%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:38:29 AM UTC 2026
% Result : Theorem 49.21s 8.58s
% Output : CNFRefutation 8.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 79
% Syntax : Number of formulae : 2468 (1204 unt; 0 typ; 0 def)
% Number of atoms : 16525 (5580 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 66593 (6698 ~;5254 |; 56 &;54006 @)
% ( 83 <=>; 496 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 177 ( 174 usr; 21 con; 0-7 aty)
% Number of variables : 11178 ( 0 ^;11158 !; 20 ?;11178 :)
% 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_SY1028,type,
sK10_SY1028: $i > $i > $i > $i ).
thf(tp_sK11_SY656,type,
sK11_SY656: $i > $i > $i ).
thf(tp_sK12_SY963,type,
sK12_SY963: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY666,type,
sK13_SY666: $i > $i > $i ).
thf(tp_sK14_SY695,type,
sK14_SY695: $i > $i > $i ).
thf(tp_sK15_SY977,type,
sK15_SY977: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY889,type,
sK16_SY889: $i > $i > $i > $i ).
thf(tp_sK17_SY749,type,
sK17_SY749: $i > $i > $i ).
thf(tp_sK18_SY1032,type,
sK18_SY1032: $i > $i > $i ).
thf(tp_sK19_SY814,type,
sK19_SY814: $i > $i > $i ).
thf(tp_sK1_SY792,type,
sK1_SY792: $i > $i > $i ).
thf(tp_sK20_SY1040,type,
sK20_SY1040: $i > $i > $i ).
thf(tp_sK21_SY863,type,
sK21_SY863: $i > $i > $i > $i ).
thf(tp_sK22_SY1012,type,
sK22_SY1012: $i > $i > $i > $i > $i > $i ).
thf(tp_sK23_SY1043,type,
sK23_SY1043: $i > $i > $i ).
thf(tp_sK24_SY901,type,
sK24_SY901: $i > $i > $i > $i ).
thf(tp_sK25_SY1036,type,
sK25_SY1036: $i > $i > $i > $i ).
thf(tp_sK26_SY942,type,
sK26_SY942: $i > $i > $i > $i ).
thf(tp_sK27_SY1057,type,
sK27_SY1057: $i > $i > $i > $i ).
thf(tp_sK28_SX0,type,
sK28_SX0: $i ).
thf(tp_sK29_SY968,type,
sK29_SY968: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY805,type,
sK2_SY805: $i > $i > $i ).
thf(tp_sK30_SY1052,type,
sK30_SY1052: $i > $i > $i ).
thf(tp_sK31_SY979,type,
sK31_SY979: $i > $i > $i > $i > $i ).
thf(tp_sK32_SY980,type,
sK32_SY980: $i > $i > $i > $i > $i ).
thf(tp_sK33_SY981,type,
sK33_SY981: $i > $i > $i > $i > $i ).
thf(tp_sK34_SY1054,type,
sK34_SY1054: $i > $i > $i > $i ).
thf(tp_sK35_SY992,type,
sK35_SY992: $i > $i > $i > $i > $i ).
thf(tp_sK36_SY999,type,
sK36_SY999: $i > $i > $i > $i > $i ).
thf(tp_sK37_SY1013,type,
sK37_SY1013: $i > $i > $i > $i > $i > $i ).
thf(tp_sK38_SY1048,type,
sK38_SY1048: $i > $i > $i ).
thf(tp_sK39_SY1060,type,
sK39_SY1060: $i > $i > $i > $i ).
thf(tp_sK3_SY721,type,
sK3_SY721: $i > $i > $i ).
thf(tp_sK40_SX0,type,
sK40_SX0: $i ).
thf(tp_sK41_SY1033,type,
sK41_SY1033: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK42_SY1062,type,
sK42_SY1062: $i ).
thf(tp_sK43_SY1063,type,
sK43_SY1063: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK44_SY1046,type,
sK44_SY1046: $i > $i > $i > $i > $i ).
thf(tp_sK45_SY1061,type,
sK45_SY1061: $i > $i > $i > $i ).
thf(tp_sK46_SY1352,type,
sK46_SY1352: $i > $i > $i ).
thf(tp_sK47_SY1408,type,
sK47_SY1408: $i > $i > $i ).
thf(tp_sK48_SY1720,type,
sK48_SY1720: $i > $i > $i ).
thf(tp_sK49_SY1581,type,
sK49_SY1581: $i > $i > $i > $i ).
thf(tp_sK4_SY915,type,
sK4_SY915: $i > $i > $i > $i ).
thf(tp_sK50_SY1725,type,
sK50_SY1725: $i > $i > $i ).
thf(tp_sK51_SY1584,type,
sK51_SY1584: $i > $i > $i > $i ).
thf(tp_sK52_SY1458,type,
sK52_SY1458: $i > $i > $i ).
thf(tp_sK53_SY1679,type,
sK53_SY1679: $i > $i > $i > $i > $i ).
thf(tp_sK54_SY1743,type,
sK54_SY1743: $i > $i > $i > $i ).
thf(tp_sK55_SY1654,type,
sK55_SY1654: $i > $i > $i > $i ).
thf(tp_sK56_SY1740,type,
sK56_SY1740: $i > $i > $i ).
thf(tp_sK57_SY1567,type,
sK57_SY1567: $i > $i > $i > $i ).
thf(tp_sK58_SY1678,type,
sK58_SY1678: $i > $i > $i > $i > $i ).
thf(tp_sK59_SY1402,type,
sK59_SY1402: $i > $i > $i ).
thf(tp_sK5_SY921,type,
sK5_SY921: $i > $i > $i > $i ).
thf(tp_sK60_SY1444,type,
sK60_SY1444: $i > $i > $i ).
thf(tp_sK61_SY1451,type,
sK61_SY1451: $i > $i > $i ).
thf(tp_sK62_SY1468,type,
sK62_SY1468: $i > $i > $i ).
thf(tp_sK63_SY1542,type,
sK63_SY1542: $i > $i > $i ).
thf(tp_sK64_SY1713,type,
sK64_SY1713: $i > $i > $i > $i > $i ).
thf(tp_sK65_SY1576,type,
sK65_SY1576: $i > $i > $i > $i ).
thf(tp_sK66_SY1751,type,
sK66_SY1751: $i > $i > $i > $i ).
thf(tp_sK67_SY1764,type,
sK67_SY1764: $i > $i > $i ).
thf(tp_sK68_SY1613,type,
sK68_SY1613: $i > $i > $i > $i ).
thf(tp_sK69_SY1767,type,
sK69_SY1767: $i > $i > $i ).
thf(tp_sK6_SY1017,type,
sK6_SY1017: $i > $i > $i ).
thf(tp_sK70_SY1632,type,
sK70_SY1632: $i > $i > $i > $i ).
thf(tp_sK71_SY1735,type,
sK71_SY1735: $i > $i > $i > $i > $i > $i ).
thf(tp_sK72_SY1770,type,
sK72_SY1770: $i > $i > $i > $i ).
thf(tp_sK73_SX0,type,
sK73_SX0: $i ).
thf(tp_sK74_SY1672,type,
sK74_SY1672: $i > $i > $i > $i > $i ).
thf(tp_sK75_SY1681,type,
sK75_SY1681: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY1773,type,
sK76_SY1773: $i > $i > $i ).
thf(tp_sK77_SY1692,type,
sK77_SY1692: $i > $i > $i > $i > $i ).
thf(tp_sK78_SY1775,type,
sK78_SY1775: $i > $i > $i > $i ).
thf(tp_sK79_SY1695,type,
sK79_SY1695: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY1021,type,
sK7_SY1021: $i > $i > $i ).
thf(tp_sK80_SY1708,type,
sK80_SY1708: $i > $i > $i > $i > $i ).
thf(tp_sK81_SY1709,type,
sK81_SY1709: $i > $i > $i > $i > $i ).
thf(tp_sK82_SY1777,type,
sK82_SY1777: $i > $i > $i > $i ).
thf(tp_sK83_SY1759,type,
sK83_SY1759: $i > $i > $i ).
thf(tp_sK84_SY1726,type,
sK84_SY1726: $i > $i > $i > $i > $i > $i ).
thf(tp_sK85_SX0,type,
sK85_SX0: $i ).
thf(tp_sK86_SY1779,type,
sK86_SY1779: $i ).
thf(tp_sK87_SY1754,type,
sK87_SY1754: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK88_SY1757,type,
sK88_SY1757: $i > $i > $i > $i > $i ).
thf(tp_sK89_SY1780,type,
sK89_SY1780: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY955,type,
sK8_SY955: $i > $i > $i > $i > $i ).
thf(tp_sK90_SY1778,type,
sK90_SY1778: $i > $i > $i > $i ).
thf(tp_sK9_SY912,type,
sK9_SY912: $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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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_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(527,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(528,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(529,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(530,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(531,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(532,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(533,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(534,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(535,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(536,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(537,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(538,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(539,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(540,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(541,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(542,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(543,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(544,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(545,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(546,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(547,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(548,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(549,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(550,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(551,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(552,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(553,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(554,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(555,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(556,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(557,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(558,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(559,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(560,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(561,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(562,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(563,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(564,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(565,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(566,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(567,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(568,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(569,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(570,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(571,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(572,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(573,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(574,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(575,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(576,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(577,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(578,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(579,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(580,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(581,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(582,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(583,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(584,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(585,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(586,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(587,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(588,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(589,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(590,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(591,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(592,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(593,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(594,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(595,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(596,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(597,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(598,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(599,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(600,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(601,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(602,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(603,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(604,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(605,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(606,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)],[604]) ).
thf(607,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)],[605]) ).
thf(608,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(copy,[status(thm)],[603]) ).
thf(609,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)],[602]) ).
thf(610,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(copy,[status(thm)],[601]) ).
thf(611,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(copy,[status(thm)],[600]) ).
thf(612,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(copy,[status(thm)],[599]) ).
thf(613,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(copy,[status(thm)],[598]) ).
thf(614,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)],[597]) ).
thf(615,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(copy,[status(thm)],[596]) ).
thf(616,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(copy,[status(thm)],[595]) ).
thf(617,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(copy,[status(thm)],[594]) ).
thf(618,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(copy,[status(thm)],[593]) ).
thf(619,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)],[592]) ).
thf(620,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(copy,[status(thm)],[591]) ).
thf(621,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)],[590]) ).
thf(622,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)],[589]) ).
thf(623,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(copy,[status(thm)],[588]) ).
thf(624,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(copy,[status(thm)],[587]) ).
thf(625,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)],[586]) ).
thf(626,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)],[585]) ).
thf(627,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(copy,[status(thm)],[584]) ).
thf(628,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(copy,[status(thm)],[583]) ).
thf(629,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(copy,[status(thm)],[582]) ).
thf(630,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(copy,[status(thm)],[581]) ).
thf(631,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(copy,[status(thm)],[580]) ).
thf(632,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(copy,[status(thm)],[579]) ).
thf(633,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)],[578]) ).
thf(634,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)],[577]) ).
thf(635,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)],[576]) ).
thf(636,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)],[575]) ).
thf(637,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(copy,[status(thm)],[574]) ).
thf(638,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(copy,[status(thm)],[573]) ).
thf(639,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)],[572]) ).
thf(640,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(copy,[status(thm)],[571]) ).
thf(641,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)],[570]) ).
thf(642,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)],[569]) ).
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 ) @ 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)],[568]) ).
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 ) @ ( 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)],[567]) ).
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 ) @ ( 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)],[566]) ).
thf(646,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)],[565]) ).
thf(647,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(copy,[status(thm)],[564]) ).
thf(648,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(copy,[status(thm)],[563]) ).
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 ) @ ( 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(copy,[status(thm)],[562]) ).
thf(650,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(copy,[status(thm)],[561]) ).
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 ) @ 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)],[560]) ).
thf(652,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)],[559]) ).
thf(653,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)],[558]) ).
thf(654,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)],[557]) ).
thf(655,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)],[556]) ).
thf(656,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)],[555]) ).
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_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)],[554]) ).
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_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)],[553]) ).
thf(659,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(copy,[status(thm)],[552]) ).
thf(660,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(copy,[status(thm)],[551]) ).
thf(661,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(copy,[status(thm)],[550]) ).
thf(662,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)],[549]) ).
thf(663,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(664,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(copy,[status(thm)],[547]) ).
thf(665,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(copy,[status(thm)],[546]) ).
thf(666,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)],[545]) ).
thf(667,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)],[544]) ).
thf(668,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(copy,[status(thm)],[543]) ).
thf(669,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)],[542]) ).
thf(670,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)],[541]) ).
thf(671,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(copy,[status(thm)],[540]) ).
thf(672,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)],[539]) ).
thf(673,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)],[538]) ).
thf(674,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(copy,[status(thm)],[537]) ).
thf(675,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)],[536]) ).
thf(676,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)],[535]) ).
thf(677,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)],[534]) ).
thf(678,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)],[533]) ).
thf(679,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(copy,[status(thm)],[532]) ).
thf(680,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(copy,[status(thm)],[531]) ).
thf(681,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(copy,[status(thm)],[530]) ).
thf(682,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(copy,[status(thm)],[529]) ).
thf(683,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)],[528]) ).
thf(684,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(copy,[status(thm)],[527]) ).
thf(685,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)],[526]) ).
thf(686,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(copy,[status(thm)],[606]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i,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 )
| ~ ( c_member @ SX3 @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ( 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ ( c_Relation_OId__on @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(689,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Transitive__Closure_Otrancl @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(691,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(692,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 = SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 ) )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX2 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(694,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 ) ) )
| ~ ! [SX7: $i,SX8: $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 @ SX7 @ SX8 ) ) @ 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 @ SX7 @ SX8 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(695,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 ) )
| ~ ( ~ ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(696,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 )
| ( SX2 != SX0 ) ) )
| ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(698,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 ) ) )
| ~ ( ~ ! [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 ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(699,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 ) )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 )
| ~ ( ( SX5 != SX3 )
| ~ ( 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 )
| ~ ( ( SX5 != SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 ) ) )
| ( 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)],[618]) ).
thf(700,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(701,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 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(702,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Wellfounded_Oacc @ SX3 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX2 ) @ SX1 )
| ( c_member @ SX3 @ SX0 @ ( c_Wellfounded_Oacc @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_member @ SX5 @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX2 ) @ ( c_Product__Type_OPair @ SX5 @ SX2 @ SX4 @ SX1 ) @ SX0 )
| ( c_member @ SX2 @ SX1 @ ( c_Relation_OImage @ SX5 @ SX2 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ! [SX5: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 )
| ~ ( c_member @ SX2 @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(706,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(707,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( c_member @ SX2 @ SX5 @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_Owf @ SX2 @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(711,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Orefl__on @ SX4 @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX2 )
| ( c_member @ SX4 @ SX0 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(713,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 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_Owf @ SX2 @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(715,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ SX0 @ ( c_Relation_OId @ SX1 ) )
| ~ ! [SX2: $i] :
( SX0
!= ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(717,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Oantisym @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(718,plain,
( ( ! [SX0: $i,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)],[637]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(720,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 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(722,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Relation_Osingle__valued @ SX5 @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX5 @ SX4 @ SX2 @ SX1 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX5 @ SX4 @ SX2 @ SX0 ) @ SX3 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(723,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(724,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(725,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX4 @ SX3 ) @ SX0 )
| ~ ( c_member @ SX1 @ SX4 @ SX2 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX4 @ SX3 ) @ SX0 )
| ~ ( c_member @ SX1 @ SX4 @ SX2 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Otrans @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX1 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX3 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(727,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_Otrancl @ SX4 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ( ~ ( c_member @ SX1 @ SX0 @ SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Otrans @ SX3 @ SX2 )
| ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ( c_Relation_Otrans @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Wellfounded_Olex__prod @ SX3 @ SX1 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(730,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Relation_OId__on @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( c_member @ SX2 @ SX3 @ SX0 )
| ( SX1
!= ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(733,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_Otrancl @ SX4 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [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 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(735,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 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(736,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 )
| ( SX2 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [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 ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(738,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 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Orefl__on @ SX4 @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX2 )
| ( c_member @ SX4 @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [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 ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(741,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX2 ) @ ( c_Product__Type_OPair @ SX6 @ SX2 @ SX4 @ SX1 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX7 @ SX2 ) @ ( c_Product__Type_OPair @ SX7 @ SX2 @ SX5 @ SX1 ) @ ( c_Relation_Orel__comp @ SX7 @ SX6 @ SX2 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ( ~ ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(744,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Transitive__Closure_Ortrancl @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [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 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(746,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 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(747,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( 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 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ SX2 @ SX1 @ SX0 )
| ( ( c_Set_Oinsert @ SX2 @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(749,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 ) )
| ~ ( ~ ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(750,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 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(751,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(752,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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 ) ) )
| ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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(unfold_def,[status(thm)],[686]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Orefl__on @ SX3 @ SX2 @ SX1 )
| ~ ( c_member @ SX3 @ SX0 @ SX2 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ( c_member @ SX3 @ SX1 @ ( c_Relation_ORange @ SX4 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(757,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ( c_member @ SX4 @ SX2 @ ( c_Relation_ODomain @ SX4 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(758,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ( ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(759,plain,
! [SV1: $i] :
( ( ! [SY348: $i] : ( c_Relation_Otrans @ SY348 @ ( c_Relation_OId__on @ SY348 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(760,plain,
! [SV2: $i] :
( ( ! [SY349: $i,SY350: $i] : ( c_member @ ( tc_prod @ SY350 @ SY350 ) @ ( c_Product__Type_OPair @ SY350 @ SY350 @ SY349 @ SY349 ) @ ( c_Transitive__Closure_Ortrancl @ SY350 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(761,plain,
! [SV3: $i] :
( ( ! [SY351: $i] : ( c_Relation_Otrans @ SY351 @ ( c_Transitive__Closure_Ortrancl @ SY351 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(762,plain,
! [SV4: $i] :
( ( ! [SY352: $i] : ( c_Relation_Otrans @ SY352 @ ( c_Transitive__Closure_Otrancl @ SY352 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(763,plain,
! [SV5: $i] :
( ( ! [SY353: $i] : ( c_member @ ( tc_prod @ SY353 @ SY353 ) @ ( c_Product__Type_OPair @ SY353 @ SY353 @ SV5 @ SV5 ) @ ( c_Relation_OId @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(764,plain,
! [SV6: $i] :
( ( c_Relation_Otrans @ SV6 @ ( c_Relation_OId @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(765,plain,
! [SV7: $i] :
( ( ! [SY354: $i,SY355: $i] : ( c_member @ SY355 @ SY354 @ ( c_Set_Oinsert @ SY355 @ SY354 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(766,plain,
! [SV8: $i] :
( ( ! [SY356: $i,SY357: $i,SY358: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY358 @ SY358 ) @ ( c_Product__Type_OPair @ SY358 @ SY358 @ SY357 @ SY356 ) @ ( c_Relation_OId__on @ SY358 @ SV8 ) )
| ~ ( ( SY357 != SY356 )
| ~ ( c_member @ SY358 @ SY357 @ SV8 ) ) )
| ~ ( ~ ~ ( ( SY357 != SY356 )
| ~ ( c_member @ SY358 @ SY357 @ SV8 ) )
| ( c_member @ ( tc_prod @ SY358 @ SY358 ) @ ( c_Product__Type_OPair @ SY358 @ SY358 @ SY357 @ SY356 ) @ ( c_Relation_OId__on @ SY358 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(767,plain,
! [SV9: $i] :
( ( ! [SY359: $i,SY360: $i,SY361: $i] :
( ( SY361 != SY360 )
| ~ ( c_member @ SY359 @ SY361 @ SV9 )
| ( c_member @ ( tc_prod @ SY359 @ SY359 ) @ ( c_Product__Type_OPair @ SY359 @ SY359 @ SY361 @ SY360 ) @ ( c_Relation_OId__on @ SY359 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(768,plain,
! [SV10: $i] :
( ( ! [SY362: $i,SY363: $i,SY364: $i,SY365: $i] :
( ~ ( c_member @ ( tc_prod @ SY365 @ SY365 ) @ ( c_Product__Type_OPair @ SY365 @ SY365 @ SY364 @ SY363 ) @ SY362 )
| ~ ( c_member @ ( tc_prod @ SY365 @ SY365 ) @ ( c_Product__Type_OPair @ SY365 @ SY365 @ SY363 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY365 @ SY362 ) )
| ( c_member @ ( tc_prod @ SY365 @ SY365 ) @ ( c_Product__Type_OPair @ SY365 @ SY365 @ SY364 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY365 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(769,plain,
! [SV11: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ( c_member @ ( tc_prod @ SY367 @ SY367 ) @ SY366 @ SV11 )
| ( c_member @ ( tc_prod @ SY367 @ SY367 ) @ SY366 @ ( c_Transitive__Closure_Otrancl @ SY367 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(770,plain,
! [SV12: $i] :
( ( ! [SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( c_member @ SY369 @ SY368 @ ( c_fequal @ SV12 ) )
| ( SY368 = SV12 ) )
| ~ ( ( SY368 != SV12 )
| ( c_member @ SY369 @ SY368 @ ( c_fequal @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(771,plain,
! [SV13: $i] :
( ( ! [SY370: $i,SY371: $i,SY372: $i] :
