV1477 @ SV1322 ) @ SV905 ) )
= $true )
| ( ( c_member @ SV1375 @ SV1477 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $true )
| ( ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4818]) ).
thf(4959,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( c_member @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4819]) ).
thf(4960,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4820]) ).
thf(4961,plain,
! [SV906: $i,SV1324: $i,SV1478: $i,SV1377: $i] :
( ( ( ~ ( c_member @ SV1377 @ SV1478 @ SV1324 ) )
= $true )
| ( ( ! [SY3631: $i] :
( ~ ( c_member @ SV1377 @ SY3631 @ SV1324 )
| ( SV1478 = SY3631 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SY3631 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3631 @ SV1478 ) @ SV906 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(4962,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1479: $i,SV1517: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV1517 @ SV1479 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SV1517 @ SV1479 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1250 = SV1059 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4822]) ).
thf(4963,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1480: $i,SV1518: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV1518 @ SV1480 @ SV1250 @ SV1168 )
!= ( c_Product__Type_OPair @ SV1518 @ SV1480 @ SV1059 @ SV907 ) ) )
= $true )
| ( ( SV1168 = SV907 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(4964,plain,
! [SV908: $i,SV1060: $i] :
( ( ( ( sK26_B_x @ SV1060 @ SV908 )
= ( sK27_SY720 @ SV1060 @ SV908 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1060 @ SV908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4965,plain,
! [SV1519: $i,SV1481: $i,SV909: $i,SV1325: $i,SV1378: $i] :
( ( ( hBOOL @ ( hAPP @ SV1378 @ ( c_Product__Type_OPair @ SV1325 @ SV909 @ SV1481 @ SV1519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1378 @ ( sK75_B_x1 @ SV1378 @ SV1325 @ SV909 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4826]) ).
thf(4966,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4828]) ).
thf(4967,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4829]) ).
thf(4968,plain,
! [SV910: $i,SV1520: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 )
| ! [SY3660: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SY3660 ) @ SV910 )
| ( SV1520 = SY3660 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4830]) ).
thf(4969,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) )
| ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(4970,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1251: $i,SV1382: $i] :
( ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) )
| ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(4971,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( c_member @ ( tc_prod @ SV1170 @ SV1062 ) @ ( c_Product__Type_OPair @ SV1170 @ SV1062 @ ( sK48_B_x @ SV1170 @ SV1062 @ SV912 ) @ ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) @ SV912 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4833]) ).
thf(4972,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
!= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4834]) ).
thf(4973,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
| ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(4974,plain,
! [SV1253: $i,SV1484: $i,SV1444: $i,SV1331: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 ) )
= $true )
| ( ( ! [SY3637: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SY3637 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SY3637 ) @ SV1253 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4837]) ).
thf(4975,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
| ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4839]) ).
thf(4976,plain,
! [SV1255: $i,SV1485: $i,SV1445: $i,SV1333: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SV1485 ) @ SV1255 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1485 @ SV1445 ) @ SV1255 )
| ( SV1445 = SV1485 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(4977,plain,
! [SV1334: $i,SV913: $i,SV1383: $i] :
( ( ( c_Relation_Otrans @ SV1383 @ SV913 )
= $false )
| ( ( c_Relation_Orefl__on @ SV1383 @ SV1334 @ SV913 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV1383 @ SV1334 @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4978,plain,
! [SV913: $i,SV1446: $i,SV1486: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV1486 @ SV1446 @ SV913 ) )
= $true )
| ( ( c_Relation_Orefl__on @ SV1486 @ SV1446 @ SV913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(4979,plain,
! [SV913: $i,SV1447: $i,SV1487: $i] :
( ( ( ~ ( c_Order__Relation_Opreorder__on @ SV1487 @ SV1447 @ SV913 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1487 @ SV913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(4980,plain,
! [SV1063: $i,SV1414: $i,SV1448: $i,SV914: $i,SV1521: $i,SV1171: $i] :
( ( ( ~ ( c_member @ SV1171 @ SV1521 @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SV1521 @ SV1414 ) @ SV1063 ) )
= $true )
| ( ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4844]) ).
thf(4981,plain,
! [SV914: $i,SV1063: $i,SV1171: $i,SV1415: $i,SV1449: $i] :
( ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(4982,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $true )
| ( ( SV1172 = SV1064 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4983,plain,
! [SV915: $i,SV1064: $i,SV1172: $i,SV1256: $i] :
( ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ ( sK45_B_y @ SV1256 @ SV1172 @ SV1064 @ SV915 ) @ SV1064 ) @ SV915 )
= $true )
| ( ( SV1172 = SV1064 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1256 @ SV1256 ) @ ( c_Product__Type_OPair @ SV1256 @ SV1256 @ SV1172 @ SV1064 ) @ ( c_Transitive__Closure_Ortrancl @ SV1256 @ SV915 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4847]) ).
thf(4984,plain,
! [SV1384: $i,SV917: $i,SV1417: $i,SV1065: $i] :
( ( ( ~ ( c_member @ SV1065 @ SV1417 @ SV917 ) )
= $true )
| ( ( c_member @ SV1065 @ SV1384 @ SV917 )
= $true )
| ( ( SV1417 = SV1384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(4985,plain,
! [SV1418: $i,SV917: $i,SV1385: $i,SV1065: $i] :
( ( ( ~ ( c_member @ SV1065 @ SV1385 @ SV917 ) )
= $true )
| ( ( c_member @ SV1065 @ SV1418 @ SV917 )
= $true )
| ( ( SV1418 = SV1385 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(4986,plain,
! [SV1173: $i,SV918: $i,SV1066: $i,SV1419: $i,SV1452: $i] :
( ( ( c_member @ ( tc_prod @ SV1452 @ SV1419 ) @ ( c_Product__Type_OPair @ SV1452 @ SV1419 @ SV1066 @ SV918 ) @ SV1173 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1452 @ SV1419 @ SV1173 ) @ SV1066 ) @ SV918 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4851]) ).
thf(4987,plain,
! [SV918: $i,SV1066: $i,SV1173: $i,SV1420: $i,SV1453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV1453 @ SV1420 @ SV1173 ) @ SV1066 ) @ SV918 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1453 @ SV1420 ) @ ( c_Product__Type_OPair @ SV1453 @ SV1420 @ SV1066 @ SV918 ) @ SV1173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4988,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1488: $i] :
( ( ( ! [SY3638: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SY3638 @ ( sK60_B_z @ SY3638 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SY3638 ) @ SV1067 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(4989,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1455: $i,SV1489: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(4990,plain,
! [SV920: $i] :
( ( ! [SY2584: $i,SY2585: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2585 @ SY2584 )
| ( SY2585 = SY2584 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2584 @ SY2585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2584 ) @ SY2585 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4855]) ).
thf(4991,plain,
! [SV920: $i] :
( ( ! [SY2586: $i,SY2587: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2587 @ SY2586 )
| ( SY2587 = SY2586 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2586 ) @ SY2587 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4856]) ).
thf(4992,plain,
! [SV920: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2589 @ SY2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2588 @ SY2589 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2588 ) @ SY2589 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4857]) ).
thf(4993,plain,
! [SV920: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2591 @ SY2590 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2590 ) @ SY2591 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4858]) ).
thf(4994,plain,
! [SV920: $i] :
( ( ! [SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) )
| ( SY2593 = SY2592 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2592 @ SY2593 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2592 ) @ SY2593 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4859]) ).
thf(4995,plain,
! [SV920: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( SY2595 = SY2594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2594 ) @ SY2595 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4860]) ).
thf(4996,plain,
! [SV920: $i] :
( ( ! [SY2596: $i,SY2597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY2596 @ SY2597 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2596 ) @ SY2597 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4861]) ).
thf(4997,plain,
! [SV920: $i] :
( ( ! [SY2598: $i,SY2599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SY2598 ) @ SY2599 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4862]) ).
thf(4998,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i,SV1456: $i,SV1522: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1522 @ SV1522 ) @ ( c_Product__Type_OPair @ SV1522 @ SV1522 @ SV1456 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SV1522 @ SV1068 ) @ SV921 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1456 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4863]) ).
thf(4999,plain,
! [SV1068: $i,SV1260: $i,SV1457: $i,SV921: $i,SV1175: $i] :
( ( ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1457 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
= $false )
| ( ( ! [SY3618: $i] : ( c_member @ ( tc_prod @ SY3618 @ SY3618 ) @ ( c_Product__Type_OPair @ SY3618 @ SY3618 @ SV1457 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SY3618 @ SV1068 ) @ SV921 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(5000,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) ) @ SV923 )
= $true )
| ( ( SV1176 = SV1069 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4865]) ).
thf(5001,plain,
! [SV923: $i,SV1069: $i,SV1176: $i,SV1261: $i] :
( ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ ( sK44_B_y @ SV1261 @ SV1176 @ SV1069 @ SV923 ) @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $true )
| ( ( SV1176 = SV1069 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1261 @ SV1261 ) @ ( c_Product__Type_OPair @ SV1261 @ SV1261 @ SV1176 @ SV1069 ) @ ( c_Transitive__Closure_Ortrancl @ SV1261 @ SV923 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4866]) ).
thf(5002,plain,
! [SV926: $i,SV1490: $i,SV1386: $i,SV1072: $i,SV1422: $i] :
( ( ( c_member @ ( tc_prod @ SV1422 @ SV1072 ) @ ( c_Product__Type_OPair @ SV1422 @ SV1072 @ SV1386 @ SV1490 ) @ SV926 )
= $false )
| ( ( c_member @ SV1422 @ SV1386 @ ( c_Relation_ODomain @ SV1422 @ SV1072 @ SV926 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4869]) ).
thf(5003,plain,
! [SV1073: $i,SV1424: $i,SV927: $i,SV1388: $i] :
( ( ( SV1388 = SV927 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1424 @ SV1424 ) @ ( c_Product__Type_OPair @ SV1424 @ SV1424 @ SV1388 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1424 @ SV1073 ) )
= $true )
| ( ( c_member @ SV1424 @ SV1388 @ ( c_Relation_ODomain @ SV1424 @ SV1424 @ SV1073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4871]) ).
thf(5004,plain,
! [SV1073: $i,SV927: $i,SV1389: $i,SV1425: $i] :
( ( ( c_member @ ( tc_prod @ SV1425 @ SV1425 ) @ ( c_Product__Type_OPair @ SV1425 @ SV1425 @ SV1389 @ SV927 ) @ ( c_Transitive__Closure_Ortrancl @ SV1425 @ SV1073 ) )
= $false )
| ( ( SV1389 = SV927 )
= $true )
| ( ( c_member @ SV1425 @ SV1389 @ ( c_Relation_ODomain @ SV1425 @ SV1425 @ SV1073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(5005,plain,
! [SV1459: $i,SV1074: $i,SV928: $i,SV1390: $i] :
( ( ( SV1390 = SV928 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1459 @ SV1390 @ SV1074 ) @ SV928 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5006,plain,
! [SV1074: $i,SV928: $i,SV1491: $i] :
( ( ( ( SV1491 != SV928 ) )
= $true )
| ( ( ! [SY3640: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3640 @ SV1491 @ SV1074 ) @ SV928 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5007,plain,
! [SV928: $i,SV1074: $i] :
( ( ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
= $false )
| ( ( ! [SY3040: $i,SY3041: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3041 @ SY3040 @ SV1074 ) @ SV928 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4875]) ).
thf(5008,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
| ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4876]) ).
thf(5009,plain,
! [SV1392: $i,SV1076: $i,SV930: $i,SV1427: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1427 @ SV930 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1076 @ SV1392 ) @ ( c_Transitive__Closure_Ortrancl @ SV1427 @ SV930 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1427 @ ( c_Set_Oinsert @ ( tc_prod @ SV1427 @ SV1427 ) @ ( c_Product__Type_OPair @ SV1427 @ SV1427 @ SV1392 @ SV1076 ) @ SV930 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5010,plain,
! [SV930: $i,SV1076: $i,SV1492: $i,SV1523: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV1523 @ ( c_Set_Oinsert @ ( tc_prod @ SV1523 @ SV1523 ) @ ( c_Product__Type_OPair @ SV1523 @ SV1523 @ SV1492 @ SV1076 ) @ SV930 ) )
| ( c_Wellfounded_Oacyclic @ SV1523 @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4878]) ).
thf(5011,plain,
! [SV930: $i,SV1076: $i,SV1493: $i,SV1524: $i] :
( ( ~ ( c_Wellfounded_Oacyclic @ SV1524 @ ( c_Set_Oinsert @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1493 @ SV1076 ) @ SV930 ) )
| ~ ( c_member @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1076 @ SV1493 ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4879]) ).
thf(5012,plain,
! [SV931: $i,SV1393: $i,SV1494: $i,SV1428: $i,SV1077: $i] :
( ( ( c_member @ ( tc_prod @ SV1077 @ SV1428 ) @ ( c_Product__Type_OPair @ SV1077 @ SV1428 @ SV1494 @ SV1393 ) @ SV931 )
= $false )
| ( ( c_member @ SV1428 @ SV1393 @ ( c_Relation_ORange @ SV1077 @ SV1428 @ SV931 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4880]) ).
thf(5013,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4882]) ).
thf(5014,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
| ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(5015,plain,
! [SV1268: $i,SV1461: $i,SV1526: $i,SV1346: $i] :
( ( ( ~ ( c_member @ SV1346 @ SV1526 @ SV1461 ) )
= $true )
| ( ( ~ ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4885]) ).