~ ( ~ ( ~ ( c_member @ SY372 @ SY371 @ ( c_Set_Oinsert @ SY372 @ SY370 @ SV13 ) )
| ( SY371 = SY370 )
| ( c_member @ SY372 @ SY371 @ SV13 ) )
| ~ ( ~ ( ( SY371 = SY370 )
| ( c_member @ SY372 @ SY371 @ SV13 ) )
| ( c_member @ SY372 @ SY371 @ ( c_Set_Oinsert @ SY372 @ SY370 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(772,plain,
! [SV14: $i] :
( ( ! [SY373: $i,SY374: $i,SY375: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SY375 @ SY375 ) @ ( c_Product__Type_OPair @ SY375 @ SY375 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SY375 @ SY374 ) )
| ~ ( c_member @ ( tc_prod @ SY375 @ SY375 ) @ ( c_Product__Type_OPair @ SY375 @ SY375 @ SY373 @ SV14 ) @ SY374 )
| ( SY373 != SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(773,plain,
! [SV15: $i] :
( ( ! [SY377: $i,SY378: $i,SY379: $i,SY380: $i,SY381: $i,SY382: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY380 @ SY379 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY378 @ SY377 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY382 @ SY381 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY382 @ SY381 @ SY380 @ SY379 )
!= ( c_Product__Type_OPair @ SY382 @ SY381 @ SY378 @ SY377 ) ) )
| ~ ! [SY383: $i,SY384: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY380 @ SY379 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY383 @ SY384 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY382 @ SY381 ) @ ( tc_prod @ SY382 @ SY381 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY383 @ SY384 ) @ ( c_Product__Type_OPair @ SY382 @ SY381 @ SY378 @ SY377 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY382 @ SY381 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(774,plain,
! [SV16: $i] :
( ( ! [SY385: $i] :
~ ( ~ ( ~ ( c_Nitpick_Orefl_H @ SY385 @ SV16 )
| ! [SY386: $i] : ( c_member @ ( tc_prod @ SY385 @ SY385 ) @ ( c_Product__Type_OPair @ SY385 @ SY385 @ SY386 @ SY386 ) @ SV16 ) )
| ~ ( ~ ! [SY387: $i] : ( c_member @ ( tc_prod @ SY385 @ SY385 ) @ ( c_Product__Type_OPair @ SY385 @ SY385 @ SY387 @ SY387 ) @ SV16 )
| ( c_Nitpick_Orefl_H @ SY385 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(775,plain,
! [SV17: $i] :
( ( ! [SY388: $i,SY389: $i,SY390: $i,SY391: $i,SY392: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY392 @ SY391 @ SY390 @ SY389 )
!= ( c_Product__Type_OPair @ SY392 @ SY391 @ SY388 @ SV17 ) )
| ~ ( ( SY390 != SY388 )
| ( SY389 != SV17 ) ) )
| ~ ( ~ ~ ( ( SY390 != SY388 )
| ( SY389 != SV17 ) )
| ( ( c_Product__Type_OPair @ SY392 @ SY391 @ SY390 @ SY389 )
= ( c_Product__Type_OPair @ SY392 @ SY391 @ SY388 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(776,plain,
! [SV18: $i] :
( ( ! [SY393: $i,SY394: $i,SY395: $i] :
( ~ ( c_member @ SY395 @ SY394 @ ( c_Relation_ORange @ SY393 @ SY395 @ SV18 ) )
| ~ ! [SY396: $i] :
~ ( c_member @ ( tc_prod @ SY393 @ SY395 ) @ ( c_Product__Type_OPair @ SY393 @ SY395 @ SY396 @ SY394 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(777,plain,
! [SV19: $i] :
( ( ! [SY397: $i] :
~ ( ~ ( ~ ( c_Relation_Oantisym @ SY397 @ SV19 )
| ! [SY398: $i,SY399: $i] :
( ~ ( c_member @ ( tc_prod @ SY397 @ SY397 ) @ ( c_Product__Type_OPair @ SY397 @ SY397 @ SY398 @ SY399 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SY397 @ SY397 ) @ ( c_Product__Type_OPair @ SY397 @ SY397 @ SY399 @ SY398 ) @ SV19 )
| ( SY398 = SY399 ) ) )
| ~ ( ~ ! [SY400: $i,SY401: $i] :
( ~ ( c_member @ ( tc_prod @ SY397 @ SY397 ) @ ( c_Product__Type_OPair @ SY397 @ SY397 @ SY400 @ SY401 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SY397 @ SY397 ) @ ( c_Product__Type_OPair @ SY397 @ SY397 @ SY401 @ SY400 ) @ SV19 )
| ( SY400 = SY401 ) )
| ( c_Relation_Oantisym @ SY397 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(778,plain,
! [SV20: $i] :
( ( ! [SY402: $i,SY403: $i,SY404: $i,SY405: $i,SY406: $i,SY407: $i,SY408: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY408 @ SY407 ) @ ( tc_prod @ SY408 @ SY407 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY408 @ SY407 ) @ ( tc_prod @ SY408 @ SY407 ) @ ( c_Product__Type_OPair @ SY408 @ SY407 @ SY406 @ SY405 ) @ ( c_Product__Type_OPair @ SY408 @ SY407 @ SY404 @ SY403 ) ) @ ( c_Wellfounded_Olex__prod @ SY408 @ SY407 @ SY402 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY408 @ SY408 ) @ ( c_Product__Type_OPair @ SY408 @ SY408 @ SY406 @ SY404 ) @ SY402 )
| ~ ( ( SY406 != SY404 )
| ~ ( c_member @ ( tc_prod @ SY407 @ SY407 ) @ ( c_Product__Type_OPair @ SY407 @ SY407 @ SY405 @ SY403 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY408 @ SY408 ) @ ( c_Product__Type_OPair @ SY408 @ SY408 @ SY406 @ SY404 ) @ SY402 )
| ~ ( ( SY406 != SY404 )
| ~ ( c_member @ ( tc_prod @ SY407 @ SY407 ) @ ( c_Product__Type_OPair @ SY407 @ SY407 @ SY405 @ SY403 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY408 @ SY407 ) @ ( tc_prod @ SY408 @ SY407 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY408 @ SY407 ) @ ( tc_prod @ SY408 @ SY407 ) @ ( c_Product__Type_OPair @ SY408 @ SY407 @ SY406 @ SY405 ) @ ( c_Product__Type_OPair @ SY408 @ SY407 @ SY404 @ SY403 ) ) @ ( c_Wellfounded_Olex__prod @ SY408 @ SY407 @ SY402 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(779,plain,
! [SV21: $i] :
( ( ! [SY409: $i,SY410: $i] :
~ ( ~ ( ~ ( c_member @ SY410 @ SY409 @ ( c_Wellfounded_Oacc @ SY410 @ SV21 ) )
| ! [SY411: $i] :
( ~ ( c_member @ ( tc_prod @ SY410 @ SY410 ) @ ( c_Product__Type_OPair @ SY410 @ SY410 @ SY411 @ SY409 ) @ SV21 )
| ( c_member @ SY410 @ SY411 @ ( c_Wellfounded_Oacc @ SY410 @ SV21 ) ) ) )
| ~ ( ~ ! [SY412: $i] :
( ~ ( c_member @ ( tc_prod @ SY410 @ SY410 ) @ ( c_Product__Type_OPair @ SY410 @ SY410 @ SY412 @ SY409 ) @ SV21 )
| ( c_member @ SY410 @ SY412 @ ( c_Wellfounded_Oacc @ SY410 @ SV21 ) ) )
| ( c_member @ SY410 @ SY409 @ ( c_Wellfounded_Oacc @ SY410 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(780,plain,
! [SV22: $i] :
( ( ! [SY413: $i,SY414: $i,SY415: $i] :
( ~ ( c_member @ ( tc_prod @ SY415 @ SY415 ) @ ( c_Product__Type_OPair @ SY415 @ SY415 @ SY414 @ SY413 ) @ ( c_Transitive__Closure_Otrancl @ SY415 @ SV22 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY415 @ SY415 ) @ ( c_Product__Type_OPair @ SY415 @ SY415 @ SY414 @ SY413 ) @ SV22 )
| ~ ! [SY416: $i] :
( ~ ( c_member @ ( tc_prod @ SY415 @ SY415 ) @ ( c_Product__Type_OPair @ SY415 @ SY415 @ SY414 @ SY416 ) @ ( c_Transitive__Closure_Otrancl @ SY415 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SY415 @ SY415 ) @ ( c_Product__Type_OPair @ SY415 @ SY415 @ SY416 @ SY413 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(781,plain,
! [SV23: $i] :
( ( ! [SY417: $i,SY418: $i,SY419: $i] :
( ~ ( c_member @ SY419 @ SY418 @ ( c_Wellfounded_Oacc @ SY419 @ SY417 ) )
| ~ ( c_member @ ( tc_prod @ SY419 @ SY419 ) @ ( c_Product__Type_OPair @ SY419 @ SY419 @ SV23 @ SY418 ) @ SY417 )
| ( c_member @ SY419 @ SV23 @ ( c_Wellfounded_Oacc @ SY419 @ SY417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(782,plain,
! [SV24: $i] :
( ( ! [SY420: $i,SY421: $i,SY422: $i,SY423: $i,SY424: $i] :
( ~ ( c_member @ SY424 @ SY423 @ SY422 )
| ~ ( c_member @ ( tc_prod @ SY424 @ SY421 ) @ ( c_Product__Type_OPair @ SY424 @ SY421 @ SY423 @ SY420 ) @ SV24 )
| ( c_member @ SY421 @ SY420 @ ( c_Relation_OImage @ SY424 @ SY421 @ SV24 @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(783,plain,
! [SV25: $i] :
( ( ! [SY425: $i,SY426: $i,SY427: $i] :
( ~ ( c_Wellfounded_Owf @ SY427 @ SY426 )
| ~ ( c_member @ ( tc_prod @ SY427 @ SY427 ) @ ( c_Product__Type_OPair @ SY427 @ SY427 @ SY425 @ SV25 ) @ SY426 )
| ~ ( c_member @ ( tc_prod @ SY427 @ SY427 ) @ ( c_Product__Type_OPair @ SY427 @ SY427 @ SV25 @ SY425 ) @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(784,plain,
! [SV26: $i] :
( ( ! [SY428: $i,SY429: $i,SY430: $i,SY431: $i] :
( ~ ( c_member @ SY431 @ SY430 @ ( c_Relation_OImage @ SY429 @ SY431 @ SY428 @ SV26 ) )
| ~ ! [SY432: $i] :
( ~ ( c_member @ ( tc_prod @ SY429 @ SY431 ) @ ( c_Product__Type_OPair @ SY429 @ SY431 @ SY432 @ SY430 ) @ SY428 )
| ~ ( c_member @ SY429 @ SY432 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(785,plain,
! [SV27: $i] :
( ( ! [SY433: $i] :
~ ( ~ ( ~ ( c_Relation_Otrans @ SY433 @ SV27 )
| ! [SY434: $i,SY435: $i] :
( ~ ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY434 @ SY435 ) @ SV27 )
| ! [SY436: $i] :
( ~ ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY435 @ SY436 ) @ SV27 )
| ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY434 @ SY436 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY437: $i,SY438: $i] :
( ~ ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY437 @ SY438 ) @ SV27 )
| ! [SY439: $i] :
( ~ ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY438 @ SY439 ) @ SV27 )
| ( c_member @ ( tc_prod @ SY433 @ SY433 ) @ ( c_Product__Type_OPair @ SY433 @ SY433 @ SY437 @ SY439 ) @ SV27 ) ) )
| ( c_Relation_Otrans @ SY433 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(786,plain,
! [SV28: $i] :
( ( ! [SY440: $i,SY441: $i,SY442: $i,SY443: $i] :
( ~ ( c_member @ ( tc_prod @ SY443 @ SY443 ) @ ( c_Product__Type_OPair @ SY443 @ SY443 @ SY442 @ SY441 ) @ SY440 )
| ~ ( c_member @ ( tc_prod @ SY443 @ SY443 ) @ ( c_Product__Type_OPair @ SY443 @ SY443 @ SY441 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY443 @ SY440 ) )
| ( c_member @ ( tc_prod @ SY443 @ SY443 ) @ ( c_Product__Type_OPair @ SY443 @ SY443 @ SY442 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY443 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(787,plain,
! [SV29: $i] :
( ( ! [SY444: $i,SY445: $i,SY446: $i,SY447: $i] :
~ ( ~ ( ~ ( c_member @ SY447 @ SY446 @ ( c_Relation_OImage @ SY445 @ SY447 @ SY444 @ SV29 ) )
| ~ ! [SY448: $i] :
~ ~ ( ~ ( c_member @ SY445 @ SY448 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SY445 @ SY447 ) @ ( c_Product__Type_OPair @ SY445 @ SY447 @ SY448 @ SY446 ) @ SY444 ) ) )
| ~ ( ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( c_member @ SY445 @ SY449 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SY445 @ SY447 ) @ ( c_Product__Type_OPair @ SY445 @ SY447 @ SY449 @ SY446 ) @ SY444 ) )
| ( c_member @ SY447 @ SY446 @ ( c_Relation_OImage @ SY445 @ SY447 @ SY444 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(788,plain,
! [SV30: $i] :
( ( ! [SY450: $i,SY451: $i] :
( ~ ( c_Wellfounded_Owf @ SY451 @ SY450 )
| ~ ( c_member @ ( tc_prod @ SY451 @ SY451 ) @ ( c_Product__Type_OPair @ SY451 @ SY451 @ SV30 @ SV30 ) @ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(789,plain,
! [SV31: $i] :
( ( ! [SY452: $i,SY453: $i,SY454: $i] :
( ~ ( c_Wellfounded_Owf @ SY454 @ SY453 )
| ~ ( c_member @ ( tc_prod @ SY454 @ SY454 ) @ ( c_Product__Type_OPair @ SY454 @ SY454 @ SY452 @ SV31 ) @ SY453 )
| ~ ( c_member @ ( tc_prod @ SY454 @ SY454 ) @ ( c_Product__Type_OPair @ SY454 @ SY454 @ SV31 @ SY452 ) @ SY453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(790,plain,
! [SV32: $i] :
( ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ( c_member @ SY457 @ SY456 @ ( c_Relation_ODomain @ SY457 @ SY455 @ SV32 ) )
| ~ ! [SY458: $i] :
~ ( c_member @ ( tc_prod @ SY457 @ SY455 ) @ ( c_Product__Type_OPair @ SY457 @ SY455 @ SY456 @ SY458 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(791,plain,
! [SV33: $i] :
( ( ! [SY459: $i,SY460: $i,SY461: $i,SY462: $i] :
( ~ ( c_Relation_Orefl__on @ SY462 @ SY461 @ SY460 )
| ~ ( c_member @ ( tc_prod @ SY462 @ SY462 ) @ ( c_Product__Type_OPair @ SY462 @ SY462 @ SY459 @ SV33 ) @ SY460 )
| ( c_member @ SY462 @ SV33 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(792,plain,
! [SV34: $i] :
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ~ ( c_member @ ( tc_prod @ SY465 @ SY465 ) @ ( c_Product__Type_OPair @ SY465 @ SY465 @ SY464 @ SY463 ) @ ( c_Transitive__Closure_Otrancl @ SY465 @ SV34 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY465 @ SY465 ) @ ( c_Product__Type_OPair @ SY465 @ SY465 @ SY464 @ SY463 ) @ SV34 )
| ~ ! [SY466: $i] :
( ~ ( c_member @ ( tc_prod @ SY465 @ SY465 ) @ ( c_Product__Type_OPair @ SY465 @ SY465 @ SY464 @ SY466 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SY465 @ SY465 ) @ ( c_Product__Type_OPair @ SY465 @ SY465 @ SY466 @ SY463 ) @ ( c_Transitive__Closure_Otrancl @ SY465 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(793,plain,
! [SV35: $i] :
( ( ! [SY467: $i,SY468: $i] :
( ~ ( c_Wellfounded_Owf @ SY468 @ SY467 )
| ~ ( c_member @ ( tc_prod @ SY468 @ SY468 ) @ ( c_Product__Type_OPair @ SY468 @ SY468 @ SV35 @ SV35 ) @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(794,plain,
! [SV36: $i] :
( ( ! [SY469: $i,SY470: $i,SY471: $i] :
( ~ ( c_member @ SY471 @ SY470 @ SY469 )
| ( c_member @ SY471 @ SY470 @ ( c_Set_Oinsert @ SY471 @ SV36 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(795,plain,
! [SV37: $i] :
( ( ! [SY472: $i] :
( ~ ( c_member @ ( tc_prod @ SY472 @ SY472 ) @ SV37 @ ( c_Relation_OId @ SY472 ) )
| ~ ! [SY473: $i] :
( SV37
!= ( c_Product__Type_OPair @ SY472 @ SY472 @ SY473 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(796,plain,
! [SV38: $i] :
( ( ! [SY474: $i,SY475: $i,SY476: $i] :
( ~ ( c_Relation_Oantisym @ SY476 @ SY475 )
| ~ ( c_member @ ( tc_prod @ SY476 @ SY476 ) @ ( c_Product__Type_OPair @ SY476 @ SY476 @ SY474 @ SV38 ) @ SY475 )
| ~ ( c_member @ ( tc_prod @ SY476 @ SY476 ) @ ( c_Product__Type_OPair @ SY476 @ SY476 @ SV38 @ SY474 ) @ SY475 )
| ( SY474 = SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(797,plain,
! [SV39: $i] :
( ( ! [SY477: $i,SY478: $i] :
( ~ ~ ( c_member @ SY478 @ SY477 @ ( c_Wellfounded_Oacc @ SY478 @ SV39 ) )
| ~ ! [SY479: $i] :
( ~ ( c_member @ ( tc_prod @ SY478 @ SY478 ) @ ( c_Product__Type_OPair @ SY478 @ SY478 @ SY479 @ SY477 ) @ SV39 )
| ( c_member @ SY478 @ SY479 @ ( c_Wellfounded_Oacc @ SY478 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(798,plain,
! [SV40: $i] :
( ( ! [SY480: $i,SY481: $i,SY482: $i] :
( ( SY482 != SY481 )
| ~ ( ~ ( ~ ( c_member @ SY480 @ SY482 @ SV40 )
| ( c_member @ SY480 @ SY481 @ SV40 ) )
| ~ ( ~ ( c_member @ SY480 @ SY481 @ SV40 )
| ( c_member @ SY480 @ SY482 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(799,plain,
! [SV41: $i] :
( ( ! [SY483: $i,SY484: $i,SY485: $i] :
( ~ ( c_member @ ( tc_prod @ SY485 @ SY485 ) @ ( c_Product__Type_OPair @ SY485 @ SY485 @ SY484 @ SY483 ) @ ( c_Transitive__Closure_Ortrancl @ SY485 @ SV41 ) )
| ~ ( ( SY484 != SY483 ) )
| ~ ! [SY486: $i] :
( ~ ( c_member @ ( tc_prod @ SY485 @ SY485 ) @ ( c_Product__Type_OPair @ SY485 @ SY485 @ SY484 @ SY486 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SY485 @ SY485 ) @ ( c_Product__Type_OPair @ SY485 @ SY485 @ SY486 @ SY483 ) @ ( c_Transitive__Closure_Ortrancl @ SY485 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(800,plain,
! [SV42: $i] :
( ( ! [SY487: $i,SY488: $i,SY489: $i] :
~ ( ~ ( ~ ( c_member @ SY489 @ SY488 @ ( c_Relation_ORange @ SY487 @ SY489 @ SV42 ) )
| ~ ! [SY490: $i] :
~ ( c_member @ ( tc_prod @ SY487 @ SY489 ) @ ( c_Product__Type_OPair @ SY487 @ SY489 @ SY490 @ SY488 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY491: $i] :
~ ( c_member @ ( tc_prod @ SY487 @ SY489 ) @ ( c_Product__Type_OPair @ SY487 @ SY489 @ SY491 @ SY488 ) @ SV42 )
| ( c_member @ SY489 @ SY488 @ ( c_Relation_ORange @ SY487 @ SY489 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(801,plain,
! [SV43: $i] :
( ( ! [SY492: $i,SY493: $i,SY494: $i,SY495: $i,SY496: $i] :
( ~ ( c_Relation_Osingle__valued @ SY496 @ SY495 @ SY494 )
| ~ ( c_member @ ( tc_prod @ SY496 @ SY495 ) @ ( c_Product__Type_OPair @ SY496 @ SY495 @ SY493 @ SY492 ) @ SY494 )
| ~ ( c_member @ ( tc_prod @ SY496 @ SY495 ) @ ( c_Product__Type_OPair @ SY496 @ SY495 @ SY493 @ SV43 ) @ SY494 )
| ( SY492 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(802,plain,
! [SV44: $i] :
( ( ! [SY497: $i,SY498: $i] :
~ ( ~ ( ~ ( c_Relation_Ototal__on @ SY498 @ SY497 @ SV44 )
| ! [SY499: $i] :
( ~ ( c_member @ SY498 @ SY499 @ SY497 )
| ! [SY500: $i] :
( ~ ( c_member @ SY498 @ SY500 @ SY497 )
| ~ ( ( SY499 != SY500 ) )
| ( c_member @ ( tc_prod @ SY498 @ SY498 ) @ ( c_Product__Type_OPair @ SY498 @ SY498 @ SY499 @ SY500 ) @ SV44 )
| ( c_member @ ( tc_prod @ SY498 @ SY498 ) @ ( c_Product__Type_OPair @ SY498 @ SY498 @ SY500 @ SY499 ) @ SV44 ) ) ) )
| ~ ( ~ ! [SY501: $i] :
( ~ ( c_member @ SY498 @ SY501 @ SY497 )
| ! [SY502: $i] :
( ~ ( c_member @ SY498 @ SY502 @ SY497 )
| ~ ( ( SY501 != SY502 ) )
| ( c_member @ ( tc_prod @ SY498 @ SY498 ) @ ( c_Product__Type_OPair @ SY498 @ SY498 @ SY501 @ SY502 ) @ SV44 )
| ( c_member @ ( tc_prod @ SY498 @ SY498 ) @ ( c_Product__Type_OPair @ SY498 @ SY498 @ SY502 @ SY501 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SY498 @ SY497 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(803,plain,
! [SV45: $i] :
( ( ! [SY503: $i,SY504: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY504 @ SY504 ) @ ( c_Product__Type_OPair @ SY504 @ SY504 @ SY503 @ SV45 ) @ ( c_Relation_OId @ SY504 ) )
| ( SY503 = SV45 ) )
| ~ ( ( SY503 != SV45 )
| ( c_member @ ( tc_prod @ SY504 @ SY504 ) @ ( c_Product__Type_OPair @ SY504 @ SY504 @ SY503 @ SV45 ) @ ( c_Relation_OId @ SY504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(804,plain,
! [SV46: $i] :
( ( ! [SY505: $i] :
~ ( ~ ( ~ ( c_Wellfounded_Owf @ SY505 @ SV46 )
| ! [SY506: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SY505 @ SX3 @ SY506 )
| ~ ! [SY508: $i] :
~ ~ ( ~ ( c_member @ SY505 @ SY508 @ SY506 )
| ~ ! [SY509: $i] :
( ~ ( c_member @ ( tc_prod @ SY505 @ SY505 ) @ ( c_Product__Type_OPair @ SY505 @ SY505 @ SY509 @ SY508 ) @ SV46 )
| ~ ( c_member @ SY505 @ SY509 @ SY506 ) ) ) ) )
| ~ ( ~ ! [SY510: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SY505 @ SX3 @ SY510 )
| ~ ! [SY512: $i] :
~ ~ ( ~ ( c_member @ SY505 @ SY512 @ SY510 )
| ~ ! [SY513: $i] :
( ~ ( c_member @ ( tc_prod @ SY505 @ SY505 ) @ ( c_Product__Type_OPair @ SY505 @ SY505 @ SY513 @ SY512 ) @ SV46 )
| ~ ( c_member @ SY505 @ SY513 @ SY510 ) ) ) )
| ( c_Wellfounded_Owf @ SY505 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(805,plain,
! [SV47: $i] :
( ( ! [SY514: $i,SY515: $i,SY516: $i,SY517: $i] :
( ~ ( c_Relation_Otrans @ SY517 @ SY516 )
| ~ ( c_member @ ( tc_prod @ SY517 @ SY517 ) @ ( c_Product__Type_OPair @ SY517 @ SY517 @ SY515 @ SY514 ) @ SY516 )
| ~ ( c_member @ ( tc_prod @ SY517 @ SY517 ) @ ( c_Product__Type_OPair @ SY517 @ SY517 @ SY514 @ SV47 ) @ SY516 )
| ( c_member @ ( tc_prod @ SY517 @ SY517 ) @ ( c_Product__Type_OPair @ SY517 @ SY517 @ SY515 @ SV47 ) @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(806,plain,
! [SV48: $i] :
( ( ! [SY518: $i,SY519: $i,SY520: $i,SY521: $i] :
( ~ ( c_member @ ( tc_prod @ SY521 @ SY521 ) @ ( c_Product__Type_OPair @ SY521 @ SY521 @ SY520 @ SY519 ) @ ( c_Transitive__Closure_Otrancl @ SY521 @ SY518 ) )
| ~ ( c_member @ ( tc_prod @ SY521 @ SY521 ) @ ( c_Product__Type_OPair @ SY521 @ SY521 @ SY519 @ SV48 ) @ SY518 )
| ( c_member @ ( tc_prod @ SY521 @ SY521 ) @ ( c_Product__Type_OPair @ SY521 @ SY521 @ SY520 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SY521 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(807,plain,
! [SV49: $i] :
( ( ! [SY522: $i,SY523: $i,SY524: $i] :
( ( SY524 != SY523 )
| ~ ( ~ ( ~ ( c_member @ SY522 @ SV49 @ SY524 )
| ( c_member @ SY522 @ SV49 @ SY523 ) )
| ~ ( ~ ( c_member @ SY522 @ SV49 @ SY523 )
| ( c_member @ SY522 @ SV49 @ SY524 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(808,plain,
! [SV50: $i] :
( ( ! [SY525: $i,SY526: $i,SY527: $i] :
( ~ ( c_Relation_Otrans @ SY527 @ SY526 )
| ~ ( c_Relation_Otrans @ SY525 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SY527 @ SY525 ) @ ( c_Wellfounded_Olex__prod @ SY527 @ SY525 @ SY526 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(809,plain,
! [SV51: $i] :
( ( ! [SY528: $i,SY529: $i,SY530: $i,SY531: $i] :
( ~ ( c_member @ ( tc_prod @ SY531 @ SY531 ) @ ( c_Product__Type_OPair @ SY531 @ SY531 @ SY530 @ SY529 ) @ SY528 )
| ~ ( c_member @ ( tc_prod @ SY531 @ SY531 ) @ ( c_Product__Type_OPair @ SY531 @ SY531 @ SY529 @ SV51 ) @ SY528 )
| ( c_member @ ( tc_prod @ SY531 @ SY531 ) @ ( c_Product__Type_OPair @ SY531 @ SY531 @ SY530 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SY531 @ SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(810,plain,
! [SV52: $i] :
( ( ! [SY532: $i,SY533: $i,SY534: $i] :
( ( SY534 != SY533 )
| ~ ( c_member @ SY532 @ SY533 @ SV52 )
| ( c_member @ SY532 @ SY534 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(811,plain,
! [SV53: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ~ ( c_member @ ( tc_prod @ SY536 @ SY536 ) @ SY535 @ ( c_Relation_OId__on @ SY536 @ SV53 ) )
| ~ ! [SY537: $i] :
( ~ ( c_member @ SY536 @ SY537 @ SV53 )
| ( SY535
!= ( c_Product__Type_OPair @ SY536 @ SY536 @ SY537 @ SY537 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(812,plain,
! [SV54: $i] :
( ( ! [SY538: $i,SY539: $i,SY540: $i,SY541: $i] :
( ~ ( c_member @ ( tc_prod @ SY541 @ SY541 ) @ ( c_Product__Type_OPair @ SY541 @ SY541 @ SY540 @ SY539 ) @ ( c_Transitive__Closure_Otrancl @ SY541 @ SY538 ) )
| ~ ( c_member @ ( tc_prod @ SY541 @ SY541 ) @ ( c_Product__Type_OPair @ SY541 @ SY541 @ SY539 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY541 @ SY538 ) )
| ( c_member @ ( tc_prod @ SY541 @ SY541 ) @ ( c_Product__Type_OPair @ SY541 @ SY541 @ SY540 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY541 @ SY538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(813,plain,
! [SV55: $i] :
( ( ! [SY542: $i,SY543: $i] :
( ~ ! [SY544: $i] :
( ~ ( c_member @ ( tc_prod @ SY543 @ SY543 ) @ ( c_Product__Type_OPair @ SY543 @ SY543 @ SY544 @ SY542 ) @ SV55 )
| ( c_member @ SY543 @ SY544 @ ( c_Wellfounded_Oacc @ SY543 @ SV55 ) ) )
| ( c_member @ SY543 @ SY542 @ ( c_Wellfounded_Oacc @ SY543 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(814,plain,
! [SV56: $i] :
( ( ! [SY545: $i,SY546: $i,SY547: $i,SY548: $i] :
( ~ ( c_member @ ( tc_prod @ SY548 @ SY548 ) @ ( c_Product__Type_OPair @ SY548 @ SY548 @ SY547 @ SY546 ) @ ( c_Transitive__Closure_Ortrancl @ SY548 @ SY545 ) )
| ~ ( c_member @ ( tc_prod @ SY548 @ SY548 ) @ ( c_Product__Type_OPair @ SY548 @ SY548 @ SY546 @ SV56 ) @ SY545 )
| ( c_member @ ( tc_prod @ SY548 @ SY548 ) @ ( c_Product__Type_OPair @ SY548 @ SY548 @ SY547 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SY548 @ SY545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(815,plain,
! [SV57: $i] :
( ( ! [SY549: $i,SY550: $i,SY551: $i,SY552: $i,SY553: $i] :
( ( ( c_Product__Type_OPair @ SY553 @ SY552 @ SY551 @ SY550 )
!= ( c_Product__Type_OPair @ SY553 @ SY552 @ SY549 @ SV57 ) )
| ~ ( ( SY551 != SY549 )
| ( SY550 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(816,plain,
! [SV58: $i] :
( ( ! [SY554: $i,SY555: $i] :
( ~ ! [SY556: $i,SY557: $i] :
( ~ ( c_member @ ( tc_prod @ SY555 @ SY554 ) @ ( c_Product__Type_OPair @ SY555 @ SY554 @ SY556 @ SY557 ) @ SV58 )
| ! [SY558: $i] :
( ~ ( c_member @ ( tc_prod @ SY555 @ SY554 ) @ ( c_Product__Type_OPair @ SY555 @ SY554 @ SY556 @ SY558 ) @ SV58 )
| ( SY557 = SY558 ) ) )
| ( c_Relation_Osingle__valued @ SY555 @ SY554 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(817,plain,
! [SV59: $i] :
( ( ! [SY559: $i,SY560: $i,SY561: $i] :
( ~ ( c_member @ ( tc_prod @ SY561 @ SY561 ) @ ( c_Product__Type_OPair @ SY561 @ SY561 @ SY560 @ SY559 ) @ ( c_Transitive__Closure_Ortrancl @ SY561 @ SV59 ) )
| ~ ( ( SY560 != SY559 ) )
| ~ ! [SY562: $i] :
( ~ ( c_member @ ( tc_prod @ SY561 @ SY561 ) @ ( c_Product__Type_OPair @ SY561 @ SY561 @ SY560 @ SY562 ) @ ( c_Transitive__Closure_Ortrancl @ SY561 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SY561 @ SY561 ) @ ( c_Product__Type_OPair @ SY561 @ SY561 @ SY562 @ SY559 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(818,plain,
! [SV60: $i] :
( ( ! [SY563: $i,SY564: $i,SY565: $i,SY566: $i] :
( ~ ( c_Relation_Orefl__on @ SY566 @ SY565 @ SY564 )
| ~ ( c_member @ ( tc_prod @ SY566 @ SY566 ) @ ( c_Product__Type_OPair @ SY566 @ SY566 @ SY563 @ SV60 ) @ SY564 )
| ( c_member @ SY566 @ SY563 @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(819,plain,
! [SV61: $i] :
( ( ! [SY567: $i] :
( ~ ! [SY568: $i,SY569: $i] :
( ~ ( c_member @ ( tc_prod @ SY567 @ SY567 ) @ ( c_Product__Type_OPair @ SY567 @ SY567 @ SY568 @ SY569 ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SY567 @ SY567 ) @ ( c_Product__Type_OPair @ SY567 @ SY567 @ SY569 @ SY568 ) @ SV61 )
| ( SY568 = SY569 ) )
| ( c_Relation_Oantisym @ SY567 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(820,plain,
! [SV62: $i] :
( ( ! [SY570: $i,SY571: $i,SY572: $i] :
( ~ ( c_member @ SY572 @ SY571 @ ( c_Set_Oinsert @ SY572 @ SY570 @ SV62 ) )
| ~ ( ( SY571 != SY570 ) )
| ( c_member @ SY572 @ SY571 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(821,plain,
! [SV63: $i] :
( ( ! [SY573: $i,SY574: $i,SY575: $i,SY576: $i,SY577: $i,SY578: $i,SY579: $i] :
( ~ ( c_member @ ( tc_prod @ SY579 @ SY578 ) @ ( c_Product__Type_OPair @ SY579 @ SY578 @ SY577 @ SY576 ) @ SY575 )
| ~ ( c_member @ ( tc_prod @ SY578 @ SY574 ) @ ( c_Product__Type_OPair @ SY578 @ SY574 @ SY576 @ SY573 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY579 @ SY574 ) @ ( c_Product__Type_OPair @ SY579 @ SY574 @ SY577 @ SY573 ) @ ( c_Relation_Orel__comp @ SY579 @ SY578 @ SY574 @ SY575 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(822,plain,
! [SV64: $i] :
( ( ! [SY580: $i,SY581: $i,SY582: $i] :
( ( SY582 != SY581 )
| ~ ( ~ ( c_member @ SY580 @ SV64 @ SY582 )
| ~ ( c_member @ SY580 @ SV64 @ SY581 ) )
| ~ ( ~ ~ ( c_member @ SY580 @ SV64 @ SY582 )
| ( c_member @ SY580 @ SV64 @ SY581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(823,plain,
! [SV65: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ~ ( c_member @ ( tc_prod @ SY584 @ SY584 ) @ SY583 @ SV65 )
| ( c_member @ ( tc_prod @ SY584 @ SY584 ) @ SY583 @ ( c_Transitive__Closure_Ortrancl @ SY584 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(824,plain,
! [SV66: $i] :
( ( ! [SY585: $i] :
( ~ ! [SY586: $i,SY587: $i] :
( ~ ( c_member @ ( tc_prod @ SY585 @ SY585 ) @ ( c_Product__Type_OPair @ SY585 @ SY585 @ SY586 @ SY587 ) @ SV66 )
| ! [SY588: $i] :
( ~ ( c_member @ ( tc_prod @ SY585 @ SY585 ) @ ( c_Product__Type_OPair @ SY585 @ SY585 @ SY587 @ SY588 ) @ SV66 )
| ( c_member @ ( tc_prod @ SY585 @ SY585 ) @ ( c_Product__Type_OPair @ SY585 @ SY585 @ SY586 @ SY588 ) @ SV66 ) ) )
| ( c_Relation_Otrans @ SY585 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(825,plain,
! [SV67: $i] :
( ( ! [SY589: $i,SY590: $i,SY591: $i] :
( ~ ~ ( c_member @ SY591 @ SY590 @ SY589 )
| ~ ~ ( c_member @ SY591 @ SY590 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY591 @ SY590 @ SY589 )
!= ( c_Set_Oinsert @ SY591 @ SY590 @ SV67 ) )
| ( SY589 = SV67 ) )
| ~ ( ( SY589 != SV67 )
| ( ( c_Set_Oinsert @ SY591 @ SY590 @ SY589 )
= ( c_Set_Oinsert @ SY591 @ SY590 @ SV67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(826,plain,
! [SV68: $i] :
( ( ! [SY592: $i,SY593: $i,SY594: $i] :
( ~ ( c_member @ ( tc_prod @ SY594 @ SY594 ) @ ( c_Product__Type_OPair @ SY594 @ SY594 @ SY593 @ SY592 ) @ SV68 )
| ( c_member @ ( tc_prod @ SY594 @ SY594 ) @ ( c_Product__Type_OPair @ SY594 @ SY594 @ SY593 @ SY592 ) @ ( c_Transitive__Closure_Otrancl @ SY594 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(827,plain,
! [SV69: $i] :
( ( ! [SY595: $i,SY596: $i] :
( ~ ( c_member @ SY596 @ SY595 @ SV69 )
| ( ( c_Set_Oinsert @ SY596 @ SY595 @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(828,plain,
! [SV70: $i] :
( ( ! [SY597: $i] :
~ ( ~ ( ~ ( c_Relation_Oirrefl @ SY597 @ SV70 )
| ! [SY598: $i] :
~ ( c_member @ ( tc_prod @ SY597 @ SY597 ) @ ( c_Product__Type_OPair @ SY597 @ SY597 @ SY598 @ SY598 ) @ SV70 ) )
| ~ ( ~ ! [SY599: $i] :
~ ( c_member @ ( tc_prod @ SY597 @ SY597 ) @ ( c_Product__Type_OPair @ SY597 @ SY597 @ SY599 @ SY599 ) @ SV70 )
| ( c_Relation_Oirrefl @ SY597 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(829,plain,
! [SV71: $i] :
( ( ! [SY600: $i,SY601: $i,SY602: $i,SY603: $i] :
( ~ ( c_member @ ( tc_prod @ SY603 @ SY603 ) @ ( c_Product__Type_OPair @ SY603 @ SY603 @ SY602 @ SY601 ) @ ( c_Transitive__Closure_Ortrancl @ SY603 @ SY600 ) )
| ~ ( c_member @ ( tc_prod @ SY603 @ SY603 ) @ ( c_Product__Type_OPair @ SY603 @ SY603 @ SY601 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY603 @ SY600 ) )
| ( c_member @ ( tc_prod @ SY603 @ SY603 ) @ ( c_Product__Type_OPair @ SY603 @ SY603 @ SY602 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY603 @ SY600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(830,plain,
! [SV72: $i] :
( ( ! [SY604: $i,SY605: $i] :
~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SY605 @ SY604 @ SV72 )
| ! [SY606: $i,SY607: $i] :
( ~ ( c_member @ ( tc_prod @ SY605 @ SY604 ) @ ( c_Product__Type_OPair @ SY605 @ SY604 @ SY606 @ SY607 ) @ SV72 )
| ! [SY608: $i] :
( ~ ( c_member @ ( tc_prod @ SY605 @ SY604 ) @ ( c_Product__Type_OPair @ SY605 @ SY604 @ SY606 @ SY608 ) @ SV72 )
| ( SY607 = SY608 ) ) ) )
| ~ ( ~ ! [SY609: $i,SY610: $i] :
( ~ ( c_member @ ( tc_prod @ SY605 @ SY604 ) @ ( c_Product__Type_OPair @ SY605 @ SY604 @ SY609 @ SY610 ) @ SV72 )
| ! [SY611: $i] :
( ~ ( c_member @ ( tc_prod @ SY605 @ SY604 ) @ ( c_Product__Type_OPair @ SY605 @ SY604 @ SY609 @ SY611 ) @ SV72 )
| ( SY610 = SY611 ) ) )
| ( c_Relation_Osingle__valued @ SY605 @ SY604 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(831,plain,
( ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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 ) ) )
| ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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_not_pos,[status(thm)],[752]) ).
thf(832,plain,
! [SV73: $i] :
( ( ! [SY612: $i,SY613: $i,SY614: $i] :
~ ( ~ ( ~ ( c_member @ SY614 @ SY613 @ ( c_Relation_ODomain @ SY614 @ SY612 @ SV73 ) )
| ~ ! [SY615: $i] :
~ ( c_member @ ( tc_prod @ SY614 @ SY612 ) @ ( c_Product__Type_OPair @ SY614 @ SY612 @ SY613 @ SY615 ) @ SV73 ) )
| ~ ( ~ ~ ! [SY616: $i] :
~ ( c_member @ ( tc_prod @ SY614 @ SY612 ) @ ( c_Product__Type_OPair @ SY614 @ SY612 @ SY613 @ SY616 ) @ SV73 )
| ( c_member @ SY614 @ SY613 @ ( c_Relation_ODomain @ SY614 @ SY612 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(833,plain,
! [SV74: $i] :
( ( ! [SY617: $i,SY618: $i,SY619: $i] :
( ~ ( c_Relation_Orefl__on @ SY619 @ SY618 @ SY617 )
| ~ ( c_member @ SY619 @ SV74 @ SY618 )
| ( c_member @ ( tc_prod @ SY619 @ SY619 ) @ ( c_Product__Type_OPair @ SY619 @ SY619 @ SV74 @ SV74 ) @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(834,plain,
! [SV75: $i] :
( ( ! [SY620: $i,SY621: $i,SY622: $i] :
( ~ ( ~ ~ ( c_member @ SY622 @ SY621 @ SY620 )
| ( SY621 = SV75 ) )
| ( c_member @ SY622 @ SY621 @ ( c_Set_Oinsert @ SY622 @ SV75 @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(835,plain,
! [SV76: $i] :
( ( ! [SY623: $i,SY624: $i,SY625: $i,SY626: $i] :
( ~ ( c_member @ ( tc_prod @ SY626 @ SY625 ) @ ( c_Product__Type_OPair @ SY626 @ SY625 @ SY624 @ SY623 ) @ SV76 )
| ( c_member @ SY625 @ SY623 @ ( c_Relation_ORange @ SY626 @ SY625 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(836,plain,
! [SV77: $i] :
( ( ! [SY627: $i,SY628: $i,SY629: $i,SY630: $i] :
( ~ ( c_member @ ( tc_prod @ SY630 @ SY629 ) @ ( c_Product__Type_OPair @ SY630 @ SY629 @ SY628 @ SY627 ) @ SV77 )
| ( c_member @ SY630 @ SY628 @ ( c_Relation_ODomain @ SY630 @ SY629 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(837,plain,
! [SV78: $i] :
( ( ! [SY631: $i] :
( ~ ( c_Relation_Otrans @ SY631 @ SV78 )
| ( ( c_Transitive__Closure_Otrancl @ SY631 @ SV78 )
= SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(838,plain,
! [SV1: $i,SV79: $i] :
( ( c_Relation_Otrans @ SV79 @ ( c_Relation_OId__on @ SV79 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(839,plain,
! [SV2: $i,SV80: $i] :
( ( ! [SY632: $i] : ( c_member @ ( tc_prod @ SY632 @ SY632 ) @ ( c_Product__Type_OPair @ SY632 @ SY632 @ SV80 @ SV80 ) @ ( c_Transitive__Closure_Ortrancl @ SY632 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(840,plain,
! [SV3: $i,SV81: $i] :
( ( c_Relation_Otrans @ SV81 @ ( c_Transitive__Closure_Ortrancl @ SV81 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(841,plain,
! [SV4: $i,SV82: $i] :
( ( c_Relation_Otrans @ SV82 @ ( c_Transitive__Closure_Otrancl @ SV82 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(842,plain,
! [SV5: $i,SV83: $i] :
( ( c_member @ ( tc_prod @ SV83 @ SV83 ) @ ( c_Product__Type_OPair @ SV83 @ SV83 @ SV5 @ SV5 ) @ ( c_Relation_OId @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(843,plain,
! [SV7: $i,SV84: $i] :
( ( ! [SY633: $i] : ( c_member @ SY633 @ SV84 @ ( c_Set_Oinsert @ SY633 @ SV84 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(844,plain,
! [SV8: $i,SV85: $i] :
( ( ! [SY634: $i,SY635: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY635 @ SY635 ) @ ( c_Product__Type_OPair @ SY635 @ SY635 @ SY634 @ SV85 ) @ ( c_Relation_OId__on @ SY635 @ SV8 ) )
| ~ ( ( SY634 != SV85 )
| ~ ( c_member @ SY635 @ SY634 @ SV8 ) ) )
| ~ ( ~ ~ ( ( SY634 != SV85 )
| ~ ( c_member @ SY635 @ SY634 @ SV8 ) )
| ( c_member @ ( tc_prod @ SY635 @ SY635 ) @ ( c_Product__Type_OPair @ SY635 @ SY635 @ SY634 @ SV85 ) @ ( c_Relation_OId__on @ SY635 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(845,plain,
! [SV9: $i,SV86: $i] :
( ( ! [SY636: $i,SY637: $i] :
( ( SY637 != SY636 )
| ~ ( c_member @ SV86 @ SY637 @ SV9 )
| ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SY637 @ SY636 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(846,plain,
! [SV10: $i,SV87: $i] :
( ( ! [SY638: $i,SY639: $i,SY640: $i] :
( ~ ( c_member @ ( tc_prod @ SY640 @ SY640 ) @ ( c_Product__Type_OPair @ SY640 @ SY640 @ SY639 @ SY638 ) @ SV87 )
| ~ ( c_member @ ( tc_prod @ SY640 @ SY640 ) @ ( c_Product__Type_OPair @ SY640 @ SY640 @ SY638 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY640 @ SV87 ) )
| ( c_member @ ( tc_prod @ SY640 @ SY640 ) @ ( c_Product__Type_OPair @ SY640 @ SY640 @ SY639 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY640 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(847,plain,
! [SV11: $i,SV88: $i] :
( ( ! [SY641: $i] :
( ~ ( c_member @ ( tc_prod @ SY641 @ SY641 ) @ SV88 @ SV11 )
| ( c_member @ ( tc_prod @ SY641 @ SY641 ) @ SV88 @ ( c_Transitive__Closure_Otrancl @ SY641 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(848,plain,
! [SV12: $i,SV89: $i] :
( ( ! [SY642: $i] :
~ ( ~ ( ~ ( c_member @ SY642 @ SV89 @ ( c_fequal @ SV12 ) )
| ( SV89 = SV12 ) )
| ~ ( ( SV89 != SV12 )
| ( c_member @ SY642 @ SV89 @ ( c_fequal @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(849,plain,
! [SV13: $i,SV90: $i] :
( ( ! [SY643: $i,SY644: $i] :
~ ( ~ ( ~ ( c_member @ SY644 @ SY643 @ ( c_Set_Oinsert @ SY644 @ SV90 @ SV13 ) )
| ( SY643 = SV90 )
| ( c_member @ SY644 @ SY643 @ SV13 ) )
| ~ ( ~ ( ( SY643 = SV90 )
| ( c_member @ SY644 @ SY643 @ SV13 ) )
| ( c_member @ SY644 @ SY643 @ ( c_Set_Oinsert @ SY644 @ SV90 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(850,plain,
! [SV14: $i,SV91: $i] :
( ( ! [SY645: $i,SY646: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SY646 @ SY646 ) @ ( c_Product__Type_OPair @ SY646 @ SY646 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SY646 @ SY645 ) )
| ~ ( c_member @ ( tc_prod @ SY646 @ SY646 ) @ ( c_Product__Type_OPair @ SY646 @ SY646 @ SV91 @ SV14 ) @ SY645 )
| ( SV91 != SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(851,plain,
! [SV15: $i,SV92: $i] :
( ( ! [SY648: $i,SY649: $i,SY650: $i,SY651: $i,SY652: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY650 @ SY649 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY648 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY652 @ SY651 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY652 @ SY651 @ SY650 @ SY649 )
!= ( c_Product__Type_OPair @ SY652 @ SY651 @ SY648 @ SV92 ) ) )
| ~ ! [SY653: $i,SY654: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY650 @ SY649 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY653 @ SY654 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY652 @ SY651 ) @ ( tc_prod @ SY652 @ SY651 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY653 @ SY654 ) @ ( c_Product__Type_OPair @ SY652 @ SY651 @ SY648 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY652 @ SY651 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(852,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
| ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) )
| ~ ( ~ ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 )
| ( c_Nitpick_Orefl_H @ SV93 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(853,plain,
! [SV17: $i,SV94: $i] :
( ( ! [SY657: $i,SY658: $i,SY659: $i,SY660: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY660 @ SY659 @ SY658 @ SY657 )
!= ( c_Product__Type_OPair @ SY660 @ SY659 @ SV94 @ SV17 ) )
| ~ ( ( SY658 != SV94 )
| ( SY657 != SV17 ) ) )
| ~ ( ~ ~ ( ( SY658 != SV94 )
| ( SY657 != SV17 ) )
| ( ( c_Product__Type_OPair @ SY660 @ SY659 @ SY658 @ SY657 )
= ( c_Product__Type_OPair @ SY660 @ SY659 @ SV94 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(854,plain,
! [SV18: $i,SV95: $i] :
( ( ! [SY661: $i,SY662: $i] :
( ~ ( c_member @ SY662 @ SY661 @ ( c_Relation_ORange @ SV95 @ SY662 @ SV18 ) )
| ~ ! [SY663: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SY662 ) @ ( c_Product__Type_OPair @ SV95 @ SY662 @ SY663 @ SY661 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(855,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Oantisym @ SV96 @ SV19 )
| ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) )
| ~ ( ~ ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) )
| ( c_Relation_Oantisym @ SV96 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(856,plain,
! [SV20: $i,SV97: $i] :
( ( ! [SY668: $i,SY669: $i,SY670: $i,SY671: $i,SY672: $i,SY673: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY673 @ SY672 ) @ ( tc_prod @ SY673 @ SY672 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY673 @ SY672 ) @ ( tc_prod @ SY673 @ SY672 ) @ ( c_Product__Type_OPair @ SY673 @ SY672 @ SY671 @ SY670 ) @ ( c_Product__Type_OPair @ SY673 @ SY672 @ SY669 @ SY668 ) ) @ ( c_Wellfounded_Olex__prod @ SY673 @ SY672 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY673 @ SY673 ) @ ( c_Product__Type_OPair @ SY673 @ SY673 @ SY671 @ SY669 ) @ SV97 )
| ~ ( ( SY671 != SY669 )
| ~ ( c_member @ ( tc_prod @ SY672 @ SY672 ) @ ( c_Product__Type_OPair @ SY672 @ SY672 @ SY670 @ SY668 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY673 @ SY673 ) @ ( c_Product__Type_OPair @ SY673 @ SY673 @ SY671 @ SY669 ) @ SV97 )
| ~ ( ( SY671 != SY669 )
| ~ ( c_member @ ( tc_prod @ SY672 @ SY672 ) @ ( c_Product__Type_OPair @ SY672 @ SY672 @ SY670 @ SY668 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY673 @ SY672 ) @ ( tc_prod @ SY673 @ SY672 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY673 @ SY672 ) @ ( tc_prod @ SY673 @ SY672 ) @ ( c_Product__Type_OPair @ SY673 @ SY672 @ SY671 @ SY670 ) @ ( c_Product__Type_OPair @ SY673 @ SY672 @ SY669 @ SY668 ) ) @ ( c_Wellfounded_Olex__prod @ SY673 @ SY672 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(857,plain,
! [SV21: $i,SV98: $i] :
( ( ! [SY674: $i] :
~ ( ~ ( ~ ( c_member @ SY674 @ SV98 @ ( c_Wellfounded_Oacc @ SY674 @ SV21 ) )
| ! [SY675: $i] :
( ~ ( c_member @ ( tc_prod @ SY674 @ SY674 ) @ ( c_Product__Type_OPair @ SY674 @ SY674 @ SY675 @ SV98 ) @ SV21 )
| ( c_member @ SY674 @ SY675 @ ( c_Wellfounded_Oacc @ SY674 @ SV21 ) ) ) )
| ~ ( ~ ! [SY676: $i] :
( ~ ( c_member @ ( tc_prod @ SY674 @ SY674 ) @ ( c_Product__Type_OPair @ SY674 @ SY674 @ SY676 @ SV98 ) @ SV21 )
| ( c_member @ SY674 @ SY676 @ ( c_Wellfounded_Oacc @ SY674 @ SV21 ) ) )
| ( c_member @ SY674 @ SV98 @ ( c_Wellfounded_Oacc @ SY674 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(858,plain,
! [SV22: $i,SV99: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ~ ( c_member @ ( tc_prod @ SY678 @ SY678 ) @ ( c_Product__Type_OPair @ SY678 @ SY678 @ SY677 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SY678 @ SV22 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY678 @ SY678 ) @ ( c_Product__Type_OPair @ SY678 @ SY678 @ SY677 @ SV99 ) @ SV22 )
| ~ ! [SY679: $i] :
( ~ ( c_member @ ( tc_prod @ SY678 @ SY678 ) @ ( c_Product__Type_OPair @ SY678 @ SY678 @ SY677 @ SY679 ) @ ( c_Transitive__Closure_Otrancl @ SY678 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SY678 @ SY678 ) @ ( c_Product__Type_OPair @ SY678 @ SY678 @ SY679 @ SV99 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(859,plain,
! [SV23: $i,SV100: $i] :
( ( ! [SY680: $i,SY681: $i] :
( ~ ( c_member @ SY681 @ SY680 @ ( c_Wellfounded_Oacc @ SY681 @ SV100 ) )
| ~ ( c_member @ ( tc_prod @ SY681 @ SY681 ) @ ( c_Product__Type_OPair @ SY681 @ SY681 @ SV23 @ SY680 ) @ SV100 )
| ( c_member @ SY681 @ SV23 @ ( c_Wellfounded_Oacc @ SY681 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(860,plain,
! [SV24: $i,SV101: $i] :
( ( ! [SY682: $i,SY683: $i,SY684: $i,SY685: $i] :
( ~ ( c_member @ SY685 @ SY684 @ SY683 )
| ~ ( c_member @ ( tc_prod @ SY685 @ SY682 ) @ ( c_Product__Type_OPair @ SY685 @ SY682 @ SY684 @ SV101 ) @ SV24 )
| ( c_member @ SY682 @ SV101 @ ( c_Relation_OImage @ SY685 @ SY682 @ SV24 @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(861,plain,
! [SV25: $i,SV102: $i] :
( ( ! [SY686: $i,SY687: $i] :
( ~ ( c_Wellfounded_Owf @ SY687 @ SY686 )
| ~ ( c_member @ ( tc_prod @ SY687 @ SY687 ) @ ( c_Product__Type_OPair @ SY687 @ SY687 @ SV102 @ SV25 ) @ SY686 )
| ~ ( c_member @ ( tc_prod @ SY687 @ SY687 ) @ ( c_Product__Type_OPair @ SY687 @ SY687 @ SV25 @ SV102 ) @ SY686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(862,plain,
! [SV26: $i,SV103: $i] :
( ( ! [SY688: $i,SY689: $i,SY690: $i] :
( ~ ( c_member @ SY690 @ SY689 @ ( c_Relation_OImage @ SY688 @ SY690 @ SV103 @ SV26 ) )
| ~ ! [SY691: $i] :
( ~ ( c_member @ ( tc_prod @ SY688 @ SY690 ) @ ( c_Product__Type_OPair @ SY688 @ SY690 @ SY691 @ SY689 ) @ SV103 )
| ~ ( c_member @ SY688 @ SY691 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(863,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Otrans @ SV104 @ SV27 )
| ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) )
| ( c_Relation_Otrans @ SV104 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(864,plain,
! [SV28: $i,SV105: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i] :
( ~ ( c_member @ ( tc_prod @ SY700 @ SY700 ) @ ( c_Product__Type_OPair @ SY700 @ SY700 @ SY699 @ SY698 ) @ SV105 )
| ~ ( c_member @ ( tc_prod @ SY700 @ SY700 ) @ ( c_Product__Type_OPair @ SY700 @ SY700 @ SY698 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY700 @ SV105 ) )
| ( c_member @ ( tc_prod @ SY700 @ SY700 ) @ ( c_Product__Type_OPair @ SY700 @ SY700 @ SY699 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY700 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(865,plain,
! [SV29: $i,SV106: $i] :
( ( ! [SY701: $i,SY702: $i,SY703: $i] :
~ ( ~ ( ~ ( c_member @ SY703 @ SY702 @ ( c_Relation_OImage @ SY701 @ SY703 @ SV106 @ SV29 ) )
| ~ ! [SY704: $i] :
~ ~ ( ~ ( c_member @ SY701 @ SY704 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SY701 @ SY703 ) @ ( c_Product__Type_OPair @ SY701 @ SY703 @ SY704 @ SY702 ) @ SV106 ) ) )
| ~ ( ~ ~ ! [SY705: $i] :
~ ~ ( ~ ( c_member @ SY701 @ SY705 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SY701 @ SY703 ) @ ( c_Product__Type_OPair @ SY701 @ SY703 @ SY705 @ SY702 ) @ SV106 ) )
| ( c_member @ SY703 @ SY702 @ ( c_Relation_OImage @ SY701 @ SY703 @ SV106 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(866,plain,
! [SV30: $i,SV107: $i] :
( ( ! [SY706: $i] :
( ~ ( c_Wellfounded_Owf @ SY706 @ SV107 )
| ~ ( c_member @ ( tc_prod @ SY706 @ SY706 ) @ ( c_Product__Type_OPair @ SY706 @ SY706 @ SV30 @ SV30 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(867,plain,
! [SV31: $i,SV108: $i] :
( ( ! [SY707: $i,SY708: $i] :
( ~ ( c_Wellfounded_Owf @ SY708 @ SY707 )
| ~ ( c_member @ ( tc_prod @ SY708 @ SY708 ) @ ( c_Product__Type_OPair @ SY708 @ SY708 @ SV108 @ SV31 ) @ SY707 )
| ~ ( c_member @ ( tc_prod @ SY708 @ SY708 ) @ ( c_Product__Type_OPair @ SY708 @ SY708 @ SV31 @ SV108 ) @ SY707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(868,plain,
! [SV32: $i,SV109: $i] :
( ( ! [SY709: $i,SY710: $i] :
( ~ ( c_member @ SY710 @ SY709 @ ( c_Relation_ODomain @ SY710 @ SV109 @ SV32 ) )
| ~ ! [SY711: $i] :
~ ( c_member @ ( tc_prod @ SY710 @ SV109 ) @ ( c_Product__Type_OPair @ SY710 @ SV109 @ SY709 @ SY711 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(869,plain,
! [SV33: $i,SV110: $i] :
( ( ! [SY712: $i,SY713: $i,SY714: $i] :
( ~ ( c_Relation_Orefl__on @ SY714 @ SY713 @ SY712 )
| ~ ( c_member @ ( tc_prod @ SY714 @ SY714 ) @ ( c_Product__Type_OPair @ SY714 @ SY714 @ SV110 @ SV33 ) @ SY712 )
| ( c_member @ SY714 @ SV33 @ SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(870,plain,
! [SV34: $i,SV111: $i] :
( ( ! [SY715: $i,SY716: $i] :
( ~ ( c_member @ ( tc_prod @ SY716 @ SY716 ) @ ( c_Product__Type_OPair @ SY716 @ SY716 @ SY715 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SY716 @ SV34 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY716 @ SY716 ) @ ( c_Product__Type_OPair @ SY716 @ SY716 @ SY715 @ SV111 ) @ SV34 )
| ~ ! [SY717: $i] :
( ~ ( c_member @ ( tc_prod @ SY716 @ SY716 ) @ ( c_Product__Type_OPair @ SY716 @ SY716 @ SY715 @ SY717 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SY716 @ SY716 ) @ ( c_Product__Type_OPair @ SY716 @ SY716 @ SY717 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SY716 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(871,plain,
! [SV35: $i,SV112: $i] :
( ( ! [SY718: $i] :
( ~ ( c_Wellfounded_Owf @ SY718 @ SV112 )
| ~ ( c_member @ ( tc_prod @ SY718 @ SY718 ) @ ( c_Product__Type_OPair @ SY718 @ SY718 @ SV35 @ SV35 ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(872,plain,
! [SV36: $i,SV113: $i] :
( ( ! [SY719: $i,SY720: $i] :
( ~ ( c_member @ SY720 @ SY719 @ SV113 )
| ( c_member @ SY720 @ SY719 @ ( c_Set_Oinsert @ SY720 @ SV36 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(873,plain,
! [SV37: $i,SV114: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) )
| ~ ! [SY721: $i] :
( SV37
!= ( c_Product__Type_OPair @ SV114 @ SV114 @ SY721 @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(874,plain,
! [SV38: $i,SV115: $i] :
( ( ! [SY722: $i,SY723: $i] :
( ~ ( c_Relation_Oantisym @ SY723 @ SY722 )
| ~ ( c_member @ ( tc_prod @ SY723 @ SY723 ) @ ( c_Product__Type_OPair @ SY723 @ SY723 @ SV115 @ SV38 ) @ SY722 )
| ~ ( c_member @ ( tc_prod @ SY723 @ SY723 ) @ ( c_Product__Type_OPair @ SY723 @ SY723 @ SV38 @ SV115 ) @ SY722 )
| ( SV115 = SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(875,plain,
! [SV39: $i,SV116: $i] :
( ( ! [SY724: $i] :
( ~ ~ ( c_member @ SY724 @ SV116 @ ( c_Wellfounded_Oacc @ SY724 @ SV39 ) )
| ~ ! [SY725: $i] :
( ~ ( c_member @ ( tc_prod @ SY724 @ SY724 ) @ ( c_Product__Type_OPair @ SY724 @ SY724 @ SY725 @ SV116 ) @ SV39 )
| ( c_member @ SY724 @ SY725 @ ( c_Wellfounded_Oacc @ SY724 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(876,plain,
! [SV40: $i,SV117: $i] :
( ( ! [SY726: $i,SY727: $i] :
( ( SY727 != SY726 )
| ~ ( ~ ( ~ ( c_member @ SV117 @ SY727 @ SV40 )
| ( c_member @ SV117 @ SY726 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SY726 @ SV40 )
| ( c_member @ SV117 @ SY727 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(877,plain,
! [SV41: $i,SV118: $i] :
( ( ! [SY728: $i,SY729: $i] :
( ~ ( c_member @ ( tc_prod @ SY729 @ SY729 ) @ ( c_Product__Type_OPair @ SY729 @ SY729 @ SY728 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SY729 @ SV41 ) )
| ~ ( ( SY728 != SV118 ) )
| ~ ! [SY730: $i] :
( ~ ( c_member @ ( tc_prod @ SY729 @ SY729 ) @ ( c_Product__Type_OPair @ SY729 @ SY729 @ SY728 @ SY730 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SY729 @ SY729 ) @ ( c_Product__Type_OPair @ SY729 @ SY729 @ SY730 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SY729 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(878,plain,
! [SV42: $i,SV119: $i] :
( ( ! [SY731: $i,SY732: $i] :
~ ( ~ ( ~ ( c_member @ SY732 @ SY731 @ ( c_Relation_ORange @ SV119 @ SY732 @ SV42 ) )
| ~ ! [SY733: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SY732 ) @ ( c_Product__Type_OPair @ SV119 @ SY732 @ SY733 @ SY731 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY734: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SY732 ) @ ( c_Product__Type_OPair @ SV119 @ SY732 @ SY734 @ SY731 ) @ SV42 )
| ( c_member @ SY732 @ SY731 @ ( c_Relation_ORange @ SV119 @ SY732 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(879,plain,
! [SV43: $i,SV120: $i] :
( ( ! [SY735: $i,SY736: $i,SY737: $i,SY738: $i] :
( ~ ( c_Relation_Osingle__valued @ SY738 @ SY737 @ SY736 )
| ~ ( c_member @ ( tc_prod @ SY738 @ SY737 ) @ ( c_Product__Type_OPair @ SY738 @ SY737 @ SY735 @ SV120 ) @ SY736 )
| ~ ( c_member @ ( tc_prod @ SY738 @ SY737 ) @ ( c_Product__Type_OPair @ SY738 @ SY737 @ SY735 @ SV43 ) @ SY736 )
| ( SV120 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(880,plain,
! [SV44: $i,SV121: $i] :
( ( ! [SY739: $i] :
~ ( ~ ( ~ ( c_Relation_Ototal__on @ SY739 @ SV121 @ SV44 )
| ! [SY740: $i] :
( ~ ( c_member @ SY739 @ SY740 @ SV121 )
| ! [SY741: $i] :
( ~ ( c_member @ SY739 @ SY741 @ SV121 )
| ~ ( ( SY740 != SY741 ) )
| ( c_member @ ( tc_prod @ SY739 @ SY739 ) @ ( c_Product__Type_OPair @ SY739 @ SY739 @ SY740 @ SY741 ) @ SV44 )
| ( c_member @ ( tc_prod @ SY739 @ SY739 ) @ ( c_Product__Type_OPair @ SY739 @ SY739 @ SY741 @ SY740 ) @ SV44 ) ) ) )
| ~ ( ~ ! [SY742: $i] :
( ~ ( c_member @ SY739 @ SY742 @ SV121 )
| ! [SY743: $i] :
( ~ ( c_member @ SY739 @ SY743 @ SV121 )
| ~ ( ( SY742 != SY743 ) )
| ( c_member @ ( tc_prod @ SY739 @ SY739 ) @ ( c_Product__Type_OPair @ SY739 @ SY739 @ SY742 @ SY743 ) @ SV44 )
| ( c_member @ ( tc_prod @ SY739 @ SY739 ) @ ( c_Product__Type_OPair @ SY739 @ SY739 @ SY743 @ SY742 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SY739 @ SV121 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(881,plain,
! [SV45: $i,SV122: $i] :
( ( ! [SY744: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY744 @ SY744 ) @ ( c_Product__Type_OPair @ SY744 @ SY744 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SY744 ) )
| ( SV122 = SV45 ) )
| ~ ( ( SV122 != SV45 )
| ( c_member @ ( tc_prod @ SY744 @ SY744 ) @ ( c_Product__Type_OPair @ SY744 @ SY744 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SY744 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(882,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ( ~ ( ~ ( c_Wellfounded_Owf @ SV123 @ SV46 )
| ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) )
| ~ ( ~ ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) )
| ( c_Wellfounded_Owf @ SV123 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(883,plain,
! [SV47: $i,SV124: $i] :
( ( ! [SY753: $i,SY754: $i,SY755: $i] :
( ~ ( c_Relation_Otrans @ SY755 @ SY754 )
| ~ ( c_member @ ( tc_prod @ SY755 @ SY755 ) @ ( c_Product__Type_OPair @ SY755 @ SY755 @ SY753 @ SV124 ) @ SY754 )
| ~ ( c_member @ ( tc_prod @ SY755 @ SY755 ) @ ( c_Product__Type_OPair @ SY755 @ SY755 @ SV124 @ SV47 ) @ SY754 )
| ( c_member @ ( tc_prod @ SY755 @ SY755 ) @ ( c_Product__Type_OPair @ SY755 @ SY755 @ SY753 @ SV47 ) @ SY754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(884,plain,
! [SV48: $i,SV125: $i] :
( ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ~ ( c_member @ ( tc_prod @ SY758 @ SY758 ) @ ( c_Product__Type_OPair @ SY758 @ SY758 @ SY757 @ SY756 ) @ ( c_Transitive__Closure_Otrancl @ SY758 @ SV125 ) )
| ~ ( c_member @ ( tc_prod @ SY758 @ SY758 ) @ ( c_Product__Type_OPair @ SY758 @ SY758 @ SY756 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SY758 @ SY758 ) @ ( c_Product__Type_OPair @ SY758 @ SY758 @ SY757 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SY758 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(885,plain,
! [SV49: $i,SV126: $i] :
( ( ! [SY759: $i,SY760: $i] :
( ( SY760 != SY759 )
| ~ ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SY760 )
| ( c_member @ SV126 @ SV49 @ SY759 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SY759 )
| ( c_member @ SV126 @ SV49 @ SY760 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(886,plain,
! [SV50: $i,SV127: $i] :
( ( ! [SY761: $i,SY762: $i] :
( ~ ( c_Relation_Otrans @ SY762 @ SY761 )
| ~ ( c_Relation_Otrans @ SV127 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SY762 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SY762 @ SV127 @ SY761 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(887,plain,
! [SV51: $i,SV128: $i] :
( ( ! [SY763: $i,SY764: $i,SY765: $i] :
( ~ ( c_member @ ( tc_prod @ SY765 @ SY765 ) @ ( c_Product__Type_OPair @ SY765 @ SY765 @ SY764 @ SY763 ) @ SV128 )
| ~ ( c_member @ ( tc_prod @ SY765 @ SY765 ) @ ( c_Product__Type_OPair @ SY765 @ SY765 @ SY763 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SY765 @ SY765 ) @ ( c_Product__Type_OPair @ SY765 @ SY765 @ SY764 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SY765 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(888,plain,
! [SV52: $i,SV129: $i] :
( ( ! [SY766: $i,SY767: $i] :
( ( SY767 != SY766 )
| ~ ( c_member @ SV129 @ SY766 @ SV52 )
| ( c_member @ SV129 @ SY767 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(889,plain,
! [SV53: $i,SV130: $i] :
( ( ! [SY768: $i] :
( ~ ( c_member @ ( tc_prod @ SY768 @ SY768 ) @ SV130 @ ( c_Relation_OId__on @ SY768 @ SV53 ) )
| ~ ! [SY769: $i] :
( ~ ( c_member @ SY768 @ SY769 @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SY768 @ SY768 @ SY769 @ SY769 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(890,plain,
! [SV54: $i,SV131: $i] :
( ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ~ ( c_member @ ( tc_prod @ SY772 @ SY772 ) @ ( c_Product__Type_OPair @ SY772 @ SY772 @ SY771 @ SY770 ) @ ( c_Transitive__Closure_Otrancl @ SY772 @ SV131 ) )
| ~ ( c_member @ ( tc_prod @ SY772 @ SY772 ) @ ( c_Product__Type_OPair @ SY772 @ SY772 @ SY770 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY772 @ SV131 ) )
| ( c_member @ ( tc_prod @ SY772 @ SY772 ) @ ( c_Product__Type_OPair @ SY772 @ SY772 @ SY771 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY772 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(891,plain,
! [SV55: $i,SV132: $i] :
( ( ! [SY773: $i] :
( ~ ! [SY774: $i] :
( ~ ( c_member @ ( tc_prod @ SY773 @ SY773 ) @ ( c_Product__Type_OPair @ SY773 @ SY773 @ SY774 @ SV132 ) @ SV55 )
| ( c_member @ SY773 @ SY774 @ ( c_Wellfounded_Oacc @ SY773 @ SV55 ) ) )
| ( c_member @ SY773 @ SV132 @ ( c_Wellfounded_Oacc @ SY773 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(892,plain,
! [SV56: $i,SV133: $i] :
( ( ! [SY775: $i,SY776: $i,SY777: $i] :
( ~ ( c_member @ ( tc_prod @ SY777 @ SY777 ) @ ( c_Product__Type_OPair @ SY777 @ SY777 @ SY776 @ SY775 ) @ ( c_Transitive__Closure_Ortrancl @ SY777 @ SV133 ) )
| ~ ( c_member @ ( tc_prod @ SY777 @ SY777 ) @ ( c_Product__Type_OPair @ SY777 @ SY777 @ SY775 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SY777 @ SY777 ) @ ( c_Product__Type_OPair @ SY777 @ SY777 @ SY776 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SY777 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(893,plain,
! [SV57: $i,SV134: $i] :
( ( ! [SY778: $i,SY779: $i,SY780: $i,SY781: $i] :
( ( ( c_Product__Type_OPair @ SY781 @ SY780 @ SY779 @ SY778 )
!= ( c_Product__Type_OPair @ SY781 @ SY780 @ SV134 @ SV57 ) )
| ~ ( ( SY779 != SV134 )
| ( SY778 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(894,plain,
! [SV58: $i,SV135: $i] :
( ( ! [SY782: $i] :
( ~ ! [SY783: $i,SY784: $i] :
( ~ ( c_member @ ( tc_prod @ SY782 @ SV135 ) @ ( c_Product__Type_OPair @ SY782 @ SV135 @ SY783 @ SY784 ) @ SV58 )
| ! [SY785: $i] :
( ~ ( c_member @ ( tc_prod @ SY782 @ SV135 ) @ ( c_Product__Type_OPair @ SY782 @ SV135 @ SY783 @ SY785 ) @ SV58 )
| ( SY784 = SY785 ) ) )
| ( c_Relation_Osingle__valued @ SY782 @ SV135 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(895,plain,
! [SV59: $i,SV136: $i] :
( ( ! [SY786: $i,SY787: $i] :
( ~ ( c_member @ ( tc_prod @ SY787 @ SY787 ) @ ( c_Product__Type_OPair @ SY787 @ SY787 @ SY786 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SY787 @ SV59 ) )
| ~ ( ( SY786 != SV136 ) )
| ~ ! [SY788: $i] :
( ~ ( c_member @ ( tc_prod @ SY787 @ SY787 ) @ ( c_Product__Type_OPair @ SY787 @ SY787 @ SY786 @ SY788 ) @ ( c_Transitive__Closure_Ortrancl @ SY787 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SY787 @ SY787 ) @ ( c_Product__Type_OPair @ SY787 @ SY787 @ SY788 @ SV136 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(896,plain,
! [SV60: $i,SV137: $i] :
( ( ! [SY789: $i,SY790: $i,SY791: $i] :
( ~ ( c_Relation_Orefl__on @ SY791 @ SY790 @ SY789 )
| ~ ( c_member @ ( tc_prod @ SY791 @ SY791 ) @ ( c_Product__Type_OPair @ SY791 @ SY791 @ SV137 @ SV60 ) @ SY789 )
| ( c_member @ SY791 @ SV137 @ SY790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(897,plain,
! [SV61: $i,SV138: $i] :
( ( ~ ! [SY792: $i,SY793: $i] :
( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY792 @ SY793 ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY793 @ SY792 ) @ SV61 )
| ( SY792 = SY793 ) )
| ( c_Relation_Oantisym @ SV138 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(898,plain,
! [SV62: $i,SV139: $i] :
( ( ! [SY794: $i,SY795: $i] :
( ~ ( c_member @ SY795 @ SY794 @ ( c_Set_Oinsert @ SY795 @ SV139 @ SV62 ) )
| ~ ( ( SY794 != SV139 ) )
| ( c_member @ SY795 @ SY794 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(899,plain,
! [SV63: $i,SV140: $i] :
( ( ! [SY796: $i,SY797: $i,SY798: $i,SY799: $i,SY800: $i,SY801: $i] :
( ~ ( c_member @ ( tc_prod @ SY801 @ SY800 ) @ ( c_Product__Type_OPair @ SY801 @ SY800 @ SY799 @ SY798 ) @ SY797 )
| ~ ( c_member @ ( tc_prod @ SY800 @ SY796 ) @ ( c_Product__Type_OPair @ SY800 @ SY796 @ SY798 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY801 @ SY796 ) @ ( c_Product__Type_OPair @ SY801 @ SY796 @ SY799 @ SV140 ) @ ( c_Relation_Orel__comp @ SY801 @ SY800 @ SY796 @ SY797 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(900,plain,
! [SV64: $i,SV141: $i] :
( ( ! [SY802: $i,SY803: $i] :
( ( SY803 != SY802 )
| ~ ( ~ ( c_member @ SV141 @ SV64 @ SY803 )
| ~ ( c_member @ SV141 @ SV64 @ SY802 ) )
| ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SY803 )
| ( c_member @ SV141 @ SV64 @ SY802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(901,plain,
! [SV65: $i,SV142: $i] :
( ( ! [SY804: $i] :
( ~ ( c_member @ ( tc_prod @ SY804 @ SY804 ) @ SV142 @ SV65 )
| ( c_member @ ( tc_prod @ SY804 @ SY804 ) @ SV142 @ ( c_Transitive__Closure_Ortrancl @ SY804 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(902,plain,
! [SV66: $i,SV143: $i] :
( ( ~ ! [SY805: $i,SY806: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY806 ) @ SV66 )
| ! [SY807: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY806 @ SY807 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY807 ) @ SV66 ) ) )
| ( c_Relation_Otrans @ SV143 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(903,plain,
! [SV67: $i,SV144: $i] :
( ( ! [SY808: $i,SY809: $i] :
( ~ ~ ( c_member @ SY809 @ SY808 @ SV144 )
| ~ ~ ( c_member @ SY809 @ SY808 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY809 @ SY808 @ SV144 )
!= ( c_Set_Oinsert @ SY809 @ SY808 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SY809 @ SY808 @ SV144 )
= ( c_Set_Oinsert @ SY809 @ SY808 @ SV67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(904,plain,
! [SV68: $i,SV145: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ~ ( c_member @ ( tc_prod @ SY811 @ SY811 ) @ ( c_Product__Type_OPair @ SY811 @ SY811 @ SY810 @ SV145 ) @ SV68 )
| ( c_member @ ( tc_prod @ SY811 @ SY811 ) @ ( c_Product__Type_OPair @ SY811 @ SY811 @ SY810 @ SV145 ) @ ( c_Transitive__Closure_Otrancl @ SY811 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(905,plain,
! [SV69: $i,SV146: $i] :
( ( ! [SY812: $i] :
( ~ ( c_member @ SY812 @ SV146 @ SV69 )
| ( ( c_Set_Oinsert @ SY812 @ SV146 @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(906,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Oirrefl @ SV147 @ SV70 )
| ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) )
| ~ ( ~ ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 )
| ( c_Relation_Oirrefl @ SV147 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(907,plain,
! [SV71: $i,SV148: $i] :
( ( ! [SY815: $i,SY816: $i,SY817: $i] :
( ~ ( c_member @ ( tc_prod @ SY817 @ SY817 ) @ ( c_Product__Type_OPair @ SY817 @ SY817 @ SY816 @ SY815 ) @ ( c_Transitive__Closure_Ortrancl @ SY817 @ SV148 ) )
| ~ ( c_member @ ( tc_prod @ SY817 @ SY817 ) @ ( c_Product__Type_OPair @ SY817 @ SY817 @ SY815 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY817 @ SV148 ) )
| ( c_member @ ( tc_prod @ SY817 @ SY817 ) @ ( c_Product__Type_OPair @ SY817 @ SY817 @ SY816 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY817 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(908,plain,
! [SV72: $i,SV149: $i] :
( ( ! [SY818: $i] :
~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SY818 @ SV149 @ SV72 )
| ! [SY819: $i,SY820: $i] :
( ~ ( c_member @ ( tc_prod @ SY818 @ SV149 ) @ ( c_Product__Type_OPair @ SY818 @ SV149 @ SY819 @ SY820 ) @ SV72 )
| ! [SY821: $i] :
( ~ ( c_member @ ( tc_prod @ SY818 @ SV149 ) @ ( c_Product__Type_OPair @ SY818 @ SV149 @ SY819 @ SY821 ) @ SV72 )
| ( SY820 = SY821 ) ) ) )
| ~ ( ~ ! [SY822: $i,SY823: $i] :
( ~ ( c_member @ ( tc_prod @ SY818 @ SV149 ) @ ( c_Product__Type_OPair @ SY818 @ SV149 @ SY822 @ SY823 ) @ SV72 )
| ! [SY824: $i] :
( ~ ( c_member @ ( tc_prod @ SY818 @ SV149 ) @ ( c_Product__Type_OPair @ SY818 @ SV149 @ SY822 @ SY824 ) @ SV72 )
| ( SY823 = SY824 ) ) )
| ( c_Relation_Osingle__valued @ SY818 @ SV149 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(909,plain,
( ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[831]) ).