thf(5016,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i,SV1495: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1495 @ SV1495 ) @ ( c_Product__Type_OPair @ SV1495 @ SV1495 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(5017,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1463: $i,SV1496: $i] :
( ( ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
!= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) ) )
= $true )
| ( ( ! [SY3643: $i] :
( ~ ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SY3643 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3643 )
= ( hAPP @ SV933 @ SY3643 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5018,plain,
! [SV1396: $i,SV1431: $i,SV934: $i,SV1080: $i] :
( ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1431 ) )
= $true )
| ( ( c_member @ SV1080 @ SV934 @ SV1396 )
= $true )
| ( ( SV1431 = SV1396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(5019,plain,
! [SV1432: $i,SV1397: $i,SV934: $i,SV1080: $i] :
( ( ( ~ ( c_member @ SV1080 @ SV934 @ SV1397 ) )
= $true )
| ( ( c_member @ SV1080 @ SV934 @ SV1432 )
= $true )
| ( ( SV1432 = SV1397 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(5020,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4890]) ).
thf(5021,plain,
! [SV935: $i,SV1081: $i,SV1182: $i,SV1270: $i] :
( ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ ( sK37_B_c @ SV1270 @ SV1182 @ SV1081 @ SV935 ) @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ SV935 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1270 @ SV1270 ) @ ( c_Product__Type_OPair @ SV1270 @ SV1270 @ SV1182 @ SV1081 ) @ ( c_Transitive__Closure_Otrancl @ SV1270 @ SV935 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4891]) ).
thf(5022,plain,
! [SV936: $i,SV1183: $i,SV1082: $i,SV1271: $i] :
( ( ( SV1271 = SV1082 )
= $false )
| ( ( ( SV1183 != SV936 ) )
= $true )
| ( ( ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5023,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) )
| ( SV1271 = SV1082 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4893]) ).
thf(5024,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) )
| ( SV1183 = SV936 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4894]) ).
thf(5025,plain,
! [SV937: $i,SV1083: $i,SV1497: $i,SV1527: $i] :
( ( ( SV1527 != SV1497 )
| ( c_member @ SV1083 @ SV937 @ SV1527 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4895]) ).
thf(5026,plain,
! [SV937: $i,SV1083: $i,SV1498: $i,SV1528: $i] :
( ( ( SV1528 != SV1498 )
| ( c_member @ SV1083 @ SV937 @ SV1528 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4896]) ).
thf(5027,plain,
! [SV937: $i,SV1083: $i,SV1499: $i,SV1529: $i] :
( ( ( SV1529 != SV1499 )
| ( c_member @ SV1083 @ SV937 @ SV1499 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4897]) ).
thf(5028,plain,
! [SV937: $i,SV1083: $i,SV1500: $i] :
( ( ( ! [SY3647: $i] : ( SY3647 != SV1500 ) )
= $true )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1500 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(5029,plain,
! [SV940: $i,SV1434: $i,SV1085: $i,SV1398: $i] :
( ( ( SV1398 = SV1085 )
= $false )
| ( ( ~ ( c_member @ SV1434 @ SV1398 @ SV940 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1434 @ SV1434 ) @ ( c_Product__Type_OPair @ SV1434 @ SV1434 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SV1434 @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5030,plain,
! [SV940: $i,SV1085: $i,SV1501: $i] :
( ( ( ! [SY3648: $i] :
~ ( c_member @ ( tc_prod @ SY3648 @ SY3648 ) @ ( c_Product__Type_OPair @ SY3648 @ SY3648 @ SV1501 @ SV1085 ) @ ( c_Relation_OId__on @ SY3648 @ SV940 ) ) )
= $true )
| ( ( SV1501 = SV1085 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5031,plain,
! [SV940: $i,SV1085: $i,SV1502: $i,SV1530: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1530 @ SV1530 ) @ ( c_Product__Type_OPair @ SV1530 @ SV1530 @ SV1502 @ SV1085 ) @ ( c_Relation_OId__on @ SV1530 @ SV940 ) )
| ( c_member @ SV1530 @ SV1502 @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4902]) ).
thf(5032,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4903]) ).
thf(5033,plain,
! [SV942: $i,SV1087: $i,SV1186: $i,SV1273: $i] :
( ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ ( sK38_B_y @ SV1273 @ SV1186 @ SV1087 @ SV942 ) @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ SV942 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1273 @ SV1273 ) @ ( c_Product__Type_OPair @ SV1273 @ SV1273 @ SV1186 @ SV1087 ) @ ( c_Transitive__Closure_Otrancl @ SV1273 @ SV942 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4904]) ).
thf(5034,plain,
! [SV943: $i,SV1088: $i,SV1503: $i] :
( ( ( ! [SY3650: $i] :
~ ( c_member @ ( tc_prod @ SY3650 @ SY3650 ) @ ( c_Product__Type_OPair @ SY3650 @ SY3650 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3650 @ SV943 ) ) )
= $true )
| ( ( ( SV1503 != SV1088 )
| ( SV1503 = SV1088 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5035,plain,
! [SV943: $i,SV1088: $i,SV1504: $i,SV1531: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1531 @ SV943 ) )
| ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1531 @ SV943 ) )
| ( SV1504 = SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4906]) ).
thf(5036,plain,
! [SV943: $i,SV1532: $i,SV1088: $i,SV1505: $i] :
( ( ( SV1505 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1532 @ SV943 ) )
| ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1532 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4907]) ).
thf(5037,plain,
! [SV943: $i,SV1088: $i,SV1506: $i] :
( ( ( ( SV1506 != SV1088 ) )
= $true )
| ( ( ! [SY3653: $i] : ( c_member @ ( tc_prod @ SY3653 @ SY3653 ) @ ( c_Product__Type_OPair @ SY3653 @ SY3653 @ SV1506 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3653 @ SV943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4908]) ).
thf(5038,plain,
! [SV945: $i,SV1090: $i,SV1188: $i,SV1277: $i,SV1351: $i,SV1399: $i] :
( ( ( c_member @ ( tc_prod @ SV1399 @ SV1399 ) @ ( c_Product__Type_OPair @ SV1399 @ SV1399 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ SV1351 ) @ SV1277 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4911]) ).
thf(5039,plain,
! [SV945: $i,SV1351: $i,SV1090: $i,SV1277: $i,SV1188: $i,SV1399: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4912]) ).
thf(5040,plain,
! [SV1352: $i,SV946: $i,SV1400: $i] :
( ( ( c_Relation_Oantisym @ SV1400 @ SV946 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV1400 @ SV1352 @ SV946 )
= $false )
| ( ( c_Order__Relation_Opartial__order__on @ SV1400 @ SV1352 @ SV946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5041,plain,
! [SV946: $i,SV1466: $i,SV1507: $i] :
( ( ( ~ ( c_Order__Relation_Opartial__order__on @ SV1507 @ SV1466 @ SV946 ) )
= $true )
| ( ( c_Order__Relation_Opreorder__on @ SV1507 @ SV1466 @ SV946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5042,plain,
! [SV946: $i,SV1467: $i,SV1508: $i] :
( ( ( ~ ( c_Order__Relation_Opartial__order__on @ SV1508 @ SV1467 @ SV946 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1508 @ SV946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(5043,plain,
! [SV1468: $i,SV1435: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1435 @ SV1468 ) @ v_L )
= $true )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1468 @ SV1435 ) @ v_L )
= $true )
| ( ( SV1435 = SV1468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4916]) ).
thf(5044,plain,
! [SV1533: $i] :
( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1533 @ SV1533 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4917]) ).
thf(5045,plain,
( ( ( ~ ( ( sK6_B_x != sK7_SY705 ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[4920]) ).
thf(5046,plain,
( ( ( ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[4920]) ).
thf(5047,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ( c_Relation_Oirrefl @ SV1401 @ SV947 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1401 @ SV947 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4921]) ).
thf(5048,plain,
! [SV947: $i] :
( ( ! [SY2741: $i,SY2742: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2742 @ SY2741 @ SV947 )
| ( c_Relation_Oirrefl @ SY2742 @ SV947 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4922]) ).
thf(5049,plain,
! [SV947: $i] :
( ( ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY2744 @ SY2743 @ SV947 )
| ( c_Relation_Otrans @ SY2744 @ SV947 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4923]) ).
thf(5050,plain,
! [SV947: $i,SV1469: $i,SV1509: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1509 @ SV1469 @ SV947 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1509 @ SV1469 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4924]) ).
thf(5051,plain,
! [SV948: $i,SV1436: $i,SV1091: $i,SV1402: $i] :
( ( ( SV1402 = SV1091 )
= $true )
| ( ( c_member @ SV1436 @ SV1402 @ SV948 )
= $true )
| ( ( c_member @ SV1436 @ SV1402 @ ( c_Set_Oinsert @ SV1436 @ SV1091 @ SV948 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(5052,plain,
! [SV948: $i,SV1091: $i,SV1510: $i] :
( ( ( ( SV1510 != SV1091 ) )
= $true )
| ( ( ! [SY3654: $i] : ( c_member @ SY3654 @ SV1510 @ ( c_Set_Oinsert @ SY3654 @ SV1091 @ SV948 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(5053,plain,
! [SV1091: $i,SV948: $i,SV1511: $i,SV1534: $i] :
( ( ~ ( c_member @ SV1534 @ SV1511 @ SV948 )
| ( c_member @ SV1534 @ SV1511 @ ( c_Set_Oinsert @ SV1534 @ SV1091 @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4927]) ).
thf(5054,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1512: $i] :
( ( ( ! [SY3656: $i] :
( ~ ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SY3656 @ ( sK55_B_z @ SY3656 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SY3656 ) @ SV1092 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(5055,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1472: $i,SV1513: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) )
= $true )
| ( ( ~ ( ~ ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(5056,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(5057,plain,
! [SV952: $i,SV1473: $i,SV1095: $i,SV1405: $i] :
( ( ( ( SV1405 != SV1095 ) )
= $true )
| ( ( SV1405 = SV1095 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1473 @ SV1473 ) @ ( c_Product__Type_OPair @ SV1473 @ SV1473 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1473 @ SV952 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(5058,plain,
! [SV952: $i,SV1095: $i,SV1406: $i,SV1438: $i] :
( ( ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Otrancl @ SV1438 @ SV952 ) )
= $true )
| ( ( SV1406 = SV1095 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1438 @ SV1438 ) @ ( c_Product__Type_OPair @ SV1438 @ SV1438 @ SV1406 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1438 @ SV952 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5059,plain,
! [SV953: $i,SV1096: $i,SV1282: $i,SV1357: $i,SV1191: $i] :
( ( ( c_member @ ( tc_prod @ SV1191 @ SV1357 ) @ ( c_Product__Type_OPair @ SV1191 @ SV1357 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV1282 ) @ SV1096 )
= $true )
| ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4936]) ).
thf(5060,plain,
! [SV953: $i,SV1096: $i,SV1282: $i,SV1357: $i,SV1191: $i] :
( ( ( c_member @ SV1191 @ ( sK23_B_x @ SV1357 @ SV1282 @ SV1191 @ SV1096 @ SV953 ) @ SV953 )
= $true )
| ( ( c_member @ SV1357 @ SV1282 @ ( c_Relation_OImage @ SV1191 @ SV1357 @ SV1096 @ SV953 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4937]) ).
thf(5061,plain,
! [SV1439: $i,SV1474: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1474 @ SV1439 )
= $false )
| ( ( ( SV1474 != SV1439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(5062,plain,
! [SV1475: $i,SV1440: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1440 @ SV1475 )
= $false )
| ( ( ( SV1475 != SV1440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4939]) ).
thf(5063,plain,
! [SV1407: $i,SV1098: $i,SV955: $i,SV1441: $i] :
( ( ( c_Wellfounded_Owf @ SV1441 @ SV955 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1098 @ SV1407 ) @ ( c_Transitive__Closure_Ortrancl @ SV1441 @ SV955 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1441 @ ( c_Set_Oinsert @ ( tc_prod @ SV1441 @ SV1441 ) @ ( c_Product__Type_OPair @ SV1441 @ SV1441 @ SV1407 @ SV1098 ) @ SV955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5064,plain,
! [SV955: $i,SV1098: $i,SV1515: $i,SV1535: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1535 @ ( c_Set_Oinsert @ ( tc_prod @ SV1535 @ SV1535 ) @ ( c_Product__Type_OPair @ SV1535 @ SV1535 @ SV1515 @ SV1098 ) @ SV955 ) )
| ( c_Wellfounded_Owf @ SV1535 @ SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4941]) ).
thf(5065,plain,
! [SV955: $i,SV1098: $i,SV1516: $i,SV1536: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV1536 @ ( c_Set_Oinsert @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1516 @ SV1098 ) @ SV955 ) )
| ~ ( c_member @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1098 @ SV1516 ) @ ( c_Transitive__Closure_Ortrancl @ SV1536 @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4942]) ).
thf(5066,plain,
! [SV1099: $i,SV1193: $i,SV795: $i,SV956: $i,SV1286: $i] :
( ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV956 @ SV795 ) @ SV1193 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV795 ) @ SV1193 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1286 @ SV1286 ) @ ( c_Product__Type_OPair @ SV1286 @ SV1286 @ SV1099 @ SV956 ) @ SV1193 )
= $false )
| ( ( c_Relation_Otrans @ SV1286 @ SV1193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5067,plain,
! [SV974: $i,SV1210: $i,SV813: $i,SV1116: $i,SV1293: $i,SV1363: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 ) )
= $true )
| ( ( SV974 = SV813 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4944]) ).