thf(910,plain,
( ( ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[831]) ).
thf(911,plain,
! [SV73: $i,SV150: $i] :
( ( ! [SY825: $i,SY826: $i] :
~ ( ~ ( ~ ( c_member @ SY826 @ SY825 @ ( c_Relation_ODomain @ SY826 @ SV150 @ SV73 ) )
| ~ ! [SY827: $i] :
~ ( c_member @ ( tc_prod @ SY826 @ SV150 ) @ ( c_Product__Type_OPair @ SY826 @ SV150 @ SY825 @ SY827 ) @ SV73 ) )
| ~ ( ~ ~ ! [SY828: $i] :
~ ( c_member @ ( tc_prod @ SY826 @ SV150 ) @ ( c_Product__Type_OPair @ SY826 @ SV150 @ SY825 @ SY828 ) @ SV73 )
| ( c_member @ SY826 @ SY825 @ ( c_Relation_ODomain @ SY826 @ SV150 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(912,plain,
! [SV74: $i,SV151: $i] :
( ( ! [SY829: $i,SY830: $i] :
( ~ ( c_Relation_Orefl__on @ SY830 @ SY829 @ SV151 )
| ~ ( c_member @ SY830 @ SV74 @ SY829 )
| ( c_member @ ( tc_prod @ SY830 @ SY830 ) @ ( c_Product__Type_OPair @ SY830 @ SY830 @ SV74 @ SV74 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(913,plain,
! [SV75: $i,SV152: $i] :
( ( ! [SY831: $i,SY832: $i] :
( ~ ( ~ ~ ( c_member @ SY832 @ SY831 @ SV152 )
| ( SY831 = SV75 ) )
| ( c_member @ SY832 @ SY831 @ ( c_Set_Oinsert @ SY832 @ SV75 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(914,plain,
! [SV76: $i,SV153: $i] :
( ( ! [SY833: $i,SY834: $i,SY835: $i] :
( ~ ( c_member @ ( tc_prod @ SY835 @ SY834 ) @ ( c_Product__Type_OPair @ SY835 @ SY834 @ SY833 @ SV153 ) @ SV76 )
| ( c_member @ SY834 @ SV153 @ ( c_Relation_ORange @ SY835 @ SY834 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(915,plain,
! [SV77: $i,SV154: $i] :
( ( ! [SY836: $i,SY837: $i,SY838: $i] :
( ~ ( c_member @ ( tc_prod @ SY838 @ SY837 ) @ ( c_Product__Type_OPair @ SY838 @ SY837 @ SY836 @ SV154 ) @ SV77 )
| ( c_member @ SY838 @ SY836 @ ( c_Relation_ODomain @ SY838 @ SY837 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(916,plain,
! [SV78: $i,SV155: $i] :
( ( ~ ( c_Relation_Otrans @ SV155 @ SV78 )
| ( ( c_Transitive__Closure_Otrancl @ SV155 @ SV78 )
= SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(917,plain,
! [SV2: $i,SV80: $i,SV156: $i] :
( ( c_member @ ( tc_prod @ SV156 @ SV156 ) @ ( c_Product__Type_OPair @ SV156 @ SV156 @ SV80 @ SV80 ) @ ( c_Transitive__Closure_Ortrancl @ SV156 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(918,plain,
! [SV7: $i,SV84: $i,SV157: $i] :
( ( c_member @ SV157 @ SV84 @ ( c_Set_Oinsert @ SV157 @ SV84 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(919,plain,
! [SV8: $i,SV85: $i,SV158: $i] :
( ( ! [SY839: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY839 @ SY839 ) @ ( c_Product__Type_OPair @ SY839 @ SY839 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SY839 @ SV8 ) )
| ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SY839 @ SV158 @ SV8 ) ) )
| ~ ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SY839 @ SV158 @ SV8 ) )
| ( c_member @ ( tc_prod @ SY839 @ SY839 ) @ ( c_Product__Type_OPair @ SY839 @ SY839 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SY839 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(920,plain,
! [SV9: $i,SV86: $i,SV159: $i] :
( ( ! [SY840: $i] :
( ( SY840 != SV159 )
| ~ ( c_member @ SV86 @ SY840 @ SV9 )
| ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SY840 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(921,plain,
! [SV10: $i,SV87: $i,SV160: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ~ ( c_member @ ( tc_prod @ SY842 @ SY842 ) @ ( c_Product__Type_OPair @ SY842 @ SY842 @ SY841 @ SV160 ) @ SV87 )
| ~ ( c_member @ ( tc_prod @ SY842 @ SY842 ) @ ( c_Product__Type_OPair @ SY842 @ SY842 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY842 @ SV87 ) )
| ( c_member @ ( tc_prod @ SY842 @ SY842 ) @ ( c_Product__Type_OPair @ SY842 @ SY842 @ SY841 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY842 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(922,plain,
! [SV11: $i,SV88: $i,SV161: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ SV11 )
| ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ ( c_Transitive__Closure_Otrancl @ SV161 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(923,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
| ( SV89 = SV12 ) )
| ~ ( ( SV89 != SV12 )
| ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(924,plain,
! [SV13: $i,SV90: $i,SV163: $i] :
( ( ! [SY843: $i] :
~ ( ~ ( ~ ( c_member @ SY843 @ SV163 @ ( c_Set_Oinsert @ SY843 @ SV90 @ SV13 ) )
| ( SV163 = SV90 )
| ( c_member @ SY843 @ SV163 @ SV13 ) )
| ~ ( ~ ( ( SV163 = SV90 )
| ( c_member @ SY843 @ SV163 @ SV13 ) )
| ( c_member @ SY843 @ SV163 @ ( c_Set_Oinsert @ SY843 @ SV90 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(925,plain,
! [SV14: $i,SV91: $i,SV164: $i] :
( ( ! [SY844: $i] :
( ~ ! [SY845: $i] :
~ ( c_member @ ( tc_prod @ SY844 @ SY844 ) @ ( c_Product__Type_OPair @ SY844 @ SY844 @ SY845 @ SY845 ) @ ( c_Transitive__Closure_Otrancl @ SY844 @ SV164 ) )
| ~ ( c_member @ ( tc_prod @ SY844 @ SY844 ) @ ( c_Product__Type_OPair @ SY844 @ SY844 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(926,plain,
! [SV15: $i,SV92: $i,SV165: $i] :
( ( ! [SY846: $i,SY847: $i,SY848: $i,SY849: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SY847 @ SY846 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY849 @ SY848 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY849 @ SY848 @ SY847 @ SY846 )
!= ( c_Product__Type_OPair @ SY849 @ SY848 @ SV165 @ SV92 ) ) )
| ~ ! [SY850: $i,SY851: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SY847 @ SY846 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SY850 @ SY851 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY849 @ SY848 ) @ ( tc_prod @ SY849 @ SY848 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SY850 @ SY851 ) @ ( c_Product__Type_OPair @ SY849 @ SY848 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY849 @ SY848 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(927,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
| ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) )
| ~ ( ~ ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 )
| ( c_Nitpick_Orefl_H @ SV93 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(928,plain,
! [SV17: $i,SV94: $i,SV166: $i] :
( ( ! [SY852: $i,SY853: $i,SY854: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY854 @ SY853 @ SY852 @ SV166 )
!= ( c_Product__Type_OPair @ SY854 @ SY853 @ SV94 @ SV17 ) )
| ~ ( ( SY852 != SV94 )
| ( SV166 != SV17 ) ) )
| ~ ( ~ ~ ( ( SY852 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SY854 @ SY853 @ SY852 @ SV166 )
= ( c_Product__Type_OPair @ SY854 @ SY853 @ SV94 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(929,plain,
! [SV18: $i,SV95: $i,SV167: $i] :
( ( ! [SY855: $i] :
( ~ ( c_member @ SY855 @ SV167 @ ( c_Relation_ORange @ SV95 @ SY855 @ SV18 ) )
| ~ ! [SY856: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SY855 ) @ ( c_Product__Type_OPair @ SV95 @ SY855 @ SY856 @ SV167 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(930,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ( ~ ( c_Relation_Oantisym @ SV96 @ SV19 )
| ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) )
| ~ ( ~ ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) )
| ( c_Relation_Oantisym @ SV96 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(931,plain,
! [SV20: $i,SV97: $i,SV168: $i] :
( ( ! [SY857: $i,SY858: $i,SY859: $i,SY860: $i,SY861: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY861 @ SY860 ) @ ( tc_prod @ SY861 @ SY860 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY861 @ SY860 ) @ ( tc_prod @ SY861 @ SY860 ) @ ( c_Product__Type_OPair @ SY861 @ SY860 @ SY859 @ SY858 ) @ ( c_Product__Type_OPair @ SY861 @ SY860 @ SY857 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY861 @ SY860 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY861 @ SY861 ) @ ( c_Product__Type_OPair @ SY861 @ SY861 @ SY859 @ SY857 ) @ SV97 )
| ~ ( ( SY859 != SY857 )
| ~ ( c_member @ ( tc_prod @ SY860 @ SY860 ) @ ( c_Product__Type_OPair @ SY860 @ SY860 @ SY858 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY861 @ SY861 ) @ ( c_Product__Type_OPair @ SY861 @ SY861 @ SY859 @ SY857 ) @ SV97 )
| ~ ( ( SY859 != SY857 )
| ~ ( c_member @ ( tc_prod @ SY860 @ SY860 ) @ ( c_Product__Type_OPair @ SY860 @ SY860 @ SY858 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY861 @ SY860 ) @ ( tc_prod @ SY861 @ SY860 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY861 @ SY860 ) @ ( tc_prod @ SY861 @ SY860 ) @ ( c_Product__Type_OPair @ SY861 @ SY860 @ SY859 @ SY858 ) @ ( c_Product__Type_OPair @ SY861 @ SY860 @ SY857 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY861 @ SY860 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(932,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
| ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
| ~ ( ~ ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
| ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(933,plain,
! [SV22: $i,SV99: $i,SV170: $i] :
( ( ! [SY864: $i] :
( ~ ( c_member @ ( tc_prod @ SY864 @ SY864 ) @ ( c_Product__Type_OPair @ SY864 @ SY864 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SY864 @ SV22 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY864 @ SY864 ) @ ( c_Product__Type_OPair @ SY864 @ SY864 @ SV170 @ SV99 ) @ SV22 )
| ~ ! [SY865: $i] :
( ~ ( c_member @ ( tc_prod @ SY864 @ SY864 ) @ ( c_Product__Type_OPair @ SY864 @ SY864 @ SV170 @ SY865 ) @ ( c_Transitive__Closure_Otrancl @ SY864 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SY864 @ SY864 ) @ ( c_Product__Type_OPair @ SY864 @ SY864 @ SY865 @ SV99 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(934,plain,
! [SV23: $i,SV100: $i,SV171: $i] :
( ( ! [SY866: $i] :
( ~ ( c_member @ SY866 @ SV171 @ ( c_Wellfounded_Oacc @ SY866 @ SV100 ) )
| ~ ( c_member @ ( tc_prod @ SY866 @ SY866 ) @ ( c_Product__Type_OPair @ SY866 @ SY866 @ SV23 @ SV171 ) @ SV100 )
| ( c_member @ SY866 @ SV23 @ ( c_Wellfounded_Oacc @ SY866 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(935,plain,
! [SV24: $i,SV101: $i,SV172: $i] :
( ( ! [SY867: $i,SY868: $i,SY869: $i] :
( ~ ( c_member @ SY869 @ SY868 @ SY867 )
| ~ ( c_member @ ( tc_prod @ SY869 @ SV172 ) @ ( c_Product__Type_OPair @ SY869 @ SV172 @ SY868 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SY869 @ SV172 @ SV24 @ SY867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(936,plain,
! [SV25: $i,SV102: $i,SV173: $i] :
( ( ! [SY870: $i] :
( ~ ( c_Wellfounded_Owf @ SY870 @ SV173 )
| ~ ( c_member @ ( tc_prod @ SY870 @ SY870 ) @ ( c_Product__Type_OPair @ SY870 @ SY870 @ SV102 @ SV25 ) @ SV173 )
| ~ ( c_member @ ( tc_prod @ SY870 @ SY870 ) @ ( c_Product__Type_OPair @ SY870 @ SY870 @ SV25 @ SV102 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(937,plain,
! [SV26: $i,SV103: $i,SV174: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ~ ( c_member @ SY872 @ SY871 @ ( c_Relation_OImage @ SV174 @ SY872 @ SV103 @ SV26 ) )
| ~ ! [SY873: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SY872 ) @ ( c_Product__Type_OPair @ SV174 @ SY872 @ SY873 @ SY871 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY873 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(938,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ( ~ ( c_Relation_Otrans @ SV104 @ SV27 )
| ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) )
| ~ ( ~ ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) )
| ( c_Relation_Otrans @ SV104 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(939,plain,
! [SV28: $i,SV105: $i,SV175: $i] :
( ( ! [SY874: $i,SY875: $i] :
( ~ ( c_member @ ( tc_prod @ SY875 @ SY875 ) @ ( c_Product__Type_OPair @ SY875 @ SY875 @ SY874 @ SV175 ) @ SV105 )
| ~ ( c_member @ ( tc_prod @ SY875 @ SY875 ) @ ( c_Product__Type_OPair @ SY875 @ SY875 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY875 @ SV105 ) )
| ( c_member @ ( tc_prod @ SY875 @ SY875 ) @ ( c_Product__Type_OPair @ SY875 @ SY875 @ SY874 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY875 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(940,plain,
! [SV29: $i,SV106: $i,SV176: $i] :
( ( ! [SY876: $i,SY877: $i] :
~ ( ~ ( ~ ( c_member @ SY877 @ SY876 @ ( c_Relation_OImage @ SV176 @ SY877 @ SV106 @ SV29 ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY878 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SY877 ) @ ( c_Product__Type_OPair @ SV176 @ SY877 @ SY878 @ SY876 ) @ SV106 ) ) )
| ~ ( ~ ~ ! [SY879: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY879 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SY877 ) @ ( c_Product__Type_OPair @ SV176 @ SY877 @ SY879 @ SY876 ) @ SV106 ) )
| ( c_member @ SY877 @ SY876 @ ( c_Relation_OImage @ SV176 @ SY877 @ SV106 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(941,plain,
! [SV30: $i,SV107: $i,SV177: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV177 @ SV107 )
| ~ ( c_member @ ( tc_prod @ SV177 @ SV177 ) @ ( c_Product__Type_OPair @ SV177 @ SV177 @ SV30 @ SV30 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(942,plain,
! [SV31: $i,SV108: $i,SV178: $i] :
( ( ! [SY880: $i] :
( ~ ( c_Wellfounded_Owf @ SY880 @ SV178 )
| ~ ( c_member @ ( tc_prod @ SY880 @ SY880 ) @ ( c_Product__Type_OPair @ SY880 @ SY880 @ SV108 @ SV31 ) @ SV178 )
| ~ ( c_member @ ( tc_prod @ SY880 @ SY880 ) @ ( c_Product__Type_OPair @ SY880 @ SY880 @ SV31 @ SV108 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(943,plain,
! [SV32: $i,SV109: $i,SV179: $i] :
( ( ! [SY881: $i] :
( ~ ( c_member @ SY881 @ SV179 @ ( c_Relation_ODomain @ SY881 @ SV109 @ SV32 ) )
| ~ ! [SY882: $i] :
~ ( c_member @ ( tc_prod @ SY881 @ SV109 ) @ ( c_Product__Type_OPair @ SY881 @ SV109 @ SV179 @ SY882 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(944,plain,
! [SV33: $i,SV110: $i,SV180: $i] :
( ( ! [SY883: $i,SY884: $i] :
( ~ ( c_Relation_Orefl__on @ SY884 @ SY883 @ SV180 )
| ~ ( c_member @ ( tc_prod @ SY884 @ SY884 ) @ ( c_Product__Type_OPair @ SY884 @ SY884 @ SV110 @ SV33 ) @ SV180 )
| ( c_member @ SY884 @ SV33 @ SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(945,plain,
! [SV34: $i,SV111: $i,SV181: $i] :
( ( ! [SY885: $i] :
( ~ ( c_member @ ( tc_prod @ SY885 @ SY885 ) @ ( c_Product__Type_OPair @ SY885 @ SY885 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SY885 @ SV34 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY885 @ SY885 ) @ ( c_Product__Type_OPair @ SY885 @ SY885 @ SV181 @ SV111 ) @ SV34 )
| ~ ! [SY886: $i] :
( ~ ( c_member @ ( tc_prod @ SY885 @ SY885 ) @ ( c_Product__Type_OPair @ SY885 @ SY885 @ SV181 @ SY886 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SY885 @ SY885 ) @ ( c_Product__Type_OPair @ SY885 @ SY885 @ SY886 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SY885 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(946,plain,
! [SV35: $i,SV112: $i,SV182: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV182 @ SV112 )
| ~ ( c_member @ ( tc_prod @ SV182 @ SV182 ) @ ( c_Product__Type_OPair @ SV182 @ SV182 @ SV35 @ SV35 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(947,plain,
! [SV36: $i,SV113: $i,SV183: $i] :
( ( ! [SY887: $i] :
( ~ ( c_member @ SY887 @ SV183 @ SV113 )
| ( c_member @ SY887 @ SV183 @ ( c_Set_Oinsert @ SY887 @ SV36 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(948,plain,
! [SV37: $i,SV114: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) ) )
= $true )
| ( ( ~ ! [SY721: $i] :
( SV37
!= ( c_Product__Type_OPair @ SV114 @ SV114 @ SY721 @ SY721 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(949,plain,
! [SV38: $i,SV115: $i,SV184: $i] :
( ( ! [SY888: $i] :
( ~ ( c_Relation_Oantisym @ SY888 @ SV184 )
| ~ ( c_member @ ( tc_prod @ SY888 @ SY888 ) @ ( c_Product__Type_OPair @ SY888 @ SY888 @ SV115 @ SV38 ) @ SV184 )
| ~ ( c_member @ ( tc_prod @ SY888 @ SY888 ) @ ( c_Product__Type_OPair @ SY888 @ SY888 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(950,plain,
! [SV39: $i,SV116: $i,SV185: $i] :
( ( ~ ~ ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
| ~ ! [SY889: $i] :
( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ SY889 @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ SY889 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(951,plain,
! [SV40: $i,SV117: $i,SV186: $i] :
( ( ! [SY890: $i] :
( ( SY890 != SV186 )
| ~ ( ~ ( ~ ( c_member @ SV117 @ SY890 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SY890 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(952,plain,
! [SV41: $i,SV118: $i,SV187: $i] :
( ( ! [SY891: $i] :
( ~ ( c_member @ ( tc_prod @ SY891 @ SY891 ) @ ( c_Product__Type_OPair @ SY891 @ SY891 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SY891 @ SV41 ) )
| ~ ( ( SV187 != SV118 ) )
| ~ ! [SY892: $i] :
( ~ ( c_member @ ( tc_prod @ SY891 @ SY891 ) @ ( c_Product__Type_OPair @ SY891 @ SY891 @ SV187 @ SY892 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SY891 @ SY891 ) @ ( c_Product__Type_OPair @ SY891 @ SY891 @ SY892 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SY891 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(953,plain,
! [SV42: $i,SV119: $i,SV188: $i] :
( ( ! [SY893: $i] :
~ ( ~ ( ~ ( c_member @ SY893 @ SV188 @ ( c_Relation_ORange @ SV119 @ SY893 @ SV42 ) )
| ~ ! [SY894: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SY893 ) @ ( c_Product__Type_OPair @ SV119 @ SY893 @ SY894 @ SV188 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY895: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SY893 ) @ ( c_Product__Type_OPair @ SV119 @ SY893 @ SY895 @ SV188 ) @ SV42 )
| ( c_member @ SY893 @ SV188 @ ( c_Relation_ORange @ SV119 @ SY893 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(954,plain,
! [SV43: $i,SV120: $i,SV189: $i] :
( ( ! [SY896: $i,SY897: $i,SY898: $i] :
( ~ ( c_Relation_Osingle__valued @ SY898 @ SY897 @ SY896 )
| ~ ( c_member @ ( tc_prod @ SY898 @ SY897 ) @ ( c_Product__Type_OPair @ SY898 @ SY897 @ SV189 @ SV120 ) @ SY896 )
| ~ ( c_member @ ( tc_prod @ SY898 @ SY897 ) @ ( c_Product__Type_OPair @ SY898 @ SY897 @ SV189 @ SV43 ) @ SY896 )
| ( SV120 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(955,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
| ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) )
| ~ ( ~ ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(956,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
| ( SV122 = SV45 ) )
| ~ ( ( SV122 != SV45 )
| ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(957,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ( ~ ( c_Wellfounded_Owf @ SV123 @ SV46 )
| ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) )
| ~ ( ~ ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) )
| ( c_Wellfounded_Owf @ SV123 @ SV46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(958,plain,
! [SV47: $i,SV124: $i,SV192: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ~ ( c_Relation_Otrans @ SY904 @ SY903 )
| ~ ( c_member @ ( tc_prod @ SY904 @ SY904 ) @ ( c_Product__Type_OPair @ SY904 @ SY904 @ SV192 @ SV124 ) @ SY903 )
| ~ ( c_member @ ( tc_prod @ SY904 @ SY904 ) @ ( c_Product__Type_OPair @ SY904 @ SY904 @ SV124 @ SV47 ) @ SY903 )
| ( c_member @ ( tc_prod @ SY904 @ SY904 ) @ ( c_Product__Type_OPair @ SY904 @ SY904 @ SV192 @ SV47 ) @ SY903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(959,plain,
! [SV48: $i,SV125: $i,SV193: $i] :
( ( ! [SY905: $i,SY906: $i] :
( ~ ( c_member @ ( tc_prod @ SY906 @ SY906 ) @ ( c_Product__Type_OPair @ SY906 @ SY906 @ SY905 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SY906 @ SV125 ) )
| ~ ( c_member @ ( tc_prod @ SY906 @ SY906 ) @ ( c_Product__Type_OPair @ SY906 @ SY906 @ SV193 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SY906 @ SY906 ) @ ( c_Product__Type_OPair @ SY906 @ SY906 @ SY905 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SY906 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(960,plain,
! [SV49: $i,SV126: $i,SV194: $i] :
( ( ! [SY907: $i] :
( ( SY907 != SV194 )
| ~ ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SY907 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SY907 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(961,plain,
! [SV50: $i,SV127: $i,SV195: $i] :
( ( ! [SY908: $i] :
( ~ ( c_Relation_Otrans @ SY908 @ SV195 )
| ~ ( c_Relation_Otrans @ SV127 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SY908 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SY908 @ SV127 @ SV195 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(962,plain,
! [SV51: $i,SV128: $i,SV196: $i] :
( ( ! [SY909: $i,SY910: $i] :
( ~ ( c_member @ ( tc_prod @ SY910 @ SY910 ) @ ( c_Product__Type_OPair @ SY910 @ SY910 @ SY909 @ SV196 ) @ SV128 )
| ~ ( c_member @ ( tc_prod @ SY910 @ SY910 ) @ ( c_Product__Type_OPair @ SY910 @ SY910 @ SV196 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SY910 @ SY910 ) @ ( c_Product__Type_OPair @ SY910 @ SY910 @ SY909 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SY910 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(963,plain,
! [SV52: $i,SV129: $i,SV197: $i] :
( ( ! [SY911: $i] :
( ( SY911 != SV197 )
| ~ ( c_member @ SV129 @ SV197 @ SV52 )
| ( c_member @ SV129 @ SY911 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(964,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
| ~ ! [SY912: $i] :
( ~ ( c_member @ SV198 @ SY912 @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ SY912 @ SY912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(965,plain,
! [SV54: $i,SV131: $i,SV199: $i] :
( ( ! [SY913: $i,SY914: $i] :
( ~ ( c_member @ ( tc_prod @ SY914 @ SY914 ) @ ( c_Product__Type_OPair @ SY914 @ SY914 @ SY913 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SY914 @ SV131 ) )
| ~ ( c_member @ ( tc_prod @ SY914 @ SY914 ) @ ( c_Product__Type_OPair @ SY914 @ SY914 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY914 @ SV131 ) )
| ( c_member @ ( tc_prod @ SY914 @ SY914 ) @ ( c_Product__Type_OPair @ SY914 @ SY914 @ SY913 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY914 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(966,plain,
! [SV55: $i,SV132: $i,SV200: $i] :
( ( ~ ! [SY915: $i] :
( ~ ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ SY915 @ SV132 ) @ SV55 )
| ( c_member @ SV200 @ SY915 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) ) )
| ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(967,plain,
! [SV56: $i,SV133: $i,SV201: $i] :
( ( ! [SY916: $i,SY917: $i] :
( ~ ( c_member @ ( tc_prod @ SY917 @ SY917 ) @ ( c_Product__Type_OPair @ SY917 @ SY917 @ SY916 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SY917 @ SV133 ) )
| ~ ( c_member @ ( tc_prod @ SY917 @ SY917 ) @ ( c_Product__Type_OPair @ SY917 @ SY917 @ SV201 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SY917 @ SY917 ) @ ( c_Product__Type_OPair @ SY917 @ SY917 @ SY916 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SY917 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(968,plain,
! [SV57: $i,SV134: $i,SV202: $i] :
( ( ! [SY918: $i,SY919: $i,SY920: $i] :
( ( ( c_Product__Type_OPair @ SY920 @ SY919 @ SY918 @ SV202 )
!= ( c_Product__Type_OPair @ SY920 @ SY919 @ SV134 @ SV57 ) )
| ~ ( ( SY918 != SV134 )
| ( SV202 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(969,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ~ ! [SY921: $i,SY922: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY922 ) @ SV58 )
| ! [SY923: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY923 ) @ SV58 )
| ( SY922 = SY923 ) ) )
| ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(970,plain,
! [SV59: $i,SV136: $i,SV204: $i] :
( ( ! [SY924: $i] :
( ~ ( c_member @ ( tc_prod @ SY924 @ SY924 ) @ ( c_Product__Type_OPair @ SY924 @ SY924 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SY924 @ SV59 ) )
| ~ ( ( SV204 != SV136 ) )
| ~ ! [SY925: $i] :
( ~ ( c_member @ ( tc_prod @ SY924 @ SY924 ) @ ( c_Product__Type_OPair @ SY924 @ SY924 @ SV204 @ SY925 ) @ ( c_Transitive__Closure_Ortrancl @ SY924 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SY924 @ SY924 ) @ ( c_Product__Type_OPair @ SY924 @ SY924 @ SY925 @ SV136 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(971,plain,
! [SV60: $i,SV137: $i,SV205: $i] :
( ( ! [SY926: $i,SY927: $i] :
( ~ ( c_Relation_Orefl__on @ SY927 @ SY926 @ SV205 )
| ~ ( c_member @ ( tc_prod @ SY927 @ SY927 ) @ ( c_Product__Type_OPair @ SY927 @ SY927 @ SV137 @ SV60 ) @ SV205 )
| ( c_member @ SY927 @ SV137 @ SY926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(972,plain,
! [SV61: $i,SV138: $i] :
( ( ( ~ ! [SY792: $i,SY793: $i] :
( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY792 @ SY793 ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY793 @ SY792 ) @ SV61 )
| ( SY792 = SY793 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(973,plain,
! [SV62: $i,SV139: $i,SV206: $i] :
( ( ! [SY928: $i] :
( ~ ( c_member @ SY928 @ SV206 @ ( c_Set_Oinsert @ SY928 @ SV139 @ SV62 ) )
| ~ ( ( SV206 != SV139 ) )
| ( c_member @ SY928 @ SV206 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(974,plain,
! [SV63: $i,SV140: $i,SV207: $i] :
( ( ! [SY929: $i,SY930: $i,SY931: $i,SY932: $i,SY933: $i] :
( ~ ( c_member @ ( tc_prod @ SY933 @ SY932 ) @ ( c_Product__Type_OPair @ SY933 @ SY932 @ SY931 @ SY930 ) @ SY929 )
| ~ ( c_member @ ( tc_prod @ SY932 @ SV207 ) @ ( c_Product__Type_OPair @ SY932 @ SV207 @ SY930 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY933 @ SV207 ) @ ( c_Product__Type_OPair @ SY933 @ SV207 @ SY931 @ SV140 ) @ ( c_Relation_Orel__comp @ SY933 @ SY932 @ SV207 @ SY929 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(975,plain,
! [SV64: $i,SV141: $i,SV208: $i] :
( ( ! [SY934: $i] :
( ( SY934 != SV208 )
| ~ ( ~ ( c_member @ SV141 @ SV64 @ SY934 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
| ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SY934 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(976,plain,
! [SV65: $i,SV142: $i,SV209: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ SV65 )
| ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ ( c_Transitive__Closure_Ortrancl @ SV209 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(977,plain,
! [SV66: $i,SV143: $i] :
( ( ( ~ ! [SY805: $i,SY806: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY806 ) @ SV66 )
| ! [SY807: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY806 @ SY807 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY807 ) @ SV66 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(978,plain,
! [SV67: $i,SV144: $i,SV210: $i] :
( ( ! [SY935: $i] :
( ~ ~ ( c_member @ SY935 @ SV210 @ SV144 )
| ~ ~ ( c_member @ SY935 @ SV210 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY935 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SY935 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SY935 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SY935 @ SV210 @ SV67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(979,plain,
! [SV68: $i,SV145: $i,SV211: $i] :
( ( ! [SY936: $i] :
( ~ ( c_member @ ( tc_prod @ SY936 @ SY936 ) @ ( c_Product__Type_OPair @ SY936 @ SY936 @ SV211 @ SV145 ) @ SV68 )
| ( c_member @ ( tc_prod @ SY936 @ SY936 ) @ ( c_Product__Type_OPair @ SY936 @ SY936 @ SV211 @ SV145 ) @ ( c_Transitive__Closure_Otrancl @ SY936 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(980,plain,
! [SV69: $i,SV146: $i,SV212: $i] :
( ( ~ ( c_member @ SV212 @ SV146 @ SV69 )
| ( ( c_Set_Oinsert @ SV212 @ SV146 @ SV69 )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(981,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ( ~ ( c_Relation_Oirrefl @ SV147 @ SV70 )
| ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) )
| ~ ( ~ ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 )
| ( c_Relation_Oirrefl @ SV147 @ SV70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(982,plain,
! [SV71: $i,SV148: $i,SV213: $i] :
( ( ! [SY937: $i,SY938: $i] :
( ~ ( c_member @ ( tc_prod @ SY938 @ SY938 ) @ ( c_Product__Type_OPair @ SY938 @ SY938 @ SY937 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SY938 @ SV148 ) )
| ~ ( c_member @ ( tc_prod @ SY938 @ SY938 ) @ ( c_Product__Type_OPair @ SY938 @ SY938 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY938 @ SV148 ) )
| ( c_member @ ( tc_prod @ SY938 @ SY938 ) @ ( c_Product__Type_OPair @ SY938 @ SY938 @ SY937 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY938 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(983,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
| ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) )
| ~ ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) )
| ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(984,plain,
( ( ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[909]) ).
thf(985,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[910]) ).
thf(986,plain,
! [SV73: $i,SV150: $i,SV215: $i] :
( ( ! [SY945: $i] :
~ ( ~ ( ~ ( c_member @ SY945 @ SV215 @ ( c_Relation_ODomain @ SY945 @ SV150 @ SV73 ) )
| ~ ! [SY946: $i] :
~ ( c_member @ ( tc_prod @ SY945 @ SV150 ) @ ( c_Product__Type_OPair @ SY945 @ SV150 @ SV215 @ SY946 ) @ SV73 ) )
| ~ ( ~ ~ ! [SY947: $i] :
~ ( c_member @ ( tc_prod @ SY945 @ SV150 ) @ ( c_Product__Type_OPair @ SY945 @ SV150 @ SV215 @ SY947 ) @ SV73 )
| ( c_member @ SY945 @ SV215 @ ( c_Relation_ODomain @ SY945 @ SV150 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(987,plain,
! [SV74: $i,SV151: $i,SV216: $i] :
( ( ! [SY948: $i] :
( ~ ( c_Relation_Orefl__on @ SY948 @ SV216 @ SV151 )
| ~ ( c_member @ SY948 @ SV74 @ SV216 )
| ( c_member @ ( tc_prod @ SY948 @ SY948 ) @ ( c_Product__Type_OPair @ SY948 @ SY948 @ SV74 @ SV74 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(988,plain,
! [SV75: $i,SV152: $i,SV217: $i] :
( ( ! [SY949: $i] :
( ~ ( ~ ~ ( c_member @ SY949 @ SV217 @ SV152 )
| ( SV217 = SV75 ) )
| ( c_member @ SY949 @ SV217 @ ( c_Set_Oinsert @ SY949 @ SV75 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(989,plain,
! [SV76: $i,SV153: $i,SV218: $i] :
( ( ! [SY950: $i,SY951: $i] :
( ~ ( c_member @ ( tc_prod @ SY951 @ SY950 ) @ ( c_Product__Type_OPair @ SY951 @ SY950 @ SV218 @ SV153 ) @ SV76 )
| ( c_member @ SY950 @ SV153 @ ( c_Relation_ORange @ SY951 @ SY950 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(990,plain,
! [SV77: $i,SV154: $i,SV219: $i] :
( ( ! [SY952: $i,SY953: $i] :
( ~ ( c_member @ ( tc_prod @ SY953 @ SY952 ) @ ( c_Product__Type_OPair @ SY953 @ SY952 @ SV219 @ SV154 ) @ SV77 )
| ( c_member @ SY953 @ SV219 @ ( c_Relation_ODomain @ SY953 @ SY952 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(991,plain,
! [SV78: $i,SV155: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV155 @ SV78 ) )
= $true )
| ( ( ( c_Transitive__Closure_Otrancl @ SV155 @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(992,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
| ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
| ~ ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
| ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(993,plain,
! [SV9: $i,SV86: $i,SV159: $i,SV221: $i] :
( ( ( SV221 != SV159 )
| ~ ( c_member @ SV86 @ SV221 @ SV9 )
| ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SV221 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(994,plain,
! [SV10: $i,SV87: $i,SV160: $i,SV222: $i] :
( ( ! [SY954: $i] :
( ~ ( c_member @ ( tc_prod @ SY954 @ SY954 ) @ ( c_Product__Type_OPair @ SY954 @ SY954 @ SV222 @ SV160 ) @ SV87 )
| ~ ( c_member @ ( tc_prod @ SY954 @ SY954 ) @ ( c_Product__Type_OPair @ SY954 @ SY954 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY954 @ SV87 ) )
| ( c_member @ ( tc_prod @ SY954 @ SY954 ) @ ( c_Product__Type_OPair @ SY954 @ SY954 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SY954 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(995,plain,
! [SV11: $i,SV88: $i,SV161: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ SV11 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ ( c_Transitive__Closure_Otrancl @ SV161 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(996,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ~ ( ~ ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
| ( SV89 = SV12 ) )
| ~ ( ( SV89 != SV12 )
| ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(997,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
| ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ~ ( ~ ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(998,plain,
! [SV14: $i,SV91: $i,SV164: $i,SV224: $i] :
( ( ~ ! [SY955: $i] :
~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SY955 @ SY955 ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) )
| ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(999,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i] :
( ( ! [SY956: $i,SY957: $i,SY958: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SY956 @ SV225 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY958 @ SY957 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY958 @ SY957 @ SY956 @ SV225 )
!= ( c_Product__Type_OPair @ SY958 @ SY957 @ SV165 @ SV92 ) ) )
| ~ ! [SY959: $i,SY960: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SY956 @ SV225 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SY959 @ SY960 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY958 @ SY957 ) @ ( tc_prod @ SY958 @ SY957 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SY959 @ SY960 ) @ ( c_Product__Type_OPair @ SY958 @ SY957 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY958 @ SY957 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1000,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
| ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1001,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ( ~ ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 )
| ( c_Nitpick_Orefl_H @ SV93 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1002,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i] :
( ( ! [SY961: $i,SY962: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY962 @ SY961 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SY962 @ SY961 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
| ~ ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SY962 @ SY961 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SY962 @ SY961 @ SV94 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1003,plain,
! [SV18: $i,SV95: $i,SV167: $i,SV227: $i] :
( ( ~ ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) )
| ~ ! [SY963: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ SY963 @ SV167 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1004,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ( ~ ( c_Relation_Oantisym @ SV96 @ SV19 )
| ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(1005,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ( ~ ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) )
| ( c_Relation_Oantisym @ SV96 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(1006,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i] :
( ( ! [SY964: $i,SY965: $i,SY966: $i,SY967: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY967 @ SY966 ) @ ( tc_prod @ SY967 @ SY966 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY967 @ SY966 ) @ ( tc_prod @ SY967 @ SY966 ) @ ( c_Product__Type_OPair @ SY967 @ SY966 @ SY965 @ SY964 ) @ ( c_Product__Type_OPair @ SY967 @ SY966 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY967 @ SY966 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY967 @ SY967 ) @ ( c_Product__Type_OPair @ SY967 @ SY967 @ SY965 @ SV228 ) @ SV97 )
| ~ ( ( SY965 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY966 @ SY966 ) @ ( c_Product__Type_OPair @ SY966 @ SY966 @ SY964 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY967 @ SY967 ) @ ( c_Product__Type_OPair @ SY967 @ SY967 @ SY965 @ SV228 ) @ SV97 )
| ~ ( ( SY965 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY966 @ SY966 ) @ ( c_Product__Type_OPair @ SY966 @ SY966 @ SY964 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY967 @ SY966 ) @ ( tc_prod @ SY967 @ SY966 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY967 @ SY966 ) @ ( tc_prod @ SY967 @ SY966 ) @ ( c_Product__Type_OPair @ SY967 @ SY966 @ SY965 @ SY964 ) @ ( c_Product__Type_OPair @ SY967 @ SY966 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY967 @ SY966 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1007,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ( ~ ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
| ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
| ~ ( ~ ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
| ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1008,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
| ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1009,plain,
! [SV23: $i,SV100: $i,SV171: $i,SV230: $i] :
( ( ~ ( c_member @ SV230 @ SV171 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
| ~ ( c_member @ ( tc_prod @ SV230 @ SV230 ) @ ( c_Product__Type_OPair @ SV230 @ SV230 @ SV23 @ SV171 ) @ SV100 )
| ( c_member @ SV230 @ SV23 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1010,plain,
! [SV24: $i,SV101: $i,SV172: $i,SV231: $i] :
( ( ! [SY969: $i,SY970: $i] :
( ~ ( c_member @ SY970 @ SY969 @ SV231 )
| ~ ( c_member @ ( tc_prod @ SY970 @ SV172 ) @ ( c_Product__Type_OPair @ SY970 @ SV172 @ SY969 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SY970 @ SV172 @ SV24 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1011,plain,
! [SV25: $i,SV102: $i,SV173: $i,SV232: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV232 @ SV173 )
| ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 )
| ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1012,plain,
! [SV26: $i,SV103: $i,SV174: $i,SV233: $i] :
( ( ! [SY971: $i] :
( ~ ( c_member @ SY971 @ SV233 @ ( c_Relation_OImage @ SV174 @ SY971 @ SV103 @ SV26 ) )
| ~ ! [SY972: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SY971 ) @ ( c_Product__Type_OPair @ SV174 @ SY971 @ SY972 @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY972 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1013,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ( ~ ( c_Relation_Otrans @ SV104 @ SV27 )
| ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1014,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ( ~ ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) )
| ( c_Relation_Otrans @ SV104 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1015,plain,
! [SV28: $i,SV105: $i,SV175: $i,SV234: $i] :
( ( ! [SY973: $i] :
( ~ ( c_member @ ( tc_prod @ SY973 @ SY973 ) @ ( c_Product__Type_OPair @ SY973 @ SY973 @ SV234 @ SV175 ) @ SV105 )
| ~ ( c_member @ ( tc_prod @ SY973 @ SY973 ) @ ( c_Product__Type_OPair @ SY973 @ SY973 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY973 @ SV105 ) )
| ( c_member @ ( tc_prod @ SY973 @ SY973 ) @ ( c_Product__Type_OPair @ SY973 @ SY973 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SY973 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1016,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i] :
( ( ! [SY974: $i] :
~ ( ~ ( ~ ( c_member @ SY974 @ SV235 @ ( c_Relation_OImage @ SV176 @ SY974 @ SV106 @ SV29 ) )
| ~ ! [SY975: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY975 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SY974 ) @ ( c_Product__Type_OPair @ SV176 @ SY974 @ SY975 @ SV235 ) @ SV106 ) ) )
| ~ ( ~ ~ ! [SY976: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY976 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SY974 ) @ ( c_Product__Type_OPair @ SV176 @ SY974 @ SY976 @ SV235 ) @ SV106 ) )
| ( c_member @ SY974 @ SV235 @ ( c_Relation_OImage @ SV176 @ SY974 @ SV106 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1017,plain,
! [SV30: $i,SV107: $i,SV177: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV177 @ SV107 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV177 @ SV177 ) @ ( c_Product__Type_OPair @ SV177 @ SV177 @ SV30 @ SV30 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1018,plain,
! [SV31: $i,SV108: $i,SV178: $i,SV236: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV236 @ SV178 )
| ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 )
| ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1019,plain,
! [SV32: $i,SV109: $i,SV179: $i,SV237: $i] :
( ( ~ ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) )
| ~ ! [SY977: $i] :
~ ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ SY977 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1020,plain,
! [SV33: $i,SV110: $i,SV180: $i,SV238: $i] :
( ( ! [SY978: $i] :
( ~ ( c_Relation_Orefl__on @ SY978 @ SV238 @ SV180 )
| ~ ( c_member @ ( tc_prod @ SY978 @ SY978 ) @ ( c_Product__Type_OPair @ SY978 @ SY978 @ SV110 @ SV33 ) @ SV180 )
| ( c_member @ SY978 @ SV33 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1021,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
| ~ ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
| ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1022,plain,
! [SV35: $i,SV112: $i,SV182: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV182 @ SV112 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV182 @ SV182 ) @ ( c_Product__Type_OPair @ SV182 @ SV182 @ SV35 @ SV35 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1023,plain,
! [SV36: $i,SV113: $i,SV183: $i,SV240: $i] :
( ( ~ ( c_member @ SV240 @ SV183 @ SV113 )
| ( c_member @ SV240 @ SV183 @ ( c_Set_Oinsert @ SV240 @ SV36 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1024,plain,
! [SV37: $i,SV114: $i] :
( ( ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) )
= $false )
| ( ( ~ ! [SY721: $i] :
( SV37
!= ( c_Product__Type_OPair @ SV114 @ SV114 @ SY721 @ SY721 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1025,plain,
! [SV38: $i,SV115: $i,SV184: $i,SV241: $i] :
( ( ~ ( c_Relation_Oantisym @ SV241 @ SV184 )
| ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
| ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1026,plain,
! [SV39: $i,SV116: $i,SV185: $i] :
( ( ( ~ ~ ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) )
= $true )
| ( ( ~ ! [SY889: $i] :
( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ SY889 @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ SY889 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1027,plain,
! [SV40: $i,SV117: $i,SV186: $i,SV242: $i] :
( ( ( SV242 != SV186 )
| ~ ( ~ ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1028,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
| ~ ( ( SV187 != SV118 ) )
| ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1029,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
| ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 )
| ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1030,plain,
! [SV43: $i,SV120: $i,SV189: $i,SV245: $i] :
( ( ! [SY983: $i,SY984: $i] :
( ~ ( c_Relation_Osingle__valued @ SY984 @ SY983 @ SV245 )
| ~ ( c_member @ ( tc_prod @ SY984 @ SY983 ) @ ( c_Product__Type_OPair @ SY984 @ SY983 @ SV189 @ SV120 ) @ SV245 )
| ~ ( c_member @ ( tc_prod @ SY984 @ SY983 ) @ ( c_Product__Type_OPair @ SY984 @ SY983 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1031,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ( ~ ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
| ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) )
| ~ ( ~ ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1032,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
| ( SV122 = SV45 ) )
| ~ ( ( SV122 != SV45 )
| ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1033,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ( ~ ( c_Wellfounded_Owf @ SV123 @ SV46 )
| ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1034,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ( ~ ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) )
| ( c_Wellfounded_Owf @ SV123 @ SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1035,plain,
! [SV47: $i,SV124: $i,SV192: $i,SV246: $i] :
( ( ! [SY985: $i] :
( ~ ( c_Relation_Otrans @ SY985 @ SV246 )
| ~ ( c_member @ ( tc_prod @ SY985 @ SY985 ) @ ( c_Product__Type_OPair @ SY985 @ SY985 @ SV192 @ SV124 ) @ SV246 )
| ~ ( c_member @ ( tc_prod @ SY985 @ SY985 ) @ ( c_Product__Type_OPair @ SY985 @ SY985 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SY985 @ SY985 ) @ ( c_Product__Type_OPair @ SY985 @ SY985 @ SV192 @ SV47 ) @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1036,plain,
! [SV48: $i,SV125: $i,SV193: $i,SV247: $i] :
( ( ! [SY986: $i] :
( ~ ( c_member @ ( tc_prod @ SY986 @ SY986 ) @ ( c_Product__Type_OPair @ SY986 @ SY986 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SY986 @ SV125 ) )
| ~ ( c_member @ ( tc_prod @ SY986 @ SY986 ) @ ( c_Product__Type_OPair @ SY986 @ SY986 @ SV193 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SY986 @ SY986 ) @ ( c_Product__Type_OPair @ SY986 @ SY986 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SY986 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1037,plain,
! [SV49: $i,SV126: $i,SV194: $i,SV248: $i] :
( ( ( SV248 != SV194 )
| ~ ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1038,plain,
! [SV50: $i,SV127: $i,SV195: $i,SV249: $i] :
( ( ~ ( c_Relation_Otrans @ SV249 @ SV195 )
| ~ ( c_Relation_Otrans @ SV127 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SV249 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SV249 @ SV127 @ SV195 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1039,plain,
! [SV51: $i,SV128: $i,SV196: $i,SV250: $i] :
( ( ! [SY987: $i] :
( ~ ( c_member @ ( tc_prod @ SY987 @ SY987 ) @ ( c_Product__Type_OPair @ SY987 @ SY987 @ SV250 @ SV196 ) @ SV128 )
| ~ ( c_member @ ( tc_prod @ SY987 @ SY987 ) @ ( c_Product__Type_OPair @ SY987 @ SY987 @ SV196 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SY987 @ SY987 ) @ ( c_Product__Type_OPair @ SY987 @ SY987 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SY987 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1040,plain,
! [SV52: $i,SV129: $i,SV197: $i,SV251: $i] :
( ( ( SV251 != SV197 )
| ~ ( c_member @ SV129 @ SV197 @ SV52 )
| ( c_member @ SV129 @ SV251 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1041,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) ) )
= $true )
| ( ( ~ ! [SY912: $i] :
( ~ ( c_member @ SV198 @ SY912 @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ SY912 @ SY912 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1042,plain,
! [SV54: $i,SV131: $i,SV199: $i,SV252: $i] :
( ( ! [SY988: $i] :
( ~ ( c_member @ ( tc_prod @ SY988 @ SY988 ) @ ( c_Product__Type_OPair @ SY988 @ SY988 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SY988 @ SV131 ) )
| ~ ( c_member @ ( tc_prod @ SY988 @ SY988 ) @ ( c_Product__Type_OPair @ SY988 @ SY988 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY988 @ SV131 ) )
| ( c_member @ ( tc_prod @ SY988 @ SY988 ) @ ( c_Product__Type_OPair @ SY988 @ SY988 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SY988 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1043,plain,
! [SV55: $i,SV132: $i,SV200: $i] :
( ( ( ~ ! [SY915: $i] :
( ~ ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ SY915 @ SV132 ) @ SV55 )
| ( c_member @ SV200 @ SY915 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) ) ) )
= $true )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1044,plain,
! [SV56: $i,SV133: $i,SV201: $i,SV253: $i] :
( ( ! [SY989: $i] :
( ~ ( c_member @ ( tc_prod @ SY989 @ SY989 ) @ ( c_Product__Type_OPair @ SY989 @ SY989 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SY989 @ SV133 ) )
| ~ ( c_member @ ( tc_prod @ SY989 @ SY989 ) @ ( c_Product__Type_OPair @ SY989 @ SY989 @ SV201 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SY989 @ SY989 ) @ ( c_Product__Type_OPair @ SY989 @ SY989 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SY989 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1045,plain,
! [SV57: $i,SV134: $i,SV202: $i,SV254: $i] :
( ( ! [SY990: $i,SY991: $i] :
( ( ( c_Product__Type_OPair @ SY991 @ SY990 @ SV254 @ SV202 )
!= ( c_Product__Type_OPair @ SY991 @ SY990 @ SV134 @ SV57 ) )
| ~ ( ( SV254 != SV134 )
| ( SV202 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1046,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ~ ! [SY921: $i,SY922: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY922 ) @ SV58 )
| ! [SY923: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY923 ) @ SV58 )
| ( SY922 = SY923 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1047,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( ( SV204 != SV136 ) )
| ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1048,plain,
! [SV60: $i,SV137: $i,SV205: $i,SV256: $i] :
( ( ! [SY993: $i] :
( ~ ( c_Relation_Orefl__on @ SY993 @ SV256 @ SV205 )
| ~ ( c_member @ ( tc_prod @ SY993 @ SY993 ) @ ( c_Product__Type_OPair @ SY993 @ SY993 @ SV137 @ SV60 ) @ SV205 )
| ( c_member @ SY993 @ SV137 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1049,plain,
! [SV61: $i,SV138: $i] :
( ( ( ! [SY792: $i,SY793: $i] :
( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY792 @ SY793 ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY793 @ SY792 ) @ SV61 )
| ( SY792 = SY793 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1050,plain,
! [SV62: $i,SV139: $i,SV206: $i,SV257: $i] :
( ( ~ ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) )
| ~ ( ( SV206 != SV139 ) )
| ( c_member @ SV257 @ SV206 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1051,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i] :
( ( ! [SY994: $i,SY995: $i,SY996: $i,SY997: $i] :
( ~ ( c_member @ ( tc_prod @ SY997 @ SY996 ) @ ( c_Product__Type_OPair @ SY997 @ SY996 @ SY995 @ SY994 ) @ SV258 )
| ~ ( c_member @ ( tc_prod @ SY996 @ SV207 ) @ ( c_Product__Type_OPair @ SY996 @ SV207 @ SY994 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY997 @ SV207 ) @ ( c_Product__Type_OPair @ SY997 @ SV207 @ SY995 @ SV140 ) @ ( c_Relation_Orel__comp @ SY997 @ SY996 @ SV207 @ SV258 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1052,plain,
! [SV64: $i,SV141: $i,SV208: $i,SV259: $i] :
( ( ( SV259 != SV208 )
| ~ ( ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
| ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1053,plain,
! [SV65: $i,SV142: $i,SV209: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ SV65 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ ( c_Transitive__Closure_Ortrancl @ SV209 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1054,plain,
! [SV66: $i,SV143: $i] :
( ( ( ! [SY805: $i,SY806: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY806 ) @ SV66 )
| ! [SY807: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY806 @ SY807 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY805 @ SY807 ) @ SV66 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1055,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV144 )
| ~ ~ ( c_member @ SV260 @ SV210 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1056,plain,
! [SV68: $i,SV145: $i,SV211: $i,SV261: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ SV68 )
| ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ ( c_Transitive__Closure_Otrancl @ SV261 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1057,plain,
! [SV69: $i,SV146: $i,SV212: $i] :
( ( ( ~ ( c_member @ SV212 @ SV146 @ SV69 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV212 @ SV146 @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1058,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ( ~ ( c_Relation_Oirrefl @ SV147 @ SV70 )
| ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1059,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ( ~ ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 )
| ( c_Relation_Oirrefl @ SV147 @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1060,plain,
! [SV71: $i,SV148: $i,SV213: $i,SV262: $i] :
( ( ! [SY998: $i] :
( ~ ( c_member @ ( tc_prod @ SY998 @ SY998 ) @ ( c_Product__Type_OPair @ SY998 @ SY998 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SY998 @ SV148 ) )
| ~ ( c_member @ ( tc_prod @ SY998 @ SY998 ) @ ( c_Product__Type_OPair @ SY998 @ SY998 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY998 @ SV148 ) )
| ( c_member @ ( tc_prod @ SY998 @ SY998 ) @ ( c_Product__Type_OPair @ SY998 @ SY998 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SY998 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1061,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ( ~ ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
| ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) )
| ~ ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) )
| ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1062,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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_not_pos,[status(thm)],[984]) ).
thf(1063,plain,
( ( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $true )
| ( ( ~ ! [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_or_pos,[status(thm)],[985]) ).