thf(5068,plain,
! [SV978: $i,SV1212: $i,SV817: $i,SV1120: $i,SV1295: $i] :
( ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
| ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(5069,plain,
! [SV1238: $i,SV1368: $i,SV1442: $i,SV857: $i,SV1017: $i,SV1312: $i,SV1152: $i,SV1408: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1442 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SV1442 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1442 @ SV1408 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4948]) ).
thf(5070,plain,
! [SV1409: $i,SV859: $i,SV1369: $i,SV1019: $i,SV1153: $i,SV1239: $i,SV1313: $i] :
( ( ( c_member @ ( tc_prod @ SV1313 @ SV1313 ) @ ( c_Product__Type_OPair @ SV1313 @ SV1313 @ SV1239 @ SV1153 ) @ ( hAPP @ SV1019 @ SV1369 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV859 @ SV1313 ) @ ( tc_prod @ SV859 @ SV1313 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1239 ) @ ( c_Product__Type_OPair @ SV859 @ SV1313 @ SV1369 @ SV1153 ) ) @ ( c_Recdef_Osame__fst @ SV859 @ SV1313 @ SV1409 @ SV1019 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1409 @ SV1369 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5071,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5072,plain,
! [SV903: $i,SV1057: $i,SV1371: $i,SV1411: $i] :
( ( ( ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV1057 )
= ( c_Set_Oinsert @ SV1411 @ SV1371 @ SV903 ) )
= $false )
| ( ( SV1057 = SV903 )
= $true )
| ( ( c_member @ SV1411 @ SV1371 @ SV903 )
= $true )
| ( ( c_member @ SV1411 @ SV1371 @ SV1057 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5073,plain,
! [SV1372: $i,SV1412: $i,SV903: $i,SV1057: $i] :
( ( ( SV1057 = SV903 )
= $false )
| ( ( ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV1057 )
= ( c_Set_Oinsert @ SV1412 @ SV1372 @ SV903 ) )
= $true )
| ( ( c_member @ SV1412 @ SV1372 @ SV903 )
= $true )
| ( ( c_member @ SV1412 @ SV1372 @ SV1057 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(5074,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1413: $i,SV1443: $i,SV1320: $i,SV1373: $i,SV904: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5075,plain,
! [SV905: $i,SV1321: $i,SV1374: $i] :
( ( ( c_member @ SV1374 @ ( sK61_B_x @ SV1374 @ SV1321 @ SV905 ) @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $false )
| ( ( c_member @ SV1374 @ SV1321 @ ( c_Wellfounded_Oacc @ SV1374 @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4957]) ).
thf(5076,plain,
! [SV905: $i,SV1322: $i,SV1477: $i,SV1375: $i] :
( ( ( c_member @ ( tc_prod @ SV1375 @ SV1375 ) @ ( c_Product__Type_OPair @ SV1375 @ SV1375 @ SV1477 @ SV1322 ) @ SV905 )
= $false )
| ( ( c_member @ SV1375 @ SV1477 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $true )
| ( ( c_member @ SV1375 @ SV1322 @ ( c_Wellfounded_Oacc @ SV1375 @ SV905 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4958]) ).
thf(5077,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
| ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4960]) ).
thf(5078,plain,
! [SV906: $i,SV1324: $i,SV1478: $i,SV1377: $i] :
( ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( ! [SY3631: $i] :
( ~ ( c_member @ SV1377 @ SY3631 @ SV1324 )
| ( SV1478 = SY3631 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SY3631 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SY3631 @ SV1478 ) @ SV906 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4961]) ).
thf(5079,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1479: $i,SV1517: $i] :
( ( ( ( c_Product__Type_OPair @ SV1517 @ SV1479 @ SV1250 @ SV1168 )
= ( c_Product__Type_OPair @ SV1517 @ SV1479 @ SV1059 @ SV907 ) )
= $false )
| ( ( SV1250 = SV1059 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(5080,plain,
! [SV907: $i,SV1059: $i,SV1168: $i,SV1250: $i,SV1480: $i,SV1518: $i] :
( ( ( ( c_Product__Type_OPair @ SV1518 @ SV1480 @ SV1250 @ SV1168 )
= ( c_Product__Type_OPair @ SV1518 @ SV1480 @ SV1059 @ SV907 ) )
= $false )
| ( ( SV1168 = SV907 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4963]) ).
thf(5081,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
| ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5082,plain,
! [SV910: $i,SV1520: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 ) )
= $true )
| ( ( ! [SY3660: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SY3660 ) @ SV910 )
| ( SV1520 = SY3660 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(5083,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4969]) ).
thf(5084,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ~ ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4969]) ).
thf(5085,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1251: $i,SV1382: $i] :
( ( ~ ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4970]) ).
thf(5086,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1061: $i,SV1251: $i,SV1382: $i] :
( ( ~ ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4970]) ).
thf(5087,plain,
! [SV912: $i,SV1062: $i,SV1170: $i] :
( ( ( ( sK49_SY727 @ SV1170 @ SV1062 @ SV912 )
= ( sK50_SY729 @ SV1170 @ SV1062 @ SV912 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1170 @ SV1062 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5088,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4973]) ).
thf(5089,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4973]) ).
thf(5090,plain,
! [SV1253: $i,SV1484: $i,SV1444: $i,SV1331: $i] :
( ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 )
= $false )
| ( ( ! [SY3637: $i] :
( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SY3637 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SY3637 ) @ SV1253 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(5091,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4975]) ).
thf(5092,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ~ ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4975]) ).
thf(5093,plain,
! [SV1255: $i,SV1485: $i,SV1445: $i,SV1333: $i] :
( ( ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SV1485 ) @ SV1255 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1485 @ SV1445 ) @ SV1255 )
| ( SV1445 = SV1485 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4976]) ).
thf(5094,plain,
! [SV913: $i,SV1446: $i,SV1486: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV1486 @ SV1446 @ SV913 )
= $false )
| ( ( c_Relation_Orefl__on @ SV1486 @ SV1446 @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5095,plain,
! [SV913: $i,SV1447: $i,SV1487: $i] :
( ( ( c_Order__Relation_Opreorder__on @ SV1487 @ SV1447 @ SV913 )
= $false )
| ( ( c_Relation_Otrans @ SV1487 @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4979]) ).
thf(5096,plain,
! [SV1063: $i,SV1414: $i,SV1448: $i,SV914: $i,SV1521: $i,SV1171: $i] :
( ( ( ~ ( c_member @ SV1171 @ SV1521 @ SV914 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SV1521 @ SV1414 ) @ SV1063 ) )
= $true )
| ( ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(5097,plain,
! [SV914: $i,SV1063: $i,SV1415: $i,SV1449: $i,SV1171: $i] :
( ( ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
| ~ ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) )
= $false )
| ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(5098,plain,
! [SV1384: $i,SV917: $i,SV1417: $i,SV1065: $i] :
( ( ( c_member @ SV1065 @ SV1417 @ SV917 )
= $false )
| ( ( c_member @ SV1065 @ SV1384 @ SV917 )
= $true )
| ( ( SV1417 = SV1384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5099,plain,
! [SV1418: $i,SV917: $i,SV1385: $i,SV1065: $i] :
( ( ( c_member @ SV1065 @ SV1385 @ SV917 )
= $false )
| ( ( c_member @ SV1065 @ SV1418 @ SV917 )
= $true )
| ( ( SV1418 = SV1385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4985]) ).
thf(5100,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1537: $i,SV1488: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4988]) ).
thf(5101,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1455: $i,SV1489: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false )
| ( ( ~ ( ~ ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5102,plain,
! [SV920: $i,SV1538: $i] :
( ( ! [SY3661: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3661 @ SV1538 )
| ( SY3661 = SV1538 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1538 @ SY3661 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1538 ) @ SY3661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4990]) ).
thf(5103,plain,
! [SV920: $i,SV1539: $i] :
( ( ! [SY3662: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3662 @ SV1539 )
| ( SY3662 = SV1539 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SY3662 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SY3662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5104,plain,
! [SV920: $i,SV1540: $i] :
( ( ! [SY3663: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3663 @ SV1540 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SY3663 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SY3663 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SY3663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4992]) ).
thf(5105,plain,
! [SV920: $i,SV1541: $i] :
( ( ! [SY3664: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SY3664 @ SV1541 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SY3664 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SY3664 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SY3664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4993]) ).
thf(5106,plain,
! [SV1542: $i,SV920: $i] :
( ( ! [SY3665: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SY3665 ) )
| ( SY3665 = SV1542 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SY3665 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SY3665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4994]) ).
thf(5107,plain,
! [SV1543: $i,SV920: $i] :
( ( ! [SY3666: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SY3666 ) )
| ( SY3666 = SV1543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SY3666 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SY3666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4995]) ).
thf(5108,plain,
! [SV1544: $i,SV920: $i] :
( ( ! [SY3667: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SY3667 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SY3667 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SY3667 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SY3667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4996]) ).
thf(5109,plain,
! [SV1545: $i,SV920: $i] :
( ( ! [SY3668: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SY3668 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SY3668 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SY3668 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SY3668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4997]) ).
thf(5110,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i,SV1456: $i,SV1522: $i] :
( ( ( c_member @ ( tc_prod @ SV1522 @ SV1522 ) @ ( c_Product__Type_OPair @ SV1522 @ SV1522 @ SV1456 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SV1522 @ SV1068 ) @ SV921 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1456 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5111,plain,
! [SV921: $i,SV1068: $i,SV1175: $i,SV1260: $i,SV1457: $i,SV1546: $i] :
( ( ( c_member @ ( tc_prod @ SV1546 @ SV1546 ) @ ( c_Product__Type_OPair @ SV1546 @ SV1546 @ SV1457 @ SV1260 ) @ ( hAPP @ ( c_Relation_Oinv__image @ SV1175 @ SV1546 @ SV1068 ) @ SV921 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1175 @ SV1175 ) @ ( c_Product__Type_OPair @ SV1175 @ SV1175 @ ( hAPP @ SV921 @ SV1457 ) @ ( hAPP @ SV921 @ SV1260 ) ) @ SV1068 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5112,plain,
! [SV1074: $i,SV928: $i,SV1491: $i] :
( ( ( SV1491 = SV928 )
= $false )
| ( ( ! [SY3640: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3640 @ SV1491 @ SV1074 ) @ SV928 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5006]) ).
thf(5113,plain,
! [SV928: $i,SV1074: $i,SV1547: $i] :
( ( ( ! [SY3669: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3669 @ SV1547 @ SV1074 ) @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5007]) ).
thf(5114,plain,
! [SV1075: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV1179: $i,SV1265: $i,SV929: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) ) )
= $true )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5115,plain,
! [SV930: $i,SV1076: $i,SV1492: $i,SV1523: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1523 @ ( c_Set_Oinsert @ ( tc_prod @ SV1523 @ SV1523 ) @ ( c_Product__Type_OPair @ SV1523 @ SV1523 @ SV1492 @ SV1076 ) @ SV930 ) ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV1523 @ SV930 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(5116,plain,
! [SV930: $i,SV1076: $i,SV1493: $i,SV1524: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ SV1524 @ ( c_Set_Oinsert @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1493 @ SV1076 ) @ SV930 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1076 @ SV1493 ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ SV930 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5117,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5118,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) ) )
= $true )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5119,plain,
! [SV1268: $i,SV1461: $i,SV1526: $i,SV1346: $i] :
( ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( ~ ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5015]) ).
thf(5120,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i,SV1495: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1495 @ SV1495 ) @ ( c_Product__Type_OPair @ SV1495 @ SV1495 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
| ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5121,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1463: $i,SV1496: $i] :
( ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
= $false )
| ( ( ! [SY3643: $i] :
( ~ ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SY3643 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SY3643 )
= ( hAPP @ SV933 @ SY3643 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5017]) ).
thf(5122,plain,
! [SV1396: $i,SV1431: $i,SV934: $i,SV1080: $i] :
( ( ( c_member @ SV1080 @ SV934 @ SV1431 )
= $false )
| ( ( c_member @ SV1080 @ SV934 @ SV1396 )
= $true )
| ( ( SV1431 = SV1396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5018]) ).
thf(5123,plain,
! [SV1432: $i,SV1397: $i,SV934: $i,SV1080: $i] :
( ( ( c_member @ SV1080 @ SV934 @ SV1397 )
= $false )
| ( ( c_member @ SV1080 @ SV934 @ SV1432 )
= $true )
| ( ( SV1432 = SV1397 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5124,plain,
! [SV1082: $i,SV1271: $i,SV936: $i,SV1183: $i] :
( ( ( SV1183 = SV936 )
= $false )
| ( ( SV1271 = SV1082 )
= $false )
| ( ( ! [SY3450: $i,SY3451: $i] :
( ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3451 @ SY3450 @ SV1082 @ SV936 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5125,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ( ! [SY3452: $i,SY3453: $i] :
( ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3453 @ SY3452 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1271 = SV1082 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5126,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i] :
( ( ( ! [SY3454: $i,SY3455: $i] :
( ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3455 @ SY3454 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1183 = SV936 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5024]) ).
thf(5127,plain,
! [SV937: $i,SV1083: $i,SV1497: $i,SV1527: $i] :
( ( ( ( SV1527 != SV1497 ) )
= $true )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1527 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5128,plain,
! [SV937: $i,SV1083: $i,SV1498: $i,SV1528: $i] :
( ( ( ( SV1528 != SV1498 ) )
= $true )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1528 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5129,plain,
! [SV937: $i,SV1083: $i,SV1499: $i,SV1529: $i] :
( ( ( ( SV1529 != SV1499 ) )
= $true )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1499 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(5130,plain,
! [SV937: $i,SV1083: $i,SV1500: $i,SV1548: $i] :
( ( ( ( SV1548 != SV1500 ) )
= $true )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1500 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1500 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5028]) ).