thf(1064,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
| ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
| ~ ( ~ ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 )
| ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1065,plain,
! [SV74: $i,SV151: $i,SV216: $i,SV264: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV264 @ SV216 @ SV151 )
| ~ ( c_member @ SV264 @ SV74 @ SV216 )
| ( c_member @ ( tc_prod @ SV264 @ SV264 ) @ ( c_Product__Type_OPair @ SV264 @ SV264 @ SV74 @ SV74 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1066,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ~ ( ~ ~ ( c_member @ SV265 @ SV217 @ SV152 )
| ( SV217 = SV75 ) )
| ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1067,plain,
! [SV76: $i,SV153: $i,SV218: $i,SV266: $i] :
( ( ! [SY1001: $i] :
( ~ ( c_member @ ( tc_prod @ SY1001 @ SV266 ) @ ( c_Product__Type_OPair @ SY1001 @ SV266 @ SV218 @ SV153 ) @ SV76 )
| ( c_member @ SV266 @ SV153 @ ( c_Relation_ORange @ SY1001 @ SV266 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1068,plain,
! [SV77: $i,SV154: $i,SV219: $i,SV267: $i] :
( ( ! [SY1002: $i] :
( ~ ( c_member @ ( tc_prod @ SY1002 @ SV267 ) @ ( c_Product__Type_OPair @ SY1002 @ SV267 @ SV219 @ SV154 ) @ SV77 )
| ( c_member @ SY1002 @ SV219 @ ( c_Relation_ODomain @ SY1002 @ SV267 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1069,plain,
! [SV78: $i,SV155: $i] :
( ( ( c_Relation_Otrans @ SV155 @ SV78 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV155 @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1070,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
| ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
| ~ ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
| ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1071,plain,
! [SV9: $i,SV86: $i,SV159: $i,SV221: $i] :
( ( ( SV221 != SV159 )
= $true )
| ( ( ~ ( c_member @ SV86 @ SV221 @ SV9 )
| ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SV221 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1072,plain,
! [SV10: $i,SV87: $i,SV160: $i,SV222: $i,SV268: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV160 ) @ SV87 )
| ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
| ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1073,plain,
! [SV11: $i,SV88: $i,SV161: $i] :
( ( ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ SV11 )
= $false )
| ( ( c_member @ ( tc_prod @ SV161 @ SV161 ) @ SV88 @ ( c_Transitive__Closure_Otrancl @ SV161 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1074,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ~ ( ~ ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
| ( SV89 = SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1075,plain,
! [SV162: $i,SV12: $i,SV89: $i] :
( ( ~ ( ( SV89 != SV12 )
| ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1076,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ~ ( ~ ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
| ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ~ ( ~ ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1077,plain,
! [SV14: $i,SV91: $i,SV164: $i,SV224: $i] :
( ( ( ~ ! [SY955: $i] :
~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SY955 @ SY955 ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1078,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1004 @ SY1003 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV165 @ SV92 ) ) )
| ~ ! [SY1005: $i,SY1006: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SY1005 @ SY1006 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1004 @ SY1003 ) @ ( tc_prod @ SY1004 @ SY1003 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SY1005 @ SY1006 ) @ ( c_Product__Type_OPair @ SY1004 @ SY1003 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1004 @ SY1003 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1079,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
| ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1080,plain,
! [SV16: $i,SV93: $i] :
( ( ~ ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 )
| ( c_Nitpick_Orefl_H @ SV93 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1081,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i] :
( ( ! [SY1007: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1007 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SY1007 @ SV270 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
| ~ ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SY1007 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SY1007 @ SV270 @ SV94 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1082,plain,
! [SV18: $i,SV95: $i,SV167: $i,SV227: $i] :
( ( ( ~ ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY963: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ SY963 @ SV167 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1083,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ( c_Relation_Oantisym @ SV96 @ SV19 )
| ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1084,plain,
! [SV19: $i,SV96: $i] :
( ( ~ ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) )
| ( c_Relation_Oantisym @ SV96 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1085,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i] :
( ( ! [SY1008: $i,SY1009: $i,SY1010: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1010 @ SY1009 ) @ ( tc_prod @ SY1010 @ SY1009 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1010 @ SY1009 ) @ ( tc_prod @ SY1010 @ SY1009 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1009 @ SY1008 @ SV271 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1009 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1010 @ SY1009 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY1010 @ SY1010 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1010 @ SY1008 @ SV228 ) @ SV97 )
| ~ ( ( SY1008 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY1009 @ SY1009 ) @ ( c_Product__Type_OPair @ SY1009 @ SY1009 @ SV271 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1010 @ SY1010 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1010 @ SY1008 @ SV228 ) @ SV97 )
| ~ ( ( SY1008 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY1009 @ SY1009 ) @ ( c_Product__Type_OPair @ SY1009 @ SY1009 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1010 @ SY1009 ) @ ( tc_prod @ SY1010 @ SY1009 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1010 @ SY1009 ) @ ( tc_prod @ SY1010 @ SY1009 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1009 @ SY1008 @ SV271 ) @ ( c_Product__Type_OPair @ SY1010 @ SY1009 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1010 @ SY1009 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1086,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ( ~ ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
| ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1087,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ( ~ ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
| ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1088,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) ) )
= $true )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
| ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1089,plain,
! [SV23: $i,SV100: $i,SV171: $i,SV230: $i] :
( ( ( ~ ( c_member @ SV230 @ SV171 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV230 @ SV230 ) @ ( c_Product__Type_OPair @ SV230 @ SV230 @ SV23 @ SV171 ) @ SV100 )
| ( c_member @ SV230 @ SV23 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1090,plain,
! [SV24: $i,SV101: $i,SV172: $i,SV231: $i,SV272: $i] :
( ( ! [SY1011: $i] :
( ~ ( c_member @ SY1011 @ SV272 @ SV231 )
| ~ ( c_member @ ( tc_prod @ SY1011 @ SV172 ) @ ( c_Product__Type_OPair @ SY1011 @ SV172 @ SV272 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SY1011 @ SV172 @ SV24 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1091,plain,
! [SV25: $i,SV102: $i,SV173: $i,SV232: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV232 @ SV173 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 )
| ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1092,plain,
! [SV26: $i,SV103: $i,SV174: $i,SV233: $i,SV273: $i] :
( ( ~ ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
| ~ ! [SY1012: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ SY1012 @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY1012 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1093,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ( c_Relation_Otrans @ SV104 @ SV27 )
| ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1094,plain,
! [SV27: $i,SV104: $i] :
( ( ~ ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) )
| ( c_Relation_Otrans @ SV104 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1095,plain,
! [SV28: $i,SV105: $i,SV175: $i,SV234: $i,SV274: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV175 ) @ SV105 )
| ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
| ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1096,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
| ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) )
| ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1097,plain,
! [SV30: $i,SV107: $i,SV177: $i] :
( ( ( c_Wellfounded_Owf @ SV177 @ SV107 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV177 @ SV177 ) @ ( c_Product__Type_OPair @ SV177 @ SV177 @ SV30 @ SV30 ) @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1098,plain,
! [SV31: $i,SV108: $i,SV178: $i,SV236: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV236 @ SV178 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 )
| ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1099,plain,
! [SV32: $i,SV109: $i,SV179: $i,SV237: $i] :
( ( ( ~ ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) ) )
= $true )
| ( ( ~ ! [SY977: $i] :
~ ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ SY977 ) @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1100,plain,
! [SV33: $i,SV110: $i,SV180: $i,SV238: $i,SV276: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV276 @ SV238 @ SV180 )
| ~ ( c_member @ ( tc_prod @ SV276 @ SV276 ) @ ( c_Product__Type_OPair @ SV276 @ SV276 @ SV110 @ SV33 ) @ SV180 )
| ( c_member @ SV276 @ SV33 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1101,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) )
= $true )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
| ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1102,plain,
! [SV35: $i,SV112: $i,SV182: $i] :
( ( ( c_Wellfounded_Owf @ SV182 @ SV112 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV182 @ SV182 ) @ ( c_Product__Type_OPair @ SV182 @ SV182 @ SV35 @ SV35 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1103,plain,
! [SV36: $i,SV113: $i,SV183: $i,SV240: $i] :
( ( ( ~ ( c_member @ SV240 @ SV183 @ SV113 ) )
= $true )
| ( ( c_member @ SV240 @ SV183 @ ( c_Set_Oinsert @ SV240 @ SV36 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1104,plain,
! [SV114: $i,SV37: $i] :
( ( ( ! [SY721: $i] :
( SV37
!= ( c_Product__Type_OPair @ SV114 @ SV114 @ SY721 @ SY721 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1105,plain,
! [SV38: $i,SV115: $i,SV184: $i,SV241: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV241 @ SV184 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
| ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1106,plain,
! [SV39: $i,SV116: $i,SV185: $i] :
( ( ( ~ ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) )
= $false )
| ( ( ~ ! [SY889: $i] :
( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ SY889 @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ SY889 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1107,plain,
! [SV40: $i,SV117: $i,SV186: $i,SV242: $i] :
( ( ( SV242 != SV186 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1108,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) )
= $true )
| ( ( ~ ( ( SV187 != SV118 ) )
| ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1109,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ~ ( ~ ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
| ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
| ~ ( ~ ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 )
| ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1110,plain,
! [SV43: $i,SV120: $i,SV189: $i,SV245: $i,SV277: $i] :
( ( ! [SY1015: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1015 @ SV277 @ SV245 )
| ~ ( c_member @ ( tc_prod @ SY1015 @ SV277 ) @ ( c_Product__Type_OPair @ SY1015 @ SV277 @ SV189 @ SV120 ) @ SV245 )
| ~ ( c_member @ ( tc_prod @ SY1015 @ SV277 ) @ ( c_Product__Type_OPair @ SY1015 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1111,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ( ~ ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
| ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1112,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ( ~ ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1113,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
| ( SV122 = SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1114,plain,
! [SV191: $i,SV45: $i,SV122: $i] :
( ( ~ ( ( SV122 != SV45 )
| ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1115,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV123 @ SV46 )
| ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1116,plain,
! [SV46: $i,SV123: $i] :
( ( ~ ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) )
| ( c_Wellfounded_Owf @ SV123 @ SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1117,plain,
! [SV47: $i,SV124: $i,SV192: $i,SV246: $i,SV278: $i] :
( ( ~ ( c_Relation_Otrans @ SV278 @ SV246 )
| ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
| ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1118,plain,
! [SV48: $i,SV125: $i,SV193: $i,SV247: $i,SV279: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
| ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV193 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1119,plain,
! [SV49: $i,SV126: $i,SV194: $i,SV248: $i] :
( ( ( SV248 != SV194 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1120,plain,
! [SV50: $i,SV127: $i,SV195: $i,SV249: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV249 @ SV195 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV127 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SV249 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SV249 @ SV127 @ SV195 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1121,plain,
! [SV51: $i,SV128: $i,SV196: $i,SV250: $i,SV280: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV196 ) @ SV128 )
| ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV196 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SV280 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1122,plain,
! [SV52: $i,SV129: $i,SV197: $i,SV251: $i] :
( ( ( SV251 != SV197 )
= $true )
| ( ( ~ ( c_member @ SV129 @ SV197 @ SV52 )
| ( c_member @ SV129 @ SV251 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1123,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false )
| ( ( ~ ! [SY912: $i] :
( ~ ( c_member @ SV198 @ SY912 @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ SY912 @ SY912 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1124,plain,
! [SV54: $i,SV131: $i,SV199: $i,SV252: $i,SV281: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
| ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
| ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1125,plain,
! [SV55: $i,SV132: $i,SV200: $i] :
( ( ( ! [SY915: $i] :
( ~ ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ SY915 @ SV132 ) @ SV55 )
| ( c_member @ SV200 @ SY915 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) ) ) )
= $false )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1126,plain,
! [SV56: $i,SV133: $i,SV201: $i,SV253: $i,SV282: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
| ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV201 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1127,plain,
! [SV57: $i,SV134: $i,SV202: $i,SV254: $i,SV283: $i] :
( ( ! [SY1016: $i] :
( ( ( c_Product__Type_OPair @ SY1016 @ SV283 @ SV254 @ SV202 )
!= ( c_Product__Type_OPair @ SY1016 @ SV283 @ SV134 @ SV57 ) )
| ~ ( ( SV254 != SV134 )
| ( SV202 != SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1128,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ! [SY921: $i,SY922: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY922 ) @ SV58 )
| ! [SY923: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ SY921 @ SY923 ) @ SV58 )
| ( SY922 = SY923 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1129,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) ) )
= $true )
| ( ( ~ ( ( SV204 != SV136 ) )
| ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1130,plain,
! [SV60: $i,SV137: $i,SV205: $i,SV256: $i,SV284: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV284 @ SV256 @ SV205 )
| ~ ( c_member @ ( tc_prod @ SV284 @ SV284 ) @ ( c_Product__Type_OPair @ SV284 @ SV284 @ SV137 @ SV60 ) @ SV205 )
| ( c_member @ SV284 @ SV137 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1131,plain,
! [SV61: $i,SV138: $i] :
( ( ( ! [SY1017: $i] :
( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK1_SY792 @ SV61 @ SV138 ) @ SY1017 ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ SY1017 @ ( sK1_SY792 @ SV61 @ SV138 ) ) @ SV61 )
| ( ( sK1_SY792 @ SV61 @ SV138 )
= SY1017 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1049]) ).
thf(1132,plain,
! [SV62: $i,SV139: $i,SV206: $i,SV257: $i] :
( ( ( ~ ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) ) )
= $true )
| ( ( ~ ( ( SV206 != SV139 ) )
| ( c_member @ SV257 @ SV206 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1133,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i] :
( ( ! [SY1018: $i,SY1019: $i,SY1020: $i] :
( ~ ( c_member @ ( tc_prod @ SY1020 @ SY1019 ) @ ( c_Product__Type_OPair @ SY1020 @ SY1019 @ SY1018 @ SV285 ) @ SV258 )
| ~ ( c_member @ ( tc_prod @ SY1019 @ SV207 ) @ ( c_Product__Type_OPair @ SY1019 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1020 @ SV207 ) @ ( c_Product__Type_OPair @ SY1020 @ SV207 @ SY1018 @ SV140 ) @ ( c_Relation_Orel__comp @ SY1020 @ SY1019 @ SV207 @ SV258 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1134,plain,
! [SV64: $i,SV141: $i,SV208: $i,SV259: $i] :
( ( ( SV259 != SV208 )
= $true )
| ( ( ~ ( ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
| ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV65: $i,SV142: $i,SV209: $i] :
( ( ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ SV65 )
= $false )
| ( ( c_member @ ( tc_prod @ SV209 @ SV209 ) @ SV142 @ ( c_Transitive__Closure_Ortrancl @ SV209 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1136,plain,
! [SV66: $i,SV143: $i] :
( ( ( ! [SY1021: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ SY1021 ) @ SV66 )
| ! [SY1022: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ SY1021 @ SY1022 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ SY1022 ) @ SV66 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1054]) ).
thf(1137,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV144 ) )
= $true )
| ( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1138,plain,
! [SV68: $i,SV145: $i,SV211: $i,SV261: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ SV68 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ ( c_Transitive__Closure_Otrancl @ SV261 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1139,plain,
! [SV69: $i,SV146: $i,SV212: $i] :
( ( ( c_member @ SV212 @ SV146 @ SV69 )
= $false )
| ( ( ( c_Set_Oinsert @ SV212 @ SV146 @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1140,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV147 @ SV70 )
| ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1141,plain,
! [SV70: $i,SV147: $i] :
( ( ~ ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 )
| ( c_Relation_Oirrefl @ SV147 @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1142,plain,
! [SV71: $i,SV148: $i,SV213: $i,SV262: $i,SV286: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
| ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
| ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1143,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ( ~ ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
| ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1144,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) )
| ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1145,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1146,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)],[1062]) ).
thf(1147,plain,
( ( ( ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $false )
| ( ( ~ ! [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_pos,[status(thm)],[1063]) ).
thf(1148,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ~ ( ~ ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
| ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
| ~ ( ~ ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 )
| ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1149,plain,
! [SV74: $i,SV151: $i,SV216: $i,SV264: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV264 @ SV216 @ SV151 ) )
= $true )
| ( ( ~ ( c_member @ SV264 @ SV74 @ SV216 )
| ( c_member @ ( tc_prod @ SV264 @ SV264 ) @ ( c_Product__Type_OPair @ SV264 @ SV264 @ SV74 @ SV74 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1150,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( c_member @ SV265 @ SV217 @ SV152 )
| ( SV217 = SV75 ) ) )
= $true )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1151,plain,
! [SV76: $i,SV153: $i,SV218: $i,SV266: $i,SV287: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV287 @ SV266 ) @ ( c_Product__Type_OPair @ SV287 @ SV266 @ SV218 @ SV153 ) @ SV76 )
| ( c_member @ SV266 @ SV153 @ ( c_Relation_ORange @ SV287 @ SV266 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1152,plain,
! [SV77: $i,SV154: $i,SV219: $i,SV267: $i,SV288: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV288 @ SV267 ) @ ( c_Product__Type_OPair @ SV288 @ SV267 @ SV219 @ SV154 ) @ SV77 )
| ( c_member @ SV288 @ SV219 @ ( c_Relation_ODomain @ SV288 @ SV267 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1153,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
| ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1154,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ~ ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
| ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1155,plain,
! [SV9: $i,SV86: $i,SV159: $i,SV221: $i] :
( ( ( SV221 = SV159 )
= $false )
| ( ( ~ ( c_member @ SV86 @ SV221 @ SV9 )
| ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SV221 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1156,plain,
! [SV10: $i,SV87: $i,SV160: $i,SV222: $i,SV268: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV160 ) @ SV87 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
| ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1157,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ~ ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
| ( SV89 = SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1158,plain,
! [SV162: $i,SV12: $i,SV89: $i] :
( ( ( SV89 != SV12 )
| ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1159,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ~ ( ~ ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
| ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1160,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ~ ( ~ ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1161,plain,
! [SV14: $i,SV91: $i,SV164: $i,SV224: $i] :
( ( ( ! [SY955: $i] :
~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SY955 @ SY955 ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1162,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i] :
( ( ! [SY1023: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1023 @ SV289 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV165 @ SV92 ) ) )
| ~ ! [SY1024: $i,SY1025: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SY1024 @ SY1025 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1023 @ SV289 ) @ ( tc_prod @ SY1023 @ SV289 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SY1024 @ SY1025 ) @ ( c_Product__Type_OPair @ SY1023 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1023 @ SV289 ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1163,plain,
! [SV16: $i,SV93: $i] :
( ( ( ~ ( c_Nitpick_Orefl_H @ SV93 @ SV16 ) )
= $true )
| ( ( ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1164,plain,
! [SV16: $i,SV93: $i] :
( ( ( ~ ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 ) )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1165,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ~ ( ~ ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
| ~ ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1166,plain,
! [SV18: $i,SV95: $i,SV167: $i,SV227: $i] :
( ( ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) )
= $false )
| ( ( ~ ! [SY963: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ SY963 @ SV167 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1167,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV96 @ SV19 ) )
= $true )
| ( ( ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1168,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1169,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i] :
( ( ! [SY1026: $i,SY1027: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1027 @ SY1026 ) @ ( tc_prod @ SY1027 @ SY1026 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1027 @ SY1026 ) @ ( tc_prod @ SY1027 @ SY1026 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1026 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1026 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1027 @ SY1026 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY1027 @ SY1027 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1027 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY1026 @ SY1026 ) @ ( c_Product__Type_OPair @ SY1026 @ SY1026 @ SV271 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1027 @ SY1027 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1027 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SY1026 @ SY1026 ) @ ( c_Product__Type_OPair @ SY1026 @ SY1026 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1027 @ SY1026 ) @ ( tc_prod @ SY1027 @ SY1026 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1027 @ SY1026 ) @ ( tc_prod @ SY1027 @ SY1026 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1026 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SY1027 @ SY1026 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1027 @ SY1026 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1170,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
| ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1171,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ~ ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
| ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1172,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
| ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1173,plain,
! [SV23: $i,SV100: $i,SV171: $i,SV230: $i] :
( ( ( c_member @ SV230 @ SV171 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV230 @ SV230 ) @ ( c_Product__Type_OPair @ SV230 @ SV230 @ SV23 @ SV171 ) @ SV100 )
| ( c_member @ SV230 @ SV23 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1174,plain,
! [SV24: $i,SV101: $i,SV172: $i,SV231: $i,SV272: $i,SV292: $i] :
( ( ~ ( c_member @ SV292 @ SV272 @ SV231 )
| ~ ( c_member @ ( tc_prod @ SV292 @ SV172 ) @ ( c_Product__Type_OPair @ SV292 @ SV172 @ SV272 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SV292 @ SV172 @ SV24 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1175,plain,
! [SV25: $i,SV102: $i,SV173: $i,SV232: $i] :
( ( ( c_Wellfounded_Owf @ SV232 @ SV173 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 )
| ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1176,plain,
! [SV26: $i,SV103: $i,SV174: $i,SV233: $i,SV273: $i] :
( ( ( ~ ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ SY1012 @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY1012 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1177,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV104 @ SV27 ) )
= $true )
| ( ( ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1178,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1179,plain,
! [SV28: $i,SV105: $i,SV175: $i,SV234: $i,SV274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV175 ) @ SV105 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
| ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1180,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ~ ( ~ ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
| ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) )
| ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1181,plain,
! [SV107: $i,SV30: $i,SV177: $i] :
( ( ( c_member @ ( tc_prod @ SV177 @ SV177 ) @ ( c_Product__Type_OPair @ SV177 @ SV177 @ SV30 @ SV30 ) @ SV107 )
= $false )
| ( ( c_Wellfounded_Owf @ SV177 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1182,plain,
! [SV31: $i,SV108: $i,SV178: $i,SV236: $i] :
( ( ( c_Wellfounded_Owf @ SV236 @ SV178 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 )
| ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1183,plain,
! [SV32: $i,SV109: $i,SV179: $i,SV237: $i] :
( ( ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) )
= $false )
| ( ( ~ ! [SY977: $i] :
~ ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ SY977 ) @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1184,plain,
! [SV33: $i,SV110: $i,SV180: $i,SV238: $i,SV276: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV276 @ SV238 @ SV180 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV276 @ SV276 ) @ ( c_Product__Type_OPair @ SV276 @ SV276 @ SV110 @ SV33 ) @ SV180 )
| ( c_member @ SV276 @ SV33 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1185,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
| ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1186,plain,
! [SV112: $i,SV35: $i,SV182: $i] :
( ( ( c_member @ ( tc_prod @ SV182 @ SV182 ) @ ( c_Product__Type_OPair @ SV182 @ SV182 @ SV35 @ SV35 ) @ SV112 )
= $false )
| ( ( c_Wellfounded_Owf @ SV182 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1187,plain,
! [SV36: $i,SV113: $i,SV183: $i,SV240: $i] :
( ( ( c_member @ SV240 @ SV183 @ SV113 )
= $false )
| ( ( c_member @ SV240 @ SV183 @ ( c_Set_Oinsert @ SV240 @ SV36 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1188,plain,
! [SV114: $i,SV37: $i] :
( ( ( SV37
!= ( c_Product__Type_OPair @ SV114 @ SV114 @ ( sK3_SY721 @ SV114 @ SV37 ) @ ( sK3_SY721 @ SV114 @ SV37 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1104]) ).
thf(1189,plain,
! [SV38: $i,SV115: $i,SV184: $i,SV241: $i] :
( ( ( c_Relation_Oantisym @ SV241 @ SV184 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
| ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1190,plain,
! [SV39: $i,SV116: $i,SV185: $i] :
( ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true )
| ( ( ~ ! [SY889: $i] :
( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ SY889 @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ SY889 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1191,plain,
! [SV40: $i,SV117: $i,SV186: $i,SV242: $i] :
( ( ( SV242 = SV186 )
= $false )
| ( ( ~ ( ~ ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1192,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false )
| ( ( ~ ( ( SV187 != SV118 ) )
| ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1193,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ~ ( ~ ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
| ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1194,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ~ ( ~ ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 )
| ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1195,plain,
! [SV43: $i,SV120: $i,SV189: $i,SV245: $i,SV277: $i,SV293: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
| ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
| ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1196,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
| ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1197,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ~ ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) )
| ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1198,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
| ( SV122 = SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1199,plain,
! [SV191: $i,SV45: $i,SV122: $i] :
( ( ( SV122 != SV45 )
| ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1200,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV123 @ SV46 ) )
= $true )
| ( ( ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1201,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1202,plain,
! [SV47: $i,SV124: $i,SV192: $i,SV246: $i,SV278: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV278 @ SV246 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
| ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1203,plain,
! [SV48: $i,SV125: $i,SV193: $i,SV247: $i,SV279: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV193 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1204,plain,
! [SV49: $i,SV126: $i,SV194: $i,SV248: $i] :
( ( ( SV248 = SV194 )
= $false )
| ( ( ~ ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1205,plain,
! [SV50: $i,SV127: $i,SV195: $i,SV249: $i] :
( ( ( c_Relation_Otrans @ SV249 @ SV195 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV127 @ SV50 )
| ( c_Relation_Otrans @ ( tc_prod @ SV249 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SV249 @ SV127 @ SV195 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1206,plain,
! [SV51: $i,SV128: $i,SV196: $i,SV250: $i,SV280: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV196 ) @ SV128 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV196 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SV280 @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1207,plain,
! [SV52: $i,SV129: $i,SV197: $i,SV251: $i] :
( ( ( SV251 = SV197 )
= $false )
| ( ( ~ ( c_member @ SV129 @ SV197 @ SV52 )
| ( c_member @ SV129 @ SV251 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1208,plain,
! [SV130: $i,SV53: $i,SV198: $i] :
( ( ( ! [SY912: $i] :
( ~ ( c_member @ SV198 @ SY912 @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ SY912 @ SY912 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1209,plain,
! [SV54: $i,SV131: $i,SV199: $i,SV252: $i,SV281: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
| ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1210,plain,
! [SV132: $i,SV55: $i,SV200: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ ( sK4_SY915 @ SV55 @ SV132 @ SV200 ) @ SV132 ) @ SV55 )
| ( c_member @ SV200 @ ( sK4_SY915 @ SV55 @ SV132 @ SV200 ) @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) ) )
= $false )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1125]) ).
thf(1211,plain,
! [SV56: $i,SV133: $i,SV201: $i,SV253: $i,SV282: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV201 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1212,plain,
! [SV57: $i,SV134: $i,SV202: $i,SV254: $i,SV283: $i,SV294: $i] :
( ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
!= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
| ~ ( ( SV254 != SV134 )
| ( SV202 != SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1213,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ! [SY1028: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ SY1028 ) @ SV58 )
| ! [SY1029: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ SY1029 ) @ SV58 )
| ( SY1028 = SY1029 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1128]) ).
thf(1214,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false )
| ( ( ~ ( ( SV204 != SV136 ) )
| ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1215,plain,
! [SV60: $i,SV137: $i,SV205: $i,SV256: $i,SV284: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV284 @ SV256 @ SV205 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV284 @ SV284 ) @ ( c_Product__Type_OPair @ SV284 @ SV284 @ SV137 @ SV60 ) @ SV205 )
| ( c_member @ SV284 @ SV137 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1216,plain,
! [SV61: $i,SV138: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK1_SY792 @ SV61 @ SV138 ) @ ( sK6_SY1017 @ SV61 @ SV138 ) ) @ SV61 )
| ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK6_SY1017 @ SV61 @ SV138 ) @ ( sK1_SY792 @ SV61 @ SV138 ) ) @ SV61 )
| ( ( sK1_SY792 @ SV61 @ SV138 )
= ( sK6_SY1017 @ SV61 @ SV138 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1217,plain,
! [SV62: $i,SV139: $i,SV206: $i,SV257: $i] :
( ( ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) )
= $false )
| ( ( ~ ( ( SV206 != SV139 ) )
| ( c_member @ SV257 @ SV206 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1218,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i,SV295: $i] :
( ( ! [SY1030: $i,SY1031: $i] :
( ~ ( c_member @ ( tc_prod @ SY1031 @ SY1030 ) @ ( c_Product__Type_OPair @ SY1031 @ SY1030 @ SV295 @ SV285 ) @ SV258 )
| ~ ( c_member @ ( tc_prod @ SY1030 @ SV207 ) @ ( c_Product__Type_OPair @ SY1030 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1031 @ SV207 ) @ ( c_Product__Type_OPair @ SY1031 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SY1031 @ SY1030 @ SV207 @ SV258 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1219,plain,
! [SV64: $i,SV141: $i,SV208: $i,SV259: $i] :
( ( ( SV259 = SV208 )
= $false )
| ( ( ~ ( ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
| ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1220,plain,
! [SV66: $i,SV143: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ ( sK7_SY1021 @ SV66 @ SV143 ) ) @ SV66 )
| ! [SY1032: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK7_SY1021 @ SV66 @ SV143 ) @ SY1032 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ SY1032 ) @ SV66 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1136]) ).
thf(1221,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ~ ( c_member @ SV260 @ SV210 @ SV144 ) )
= $false )
| ( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1222,plain,
! [SV68: $i,SV145: $i,SV211: $i,SV261: $i] :
( ( ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ SV68 )
= $false )
| ( ( c_member @ ( tc_prod @ SV261 @ SV261 ) @ ( c_Product__Type_OPair @ SV261 @ SV261 @ SV211 @ SV145 ) @ ( c_Transitive__Closure_Otrancl @ SV261 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1223,plain,
! [SV70: $i,SV147: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV147 @ SV70 ) )
= $true )
| ( ( ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1224,plain,
! [SV70: $i,SV147: $i] :
( ( ( ~ ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1225,plain,
! [SV71: $i,SV148: $i,SV213: $i,SV262: $i,SV286: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
| ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1226,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
| ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1227,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) )
| ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1228,plain,
( ( ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1230,plain,
( ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
= $true )
| ( ( ~ ! [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)],[1147]) ).
thf(1231,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ~ ( ~ ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
| ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1232,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ~ ( ~ ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 )
| ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1233,plain,
! [SV74: $i,SV151: $i,SV216: $i,SV264: $i] :
( ( ( c_Relation_Orefl__on @ SV264 @ SV216 @ SV151 )
= $false )
| ( ( ~ ( c_member @ SV264 @ SV74 @ SV216 )
| ( c_member @ ( tc_prod @ SV264 @ SV264 ) @ ( c_Product__Type_OPair @ SV264 @ SV264 @ SV74 @ SV74 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1234,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ( ~ ~ ( c_member @ SV265 @ SV217 @ SV152 )
| ( SV217 = SV75 ) )
= $false )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1235,plain,
! [SV76: $i,SV153: $i,SV218: $i,SV266: $i,SV287: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV287 @ SV266 ) @ ( c_Product__Type_OPair @ SV287 @ SV266 @ SV218 @ SV153 ) @ SV76 ) )
= $true )
| ( ( c_member @ SV266 @ SV153 @ ( c_Relation_ORange @ SV287 @ SV266 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1236,plain,
! [SV77: $i,SV154: $i,SV219: $i,SV267: $i,SV288: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV288 @ SV267 ) @ ( c_Product__Type_OPair @ SV288 @ SV267 @ SV219 @ SV154 ) @ SV77 ) )
= $true )
| ( ( c_member @ SV288 @ SV219 @ ( c_Relation_ODomain @ SV288 @ SV267 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1237,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
| ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1238,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
| ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1239,plain,
! [SV159: $i,SV9: $i,SV221: $i,SV86: $i] :
( ( ( ~ ( c_member @ SV86 @ SV221 @ SV9 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SV221 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) )
= $true )
| ( ( SV221 = SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1240,plain,
! [SV10: $i,SV87: $i,SV160: $i,SV222: $i,SV268: $i] :
( ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV160 ) @ SV87 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
| ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1241,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ( ~ ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) ) )
= $true )
| ( ( SV89 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1242,plain,
! [SV162: $i,SV12: $i,SV89: $i] :
( ( ( SV89 != SV12 )
= $true )
| ( ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1243,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ~ ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
| ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1244,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ~ ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
| ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1245,plain,
! [SV164: $i,SV91: $i,SV14: $i,SV224: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1161]) ).
thf(1246,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
| ~ ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) )
| ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1247,plain,
! [SV16: $i,SV93: $i] :
( ( ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
= $false )
| ( ( ! [SY655: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY655 @ SY655 ) @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1248,plain,
! [SV16: $i,SV93: $i] :
( ( ( ! [SY656: $i] : ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SY656 @ SY656 ) @ SV16 ) )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1249,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ~ ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
| ~ ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1250,plain,
! [SV18: $i,SV167: $i,SV227: $i,SV95: $i] :
( ( ( ! [SY963: $i] :
~ ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ SY963 @ SV167 ) @ SV18 ) )
= $false )
| ( ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1251,plain,
! [SV19: $i,SV96: $i] :
( ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false )
| ( ( ! [SY664: $i,SY665: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY664 @ SY665 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY665 @ SY664 ) @ SV19 )
| ( SY664 = SY665 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1252,plain,
! [SV19: $i,SV96: $i] :
( ( ( ! [SY666: $i,SY667: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY666 @ SY667 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY667 @ SY666 ) @ SV19 )
| ( SY666 = SY667 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1253,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i] :
( ( ! [SY1035: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1035 @ SV297 ) @ ( tc_prod @ SY1035 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1035 @ SV297 ) @ ( tc_prod @ SY1035 @ SV297 ) @ ( c_Product__Type_OPair @ SY1035 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SY1035 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1035 @ SV297 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SY1035 @ SY1035 ) @ ( c_Product__Type_OPair @ SY1035 @ SY1035 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1035 @ SY1035 ) @ ( c_Product__Type_OPair @ SY1035 @ SY1035 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1035 @ SV297 ) @ ( tc_prod @ SY1035 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1035 @ SV297 ) @ ( tc_prod @ SY1035 @ SV297 ) @ ( c_Product__Type_OPair @ SY1035 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SY1035 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SY1035 @ SV297 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1254,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ( ~ ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
= $true )
| ( ( ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1255,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ( ~ ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $true )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1256,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 ) )
= $true )
| ( ( ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1257,plain,
! [SV100: $i,SV171: $i,SV23: $i,SV230: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV230 @ SV230 ) @ ( c_Product__Type_OPair @ SV230 @ SV230 @ SV23 @ SV171 ) @ SV100 ) )
= $true )
| ( ( c_member @ SV230 @ SV23 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
= $true )
| ( ( c_member @ SV230 @ SV171 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1258,plain,
! [SV24: $i,SV101: $i,SV172: $i,SV231: $i,SV272: $i,SV292: $i] :
( ( ( ~ ( c_member @ SV292 @ SV272 @ SV231 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV292 @ SV172 ) @ ( c_Product__Type_OPair @ SV292 @ SV172 @ SV272 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SV292 @ SV172 @ SV24 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1259,plain,
! [SV173: $i,SV25: $i,SV102: $i,SV232: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV232 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1260,plain,
! [SV26: $i,SV103: $i,SV174: $i,SV233: $i,SV273: $i] :
( ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ SY1012 @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY1012 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1261,plain,
! [SV27: $i,SV104: $i] :
( ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false )
| ( ( ! [SY692: $i,SY693: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY693 ) @ SV27 )
| ! [SY694: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY693 @ SY694 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY692 @ SY694 ) @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1262,plain,
! [SV27: $i,SV104: $i] :
( ( ( ! [SY695: $i,SY696: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY696 ) @ SV27 )
| ! [SY697: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY696 @ SY697 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY695 @ SY697 ) @ SV27 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1263,plain,
! [SV28: $i,SV105: $i,SV175: $i,SV234: $i,SV274: $i] :
( ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV175 ) @ SV105 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
| ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1264,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ~ ( ~ ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
| ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1265,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) )
| ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1266,plain,
! [SV178: $i,SV31: $i,SV108: $i,SV236: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV236 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1267,plain,
! [SV32: $i,SV179: $i,SV109: $i,SV237: $i] :
( ( ( ! [SY977: $i] :
~ ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ SY977 ) @ SV32 ) )
= $false )
| ( ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1268,plain,
! [SV33: $i,SV110: $i,SV180: $i,SV238: $i,SV276: $i] :
( ( ( c_Relation_Orefl__on @ SV276 @ SV238 @ SV180 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV276 @ SV276 ) @ ( c_Product__Type_OPair @ SV276 @ SV276 @ SV110 @ SV33 ) @ SV180 )
| ( c_member @ SV276 @ SV33 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1269,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 ) )
= $true )
| ( ( ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1270,plain,
! [SV114: $i,SV37: $i] :
( ( ( SV37
= ( c_Product__Type_OPair @ SV114 @ SV114 @ ( sK3_SY721 @ SV114 @ SV37 ) @ ( sK3_SY721 @ SV114 @ SV37 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV114 @ SV114 ) @ SV37 @ ( c_Relation_OId @ SV114 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1271,plain,
! [SV184: $i,SV38: $i,SV115: $i,SV241: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV241 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1272,plain,
! [SV39: $i,SV116: $i,SV185: $i] :
( ( ( ! [SY889: $i] :
( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ SY889 @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ SY889 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) ) )
= $false )
| ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1273,plain,
! [SV186: $i,SV40: $i,SV242: $i,SV117: $i] :
( ( ( ~ ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
| ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) ) )
= $false )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1274,plain,
! [SV41: $i,SV243: $i,SV118: $i,SV187: $i] :
( ( ( ~ ( ( SV187 != SV118 ) ) )
= $true )
| ( ( ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1275,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ~ ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
| ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1276,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ~ ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 )
| ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1277,plain,
! [SV43: $i,SV120: $i,SV189: $i,SV245: $i,SV277: $i,SV293: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
| ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1278,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ( ~ ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 ) )
= $true )
| ( ( ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1279,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ( ~ ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1280,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) ) )
= $true )
| ( ( SV122 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1281,plain,
! [SV191: $i,SV45: $i,SV122: $i] :
( ( ( SV122 != SV45 )
= $true )
| ( ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1282,plain,
! [SV46: $i,SV123: $i] :
( ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false )
| ( ( ! [SY745: $i] :
( ~ ~ ! [SY746: $i] :
~ ( c_member @ SV123 @ SY746 @ SY745 )
| ~ ! [SY747: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY747 @ SY745 )
| ~ ! [SY748: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY748 @ SY747 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY748 @ SY745 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1283,plain,
! [SV46: $i,SV123: $i] :
( ( ( ! [SY749: $i] :
( ~ ~ ! [SY750: $i] :
~ ( c_member @ SV123 @ SY750 @ SY749 )
| ~ ! [SY751: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY751 @ SY749 )
| ~ ! [SY752: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY752 @ SY751 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY752 @ SY749 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1284,plain,
! [SV47: $i,SV124: $i,SV192: $i,SV246: $i,SV278: $i] :
( ( ( c_Relation_Otrans @ SV278 @ SV246 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
| ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1285,plain,
! [SV48: $i,SV125: $i,SV193: $i,SV247: $i,SV279: $i] :
( ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV193 @ SV48 ) @ SV125 )
| ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1286,plain,
! [SV194: $i,SV248: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
| ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) ) )
= $false )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1287,plain,
! [SV195: $i,SV249: $i,SV50: $i,SV127: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV127 @ SV50 ) )
= $true )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV249 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SV249 @ SV127 @ SV195 @ SV50 ) )
= $true )
| ( ( c_Relation_Otrans @ SV249 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1288,plain,
! [SV51: $i,SV128: $i,SV196: $i,SV250: $i,SV280: $i] :
( ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV196 ) @ SV128 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV196 @ SV51 ) @ SV128 )
| ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SV280 @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1289,plain,
! [SV251: $i,SV52: $i,SV197: $i,SV129: $i] :
( ( ( ~ ( c_member @ SV129 @ SV197 @ SV52 ) )
= $true )
| ( ( c_member @ SV129 @ SV251 @ SV52 )
= $true )
| ( ( SV251 = SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1290,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ( ~ ( c_member @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ SV53 )
| ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1208]) ).
thf(1291,plain,
! [SV54: $i,SV131: $i,SV199: $i,SV252: $i,SV281: $i] :
( ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
| ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1292,plain,
! [SV132: $i,SV55: $i,SV200: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ ( sK4_SY915 @ SV55 @ SV132 @ SV200 ) @ SV132 ) @ SV55 ) )
= $false )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1293,plain,
! [SV132: $i,SV55: $i,SV200: $i] :
( ( ( c_member @ SV200 @ ( sK4_SY915 @ SV55 @ SV132 @ SV200 ) @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $false )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1294,plain,
! [SV56: $i,SV133: $i,SV201: $i,SV253: $i,SV282: $i] :
( ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV201 @ SV56 ) @ SV133 )
| ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1295,plain,
! [SV57: $i,SV134: $i,SV202: $i,SV254: $i,SV283: $i,SV294: $i] :
( ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
!= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $true )
| ( ( ~ ( ( SV254 != SV134 )
| ( SV202 != SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1296,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK10_SY1028 @ SV58 @ SV135 @ SV203 ) ) @ SV58 )
| ! [SY1036: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ SY1036 ) @ SV58 )
| ( ( sK10_SY1028 @ SV58 @ SV135 @ SV203 )
= SY1036 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1213]) ).
thf(1297,plain,
! [SV59: $i,SV255: $i,SV136: $i,SV204: $i] :
( ( ( ~ ( ( SV204 != SV136 ) ) )
= $true )
| ( ( ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1298,plain,
! [SV60: $i,SV137: $i,SV205: $i,SV256: $i,SV284: $i] :
( ( ( c_Relation_Orefl__on @ SV284 @ SV256 @ SV205 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV284 @ SV284 ) @ ( c_Product__Type_OPair @ SV284 @ SV284 @ SV137 @ SV60 ) @ SV205 )
| ( c_member @ SV284 @ SV137 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1299,plain,
! [SV61: $i,SV138: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK1_SY792 @ SV61 @ SV138 ) @ ( sK6_SY1017 @ SV61 @ SV138 ) ) @ SV61 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1300,plain,
! [SV61: $i,SV138: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK6_SY1017 @ SV61 @ SV138 ) @ ( sK1_SY792 @ SV61 @ SV138 ) ) @ SV61 )
| ( ( sK1_SY792 @ SV61 @ SV138 )
= ( sK6_SY1017 @ SV61 @ SV138 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1301,plain,
! [SV62: $i,SV257: $i,SV139: $i,SV206: $i] :
( ( ( ~ ( ( SV206 != SV139 ) ) )
= $true )
| ( ( c_member @ SV257 @ SV206 @ SV62 )
= $true )
| ( ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1302,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i,SV295: $i,SV298: $i] :
( ( ! [SY1037: $i] :
( ~ ( c_member @ ( tc_prod @ SY1037 @ SV298 ) @ ( c_Product__Type_OPair @ SY1037 @ SV298 @ SV295 @ SV285 ) @ SV258 )
| ~ ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SY1037 @ SV207 ) @ ( c_Product__Type_OPair @ SY1037 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SY1037 @ SV298 @ SV207 @ SV258 @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1303,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1304,plain,
! [SV66: $i,SV143: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ ( sK7_SY1021 @ SV66 @ SV143 ) ) @ SV66 ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1305,plain,
! [SV66: $i,SV143: $i] :
( ( ( ! [SY1032: $i] :
( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK7_SY1021 @ SV66 @ SV143 ) @ SY1032 ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ SY1032 ) @ SV66 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1306,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true )
| ( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV67 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1307,plain,
! [SV70: $i,SV147: $i] :
( ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $false )
| ( ( ! [SY813: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY813 @ SY813 ) @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1308,plain,
! [SV70: $i,SV147: $i] :
( ( ( ! [SY814: $i] :
~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SY814 @ SY814 ) @ SV70 ) )
= $false )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1309,plain,
! [SV71: $i,SV148: $i,SV213: $i,SV262: $i,SV286: $i] :
( ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
| ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1310,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1311,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1312,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1313,plain,
! [SV299: $i] :
( ( ! [SY1038: $i] :
( ~ ( ( SV299 != SY1038 ) )
| ( 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 @ SY1038 @ SV299 ) @ 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 @ SV299 @ SY1038 ) @ v_L ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1314,plain,
( ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true )
| ( ( ~ ! [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 )
| ( ( ~ ! [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_or_pos,[status(thm)],[1230]) ).
thf(1315,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ~ ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
| ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1316,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ~ ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 )
| ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1317,plain,
! [SV151: $i,SV216: $i,SV74: $i,SV264: $i] :
( ( ( ~ ( c_member @ SV264 @ SV74 @ SV216 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV264 @ SV264 ) @ ( c_Product__Type_OPair @ SV264 @ SV264 @ SV74 @ SV74 ) @ SV151 )
= $true )
| ( ( c_Relation_Orefl__on @ SV264 @ SV216 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1318,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ( ~ ~ ( c_member @ SV265 @ SV217 @ SV152 ) )
= $false )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1319,plain,
! [SV152: $i,SV265: $i,SV75: $i,SV217: $i] :
( ( ( SV217 = SV75 )
= $false )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1320,plain,
! [SV76: $i,SV153: $i,SV218: $i,SV266: $i,SV287: $i] :
( ( ( c_member @ ( tc_prod @ SV287 @ SV266 ) @ ( c_Product__Type_OPair @ SV287 @ SV266 @ SV218 @ SV153 ) @ SV76 )
= $false )
| ( ( c_member @ SV266 @ SV153 @ ( c_Relation_ORange @ SV287 @ SV266 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1321,plain,
! [SV77: $i,SV154: $i,SV219: $i,SV267: $i,SV288: $i] :
( ( ( c_member @ ( tc_prod @ SV288 @ SV267 ) @ ( c_Product__Type_OPair @ SV288 @ SV267 @ SV219 @ SV154 ) @ SV77 )
= $false )
| ( ( c_member @ SV288 @ SV219 @ ( c_Relation_ODomain @ SV288 @ SV267 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1322,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) ) )
= $true )
| ( ( ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1323,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( ~ ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1324,plain,
! [SV159: $i,SV9: $i,SV221: $i,SV86: $i] :
( ( ( c_member @ SV86 @ SV221 @ SV9 )
= $false )
| ( ( c_member @ ( tc_prod @ SV86 @ SV86 ) @ ( c_Product__Type_OPair @ SV86 @ SV86 @ SV221 @ SV159 ) @ ( c_Relation_OId__on @ SV86 @ SV9 ) )
= $true )
| ( ( SV221 = SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1325,plain,
! [SV222: $i,SV87: $i,SV10: $i,SV160: $i,SV268: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV160 ) @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1326,plain,
! [SV12: $i,SV89: $i,SV162: $i] :
( ( ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
= $false )
| ( ( SV89 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1327,plain,
! [SV162: $i,SV12: $i,SV89: $i] :
( ( ( SV89 = SV12 )
= $false )
| ( ( c_member @ SV162 @ SV89 @ ( c_fequal @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1328,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ( ~ ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) ) )
= $true )
| ( ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1329,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ( ~ ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) ) )
= $true )
| ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1330,plain,
! [SV164: $i,SV91: $i,SV14: $i,SV224: $i] :
( ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
| ( SV91 != SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1331,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) )
= $true )
| ( ( ~ ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) )
| ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1332,plain,
! [SV16: $i,SV300: $i,SV93: $i] :
( ( ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ SV300 @ SV300 ) @ SV16 )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1333,plain,
! [SV16: $i,SV93: $i] :
( ( ( c_member @ ( tc_prod @ SV93 @ SV93 ) @ ( c_Product__Type_OPair @ SV93 @ SV93 @ ( sK11_SY656 @ SV16 @ SV93 ) @ ( sK11_SY656 @ SV16 @ SV93 ) ) @ SV16 )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV93 @ SV16 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1248]) ).
thf(1334,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ~ ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1335,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ~ ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1336,plain,
! [SV167: $i,SV18: $i,SV227: $i,SV95: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ ( sK12_SY963 @ SV18 @ SV167 @ SV227 @ SV95 ) @ SV167 ) @ SV18 ) )
= $false )
| ( ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1250]) ).
thf(1337,plain,
! [SV19: $i,SV301: $i,SV96: $i] :
( ( ( ! [SY1039: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SY1039 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY1039 @ SV301 ) @ SV19 )
| ( SV301 = SY1039 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1338,plain,
! [SV19: $i,SV96: $i] :
( ( ( ! [SY1040: $i] :
( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK13_SY666 @ SV19 @ SV96 ) @ SY1040 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SY1040 @ ( sK13_SY666 @ SV19 @ SV96 ) ) @ SV19 )
| ( ( sK13_SY666 @ SV19 @ SV96 )
= SY1040 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1252]) ).
thf(1339,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1340,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $false )
| ( ( ! [SY862: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY862 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY862 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1341,plain,
! [SV21: $i,SV98: $i,SV169: $i] :
( ( ( ! [SY863: $i] :
( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SY863 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SY863 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) ) )
= $false )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1342,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 ) )
= $false )
| ( ( ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1343,plain,
! [SV100: $i,SV171: $i,SV23: $i,SV230: $i] :
( ( ( c_member @ ( tc_prod @ SV230 @ SV230 ) @ ( c_Product__Type_OPair @ SV230 @ SV230 @ SV23 @ SV171 ) @ SV100 )
= $false )
| ( ( c_member @ SV230 @ SV23 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
= $true )
| ( ( c_member @ SV230 @ SV171 @ ( c_Wellfounded_Oacc @ SV230 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1344,plain,
! [SV24: $i,SV101: $i,SV172: $i,SV231: $i,SV272: $i,SV292: $i] :
( ( ( c_member @ SV292 @ SV272 @ SV231 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV292 @ SV172 ) @ ( c_Product__Type_OPair @ SV292 @ SV172 @ SV272 @ SV101 ) @ SV24 )
| ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SV292 @ SV172 @ SV24 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1345,plain,
! [SV173: $i,SV25: $i,SV102: $i,SV232: $i] :
( ( ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV232 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1346,plain,
! [SV26: $i,SV103: $i,SV233: $i,SV273: $i,SV174: $i] :
( ( ( ! [SY1012: $i] :
( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ SY1012 @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ SY1012 @ SV26 ) ) )
= $false )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1347,plain,
! [SV27: $i,SV303: $i,SV104: $i] :
( ( ( ! [SY1041: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SY1041 ) @ SV27 )
| ! [SY1042: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY1041 @ SY1042 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SY1042 ) @ SV27 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1348,plain,
! [SV27: $i,SV104: $i] :
( ( ( ! [SY1043: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ SY1043 ) @ SV27 )
| ! [SY1044: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SY1043 @ SY1044 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ SY1044 ) @ SV27 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1262]) ).
thf(1349,plain,
! [SV234: $i,SV105: $i,SV28: $i,SV175: $i,SV274: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV175 ) @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1350,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ~ ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
| ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1351,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) )
| ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1352,plain,
! [SV178: $i,SV31: $i,SV108: $i,SV236: $i] :
( ( ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV236 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1353,plain,
! [SV32: $i,SV179: $i,SV109: $i,SV237: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ ( sK15_SY977 @ SV32 @ SV179 @ SV109 @ SV237 ) ) @ SV32 ) )
= $false )
| ( ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1267]) ).
thf(1354,plain,
! [SV238: $i,SV180: $i,SV33: $i,SV110: $i,SV276: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV276 @ SV276 ) @ ( c_Product__Type_OPair @ SV276 @ SV276 @ SV110 @ SV33 ) @ SV180 ) )
= $true )
| ( ( c_member @ SV276 @ SV33 @ SV238 )
= $true )
| ( ( c_Relation_Orefl__on @ SV276 @ SV238 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1355,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 ) )
= $false )
| ( ( ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1356,plain,
! [SV184: $i,SV38: $i,SV115: $i,SV241: $i] :
( ( ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
| ( SV115 = SV38 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV241 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1357,plain,
! [SV116: $i,SV39: $i,SV185: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ ( sK16_SY889 @ SV39 @ SV116 @ SV185 ) @ SV116 ) @ SV39 )
| ( c_member @ SV185 @ ( sK16_SY889 @ SV39 @ SV116 @ SV185 ) @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) ) )
= $false )
| ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1272]) ).
thf(1358,plain,
! [SV186: $i,SV40: $i,SV242: $i,SV117: $i] :
( ( ( ~ ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) ) )
= $false )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1359,plain,
! [SV242: $i,SV40: $i,SV186: $i,SV117: $i] :
( ( ( ~ ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) ) )
= $false )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1360,plain,
! [SV41: $i,SV243: $i,SV118: $i,SV187: $i] :
( ( ( SV187 != SV118 )
= $false )
| ( ( ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1361,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ( ~ ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) ) )
= $true )
| ( ( ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1362,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ( ~ ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 ) )
= $true )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1363,plain,
! [SV43: $i,SV120: $i,SV189: $i,SV245: $i,SV277: $i,SV293: $i] :
( ( ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
| ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1364,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false )
| ( ( ! [SY899: $i] :
( ~ ( c_member @ SV190 @ SY899 @ SV121 )
| ! [SY900: $i] :
( ~ ( c_member @ SV190 @ SY900 @ SV121 )
| ~ ( ( SY899 != SY900 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY899 @ SY900 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY900 @ SY899 ) @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1365,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ( ! [SY901: $i] :
( ~ ( c_member @ SV190 @ SY901 @ SV121 )
| ! [SY902: $i] :
( ~ ( c_member @ SV190 @ SY902 @ SV121 )
| ~ ( ( SY901 != SY902 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY901 @ SY902 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY902 @ SY901 ) @ SV44 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1366,plain,
! [SV45: $i,SV122: $i,SV191: $i] :
( ( ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
= $false )
| ( ( SV122 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1367,plain,
! [SV191: $i,SV45: $i,SV122: $i] :
( ( ( SV122 = SV45 )
= $false )
| ( ( c_member @ ( tc_prod @ SV191 @ SV191 ) @ ( c_Product__Type_OPair @ SV191 @ SV191 @ SV122 @ SV45 ) @ ( c_Relation_OId @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1368,plain,
! [SV46: $i,SV304: $i,SV123: $i] :
( ( ( ~ ~ ! [SY1045: $i] :
~ ( c_member @ SV123 @ SY1045 @ SV304 )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1369,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ~ ! [SY1048: $i] :
~ ( c_member @ SV123 @ SY1048 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1049: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1049 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1050: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1050 @ SY1049 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1050 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1283]) ).
thf(1370,plain,
! [SV47: $i,SV246: $i,SV124: $i,SV192: $i,SV278: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 ) )
= $true )
| ( ( c_Relation_Otrans @ SV278 @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1371,plain,
! [SV247: $i,SV125: $i,SV48: $i,SV193: $i,SV279: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV193 @ SV48 ) @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1372,plain,
! [SV194: $i,SV248: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) ) )
= $false )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1373,plain,
! [SV248: $i,SV194: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) ) )
= $false )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1374,plain,
! [SV195: $i,SV249: $i,SV50: $i,SV127: $i] :
( ( ( c_Relation_Otrans @ SV127 @ SV50 )
= $false )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV249 @ SV127 ) @ ( c_Wellfounded_Olex__prod @ SV249 @ SV127 @ SV195 @ SV50 ) )
= $true )
| ( ( c_Relation_Otrans @ SV249 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1375,plain,
! [SV250: $i,SV128: $i,SV51: $i,SV196: $i,SV280: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV196 @ SV51 ) @ SV128 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SV280 @ SV128 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV196 ) @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1376,plain,
! [SV251: $i,SV52: $i,SV197: $i,SV129: $i] :
( ( ( c_member @ SV129 @ SV197 @ SV52 )
= $false )
| ( ( c_member @ SV129 @ SV251 @ SV52 )
= $true )
| ( ( SV251 = SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1377,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ( ~ ( c_member @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ SV53 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1378,plain,
! [SV53: $i,SV198: $i,SV130: $i] :
( ( ( SV130
!= ( c_Product__Type_OPair @ SV198 @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1379,plain,
! [SV252: $i,SV131: $i,SV54: $i,SV199: $i,SV281: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1380,plain,
! [SV132: $i,SV55: $i,SV200: $i] :
( ( ( c_member @ ( tc_prod @ SV200 @ SV200 ) @ ( c_Product__Type_OPair @ SV200 @ SV200 @ ( sK4_SY915 @ SV55 @ SV132 @ SV200 ) @ SV132 ) @ SV55 )
= $true )
| ( ( c_member @ SV200 @ SV132 @ ( c_Wellfounded_Oacc @ SV200 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1381,plain,
! [SV253: $i,SV133: $i,SV56: $i,SV201: $i,SV282: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV201 @ SV56 ) @ SV133 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1382,plain,
! [SV57: $i,SV134: $i,SV202: $i,SV254: $i,SV283: $i,SV294: $i] :
( ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false )
| ( ( ~ ( ( SV254 != SV134 )
| ( SV202 != SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1383,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK10_SY1028 @ SV58 @ SV135 @ SV203 ) ) @ SV58 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1384,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ! [SY1036: $i] :
( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ SY1036 ) @ SV58 )
| ( ( sK10_SY1028 @ SV58 @ SV135 @ SV203 )
= SY1036 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1385,plain,
! [SV59: $i,SV255: $i,SV136: $i,SV204: $i] :
( ( ( SV204 != SV136 )
= $false )
| ( ( ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1386,plain,
! [SV256: $i,SV205: $i,SV60: $i,SV137: $i,SV284: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV284 @ SV284 ) @ ( c_Product__Type_OPair @ SV284 @ SV284 @ SV137 @ SV60 ) @ SV205 ) )
= $true )
| ( ( c_member @ SV284 @ SV137 @ SV256 )
= $true )
| ( ( c_Relation_Orefl__on @ SV284 @ SV256 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1387,plain,
! [SV61: $i,SV138: $i] :
( ( ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK1_SY792 @ SV61 @ SV138 ) @ ( sK6_SY1017 @ SV61 @ SV138 ) ) @ SV61 )
= $true )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1388,plain,
! [SV61: $i,SV138: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK6_SY1017 @ SV61 @ SV138 ) @ ( sK1_SY792 @ SV61 @ SV138 ) ) @ SV61 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1389,plain,
! [SV138: $i,SV61: $i] :
( ( ( ( sK1_SY792 @ SV61 @ SV138 )
= ( sK6_SY1017 @ SV61 @ SV138 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1390,plain,
! [SV62: $i,SV257: $i,SV139: $i,SV206: $i] :
( ( ( SV206 != SV139 )
= $false )
| ( ( c_member @ SV257 @ SV206 @ SV62 )
= $true )
| ( ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1391,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i,SV295: $i,SV298: $i,SV305: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV305 @ SV298 ) @ ( c_Product__Type_OPair @ SV305 @ SV298 @ SV295 @ SV285 ) @ SV258 )
| ~ ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV305 @ SV207 ) @ ( c_Product__Type_OPair @ SV305 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SV305 @ SV298 @ SV207 @ SV258 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1392,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1393,plain,
! [SV66: $i,SV143: $i] :
( ( ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ ( sK7_SY1021 @ SV66 @ SV143 ) ) @ SV66 )
= $true )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1394,plain,
! [SV66: $i,SV143: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK7_SY1021 @ SV66 @ SV143 ) @ ( sK18_SY1032 @ SV66 @ SV143 ) ) @ SV66 )
| ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ ( sK18_SY1032 @ SV66 @ SV143 ) ) @ SV66 ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1305]) ).
thf(1395,plain,
! [SV144: $i,SV67: $i,SV210: $i,SV260: $i] :
( ( ( ~ ~ ( c_member @ SV260 @ SV210 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1396,plain,
! [SV70: $i,SV306: $i,SV147: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SV306 @ SV306 ) @ SV70 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1397,plain,
! [SV70: $i,SV147: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ ( sK19_SY814 @ SV70 @ SV147 ) @ ( sK19_SY814 @ SV70 @ SV147 ) ) @ SV70 ) )
= $false )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1308]) ).
thf(1398,plain,
! [SV262: $i,SV148: $i,SV71: $i,SV213: $i,SV286: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1399,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY940 ) @ SV72 )
| ! [SY941: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY939 @ SY941 ) @ SV72 )
| ( SY940 = SY941 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1400,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ! [SY942: $i,SY943: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY943 ) @ SV72 )
| ! [SY944: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SY942 @ SY944 ) @ SV72 )
| ( SY943 = SY944 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1401,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1402,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)],[1312]) ).
thf(1403,plain,
! [SV307: $i,SV299: $i] :
( ( ~ ( ( SV299 != SV307 ) )
| ( 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 @ SV307 @ SV299 ) @ 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 @ SV299 @ SV307 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1404,plain,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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 )
| ( ( ~ ! [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_pos,[status(thm)],[1314]) ).
thf(1405,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ( ~ ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) ) )
= $true )
| ( ( ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1406,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ~ ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 ) )
= $true )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1407,plain,
! [SV151: $i,SV216: $i,SV74: $i,SV264: $i] :
( ( ( c_member @ SV264 @ SV74 @ SV216 )
= $false )
| ( ( c_member @ ( tc_prod @ SV264 @ SV264 ) @ ( c_Product__Type_OPair @ SV264 @ SV264 @ SV74 @ SV74 ) @ SV151 )
= $true )
| ( ( c_Relation_Orefl__on @ SV264 @ SV216 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1408,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ( ~ ( c_member @ SV265 @ SV217 @ SV152 ) )
= $true )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1409,plain,
! [SV8: $i,SV85: $i,SV158: $i,SV220: $i] :
( ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false )
| ( ( ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1410,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( ~ ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1411,plain,
! [SV222: $i,SV87: $i,SV10: $i,SV160: $i,SV268: $i] :
( ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV160 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV10 ) @ ( c_Transitive__Closure_Ortrancl @ SV268 @ SV87 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV268 @ SV268 ) @ ( c_Product__Type_OPair @ SV268 @ SV268 @ SV222 @ SV160 ) @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1412,plain,
! [SV13: $i,SV90: $i,SV163: $i,SV223: $i] :
( ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $false )
| ( ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1413,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ( ( SV163 = SV90 )
| ( c_member @ SV223 @ SV163 @ SV13 ) )
= $false )
| ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1414,plain,
! [SV164: $i,SV14: $i,SV91: $i,SV224: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 ) )
= $true )
| ( ( SV91 != SV14 )
= $true )
| ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1415,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false )
| ( ( ~ ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) )
| ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1416,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
| ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1417,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
| ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1418,plain,
! [SV167: $i,SV18: $i,SV227: $i,SV95: $i] :
( ( ( c_member @ ( tc_prod @ SV95 @ SV227 ) @ ( c_Product__Type_OPair @ SV95 @ SV227 @ ( sK12_SY963 @ SV18 @ SV167 @ SV227 @ SV95 ) @ SV167 ) @ SV18 )
= $true )
| ( ( c_member @ SV227 @ SV167 @ ( c_Relation_ORange @ SV95 @ SV227 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1419,plain,
! [SV19: $i,SV308: $i,SV301: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SV308 ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV308 @ SV301 ) @ SV19 )
| ( SV301 = SV308 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1420,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK13_SY666 @ SV19 @ SV96 ) @ ( sK20_SY1040 @ SV19 @ SV96 ) ) @ SV19 )
| ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK20_SY1040 @ SV19 @ SV96 ) @ ( sK13_SY666 @ SV19 @ SV96 ) ) @ SV19 )
| ( ( sK13_SY666 @ SV19 @ SV96 )
= ( sK20_SY1040 @ SV19 @ SV96 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1338]) ).