thf(5131,plain,
! [SV1085: $i,SV940: $i,SV1398: $i,SV1434: $i] :
( ( ( c_member @ SV1434 @ SV1398 @ SV940 )
= $false )
| ( ( SV1398 = SV1085 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1434 @ SV1434 ) @ ( c_Product__Type_OPair @ SV1434 @ SV1434 @ SV1398 @ SV1085 ) @ ( c_Relation_OId__on @ SV1434 @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5132,plain,
! [SV940: $i,SV1085: $i,SV1501: $i,SV1549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1549 @ SV1549 ) @ ( c_Product__Type_OPair @ SV1549 @ SV1549 @ SV1501 @ SV1085 ) @ ( c_Relation_OId__on @ SV1549 @ SV940 ) ) )
= $true )
| ( ( SV1501 = SV1085 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5030]) ).
thf(5133,plain,
! [SV940: $i,SV1085: $i,SV1502: $i,SV1530: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1530 @ SV1530 ) @ ( c_Product__Type_OPair @ SV1530 @ SV1530 @ SV1502 @ SV1085 ) @ ( c_Relation_OId__on @ SV1530 @ SV940 ) ) )
= $true )
| ( ( c_member @ SV1530 @ SV1502 @ SV940 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5031]) ).
thf(5134,plain,
! [SV943: $i,SV1088: $i,SV1503: $i,SV1550: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1550 @ SV1550 ) @ ( c_Product__Type_OPair @ SV1550 @ SV1550 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1550 @ SV943 ) ) )
= $true )
| ( ( ( SV1503 != SV1088 )
| ( SV1503 = SV1088 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5034]) ).
thf(5135,plain,
! [SV943: $i,SV1088: $i,SV1504: $i,SV1531: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1531 @ SV943 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1531 @ SV943 ) )
| ( SV1504 = SV1088 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5035]) ).
thf(5136,plain,
! [SV943: $i,SV1532: $i,SV1088: $i,SV1505: $i] :
( ( ( ( SV1505 = SV1088 )
| ~ ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1532 @ SV943 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1532 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5036]) ).
thf(5137,plain,
! [SV943: $i,SV1088: $i,SV1506: $i] :
( ( ( SV1506 = SV1088 )
= $false )
| ( ( ! [SY3653: $i] : ( c_member @ ( tc_prod @ SY3653 @ SY3653 ) @ ( c_Product__Type_OPair @ SY3653 @ SY3653 @ SV1506 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SY3653 @ SV943 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5138,plain,
! [SV945: $i,SV1351: $i,SV1090: $i,SV1277: $i,SV1188: $i,SV1399: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) @ ( hAPP @ SV945 @ ( sK56_B_z @ SV1399 @ SV1351 @ SV1277 @ SV1188 @ SV1090 @ SV945 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1399 @ SV1188 @ SV1277 @ SV1090 @ SV1351 @ ( hAPP @ ( hAPP @ SV1090 @ SV945 ) @ SV1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5139,plain,
! [SV946: $i,SV1466: $i,SV1507: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ SV1507 @ SV1466 @ SV946 )
= $false )
| ( ( c_Order__Relation_Opreorder__on @ SV1507 @ SV1466 @ SV946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5140,plain,
! [SV946: $i,SV1467: $i,SV1508: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ SV1508 @ SV1467 @ SV946 )
= $false )
| ( ( c_Relation_Oantisym @ SV1508 @ SV946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5141,plain,
! [SV1533: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ SV1533 @ SV1533 ) @ v_L )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5142,plain,
( ( ( ( sK6_B_x != sK7_SY705 ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[5045]) ).
thf(5143,plain,
( ( ( ~ ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[5046]) ).
thf(5144,plain,
! [SV1353: $i,SV947: $i,SV1401: $i] :
( ( ( c_Relation_Otrans @ SV1401 @ SV947 )
= $false )
| ( ( c_Relation_Oirrefl @ SV1401 @ SV947 )
= $false )
| ( ( ~ ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5047]) ).
thf(5145,plain,
! [SV947: $i,SV1551: $i] :
( ( ! [SY3670: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY3670 @ SV1551 @ SV947 )
| ( c_Relation_Oirrefl @ SY3670 @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5048]) ).
thf(5146,plain,
! [SV947: $i,SV1552: $i] :
( ( ! [SY3671: $i] :
( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SY3671 @ SV1552 @ SV947 )
| ( c_Relation_Otrans @ SY3671 @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5049]) ).
thf(5147,plain,
! [SV947: $i,SV1469: $i,SV1509: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1509 @ SV1469 @ SV947 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1509 @ SV1469 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5050]) ).
thf(5148,plain,
! [SV948: $i,SV1091: $i,SV1510: $i] :
( ( ( SV1510 = SV1091 )
= $false )
| ( ( ! [SY3654: $i] : ( c_member @ SY3654 @ SV1510 @ ( c_Set_Oinsert @ SY3654 @ SV1091 @ SV948 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5149,plain,
! [SV1091: $i,SV948: $i,SV1511: $i,SV1534: $i] :
( ( ( ~ ( c_member @ SV1534 @ SV1511 @ SV948 ) )
= $true )
| ( ( c_member @ SV1534 @ SV1511 @ ( c_Set_Oinsert @ SV1534 @ SV1091 @ SV948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5053]) ).
thf(5150,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1553: $i,SV1512: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5054]) ).
thf(5151,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1472: $i,SV1513: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false )
| ( ( ~ ( ~ ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5152,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5153,plain,
! [SV952: $i,SV1473: $i,SV1095: $i,SV1405: $i] :
( ( ( SV1405 = SV1095 )
= $false )
| ( ( SV1405 = SV1095 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1473 @ SV1473 ) @ ( c_Product__Type_OPair @ SV1473 @ SV1473 @ SV1405 @ SV1095 ) @ ( c_Transitive__Closure_Ortrancl @ SV1473 @ SV952 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5154,plain,
! [SV1439: $i,SV1474: $i] :
( ( ( SV1474 = SV1439 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1474 @ SV1439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5155,plain,
! [SV1440: $i,SV1475: $i] :
( ( ( SV1475 = SV1440 )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1440 @ SV1475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5156,plain,
! [SV955: $i,SV1098: $i,SV1515: $i,SV1535: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1535 @ ( c_Set_Oinsert @ ( tc_prod @ SV1535 @ SV1535 ) @ ( c_Product__Type_OPair @ SV1535 @ SV1535 @ SV1515 @ SV1098 ) @ SV955 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1535 @ SV955 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(5157,plain,
! [SV955: $i,SV1098: $i,SV1516: $i,SV1536: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1536 @ ( c_Set_Oinsert @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1516 @ SV1098 ) @ SV955 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1098 @ SV1516 ) @ ( c_Transitive__Closure_Ortrancl @ SV1536 @ SV955 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(5158,plain,
! [SV974: $i,SV1210: $i,SV813: $i,SV1116: $i,SV1293: $i,SV1363: $i] :
( ( ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV813 ) @ SV1210 )
= $false )
| ( ( SV974 = SV813 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1363 @ SV1293 ) @ ( c_Product__Type_OPair @ SV1363 @ SV1293 @ SV1116 @ SV974 ) @ SV1210 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1363 @ SV1293 @ SV1210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5067]) ).
thf(5159,plain,
! [SV1120: $i,SV1212: $i,SV817: $i,SV978: $i,SV1295: $i] :
( ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV978 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV817 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV817 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1295 @ SV1295 ) @ ( c_Product__Type_OPair @ SV1295 @ SV1295 @ SV1120 @ SV978 ) @ ( c_Transitive__Closure_Ortrancl @ SV1295 @ SV1212 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1295 @ SV1295 @ SV1212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5160,plain,
! [SV1238: $i,SV1368: $i,SV1442: $i,SV857: $i,SV1017: $i,SV1312: $i,SV1152: $i,SV1408: $i] :
( ( ( c_member @ ( tc_prod @ SV1408 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1408 @ SV1152 @ SV1312 @ SV1017 ) @ SV857 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1442 @ SV1152 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1152 @ SV1368 @ SV1017 ) @ ( c_Relation_Orel__comp @ SV1442 @ SV1408 @ SV1152 @ SV1238 @ SV857 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1442 @ SV1408 ) @ ( c_Product__Type_OPair @ SV1442 @ SV1408 @ SV1368 @ SV1312 ) @ SV1238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5069]) ).
thf(5161,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5071]) ).
thf(5162,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5071]) ).
thf(5163,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1413: $i,SV1443: $i,SV1320: $i,SV1373: $i,SV904: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5074]) ).
thf(5164,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5077]) ).
thf(5165,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5077]) ).
thf(5166,plain,
! [SV906: $i,SV1478: $i,SV1324: $i,SV1554: $i,SV1377: $i] :
( ( ( ~ ( c_member @ SV1377 @ SV1554 @ SV1324 )
| ( SV1478 = SV1554 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SV1554 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1554 @ SV1478 ) @ SV906 ) )
= $true )
| ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5078]) ).
thf(5167,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5081]) ).
thf(5168,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ~ ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5081]) ).
thf(5169,plain,
! [SV910: $i,SV1520: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 )
= $false )
| ( ( ! [SY3660: $i] :
( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SY3660 ) @ SV910 )
| ( SV1520 = SY3660 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5170,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ! [SY3562: $i,SY3563: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3563 @ SY3562 ) @ ( tc_prod @ SY3563 @ SY3562 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3562 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3563 @ SY3562 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3563 @ SY3563 ) @ ( c_Product__Type_OPair @ SY3563 @ SY3563 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5083]) ).
thf(5171,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i] :
( ( ! [SY3564: $i,SY3565: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3565 @ SY3564 ) @ ( tc_prod @ SY3565 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3564 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3565 @ SY3564 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SY3564 @ SY3564 ) @ ( c_Product__Type_OPair @ SY3564 @ SY3564 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3565 @ SY3565 ) @ ( c_Product__Type_OPair @ SY3565 @ SY3565 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5084]) ).
thf(5172,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1251: $i,SV1382: $i] :
( ( ! [SY3566: $i] :
( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SY3566 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3566 @ SY3566 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3567: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3567 @ SY3566 ) @ ( tc_prod @ SY3567 @ SY3566 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3567 @ SY3566 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3567 @ SY3566 @ SV1061 @ SV911 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5085]) ).
thf(5173,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1061: $i,SV1251: $i,SV1382: $i] :
( ( ! [SY3568: $i,SY3569: $i] :
( ~ ( c_member @ ( tc_prod @ SY3569 @ SY3569 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3569 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3569 @ SY3568 ) @ ( tc_prod @ SY3569 @ SY3568 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3569 @ SY3568 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3569 @ SY3568 @ SV1061 @ SV911 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5086]) ).
thf(5174,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK78_SY740 @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
= $true )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5088]) ).
thf(5175,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5089]) ).
thf(5176,plain,
! [SV1444: $i,SV1253: $i,SV1555: $i,SV1484: $i,SV1331: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SV1555 ) @ SV1253 )
| ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1555 ) @ SV1253 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 )
= $false )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5090]) ).
thf(5177,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( c_member @ ( tc_prod @ SV1332 @ SV1332 ) @ ( c_Product__Type_OPair @ SV1332 @ SV1332 @ ( sK34_SY725 @ SV1332 @ SV1254 ) @ ( sK33_B_x @ SV1332 @ SV1254 ) ) @ SV1254 )
= $true )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5091]) ).
thf(5178,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ( ( sK33_B_x @ SV1332 @ SV1254 )
!= ( sK34_SY725 @ SV1332 @ SV1254 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5092]) ).
thf(5179,plain,
! [SV1255: $i,SV1445: $i,SV1485: $i,SV1333: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1485 @ SV1445 ) @ SV1255 ) )
= $true )
| ( ( SV1445 = SV1485 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SV1485 ) @ SV1255 )
= $false )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5180,plain,
! [SV1063: $i,SV1414: $i,SV1448: $i,SV914: $i,SV1521: $i,SV1171: $i] :
( ( ( c_member @ SV1171 @ SV1521 @ SV914 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SV1521 @ SV1414 ) @ SV1063 ) )
= $true )
| ( ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5096]) ).
thf(5181,plain,
! [SV914: $i,SV1063: $i,SV1415: $i,SV1449: $i,SV1171: $i] :
( ( ( ~ ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 ) )
= $false )
| ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5097]) ).
thf(5182,plain,
! [SV914: $i,SV1063: $i,SV1415: $i,SV1449: $i,SV1171: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 ) )
= $false )
| ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5097]) ).
thf(5183,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1537: $i,SV1488: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(5184,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1489: $i] :
( ( ( ~ ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) )
| ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5185,plain,
! [SV920: $i,SV1538: $i,SV1556: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1556 @ SV1538 )
| ( SV1556 = SV1538 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1538 @ SV1556 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1538 ) @ SV1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5102]) ).
thf(5186,plain,
! [SV920: $i,SV1539: $i,SV1557: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1557 @ SV1539 )
| ( SV1557 = SV1539 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5103]) ).
thf(5187,plain,
! [SV920: $i,SV1540: $i,SV1558: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1558 @ SV1540 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SV1558 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5104]) ).
thf(5188,plain,
! [SV920: $i,SV1541: $i,SV1559: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5105]) ).
thf(5189,plain,
! [SV1560: $i,SV1542: $i,SV920: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) )
| ( SV1560 = SV1542 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SV1560 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5106]) ).
thf(5190,plain,
! [SV1561: $i,SV1543: $i,SV920: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
| ( SV1561 = SV1543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5107]) ).
thf(5191,plain,
! [SV1562: $i,SV1544: $i,SV920: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5108]) ).
thf(5192,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5109]) ).
thf(5193,plain,
! [SV928: $i,SV1074: $i,SV1491: $i,SV1564: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1564 @ SV1491 @ SV1074 ) @ SV928 ) )
= $true )
| ( ( SV1491 = SV928 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5112]) ).
thf(5194,plain,
! [SV928: $i,SV1074: $i,SV1547: $i,SV1565: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1565 @ SV1547 @ SV1074 ) @ SV928 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1074 @ SV928 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5113]) ).
thf(5195,plain,
! [SV1075: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV1179: $i,SV1265: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5196,plain,
! [SV930: $i,SV1076: $i,SV1492: $i,SV1523: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1523 @ ( c_Set_Oinsert @ ( tc_prod @ SV1523 @ SV1523 ) @ ( c_Product__Type_OPair @ SV1523 @ SV1523 @ SV1492 @ SV1076 ) @ SV930 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV1523 @ SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5197,plain,
! [SV930: $i,SV1076: $i,SV1493: $i,SV1524: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1524 @ ( c_Set_Oinsert @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1493 @ SV1076 ) @ SV930 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1076 @ SV1493 ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ SV930 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5198,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5117]) ).
thf(5199,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5117]) ).
thf(5200,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 )
| ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $false )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5201,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) )
| ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) )
= $false )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5202,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i,SV1495: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1495 @ SV1495 ) @ ( c_Product__Type_OPair @ SV1495 @ SV1495 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5120]) ).
thf(5203,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1462: $i,SV1495: $i,SV1269: $i] :
( ( ( ~ ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5120]) ).
thf(5204,plain,
! [SV1463: $i,SV933: $i,SV1269: $i,SV1181: $i,SV1079: $i,SV1566: $i,SV1496: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SV1566 @ SV1079 ) @ SV1181 )
| ( ( hAPP @ SV1269 @ SV1566 )
= ( hAPP @ SV933 @ SV1566 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5121]) ).
thf(5205,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1567: $i] :
( ( ( ! [SY3672: $i] :
( ( c_Product__Type_OPair @ SY3672 @ SV1567 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SY3672 @ SV1567 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1271 = SV1082 )
= $false )
| ( ( SV1183 = SV936 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5124]) ).
thf(5206,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1568: $i] :
( ( ( ! [SY3673: $i] :
( ( c_Product__Type_OPair @ SY3673 @ SV1568 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3673 @ SV1568 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1271 = SV1082 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5125]) ).
thf(5207,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1569: $i] :
( ( ( ! [SY3674: $i] :
( ( c_Product__Type_OPair @ SY3674 @ SV1569 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SY3674 @ SV1569 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1183 = SV936 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5126]) ).
thf(5208,plain,
! [SV937: $i,SV1083: $i,SV1497: $i,SV1527: $i] :
( ( ( SV1527 = SV1497 )
= $false )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1527 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5127]) ).
thf(5209,plain,
! [SV937: $i,SV1083: $i,SV1498: $i,SV1528: $i] :
( ( ( SV1528 = SV1498 )
= $false )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1528 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5210,plain,
! [SV937: $i,SV1083: $i,SV1499: $i,SV1529: $i] :
( ( ( SV1529 = SV1499 )
= $false )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1499 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5129]) ).
thf(5211,plain,
! [SV937: $i,SV1083: $i,SV1500: $i,SV1548: $i] :
( ( ( SV1548 = SV1500 )
= $false )
| ( ( ( c_member @ SV1083 @ SV937 @ SV1500 )
| ~ ( c_member @ SV1083 @ SV937 @ SV1500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5130]) ).
thf(5212,plain,
! [SV940: $i,SV1085: $i,SV1501: $i,SV1549: $i] :
( ( ( c_member @ ( tc_prod @ SV1549 @ SV1549 ) @ ( c_Product__Type_OPair @ SV1549 @ SV1549 @ SV1501 @ SV1085 ) @ ( c_Relation_OId__on @ SV1549 @ SV940 ) )
= $false )
| ( ( SV1501 = SV1085 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5132]) ).
thf(5213,plain,
! [SV940: $i,SV1085: $i,SV1502: $i,SV1530: $i] :
( ( ( c_member @ ( tc_prod @ SV1530 @ SV1530 ) @ ( c_Product__Type_OPair @ SV1530 @ SV1530 @ SV1502 @ SV1085 ) @ ( c_Relation_OId__on @ SV1530 @ SV940 ) )
= $false )
| ( ( c_member @ SV1530 @ SV1502 @ SV940 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5133]) ).
thf(5214,plain,
! [SV943: $i,SV1088: $i,SV1503: $i,SV1550: $i] :
( ( ( c_member @ ( tc_prod @ SV1550 @ SV1550 ) @ ( c_Product__Type_OPair @ SV1550 @ SV1550 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1550 @ SV943 ) )
= $false )
| ( ( ( SV1503 != SV1088 )
| ( SV1503 = SV1088 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5134]) ).
thf(5215,plain,
! [SV943: $i,SV1088: $i,SV1504: $i,SV1531: $i] :
( ( ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1531 @ SV943 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1531 @ SV943 ) )
| ( SV1504 = SV1088 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5135]) ).
thf(5216,plain,
! [SV943: $i,SV1532: $i,SV1088: $i,SV1505: $i] :
( ( ( SV1505 = SV1088 )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1532 @ SV943 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1532 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5217,plain,
! [SV943: $i,SV1088: $i,SV1506: $i,SV1570: $i] :
( ( ( c_member @ ( tc_prod @ SV1570 @ SV1570 ) @ ( c_Product__Type_OPair @ SV1570 @ SV1570 @ SV1506 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1570 @ SV943 ) )
= $true )
| ( ( SV1506 = SV1088 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5137]) ).
thf(5218,plain,
( ( ( sK6_B_x = sK7_SY705 )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5219,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
| ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5220,plain,
! [SV947: $i,SV1353: $i,SV1401: $i] :
( ( ( c_Relation_Ototal__on @ SV1401 @ SV1353 @ SV947 )
= $false )
| ( ( c_Relation_Oirrefl @ SV1401 @ SV947 )
= $false )
| ( ( c_Relation_Otrans @ SV1401 @ SV947 )
= $false )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1401 @ SV1353 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5221,plain,
! [SV947: $i,SV1551: $i,SV1571: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1571 @ SV1551 @ SV947 )
| ( c_Relation_Oirrefl @ SV1571 @ SV947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5145]) ).
thf(5222,plain,
! [SV947: $i,SV1552: $i,SV1572: $i] :
( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1572 @ SV1552 @ SV947 )
| ( c_Relation_Otrans @ SV1572 @ SV947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5146]) ).
thf(5223,plain,
! [SV948: $i,SV1091: $i,SV1510: $i,SV1573: $i] :
( ( ( c_member @ SV1573 @ SV1510 @ ( c_Set_Oinsert @ SV1573 @ SV1091 @ SV948 ) )
= $true )
| ( ( SV1510 = SV1091 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5148]) ).
thf(5224,plain,
! [SV1091: $i,SV948: $i,SV1511: $i,SV1534: $i] :
( ( ( c_member @ SV1534 @ SV1511 @ SV948 )
= $false )
| ( ( c_member @ SV1534 @ SV1511 @ ( c_Set_Oinsert @ SV1534 @ SV1091 @ SV948 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5149]) ).
thf(5225,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1553: $i,SV1512: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) ) )
= $true )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5226,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1513: $i] :
( ( ( ~ ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) )
| ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5227,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5152]) ).
thf(5228,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5152]) ).
thf(5229,plain,
! [SV955: $i,SV1098: $i,SV1515: $i,SV1535: $i] :
( ( ( c_Wellfounded_Owf @ SV1535 @ ( c_Set_Oinsert @ ( tc_prod @ SV1535 @ SV1535 ) @ ( c_Product__Type_OPair @ SV1535 @ SV1535 @ SV1515 @ SV1098 ) @ SV955 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1535 @ SV955 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5230,plain,
! [SV955: $i,SV1098: $i,SV1516: $i,SV1536: $i] :
( ( ( c_Wellfounded_Owf @ SV1536 @ ( c_Set_Oinsert @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1516 @ SV1098 ) @ SV955 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1098 @ SV1516 ) @ ( c_Transitive__Closure_Ortrancl @ SV1536 @ SV955 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5157]) ).
thf(5231,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) @ SV1056 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5161]) ).
thf(5232,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5162]) ).
thf(5233,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5163]) ).
thf(5234,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( c_member @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ SV1323 )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5164]) ).
thf(5235,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5165]) ).
thf(5236,plain,
! [SV906: $i,SV1478: $i,SV1324: $i,SV1554: $i,SV1377: $i] :
( ( ( ~ ( c_member @ SV1377 @ SV1554 @ SV1324 ) )
= $true )
| ( ( ( SV1478 = SV1554 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SV1554 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1554 @ SV1478 ) @ SV906 ) )
= $true )
| ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5166]) ).
thf(5237,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( c_member @ ( tc_prod @ SV1380 @ SV1327 ) @ ( c_Product__Type_OPair @ SV1380 @ SV1327 @ ( sK51_B_x @ SV1380 @ SV1327 @ SV910 ) @ ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) @ SV910 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5167]) ).
thf(5238,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
!= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5168]) ).
thf(5239,plain,
! [SV1520: $i,SV910: $i,SV1574: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1574 ) @ SV910 )
| ( SV1520 = SV1574 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5169]) ).
thf(5240,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1575: $i] :
( ( ! [SY3675: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3675 @ SV1575 ) @ ( tc_prod @ SY3675 @ SV1575 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3675 @ SV1575 ) @ ( tc_prod @ SY3675 @ SV1575 ) @ ( c_Product__Type_OPair @ SY3675 @ SV1575 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3675 @ SV1575 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3675 @ SV1575 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SY3675 @ SY3675 ) @ ( c_Product__Type_OPair @ SY3675 @ SY3675 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5170]) ).
thf(5241,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1576: $i] :
( ( ! [SY3676: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY3676 @ SV1576 ) @ ( tc_prod @ SY3676 @ SV1576 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3676 @ SV1576 ) @ ( tc_prod @ SY3676 @ SV1576 ) @ ( c_Product__Type_OPair @ SY3676 @ SV1576 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3676 @ SV1576 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3676 @ SV1576 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SV1576 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1576 @ SV1576 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SY3676 @ SY3676 ) @ ( c_Product__Type_OPair @ SY3676 @ SY3676 @ SV1382 @ SV1251 ) @ SV1061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5171]) ).
thf(5242,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1577: $i,SV1251: $i,SV1382: $i] :
( ( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 )
| ! [SY3677: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3677 @ SV1577 @ SV1061 @ SV911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5172]) ).
thf(5243,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1578: $i,SV1061: $i,SV1251: $i,SV1382: $i] :
( ( ! [SY3678: $i] :
( ~ ( c_member @ ( tc_prod @ SY3678 @ SY3678 ) @ ( c_Product__Type_OPair @ SY3678 @ SY3678 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY3678 @ SV1578 ) @ ( tc_prod @ SY3678 @ SV1578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3678 @ SV1578 ) @ ( tc_prod @ SY3678 @ SV1578 ) @ ( c_Product__Type_OPair @ SY3678 @ SV1578 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3678 @ SV1578 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3678 @ SV1578 @ SV1061 @ SV911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5173]) ).
thf(5244,plain,
! [SV1252: $i,SV1330: $i] :
( ( ( c_member @ ( tc_prod @ SV1330 @ SV1330 ) @ ( c_Product__Type_OPair @ SV1330 @ SV1330 @ ( sK77_B_x @ SV1330 @ SV1252 ) @ ( sK79_SY742 @ SV1330 @ SV1252 ) ) @ SV1252 )
= $false )
| ( ( c_Relation_Otrans @ SV1330 @ SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5175]) ).
thf(5245,plain,
! [SV1444: $i,SV1253: $i,SV1555: $i,SV1484: $i,SV1331: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SV1555 ) @ SV1253 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1555 ) @ SV1253 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 )
= $false )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5176]) ).
thf(5246,plain,
! [SV1254: $i,SV1332: $i] :
( ( ( ( sK33_B_x @ SV1332 @ SV1254 )
= ( sK34_SY725 @ SV1332 @ SV1254 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1332 @ SV1254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5178]) ).
thf(5247,plain,
! [SV1255: $i,SV1445: $i,SV1485: $i,SV1333: $i] :
( ( ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1485 @ SV1445 ) @ SV1255 )
= $false )
| ( ( SV1445 = SV1485 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1333 @ SV1333 ) @ ( c_Product__Type_OPair @ SV1333 @ SV1333 @ SV1445 @ SV1485 ) @ SV1255 )
= $false )
| ( ( c_Relation_Oantisym @ SV1333 @ SV1255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5248,plain,
! [SV914: $i,SV1063: $i,SV1414: $i,SV1521: $i,SV1448: $i,SV1171: $i] :
( ( ( c_member @ ( tc_prod @ SV1171 @ SV1448 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1448 @ SV1521 @ SV1414 ) @ SV1063 )
= $false )
| ( ( c_member @ SV1171 @ SV1521 @ SV914 )
= $false )
| ( ( c_member @ SV1448 @ SV1414 @ ( c_Relation_OImage @ SV1171 @ SV1448 @ SV1063 @ SV914 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5249,plain,
! [SV914: $i,SV1063: $i,SV1415: $i,SV1449: $i,SV1171: $i] :
( ( ( c_member @ SV1171 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV914 )
= $true )
| ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5181]) ).
thf(5250,plain,
! [SV914: $i,SV1063: $i,SV1415: $i,SV1449: $i,SV1171: $i] :
( ( ( c_member @ ( tc_prod @ SV1171 @ SV1449 ) @ ( c_Product__Type_OPair @ SV1171 @ SV1449 @ ( sK24_B_x @ SV1449 @ SV1415 @ SV1171 @ SV1063 @ SV914 ) @ SV1415 ) @ SV1063 )
= $true )
| ( ( c_member @ SV1449 @ SV1415 @ ( c_Relation_OImage @ SV1171 @ SV1449 @ SV1063 @ SV914 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5182]) ).
thf(5251,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1537: $i,SV1488: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5252,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1489: $i] :
( ( ( ~ ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5184]) ).
thf(5253,plain,
! [SV1259: $i,SV1455: $i,SV1489: $i,SV1067: $i,SV919: $i,SV1174: $i] :
( ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5184]) ).
thf(5254,plain,
! [SV920: $i,SV1538: $i,SV1556: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1556 @ SV1538 )
= $true )
| ( ( ( SV1556 = SV1538 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1538 @ SV1556 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1538 ) @ SV1556 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5185]) ).
thf(5255,plain,
! [SV920: $i,SV1539: $i,SV1557: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1557 @ SV1539 )
= $true )
| ( ( ( SV1557 = SV1539 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(5256,plain,
! [SV920: $i,SV1540: $i,SV1558: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1558 @ SV1540 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SV1558 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5257,plain,
! [SV920: $i,SV1541: $i,SV1559: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(5258,plain,
! [SV1560: $i,SV1542: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) ) )
= $true )
| ( ( ( SV1560 = SV1542 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SV1560 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5259,plain,
! [SV1561: $i,SV1543: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true )
| ( ( ( SV1561 = SV1543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5260,plain,
! [SV1562: $i,SV1544: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5261,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5192]) ).
thf(5262,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5263,plain,
! [SV930: $i,SV1493: $i,SV1076: $i,SV1524: $i] :
( ( ( c_member @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1076 @ SV1493 ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ SV930 ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV1524 @ ( c_Set_Oinsert @ ( tc_prod @ SV1524 @ SV1524 ) @ ( c_Product__Type_OPair @ SV1524 @ SV1524 @ SV1493 @ SV1076 ) @ SV930 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5264,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) ) @ SV932 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5198]) ).
thf(5265,plain,
! [SV932: $i,SV1078: $i,SV1180: $i,SV1266: $i,SV1344: $i,SV1395: $i,SV1430: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ ( sK46_B_a @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) @ ( sK47_SY726 @ SV1430 @ SV1395 @ SV1344 @ SV1266 @ SV1180 @ SV1078 @ SV932 ) ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 )
= ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1430 @ SV1395 ) @ ( tc_prod @ SV1430 @ SV1395 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1344 @ SV1266 ) @ ( c_Product__Type_OPair @ SV1430 @ SV1395 @ SV1180 @ SV1078 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1430 @ SV1395 ) @ SV932 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5199]) ).
thf(5266,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 ) )
= $false )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5200]) ).
thf(5267,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( ~ ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $false )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5200]) ).
thf(5268,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ~ ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) ) )
= $false )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5201]) ).
thf(5269,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ~ ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 ) )
= $false )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5201]) ).
thf(5270,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1269: $i,SV1462: $i,SV1495: $i] :
( ( ( c_member @ ( tc_prod @ SV1495 @ SV1495 ) @ ( c_Product__Type_OPair @ SV1495 @ SV1495 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) @ SV1079 ) @ SV1181 )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5202]) ).
thf(5271,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1462: $i,SV1495: $i,SV1269: $i] :
( ( ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
!= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5203]) ).
thf(5272,plain,
! [SV1463: $i,SV933: $i,SV1269: $i,SV1181: $i,SV1079: $i,SV1566: $i,SV1496: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SV1566 @ SV1079 ) @ SV1181 ) )
= $true )
| ( ( ( hAPP @ SV1269 @ SV1566 )
= ( hAPP @ SV933 @ SV1566 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5204]) ).
thf(5273,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1567: $i,SV1579: $i] :
( ( ( ( c_Product__Type_OPair @ SV1579 @ SV1567 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SV1579 @ SV1567 @ SV1082 @ SV936 ) )
= $true )
| ( ( SV1271 = SV1082 )
= $false )
| ( ( SV1183 = SV936 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5205]) ).
thf(5274,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1568: $i,SV1580: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV1580 @ SV1568 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SV1580 @ SV1568 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1271 = SV1082 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5206]) ).
thf(5275,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1569: $i,SV1581: $i] :
( ( ( ( ( c_Product__Type_OPair @ SV1581 @ SV1569 @ SV1271 @ SV1183 )
!= ( c_Product__Type_OPair @ SV1581 @ SV1569 @ SV1082 @ SV936 ) ) )
= $true )
| ( ( SV1183 = SV936 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5207]) ).
thf(5276,plain,
! [SV1497: $i,SV1527: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1527 )
= $true )
| ( ( ~ ( c_member @ SV1083 @ SV937 @ SV1527 ) )
= $true )
| ( ( SV1527 = SV1497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5208]) ).
thf(5277,plain,
! [SV1498: $i,SV1528: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1528 )
= $true )
| ( ( ~ ( c_member @ SV1083 @ SV937 @ SV1498 ) )
= $true )
| ( ( SV1528 = SV1498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5278,plain,
! [SV1529: $i,SV1499: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1499 )
= $true )
| ( ( ~ ( c_member @ SV1083 @ SV937 @ SV1529 ) )
= $true )
| ( ( SV1529 = SV1499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5279,plain,
! [SV1548: $i,SV1500: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1500 )
= $true )
| ( ( ~ ( c_member @ SV1083 @ SV937 @ SV1500 ) )
= $true )
| ( ( SV1548 = SV1500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5211]) ).
thf(5280,plain,
! [SV943: $i,SV1550: $i,SV1088: $i,SV1503: $i] :
( ( ( ( SV1503 != SV1088 ) )
= $true )
| ( ( SV1503 = SV1088 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1550 @ SV1550 ) @ ( c_Product__Type_OPair @ SV1550 @ SV1550 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1550 @ SV943 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5214]) ).
thf(5281,plain,
! [SV943: $i,SV1088: $i,SV1504: $i,SV1531: $i] :
( ( ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1531 @ SV943 ) )
= $true )
| ( ( SV1504 = SV1088 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1531 @ SV1531 ) @ ( c_Product__Type_OPair @ SV1531 @ SV1531 @ SV1504 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1531 @ SV943 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5282,plain,
! [SV943: $i,SV1088: $i,SV1505: $i,SV1532: $i] :
( ( ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Otrancl @ SV1532 @ SV943 ) )
= $false )
| ( ( SV1505 = SV1088 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1532 @ SV1532 ) @ ( c_Product__Type_OPair @ SV1532 @ SV1532 @ SV1505 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1532 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5216]) ).
thf(5283,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[5219]) ).
thf(5284,plain,
( ( ( ~ ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[5219]) ).
thf(5285,plain,
! [SV947: $i,SV1551: $i,SV1571: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1571 @ SV1551 @ SV947 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV1571 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5286,plain,
! [SV947: $i,SV1552: $i,SV1572: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1572 @ SV1552 @ SV947 ) )
= $true )
| ( ( c_Relation_Otrans @ SV1572 @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5222]) ).
thf(5287,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1553: $i,SV1512: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
| ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
= $false )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5225]) ).
thf(5288,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1513: $i] :
( ( ( ~ ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5226]) ).
thf(5289,plain,
! [SV1092: $i,SV1280: $i,SV1472: $i,SV1513: $i,SV1189: $i,SV949: $i] :
( ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5226]) ).
thf(5290,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5227]) ).
thf(5291,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5228]) ).
thf(5292,plain,
! [SV955: $i,SV1516: $i,SV1098: $i,SV1536: $i] :
( ( ( c_member @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1098 @ SV1516 ) @ ( c_Transitive__Closure_Ortrancl @ SV1536 @ SV955 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV1536 @ ( c_Set_Oinsert @ ( tc_prod @ SV1536 @ SV1536 ) @ ( c_Product__Type_OPair @ SV1536 @ SV1536 @ SV1516 @ SV1098 ) @ SV955 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5230]) ).
thf(5293,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5232]) ).
thf(5294,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5233]) ).
thf(5295,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
| ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5235]) ).
thf(5296,plain,
! [SV906: $i,SV1478: $i,SV1324: $i,SV1554: $i,SV1377: $i] :
( ( ( c_member @ SV1377 @ SV1554 @ SV1324 )
= $false )
| ( ( ( SV1478 = SV1554 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SV1554 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1554 @ SV1478 ) @ SV906 ) )
= $true )
| ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5236]) ).
thf(5297,plain,
! [SV910: $i,SV1327: $i,SV1380: $i] :
( ( ( ( sK52_SY730 @ SV1380 @ SV1327 @ SV910 )
= ( sK53_SY732 @ SV1380 @ SV1327 @ SV910 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1380 @ SV1327 @ SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5298,plain,
! [SV1520: $i,SV910: $i,SV1574: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1574 ) @ SV910 ) )
= $true )
| ( ( SV1520 = SV1574 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5239]) ).
thf(5299,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1575: $i,SV1582: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1582 @ SV1575 @ SV1061 @ SV911 ) )
| ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SV1582 @ SV1582 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1582 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5240]) ).
thf(5300,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1576: $i,SV1583: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1583 @ SV1576 @ SV1061 @ SV911 ) )
| ( c_member @ ( tc_prod @ SV1576 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1576 @ SV1576 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SV1583 @ SV1583 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1583 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5241]) ).
thf(5301,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1577: $i,SV1251: $i,SV1382: $i] :
( ( ( ( SV1382 != SV1251 )
| ~ ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 ) )
= $true )
| ( ( ! [SY3677: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3677 @ SV1577 @ SV1061 @ SV911 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5242]) ).
thf(5302,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1578: $i,SV1061: $i,SV1251: $i,SV1382: $i,SV1584: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV1584 @ SV1584 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1584 @ SV1382 @ SV1251 ) @ SV1061 )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1584 @ SV1578 @ SV1061 @ SV911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5243]) ).
thf(5303,plain,
! [SV1444: $i,SV1253: $i,SV1555: $i,SV1484: $i,SV1331: $i] :
( ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1484 @ SV1555 ) @ SV1253 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1555 ) @ SV1253 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1331 @ SV1331 ) @ ( c_Product__Type_OPair @ SV1331 @ SV1331 @ SV1444 @ SV1484 ) @ SV1253 )
= $false )
| ( ( c_Relation_Otrans @ SV1331 @ SV1253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5245]) ).
thf(5304,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1537: $i,SV1488: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5251]) ).
thf(5305,plain,
! [SV919: $i,SV1067: $i,SV1537: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1488: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5251]) ).
thf(5306,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1489: $i] :
( ( ( ! [SY3639: $i] :
( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SY3639 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SY3639 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SY3639 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5252]) ).
thf(5307,plain,
! [SV1259: $i,SV1455: $i,SV1489: $i,SV1067: $i,SV919: $i,SV1174: $i] :
( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
= ( hAPP @ ( hAPP @ SV1174 @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) @ SV1067 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5253]) ).
thf(5308,plain,
! [SV920: $i,SV1538: $i,SV1556: $i] :
( ( ( SV1556 = SV1538 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1538 @ SV1556 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1538 ) @ SV1556 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1556 @ SV1538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5309,plain,
! [SV920: $i,SV1539: $i,SV1557: $i] :
( ( ( SV1557 = SV1539 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1557 @ SV1539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5310,plain,
! [SV1558: $i,SV1540: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SV1558 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1558 @ SV1540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5256]) ).
thf(5311,plain,
! [SV1559: $i,SV1541: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5257]) ).
thf(5312,plain,
! [SV1560: $i,SV1542: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) )
= $false )
| ( ( ( SV1560 = SV1542 )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SV1560 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5313,plain,
! [SV1561: $i,SV1543: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $false )
| ( ( ( SV1561 = SV1543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5259]) ).
thf(5314,plain,
! [SV1562: $i,SV1544: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5260]) ).
thf(5315,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5261]) ).
thf(5316,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
| ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5317,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 )
= $true )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5266]) ).
thf(5318,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
= $true )
| ( ( ~ ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5267]) ).
thf(5319,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( ! [SY3620: $i] :
( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SY3620 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SY3620 @ SV1461 ) ) )
= $true )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5268]) ).
thf(5320,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1346: $i] :
( ( ( c_member @ SV1346 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) @ SV1461 )
= $true )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5269]) ).
thf(5321,plain,
! [SV933: $i,SV1079: $i,SV1181: $i,SV1462: $i,SV1495: $i,SV1269: $i] :
( ( ( ( hAPP @ SV1269 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) )
= ( hAPP @ SV933 @ ( sK43_B_y @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 @ SV933 ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1495 @ SV1462 @ SV933 @ SV1181 @ SV1079 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5322,plain,
! [SV1463: $i,SV933: $i,SV1269: $i,SV1181: $i,SV1079: $i,SV1566: $i,SV1496: $i] :
( ( ( c_member @ ( tc_prod @ SV1496 @ SV1496 ) @ ( c_Product__Type_OPair @ SV1496 @ SV1496 @ SV1566 @ SV1079 ) @ SV1181 )
= $false )
| ( ( ( hAPP @ SV1269 @ SV1566 )
= ( hAPP @ SV933 @ SV1566 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV1269 @ SV1181 @ SV1079 )
= ( c_Recdef_Ocut @ SV1496 @ SV1463 @ SV933 @ SV1181 @ SV1079 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5323,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1568: $i,SV1580: $i] :
( ( ( ( c_Product__Type_OPair @ SV1580 @ SV1568 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SV1580 @ SV1568 @ SV1082 @ SV936 ) )
= $false )
| ( ( SV1271 = SV1082 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5324,plain,
! [SV936: $i,SV1082: $i,SV1183: $i,SV1271: $i,SV1569: $i,SV1581: $i] :
( ( ( ( c_Product__Type_OPair @ SV1581 @ SV1569 @ SV1271 @ SV1183 )
= ( c_Product__Type_OPair @ SV1581 @ SV1569 @ SV1082 @ SV936 ) )
= $false )
| ( ( SV1183 = SV936 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5325,plain,
! [SV1497: $i,SV1527: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1527 )
= $false )
| ( ( c_member @ SV1083 @ SV937 @ SV1527 )
= $true )
| ( ( SV1527 = SV1497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5326,plain,
! [SV1528: $i,SV1498: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1498 )
= $false )
| ( ( c_member @ SV1083 @ SV937 @ SV1528 )
= $true )
| ( ( SV1528 = SV1498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5277]) ).
thf(5327,plain,
! [SV1499: $i,SV1529: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1529 )
= $false )
| ( ( c_member @ SV1083 @ SV937 @ SV1499 )
= $true )
| ( ( SV1529 = SV1499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(5328,plain,
! [SV1548: $i,SV1500: $i,SV937: $i,SV1083: $i] :
( ( ( c_member @ SV1083 @ SV937 @ SV1500 )
= $false )
| ( ( c_member @ SV1083 @ SV937 @ SV1500 )
= $true )
| ( ( SV1548 = SV1500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5329,plain,
! [SV943: $i,SV1550: $i,SV1088: $i,SV1503: $i] :
( ( ( SV1503 = SV1088 )
= $false )
| ( ( SV1503 = SV1088 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1550 @ SV1550 ) @ ( c_Product__Type_OPair @ SV1550 @ SV1550 @ SV1503 @ SV1088 ) @ ( c_Transitive__Closure_Ortrancl @ SV1550 @ SV943 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5330,plain,
( ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[5283]) ).
thf(5331,plain,
( ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[5284]) ).
thf(5332,plain,
! [SV947: $i,SV1551: $i,SV1571: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1571 @ SV1551 @ SV947 )
= $false )
| ( ( c_Relation_Oirrefl @ SV1571 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5333,plain,
! [SV947: $i,SV1552: $i,SV1572: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1572 @ SV1552 @ SV947 )
= $false )
| ( ( c_Relation_Otrans @ SV1572 @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5334,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1553: $i,SV1512: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 ) )
= $false )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5335,plain,
! [SV949: $i,SV1092: $i,SV1553: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1512: $i] :
( ( ( ~ ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
= $false )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5336,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1513: $i] :
( ( ( ! [SY3657: $i] :
( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SY3657 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SY3657 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SY3657 ) ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5288]) ).
thf(5337,plain,
! [SV1092: $i,SV1280: $i,SV1472: $i,SV1513: $i,SV1189: $i,SV949: $i] :
( ( ( SV949
= ( hAPP @ ( hAPP @ SV1189 @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) @ SV1092 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5289]) ).
thf(5338,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(5339,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5293]) ).
thf(5340,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5293]) ).
thf(5341,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5294]) ).
thf(5342,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5294]) ).
thf(5343,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5295]) ).
thf(5344,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5295]) ).
thf(5345,plain,
! [SV1324: $i,SV906: $i,SV1377: $i,SV1554: $i,SV1478: $i] :
( ( ( SV1478 = SV1554 )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SV1554 ) @ SV906 )
| ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1554 @ SV1478 ) @ SV906 ) )
= $true )
| ( ( c_member @ SV1377 @ SV1554 @ SV1324 )
= $false )
| ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5346,plain,
! [SV1520: $i,SV910: $i,SV1574: $i,SV1483: $i,SV1328: $i,SV1381: $i] :
( ( ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1574 ) @ SV910 )
= $false )
| ( ( SV1520 = SV1574 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1381 @ SV1328 ) @ ( c_Product__Type_OPair @ SV1381 @ SV1328 @ SV1483 @ SV1520 ) @ SV910 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1381 @ SV1328 @ SV910 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5347,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1575: $i,SV1582: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1582 @ SV1575 @ SV1061 @ SV911 ) ) )
= $true )
| ( ( ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SV1582 @ SV1582 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1582 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5348,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1576: $i,SV1583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1583 @ SV1576 @ SV1061 @ SV911 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV1576 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1576 @ SV1576 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SV1583 @ SV1583 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1583 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5349,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1577: $i,SV1251: $i,SV1382: $i] :
( ( ( ( SV1382 != SV1251 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 ) )
= $true )
| ( ( ! [SY3677: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3677 @ SV1577 @ SV1061 @ SV911 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5301]) ).
thf(5350,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1578: $i,SV1061: $i,SV1251: $i,SV1382: $i,SV1584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1584 @ SV1584 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1584 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1584 @ SV1578 @ SV1061 @ SV911 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5302]) ).
thf(5351,plain,
! [SV919: $i,SV1067: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1537: $i,SV1488: $i] :
( ( ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5304]) ).
thf(5352,plain,
! [SV919: $i,SV1067: $i,SV1537: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1488: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5305]) ).
thf(5353,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1585: $i,SV1489: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SV1585 @ SV1067 ) @ SV1259 )
| ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1585 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1585 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5306]) ).
thf(5354,plain,
! [SV920: $i,SV1556: $i,SV1538: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1538 @ SV1556 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1538 ) @ SV1556 ) )
= $true )
| ( ( SV1556 = SV1538 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1556 @ SV1538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5355,plain,
! [SV1557: $i,SV1539: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
= $true )
| ( ( SV1557 = SV1539 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1557 @ SV1539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(5356,plain,
! [SV1558: $i,SV1540: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SV1558 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1558 @ SV1540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(5357,plain,
! [SV1559: $i,SV1541: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(5358,plain,
! [SV920: $i,SV1542: $i,SV1560: $i] :
( ( ( SV1560 = SV1542 )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SV1560 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(5359,plain,
! [SV920: $i,SV1543: $i,SV1561: $i] :
( ( ( SV1561 = SV1543 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(5360,plain,
! [SV1562: $i,SV1544: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5314]) ).
thf(5361,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5315]) ).
thf(5362,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5316]) ).
thf(5363,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5316]) ).
thf(5364,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1345 @ SV1345 ) @ ( c_Product__Type_OPair @ SV1345 @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ SV1525 ) @ SV1267 )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5365,plain,
! [SV1267: $i,SV1525: $i,SV1345: $i] :
( ( ( c_member @ SV1345 @ SV1525 @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
= $false )
| ( ( c_member @ SV1345 @ ( sK30_SY724 @ SV1525 @ SV1345 @ SV1267 ) @ ( sK29_B_Q @ SV1345 @ SV1267 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV1345 @ SV1267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5366,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1586: $i,SV1346: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SV1586 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
| ~ ( c_member @ SV1346 @ SV1586 @ SV1461 ) )
= $true )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5319]) ).
thf(5367,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK7_SY705 @ sK6_B_x ) @ v_L )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(5368,plain,
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ sK6_B_x @ sK7_SY705 ) @ v_L )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5369,plain,
! [SV949: $i,SV1092: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1553: $i,SV1512: $i] :
( ( ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
= $true )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5334]) ).
thf(5370,plain,
! [SV949: $i,SV1092: $i,SV1553: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1512: $i] :
( ( ( ~ ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) ) )
= $true )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5335]) ).
thf(5371,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1587: $i,SV1513: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SV1587 @ SV1092 ) @ SV1280 )
| ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1587 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1587 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5336]) ).
thf(5372,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5338]) ).
thf(5373,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5338]) ).
thf(5374,plain,
! [SV902: $i,SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i] :
( ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5339]) ).
thf(5375,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5340]) ).
thf(5376,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5341]) ).
thf(5377,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5342]) ).
thf(5378,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
!= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5343]) ).
thf(5379,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5344]) ).
thf(5380,plain,
! [SV1324: $i,SV906: $i,SV1554: $i,SV1478: $i,SV1377: $i] :
( ( ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1478 @ SV1554 ) @ SV906 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1377 @ SV1377 ) @ ( c_Product__Type_OPair @ SV1377 @ SV1377 @ SV1554 @ SV1478 ) @ SV906 )
= $true )
| ( ( SV1478 = SV1554 )
= $true )
| ( ( c_member @ SV1377 @ SV1554 @ SV1324 )
= $false )
| ( ( c_member @ SV1377 @ SV1478 @ SV1324 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1377 @ SV1324 @ SV906 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5345]) ).
thf(5381,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1575: $i,SV1582: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1582 @ SV1575 @ SV1061 @ SV911 ) )
= $false )
| ( ( ( SV1382 = SV1251 )
| ( c_member @ ( tc_prod @ SV1582 @ SV1582 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1582 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5382,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1576: $i,SV1583: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1583 @ SV1576 @ SV1061 @ SV911 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV1576 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1576 @ SV1576 @ SV1329 @ SV1169 ) @ SV911 )
| ( c_member @ ( tc_prod @ SV1583 @ SV1583 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1583 @ SV1382 @ SV1251 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5383,plain,
! [SV1061: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1577: $i,SV1251: $i,SV1382: $i] :
( ( ( SV1382 = SV1251 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 ) )
= $true )
| ( ( ! [SY3677: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3677 @ SV1577 @ SV1061 @ SV911 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5384,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1578: $i,SV1061: $i,SV1251: $i,SV1382: $i,SV1584: $i] :
( ( ( c_member @ ( tc_prod @ SV1584 @ SV1584 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1584 @ SV1382 @ SV1251 ) @ SV1061 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1584 @ SV1578 ) @ ( tc_prod @ SV1584 @ SV1578 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1584 @ SV1578 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1584 @ SV1578 @ SV1061 @ SV911 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5385,plain,
! [SV1259: $i,SV1454: $i,SV1488: $i,SV1537: $i,SV1067: $i,SV919: $i,SV1174: $i] :
( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1488 @ SV1488 ) @ ( c_Product__Type_OPair @ SV1488 @ SV1488 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1067 ) @ SV1259 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5351]) ).
thf(5386,plain,
! [SV919: $i,SV1067: $i,SV1537: $i,SV1174: $i,SV1259: $i,SV1454: $i,SV1488: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
!= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(5387,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1585: $i,SV1489: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SV1585 @ SV1067 ) @ SV1259 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1585 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1585 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5353]) ).
thf(5388,plain,
! [SV1557: $i,SV1539: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1539 ) @ SV1557 ) )
= $true )
| ( ( SV1557 = SV1539 )
= $true )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1557 @ SV1539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5389,plain,
! [SV920: $i,SV1558: $i,SV1540: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1540 @ SV1558 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1540 ) @ SV1558 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1558 @ SV1540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5356]) ).
thf(5390,plain,
! [SV1559: $i,SV1541: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(5391,plain,
! [SV920: $i,SV1560: $i,SV1542: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1542 @ SV1560 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) )
= $true )
| ( ( SV1560 = SV1542 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1542 ) @ SV1560 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5358]) ).
thf(5392,plain,
! [SV1561: $i,SV1543: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $true )
| ( ( SV1561 = SV1543 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5359]) ).
thf(5393,plain,
! [SV1562: $i,SV1544: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false )
| ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5360]) ).
thf(5394,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5395,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) @ SV1075 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5362]) ).
thf(5396,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5363]) ).
thf(5397,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1586: $i,SV1346: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SV1586 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 ) )
= $true )
| ( ( ~ ( c_member @ SV1346 @ SV1586 @ SV1461 ) )
= $true )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5366]) ).
thf(5398,plain,
! [SV1280: $i,SV1471: $i,SV1512: $i,SV1092: $i,SV1553: $i,SV1189: $i,SV949: $i] :
( ( ( SV949
= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1512 @ SV1512 ) @ ( c_Product__Type_OPair @ SV1512 @ SV1512 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1092 ) @ SV1280 )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(5399,plain,
! [SV949: $i,SV1092: $i,SV1553: $i,SV1189: $i,SV1280: $i,SV1471: $i,SV1512: $i] :
( ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) )
= $false )
| ( ( ( SV949
!= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5370]) ).
thf(5400,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1587: $i,SV1513: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SV1587 @ SV1092 ) @ SV1280 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1587 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1587 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5371]) ).
thf(5401,plain,
! [SV951: $i,SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i] :
( ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) @ SV1094 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5372]) ).
thf(5402,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5373]) ).
thf(5403,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5404,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5405,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ( sK67_B_x @ SV1376 @ SV1323 @ SV906 )
= ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5378]) ).
thf(5406,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
| ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5379]) ).
thf(5407,plain,
! [SV911: $i,SV1169: $i,SV1329: $i,SV1575: $i,SV1061: $i,SV1582: $i,SV1251: $i,SV1382: $i] :
( ( ( SV1382 = SV1251 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1582 @ SV1582 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1582 @ SV1382 @ SV1251 ) @ SV1061 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1582 @ SV1575 ) @ ( tc_prod @ SV1582 @ SV1575 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1582 @ SV1575 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1582 @ SV1575 @ SV1061 @ SV911 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5381]) ).
thf(5408,plain,
! [SV1061: $i,SV1251: $i,SV1382: $i,SV1583: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1576: $i] :
( ( ( c_member @ ( tc_prod @ SV1576 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1576 @ SV1576 @ SV1329 @ SV1169 ) @ SV911 )
= $true )
| ( ( c_member @ ( tc_prod @ SV1583 @ SV1583 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1583 @ SV1382 @ SV1251 ) @ SV1061 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1583 @ SV1576 ) @ ( tc_prod @ SV1583 @ SV1576 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1583 @ SV1576 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1583 @ SV1576 @ SV1061 @ SV911 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5382]) ).
thf(5409,plain,
! [SV1061: $i,SV1251: $i,SV1382: $i,SV911: $i,SV1169: $i,SV1329: $i,SV1577: $i] :
( ( ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 )
= $false )
| ( ( SV1382 = SV1251 )
= $false )
| ( ( ! [SY3677: $i] : ( c_member @ ( tc_prod @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY3677 @ SV1577 ) @ ( tc_prod @ SY3677 @ SV1577 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SY3677 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SY3677 @ SV1577 @ SV1061 @ SV911 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5410,plain,
! [SV1259: $i,SV1454: $i,SV1488: $i,SV1537: $i,SV1067: $i,SV919: $i,SV1174: $i] :
( ( ( ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 )
= ( hAPP @ ( hAPP @ SV1174 @ SV1537 ) @ SV1067 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ ( hAPP @ SV1537 @ ( sK60_B_z @ SV1537 @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1488 @ SV1454 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5386]) ).
thf(5411,plain,
! [SV919: $i,SV1174: $i,SV1455: $i,SV1259: $i,SV1067: $i,SV1585: $i,SV1489: $i] :
( ( ( c_member @ ( tc_prod @ SV1489 @ SV1489 ) @ ( c_Product__Type_OPair @ SV1489 @ SV1489 @ SV1585 @ SV1067 ) @ SV1259 )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1585 @ ( hAPP @ ( sK59_B_g @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ SV919 ) @ SV1585 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1489 @ SV1455 @ SV1259 @ SV1174 @ SV1067 @ ( hAPP @ ( hAPP @ SV1174 @ SV919 ) @ SV1067 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5387]) ).
thf(5412,plain,
! [SV1559: $i,SV1541: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1541 ) @ SV1559 ) )
= $false )
| ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1559 @ SV1541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5413,plain,
! [SV1561: $i,SV1543: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $true )
| ( ( SV1561 = SV1543 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1543 ) @ SV1561 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5414,plain,
! [SV920: $i,SV1562: $i,SV1544: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ SV1544 @ SV1562 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1544 ) @ SV1562 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5393]) ).
thf(5415,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5394]) ).
thf(5416,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5417,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1586: $i,SV1346: $i] :
( ( ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SV1586 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
= $false )
| ( ( ~ ( c_member @ SV1346 @ SV1586 @ SV1461 ) )
= $true )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5418,plain,
! [SV1280: $i,SV1471: $i,SV1512: $i,SV1092: $i,SV1553: $i,SV1189: $i,SV949: $i] :
( ( ( SV949
= ( hAPP @ ( hAPP @ SV1189 @ SV1553 ) @ SV1092 ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ ( hAPP @ SV1553 @ ( sK55_B_z @ SV1553 @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) ) )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1512 @ SV1471 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5399]) ).
thf(5419,plain,
! [SV949: $i,SV1189: $i,SV1472: $i,SV1280: $i,SV1092: $i,SV1587: $i,SV1513: $i] :
( ( ( c_member @ ( tc_prod @ SV1513 @ SV1513 ) @ ( c_Product__Type_OPair @ SV1513 @ SV1513 @ SV1587 @ SV1092 ) @ SV1280 )
= $false )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1587 @ ( hAPP @ ( sK54_B_g @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 ) @ SV1587 ) )
= $true )
| ( ( c_Recdef_Owfrec__rel @ SV1513 @ SV1472 @ SV1280 @ SV1189 @ SV1092 @ SV949 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5400]) ).
thf(5420,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5402]) ).
thf(5421,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5403]) ).
thf(5422,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5403]) ).
thf(5423,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5424,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5425,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5406]) ).
thf(5426,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5406]) ).
thf(5427,plain,
! [SV911: $i,SV1061: $i,SV1169: $i,SV1251: $i,SV1329: $i,SV1382: $i,SV1577: $i,SV1588: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1588 @ SV1577 ) @ ( tc_prod @ SV1588 @ SV1577 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1588 @ SV1577 ) @ ( tc_prod @ SV1588 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1588 @ SV1577 @ SV1382 @ SV1329 ) @ ( c_Product__Type_OPair @ SV1588 @ SV1577 @ SV1251 @ SV1169 ) ) @ ( c_Wellfounded_Olex__prod @ SV1588 @ SV1577 @ SV1061 @ SV911 ) )
= $true )
| ( ( SV1382 = SV1251 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1577 @ SV1577 ) @ ( c_Product__Type_OPair @ SV1577 @ SV1577 @ SV1329 @ SV1169 ) @ SV911 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5409]) ).
thf(5428,plain,
! [SV1563: $i,SV1545: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV1545 ) @ SV1563 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5429,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5416]) ).
thf(5430,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5416]) ).
thf(5431,plain,
! [SV1526: $i,SV1268: $i,SV1461: $i,SV1586: $i,SV1346: $i] :
( ( ( c_member @ SV1346 @ SV1586 @ SV1461 )
= $false )
| ( ( c_member @ ( tc_prod @ SV1346 @ SV1346 ) @ ( c_Product__Type_OPair @ SV1346 @ SV1346 @ SV1586 @ ( sK28_B_x @ SV1461 @ SV1346 @ SV1268 ) ) @ SV1268 )
= $false )
| ( ( c_member @ SV1346 @ SV1526 @ SV1461 )
= $false )
| ( ( c_Wellfounded_Owf @ SV1346 @ SV1268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5432,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5420]) ).
thf(5433,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5420]) ).
thf(5434,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( hBOOL @ ( hAPP @ SV902 @ ( sK13_SY707 @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5421]) ).
thf(5435,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5422]) ).
thf(5436,plain,
! [SV904: $i,SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) @ SV1058 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5423]) ).
thf(5437,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5424]) ).
thf(5438,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5425]) ).
thf(5439,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5426]) ).
thf(5440,plain,
! [SV929: $i,SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5429]) ).
thf(5441,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5430]) ).
thf(5442,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( hBOOL @ ( hAPP @ SV951 @ ( sK10_B_y @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5432]) ).
thf(5443,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5433]) ).
thf(5444,plain,
! [SV1056: $i,SV1166: $i,SV1248: $i,SV1319: $i,SV902: $i] :
( ( ( hBOOL @ ( hAPP @ SV902 @ ( sK12_B_y @ SV1319 @ SV1248 @ SV1166 @ SV1056 @ SV902 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1248 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV902 @ SV1166 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1319 @ SV1319 ) @ ( c_Product__Type_OPair @ SV1319 @ SV1319 @ SV1248 @ SV1166 ) @ ( c_Transitive__Closure_Ortrancl @ SV1319 @ SV1056 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5445,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5446,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5447,plain,
! [SV906: $i,SV1323: $i,SV1376: $i] :
( ( ( c_member @ ( tc_prod @ SV1376 @ SV1376 ) @ ( c_Product__Type_OPair @ SV1376 @ SV1376 @ ( sK68_SY735 @ SV1376 @ SV1323 @ SV906 ) @ ( sK67_B_x @ SV1376 @ SV1323 @ SV906 ) ) @ SV906 )
= $false )
| ( ( c_Relation_Ototal__on @ SV1376 @ SV1323 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5448,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5449,plain,
! [SV1094: $i,SV1190: $i,SV1281: $i,SV1356: $i,SV951: $i] :
( ( ( hBOOL @ ( hAPP @ SV951 @ ( sK11_SY706 @ SV1356 @ SV1281 @ SV1190 @ SV1094 @ SV951 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV951 @ SV1281 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV1356 @ SV1356 ) @ ( c_Product__Type_OPair @ SV1356 @ SV1356 @ SV1281 @ SV1190 ) @ ( c_Transitive__Closure_Ortrancl @ SV1356 @ SV1094 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5450,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5445]) ).
thf(5451,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5445]) ).
thf(5452,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5448]) ).
thf(5453,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5448]) ).
thf(5454,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK18_B_a @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK19_SY714 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5450]) ).
thf(5455,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5451]) ).
thf(5456,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK16_SY711 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK17_SY713 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5452]) ).
thf(5457,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5453]) ).
thf(5458,plain,
! [SV1058: $i,SV1167: $i,SV1249: $i,SV1320: $i,SV1373: $i,SV1413: $i,SV1443: $i,SV904: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ ( sK20_SY717 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) @ ( sK21_SY719 @ SV1443 @ SV1413 @ SV1373 @ SV1320 @ SV1249 @ SV1167 @ SV1058 @ SV904 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1249 ) @ SV1167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV904 @ SV1373 ) @ SV1320 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1443 @ SV1413 ) @ ( tc_prod @ SV1443 @ SV1413 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1373 @ SV1320 ) @ ( c_Product__Type_OPair @ SV1443 @ SV1413 @ SV1249 @ SV1167 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1443 @ SV1413 ) @ SV1058 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5459,plain,
! [SV1075: $i,SV1179: $i,SV1265: $i,SV1343: $i,SV1391: $i,SV1426: $i,SV1460: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ ( sK14_B_a @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) @ ( sK15_SY708 @ SV1460 @ SV1426 @ SV1391 @ SV1343 @ SV1265 @ SV1179 @ SV1075 @ SV929 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1391 ) @ SV1343 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV929 @ SV1265 ) @ SV1179 ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV1460 @ SV1426 ) @ ( tc_prod @ SV1460 @ SV1426 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1391 @ SV1343 ) @ ( c_Product__Type_OPair @ SV1460 @ SV1426 @ SV1265 @ SV1179 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV1460 @ SV1426 ) @ SV1075 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5457]) ).
thf(5460,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[3265,5459,5458,5456,5454,5449,5447,5446,5444,5442,5440,5436,5434,5431,5428,5427,5419,5418,5414,5413,5412,5411,5410,5408,5407,5405,5401,5398,5395,5391,5389,5388,5385,5384,5380,5376,5374,5368,5367,5365,5364,5354,5346,5337,5333,5332,5329,5328,5327,5326,5325,5324,5323,5322,5321,5320,5307,5303,5297,5292,5290,5282,5281,5273,5270,5265,5264,5263,5250,5249,5248,5247,5246,5244,5237,5234,5231,5229,5224,5223,5220,5218,5217,5213,5212,5196,5194,5193,5177,5174,5160,5159,5158,5155,5154,5153,5147,5141,5140,5139,5138,5131,5123,5122,5111,5110,5099,5098,5095,5094,5087,5080,5079,5076,5075,5073,5072,5070,5066,5063,5060,5059,5058,5051,5043,5040,5038,5033,5032,5021,5020,5012,5009,5005,5004,5003,5002,5001,5000,4987,4986,4983,4982,4977,4971,4966,4965,4964,4959,4956,4951,4950,4947,4946,4932,4931,4928,4919,4918,4910,4909,4899,4883,4881,4870,4868,4867,4850,4838,4835,4827,4824,4810,4805,4804,4802,4801,4800,4799,4798,4797,4796,4795,4794,4793,4792,4789,4788,4783,4782,4755,4747,4743,4742,4740,4711,4710,4706,4705,4691,4690,4650,4648,4647,4638,4632,4631,4628,4627,4626,4625,4624,4618,4616,4613,4588,4580,4545,4544,4511,4493,4492,4491,4489,4488,4487,4480,4455,4453,4432,4364,4341,4329,4328,4323,4316,4313,4311,4298,4296,4291,4283,4282,4281,4276,4275,4162,4161,4160,4149,4143,4141,4140,4127,4119,3998,3997,3994,3991,3986,3985,3983,3982,3977,3974,3961,3950,3833,3829,3817,3799,3793,3772,3675,3667,3665,3660,3656,3652,3651,3650,3649,3648,3647,3643,3642,3641,3620,3608,3603,3585,3503,3496,3487,3483,3450,3337,3336,3335,3334,3333,3332,3331,3330,3328,3327,3313,3312,3309]) ).
thf(5461,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5460,3155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT105+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 02:21:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59 .............
% 2.72/2.92
% 2.72/2.92 No.of.Axioms: 522
% 2.72/2.92
% 2.72/2.92 Length.of.Defs: 0
% 2.72/2.92
% 2.72/2.92 Contains.Choice.Funs: false
% 2.92/3.10 ...........................
% 4.08/4.27 (rf:2,axioms:184,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:524,loop_count:0,foatp_calls:0,translation:fof_full)..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
% 15.26/15.50
% 15.26/15.50 ********************************
% 15.26/15.50 * All subproblems solved! *
% 15.26/15.50 ********************************
% 15.26/15.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:184,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5460,loop_count:0,foatp_calls:1,translation:fof_full)
% 24.95/25.18
% 24.95/25.18 %**** Beginning of derivation protocol ****
% 24.95/25.18 % SZS output start CNFRefutation
% See solution above
% 24.99/25.21
% 24.99/25.21 %**** End of derivation protocol ****
% 24.99/25.21 %**** no. of clauses in derivation: 5123 ****
% 24.99/25.21 %**** clause counter: 5460 ****
% 24.99/25.21
% 24.99/25.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:184,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5460,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------