thf(1421,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1422,plain,
! [SV21: $i,SV98: $i,SV309: $i,SV169: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SV309 @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ SV309 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
= $true )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1423,plain,
! [SV98: $i,SV21: $i,SV169: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ ( sK21_SY863 @ SV21 @ SV98 @ SV169 ) @ SV98 ) @ SV21 )
| ( c_member @ SV169 @ ( sK21_SY863 @ SV21 @ SV98 @ SV169 ) @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) ) )
= $false )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1341]) ).
thf(1424,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( ~ ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1425,plain,
! [SV231: $i,SV24: $i,SV101: $i,SV272: $i,SV172: $i,SV292: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV292 @ SV172 ) @ ( c_Product__Type_OPair @ SV292 @ SV172 @ SV272 @ SV101 ) @ SV24 ) )
= $true )
| ( ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SV292 @ SV172 @ SV24 @ SV231 ) )
= $true )
| ( ( c_member @ SV292 @ SV272 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1426,plain,
! [SV173: $i,SV102: $i,SV25: $i,SV232: $i] :
( ( ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV25 @ SV102 ) @ SV173 )
= $false )
| ( ( c_member @ ( tc_prod @ SV232 @ SV232 ) @ ( c_Product__Type_OPair @ SV232 @ SV232 @ SV102 @ SV25 ) @ SV173 )
= $false )
| ( ( c_Wellfounded_Owf @ SV232 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1427,plain,
! [SV233: $i,SV103: $i,SV26: $i,SV273: $i,SV174: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV233 ) @ SV103 )
| ~ ( c_member @ SV174 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV26 ) )
= $false )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1346]) ).
thf(1428,plain,
! [SV27: $i,SV310: $i,SV303: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 )
| ! [SY1051: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SY1051 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SY1051 ) @ SV27 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1429,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ ( sK23_SY1043 @ SV27 @ SV104 ) ) @ SV27 )
| ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK23_SY1043 @ SV27 @ SV104 ) @ SY1052 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ SY1052 ) @ SV27 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1348]) ).
thf(1430,plain,
! [SV234: $i,SV105: $i,SV28: $i,SV175: $i,SV274: $i] :
( ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV175 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV28 ) @ ( c_Transitive__Closure_Otrancl @ SV274 @ SV105 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV274 @ SV274 ) @ ( c_Product__Type_OPair @ SV274 @ SV274 @ SV234 @ SV175 ) @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1431,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ( ~ ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) ) )
= $true )
| ( ( ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1432,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1433,plain,
! [SV178: $i,SV108: $i,SV31: $i,SV236: $i] :
( ( ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV31 @ SV108 ) @ SV178 )
= $false )
| ( ( c_member @ ( tc_prod @ SV236 @ SV236 ) @ ( c_Product__Type_OPair @ SV236 @ SV236 @ SV108 @ SV31 ) @ SV178 )
= $false )
| ( ( c_Wellfounded_Owf @ SV236 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1434,plain,
! [SV32: $i,SV179: $i,SV109: $i,SV237: $i] :
( ( ( c_member @ ( tc_prod @ SV237 @ SV109 ) @ ( c_Product__Type_OPair @ SV237 @ SV109 @ SV179 @ ( sK15_SY977 @ SV32 @ SV179 @ SV109 @ SV237 ) ) @ SV32 )
= $true )
| ( ( c_member @ SV237 @ SV179 @ ( c_Relation_ODomain @ SV237 @ SV109 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1435,plain,
! [SV238: $i,SV180: $i,SV33: $i,SV110: $i,SV276: $i] :
( ( ( c_member @ ( tc_prod @ SV276 @ SV276 ) @ ( c_Product__Type_OPair @ SV276 @ SV276 @ SV110 @ SV33 ) @ SV180 )
= $false )
| ( ( c_member @ SV276 @ SV33 @ SV238 )
= $true )
| ( ( c_Relation_Orefl__on @ SV276 @ SV238 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1436,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( ~ ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1437,plain,
! [SV184: $i,SV115: $i,SV38: $i,SV241: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 ) )
= $true )
| ( ( SV115 = SV38 )
= $true )
| ( ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
= $false )
| ( ( c_Relation_Oantisym @ SV241 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1438,plain,
! [SV116: $i,SV39: $i,SV185: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ ( sK16_SY889 @ SV39 @ SV116 @ SV185 ) @ SV116 ) @ SV39 ) )
= $false )
| ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1439,plain,
! [SV116: $i,SV39: $i,SV185: $i] :
( ( ( c_member @ SV185 @ ( sK16_SY889 @ SV39 @ SV116 @ SV185 ) @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $false )
| ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1440,plain,
! [SV186: $i,SV40: $i,SV242: $i,SV117: $i] :
( ( ( ~ ( c_member @ SV117 @ SV242 @ SV40 )
| ( c_member @ SV117 @ SV186 @ SV40 ) )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1441,plain,
! [SV242: $i,SV40: $i,SV186: $i,SV117: $i] :
( ( ( ~ ( c_member @ SV117 @ SV186 @ SV40 )
| ( c_member @ SV117 @ SV242 @ SV40 ) )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1442,plain,
! [SV41: $i,SV243: $i,SV118: $i,SV187: $i] :
( ( ( SV187 = SV118 )
= $true )
| ( ( ~ ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1443,plain,
! [SV42: $i,SV119: $i,SV188: $i,SV244: $i] :
( ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $false )
| ( ( ~ ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1444,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ( ~ ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 ) )
= $false )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1445,plain,
! [SV43: $i,SV245: $i,SV120: $i,SV189: $i,SV277: $i,SV293: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1446,plain,
! [SV44: $i,SV121: $i,SV311: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ SV311 @ SV121 )
| ! [SY1053: $i] :
( ~ ( c_member @ SV190 @ SY1053 @ SV121 )
| ~ ( ( SV311 != SY1053 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SY1053 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY1053 @ SV311 ) @ SV44 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1447,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ SV121 )
| ! [SY1054: $i] :
( ~ ( c_member @ SV190 @ SY1054 @ SV121 )
| ~ ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= SY1054 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ SY1054 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY1054 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1365]) ).
thf(1448,plain,
! [SV46: $i,SV304: $i,SV123: $i] :
( ( ( ~ ~ ! [SY1045: $i] :
~ ( c_member @ SV123 @ SY1045 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1449,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ~ ! [SY1048: $i] :
~ ( c_member @ SV123 @ SY1048 @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1450,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ! [SY1049: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1049 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1050: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1050 @ SY1049 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1050 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1451,plain,
! [SV47: $i,SV246: $i,SV124: $i,SV192: $i,SV278: $i] :
( ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
| ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 ) )
= $true )
| ( ( c_Relation_Otrans @ SV278 @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1452,plain,
! [SV247: $i,SV125: $i,SV48: $i,SV193: $i,SV279: $i] :
( ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV193 @ SV48 ) @ SV125 )
= $false )
| ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV48 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV279 @ SV279 ) @ ( c_Product__Type_OPair @ SV279 @ SV279 @ SV247 @ SV193 ) @ ( c_Transitive__Closure_Otrancl @ SV279 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1453,plain,
! [SV194: $i,SV248: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( c_member @ SV126 @ SV49 @ SV248 )
| ( c_member @ SV126 @ SV49 @ SV194 ) )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1454,plain,
! [SV248: $i,SV194: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( c_member @ SV126 @ SV49 @ SV194 )
| ( c_member @ SV126 @ SV49 @ SV248 ) )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1455,plain,
! [SV250: $i,SV128: $i,SV51: $i,SV196: $i,SV280: $i] :
( ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV196 @ SV51 ) @ SV128 )
= $false )
| ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV51 ) @ ( c_Transitive__Closure_Otrancl @ SV280 @ SV128 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV280 @ SV280 ) @ ( c_Product__Type_OPair @ SV280 @ SV280 @ SV250 @ SV196 ) @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1456,plain,
! [SV53: $i,SV130: $i,SV198: $i] :
( ( ( c_member @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ SV53 )
= $true )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1457,plain,
! [SV53: $i,SV198: $i,SV130: $i] :
( ( ( SV130
= ( c_Product__Type_OPair @ SV198 @ SV198 @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) @ ( sK9_SY912 @ SV130 @ SV53 @ SV198 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV198 @ SV198 ) @ SV130 @ ( c_Relation_OId__on @ SV198 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1458,plain,
! [SV252: $i,SV131: $i,SV54: $i,SV199: $i,SV281: $i] :
( ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV199 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV54 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV281 @ SV281 ) @ ( c_Product__Type_OPair @ SV281 @ SV281 @ SV252 @ SV199 ) @ ( c_Transitive__Closure_Otrancl @ SV281 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1459,plain,
! [SV253: $i,SV133: $i,SV56: $i,SV201: $i,SV282: $i] :
( ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV201 @ SV56 ) @ SV133 )
= $false )
| ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV56 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV282 @ SV282 ) @ ( c_Product__Type_OPair @ SV282 @ SV282 @ SV253 @ SV201 ) @ ( c_Transitive__Closure_Ortrancl @ SV282 @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1460,plain,
! [SV283: $i,SV294: $i,SV57: $i,SV202: $i,SV134: $i,SV254: $i] :
( ( ( ( SV254 != SV134 )
| ( SV202 != SV57 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1461,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK10_SY1028 @ SV58 @ SV135 @ SV203 ) ) @ SV58 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1462,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK25_SY1036 @ SV58 @ SV135 @ SV203 ) ) @ SV58 )
| ( ( sK10_SY1028 @ SV58 @ SV135 @ SV203 )
= ( sK25_SY1036 @ SV58 @ SV135 @ SV203 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1384]) ).
thf(1463,plain,
! [SV59: $i,SV255: $i,SV136: $i,SV204: $i] :
( ( ( SV204 = SV136 )
= $true )
| ( ( ~ ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1464,plain,
! [SV256: $i,SV205: $i,SV60: $i,SV137: $i,SV284: $i] :
( ( ( c_member @ ( tc_prod @ SV284 @ SV284 ) @ ( c_Product__Type_OPair @ SV284 @ SV284 @ SV137 @ SV60 ) @ SV205 )
= $false )
| ( ( c_member @ SV284 @ SV137 @ SV256 )
= $true )
| ( ( c_Relation_Orefl__on @ SV284 @ SV256 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1465,plain,
! [SV61: $i,SV138: $i] :
( ( ( c_member @ ( tc_prod @ SV138 @ SV138 ) @ ( c_Product__Type_OPair @ SV138 @ SV138 @ ( sK6_SY1017 @ SV61 @ SV138 ) @ ( sK1_SY792 @ SV61 @ SV138 ) ) @ SV61 )
= $true )
| ( ( c_Relation_Oantisym @ SV138 @ SV61 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1466,plain,
! [SV62: $i,SV257: $i,SV139: $i,SV206: $i] :
( ( ( SV206 = SV139 )
= $true )
| ( ( c_member @ SV257 @ SV206 @ SV62 )
= $true )
| ( ( c_member @ SV257 @ SV206 @ ( c_Set_Oinsert @ SV257 @ SV139 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1467,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i,SV295: $i,SV298: $i,SV305: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV305 @ SV298 ) @ ( c_Product__Type_OPair @ SV305 @ SV298 @ SV295 @ SV285 ) @ SV258 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV305 @ SV207 ) @ ( c_Product__Type_OPair @ SV305 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SV305 @ SV298 @ SV207 @ SV258 @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1468,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( c_member @ SV141 @ SV64 @ SV259 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1469,plain,
! [SV259: $i,SV208: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( c_member @ SV141 @ SV64 @ SV208 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1470,plain,
! [SV66: $i,SV143: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK7_SY1021 @ SV66 @ SV143 ) @ ( sK18_SY1032 @ SV66 @ SV143 ) ) @ SV66 ) )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1394]) ).
thf(1471,plain,
! [SV66: $i,SV143: $i] :
( ( ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK2_SY805 @ SV66 @ SV143 ) @ ( sK18_SY1032 @ SV66 @ SV143 ) ) @ SV66 )
= $false )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1394]) ).
thf(1472,plain,
! [SV144: $i,SV67: $i,SV210: $i,SV260: $i] :
( ( ( ~ ( c_member @ SV260 @ SV210 @ SV67 ) )
= $false )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1473,plain,
! [SV70: $i,SV306: $i,SV147: $i] :
( ( ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ SV306 @ SV306 ) @ SV70 )
= $false )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1474,plain,
! [SV70: $i,SV147: $i] :
( ( ( c_member @ ( tc_prod @ SV147 @ SV147 ) @ ( c_Product__Type_OPair @ SV147 @ SV147 @ ( sK19_SY814 @ SV70 @ SV147 ) @ ( sK19_SY814 @ SV70 @ SV147 ) ) @ SV70 )
= $true )
| ( ( c_Relation_Oirrefl @ SV147 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1475,plain,
! [SV262: $i,SV148: $i,SV71: $i,SV213: $i,SV286: $i] :
( ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV213 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV71 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV286 @ SV286 ) @ ( c_Product__Type_OPair @ SV286 @ SV286 @ SV262 @ SV213 ) @ ( c_Transitive__Closure_Ortrancl @ SV286 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1476,plain,
! [SV72: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( ! [SY1055: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SY1055 ) @ SV72 )
| ! [SY1056: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SY1056 ) @ SV72 )
| ( SY1055 = SY1056 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1477,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ! [SY1057: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ SY1057 ) @ SV72 )
| ! [SY1058: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ SY1058 ) @ SV72 )
| ( SY1057 = SY1058 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1400]) ).
thf(1478,plain,
( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1479,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)],[1402]) ).
thf(1480,plain,
! [SV307: $i,SV299: $i] :
( ( ( ~ ( ( SV299 != SV307 ) ) )
= $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 @ SV307 @ SV299 ) @ 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 @ SV299 @ SV307 ) @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1481,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 )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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_pos,[status(thm)],[1404]) ).
thf(1482,plain,
! [SV73: $i,SV150: $i,SV215: $i,SV263: $i] :
( ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $false )
| ( ( ~ ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1483,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ~ ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 ) )
= $false )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1484,plain,
! [SV75: $i,SV152: $i,SV217: $i,SV265: $i] :
( ( ( c_member @ SV265 @ SV217 @ SV152 )
= $false )
| ( ( c_member @ SV265 @ SV217 @ ( c_Set_Oinsert @ SV265 @ SV75 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1485,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1486,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( ( SV158 != SV85 )
| ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1487,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ( SV163 = SV90 )
= $true )
| ( ( c_member @ SV223 @ SV163 @ SV13 )
= $true )
| ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1488,plain,
! [SV13: $i,SV223: $i,SV90: $i,SV163: $i] :
( ( ( SV163 = SV90 )
= $false )
| ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1489,plain,
! [SV90: $i,SV13: $i,SV163: $i,SV223: $i] :
( ( ( c_member @ SV223 @ SV163 @ SV13 )
= $false )
| ( ( c_member @ SV223 @ SV163 @ ( c_Set_Oinsert @ SV223 @ SV90 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1490,plain,
! [SV164: $i,SV14: $i,SV91: $i,SV224: $i] :
( ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
= $false )
| ( ( SV91 != SV14 )
= $true )
| ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1491,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ~ ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) ) )
= $true )
| ( ( ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1492,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
!= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true )
| ( ( ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1493,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( ~ ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1494,plain,
! [SV19: $i,SV308: $i,SV301: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SV308 ) @ SV19 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV308 @ SV301 ) @ SV19 )
| ( SV301 = SV308 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1495,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK13_SY666 @ SV19 @ SV96 ) @ ( sK20_SY1040 @ SV19 @ SV96 ) ) @ SV19 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1496,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK20_SY1040 @ SV19 @ SV96 ) @ ( sK13_SY666 @ SV19 @ SV96 ) ) @ SV19 )
| ( ( sK13_SY666 @ SV19 @ SV96 )
= ( sK20_SY1040 @ SV19 @ SV96 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1497,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1498,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ~ ( ~ ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1499,plain,
! [SV21: $i,SV98: $i,SV309: $i,SV169: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SV309 @ SV98 ) @ SV21 ) )
= $true )
| ( ( c_member @ SV169 @ SV309 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1500,plain,
! [SV98: $i,SV21: $i,SV169: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ ( sK21_SY863 @ SV21 @ SV98 @ SV169 ) @ SV98 ) @ SV21 ) )
= $false )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1501,plain,
! [SV98: $i,SV21: $i,SV169: $i] :
( ( ( c_member @ SV169 @ ( sK21_SY863 @ SV21 @ SV98 @ SV169 ) @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $false )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1502,plain,
! [SV99: $i,SV22: $i,SV170: $i,SV229: $i] :
( ( ( ! [SY968: $i] :
( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SY968 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SY968 @ SV99 ) @ SV22 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1503,plain,
! [SV231: $i,SV24: $i,SV101: $i,SV272: $i,SV172: $i,SV292: $i] :
( ( ( c_member @ ( tc_prod @ SV292 @ SV172 ) @ ( c_Product__Type_OPair @ SV292 @ SV172 @ SV272 @ SV101 ) @ SV24 )
= $false )
| ( ( c_member @ SV172 @ SV101 @ ( c_Relation_OImage @ SV292 @ SV172 @ SV24 @ SV231 ) )
= $true )
| ( ( c_member @ SV292 @ SV272 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1504,plain,
! [SV233: $i,SV103: $i,SV26: $i,SV273: $i,SV174: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV233 ) @ SV103 ) )
= $false )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1505,plain,
! [SV273: $i,SV233: $i,SV103: $i,SV26: $i,SV174: $i] :
( ( ( ~ ( c_member @ SV174 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV26 ) )
= $false )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1506,plain,
! [SV27: $i,SV310: $i,SV303: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 ) )
= $true )
| ( ( ! [SY1051: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SY1051 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SY1051 ) @ SV27 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1507,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ ( sK23_SY1043 @ SV27 @ SV104 ) ) @ SV27 ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1508,plain,
! [SV27: $i,SV104: $i] :
( ( ( ! [SY1052: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK23_SY1043 @ SV27 @ SV104 ) @ SY1052 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ SY1052 ) @ SV27 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1509,plain,
! [SV29: $i,SV106: $i,SV176: $i,SV235: $i,SV275: $i] :
( ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false )
| ( ( ~ ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1510,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1511,plain,
! [SV111: $i,SV34: $i,SV181: $i,SV239: $i] :
( ( ( ! [SY979: $i] :
( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SY979 ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SY979 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1512,plain,
! [SV184: $i,SV115: $i,SV38: $i,SV241: $i] :
( ( ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV38 @ SV115 ) @ SV184 )
= $false )
| ( ( SV115 = SV38 )
= $true )
| ( ( c_member @ ( tc_prod @ SV241 @ SV241 ) @ ( c_Product__Type_OPair @ SV241 @ SV241 @ SV115 @ SV38 ) @ SV184 )
= $false )
| ( ( c_Relation_Oantisym @ SV241 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1513,plain,
! [SV116: $i,SV39: $i,SV185: $i] :
( ( ( c_member @ ( tc_prod @ SV185 @ SV185 ) @ ( c_Product__Type_OPair @ SV185 @ SV185 @ ( sK16_SY889 @ SV39 @ SV116 @ SV185 ) @ SV116 ) @ SV39 )
= $true )
| ( ( c_member @ SV185 @ SV116 @ ( c_Wellfounded_Oacc @ SV185 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1514,plain,
! [SV186: $i,SV40: $i,SV242: $i,SV117: $i] :
( ( ( ~ ( c_member @ SV117 @ SV242 @ SV40 ) )
= $true )
| ( ( c_member @ SV117 @ SV186 @ SV40 )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1515,plain,
! [SV242: $i,SV40: $i,SV186: $i,SV117: $i] :
( ( ( ~ ( c_member @ SV117 @ SV186 @ SV40 ) )
= $true )
| ( ( c_member @ SV117 @ SV242 @ SV40 )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1516,plain,
! [SV118: $i,SV41: $i,SV187: $i,SV243: $i] :
( ( ( ! [SY980: $i] :
( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SY980 ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SY980 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) ) )
= $false )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1517,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ( ! [SY981: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY981 @ SV188 ) @ SV42 ) )
= $false )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1518,plain,
! [SV42: $i,SV188: $i,SV244: $i,SV119: $i] :
( ( ( ! [SY982: $i] :
~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SY982 @ SV188 ) @ SV42 ) )
= $true )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1519,plain,
! [SV43: $i,SV245: $i,SV120: $i,SV189: $i,SV277: $i,SV293: $i] :
( ( ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
| ( SV120 = SV43 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1520,plain,
! [SV44: $i,SV121: $i,SV311: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ SV311 @ SV121 ) )
= $true )
| ( ( ! [SY1053: $i] :
( ~ ( c_member @ SV190 @ SY1053 @ SV121 )
| ~ ( ( SV311 != SY1053 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SY1053 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY1053 @ SV311 ) @ SV44 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1521,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ SV121 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1522,plain,
! [SV44: $i,SV121: $i,SV190: $i] :
( ( ( ! [SY1054: $i] :
( ~ ( c_member @ SV190 @ SY1054 @ SV121 )
| ~ ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= SY1054 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ SY1054 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY1054 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1523,plain,
! [SV46: $i,SV304: $i,SV123: $i] :
( ( ( ~ ! [SY1045: $i] :
~ ( c_member @ SV123 @ SY1045 @ SV304 ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1524,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ! [SY1048: $i] :
~ ( c_member @ SV123 @ SY1048 @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1525,plain,
! [SV46: $i,SV123: $i] :
( ( ( ! [SY1049: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1049 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1050: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1050 @ SY1049 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1050 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1526,plain,
! [SV192: $i,SV246: $i,SV47: $i,SV124: $i,SV278: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 )
= $true )
| ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
= $false )
| ( ( c_Relation_Otrans @ SV278 @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1527,plain,
! [SV194: $i,SV248: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( c_member @ SV126 @ SV49 @ SV248 ) )
= $true )
| ( ( c_member @ SV126 @ SV49 @ SV194 )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1528,plain,
! [SV248: $i,SV194: $i,SV49: $i,SV126: $i] :
( ( ( ~ ( c_member @ SV126 @ SV49 @ SV194 ) )
= $true )
| ( ( c_member @ SV126 @ SV49 @ SV248 )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1529,plain,
! [SV57: $i,SV202: $i,SV283: $i,SV294: $i,SV134: $i,SV254: $i] :
( ( ( SV254 != SV134 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1530,plain,
! [SV134: $i,SV254: $i,SV283: $i,SV294: $i,SV57: $i,SV202: $i] :
( ( ( SV202 != SV57 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1531,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK25_SY1036 @ SV58 @ SV135 @ SV203 ) ) @ SV58 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1532,plain,
! [SV203: $i,SV135: $i,SV58: $i] :
( ( ( ( sK10_SY1028 @ SV58 @ SV135 @ SV203 )
= ( sK25_SY1036 @ SV58 @ SV135 @ SV203 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1533,plain,
! [SV136: $i,SV59: $i,SV204: $i,SV255: $i] :
( ( ( ! [SY992: $i] :
( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SY992 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SY992 @ SV136 ) @ SV59 ) ) )
= $false )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1534,plain,
! [SV63: $i,SV140: $i,SV207: $i,SV258: $i,SV285: $i,SV295: $i,SV298: $i,SV305: $i] :
( ( ( c_member @ ( tc_prod @ SV305 @ SV298 ) @ ( c_Product__Type_OPair @ SV305 @ SV298 @ SV295 @ SV285 ) @ SV258 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 )
| ( c_member @ ( tc_prod @ SV305 @ SV207 ) @ ( c_Product__Type_OPair @ SV305 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SV305 @ SV298 @ SV207 @ SV258 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1535,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1536,plain,
! [SV259: $i,SV208: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) ) )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1537,plain,
! [SV66: $i,SV143: $i] :
( ( ( c_member @ ( tc_prod @ SV143 @ SV143 ) @ ( c_Product__Type_OPair @ SV143 @ SV143 @ ( sK7_SY1021 @ SV66 @ SV143 ) @ ( sK18_SY1032 @ SV66 @ SV143 ) ) @ SV66 )
= $true )
| ( ( c_Relation_Otrans @ SV143 @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1538,plain,
! [SV144: $i,SV67: $i,SV210: $i,SV260: $i] :
( ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1539,plain,
! [SV72: $i,SV313: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 )
| ! [SY1059: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SY1059 ) @ SV72 )
| ( SV313 = SY1059 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1540,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK27_SY1057 @ SV72 @ SV149 @ SV214 ) ) @ SV72 )
| ! [SY1060: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ SY1060 ) @ SV72 )
| ( ( sK27_SY1057 @ SV72 @ SV149 @ SV214 )
= SY1060 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1477]) ).
thf(1541,plain,
! [SV314: $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 @ SV314 @ SV314 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1542,plain,
! [SV307: $i,SV299: $i] :
( ( ( SV299 != SV307 )
= $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 @ SV307 @ SV299 ) @ 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 @ SV299 @ SV307 ) @ v_L ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1543,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 @ sK28_SX0 @ sK28_SX0 ) @ v_L ) )
= $false )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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_forall_neg,[status(esa)],[1481]) ).
thf(1544,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ! [SY999: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY999 ) @ SV73 ) )
= $false )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1545,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ! [SY1000: $i] :
~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SY1000 ) @ SV73 ) )
= $true )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1546,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( SV158 != SV85 )
= $false )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1547,plain,
! [SV85: $i,SV8: $i,SV158: $i,SV220: $i] :
( ( ( ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1548,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( SV158 != SV85 )
= $true )
| ( ( ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1549,plain,
! [SV164: $i,SV224: $i,SV14: $i,SV91: $i] :
( ( ( SV91 = SV14 )
= $false )
| ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ SV91 @ SV14 ) @ SV164 )
= $false )
| ( ( c_member @ ( tc_prod @ SV224 @ SV224 ) @ ( c_Product__Type_OPair @ SV224 @ SV224 @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) @ ( sK8_SY955 @ SV14 @ SV91 @ SV164 @ SV224 ) ) @ ( c_Transitive__Closure_Otrancl @ SV224 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1550,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
!= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $false )
| ( ( ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1551,plain,
! [SV17: $i,SV94: $i,SV166: $i,SV226: $i,SV270: $i,SV290: $i] :
( ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false )
| ( ( ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1552,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( ~ ( ( SV226 != SV94 )
| ( SV166 != SV17 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1553,plain,
! [SV19: $i,SV308: $i,SV301: $i,SV96: $i] :
( ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SV308 ) @ SV19 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV308 @ SV301 ) @ SV19 )
| ( SV301 = SV308 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1554,plain,
! [SV19: $i,SV96: $i] :
( ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK13_SY666 @ SV19 @ SV96 ) @ ( sK20_SY1040 @ SV19 @ SV96 ) ) @ SV19 )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1555,plain,
! [SV19: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK20_SY1040 @ SV19 @ SV96 ) @ ( sK13_SY666 @ SV19 @ SV96 ) ) @ SV19 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1556,plain,
! [SV96: $i,SV19: $i] :
( ( ( ( sK13_SY666 @ SV19 @ SV96 )
= ( sK20_SY1040 @ SV19 @ SV96 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1557,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
| ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1558,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ~ ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1559,plain,
! [SV21: $i,SV98: $i,SV309: $i,SV169: $i] :
( ( ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ SV309 @ SV98 ) @ SV21 )
= $false )
| ( ( c_member @ SV169 @ SV309 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1560,plain,
! [SV98: $i,SV21: $i,SV169: $i] :
( ( ( c_member @ ( tc_prod @ SV169 @ SV169 ) @ ( c_Product__Type_OPair @ SV169 @ SV169 @ ( sK21_SY863 @ SV21 @ SV98 @ SV169 ) @ SV98 ) @ SV21 )
= $true )
| ( ( c_member @ SV169 @ SV98 @ ( c_Wellfounded_Oacc @ SV169 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1561,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
| ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) @ SV99 ) @ SV22 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1502]) ).
thf(1562,plain,
! [SV233: $i,SV103: $i,SV26: $i,SV273: $i,SV174: $i] :
( ( ( c_member @ ( tc_prod @ SV174 @ SV273 ) @ ( c_Product__Type_OPair @ SV174 @ SV273 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV233 ) @ SV103 )
= $true )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1563,plain,
! [SV273: $i,SV233: $i,SV103: $i,SV26: $i,SV174: $i] :
( ( ( c_member @ SV174 @ ( sK22_SY1012 @ SV26 @ SV103 @ SV233 @ SV273 @ SV174 ) @ SV26 )
= $true )
| ( ( c_member @ SV273 @ SV233 @ ( c_Relation_OImage @ SV174 @ SV273 @ SV103 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1564,plain,
! [SV27: $i,SV310: $i,SV303: $i,SV104: $i] :
( ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 )
= $false )
| ( ( ! [SY1051: $i] :
( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SY1051 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SY1051 ) @ SV27 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1565,plain,
! [SV27: $i,SV104: $i] :
( ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ ( sK23_SY1043 @ SV27 @ SV104 ) ) @ SV27 )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1566,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK23_SY1043 @ SV27 @ SV104 ) @ ( sK30_SY1052 @ SV27 @ SV104 ) ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ ( sK30_SY1052 @ SV27 @ SV104 ) ) @ SV27 ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1508]) ).
thf(1567,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ( ! [SY1013: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1013 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1013 @ SV235 ) @ SV106 ) ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1568,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV176: $i] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( c_member @ SV176 @ SY1014 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SY1014 @ SV235 ) @ SV106 ) ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1569,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) ) @ SV34 )
| ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1511]) ).
thf(1570,plain,
! [SV186: $i,SV40: $i,SV242: $i,SV117: $i] :
( ( ( c_member @ SV117 @ SV242 @ SV40 )
= $false )
| ( ( c_member @ SV117 @ SV186 @ SV40 )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1571,plain,
! [SV242: $i,SV40: $i,SV186: $i,SV117: $i] :
( ( ( c_member @ SV117 @ SV186 @ SV40 )
= $false )
| ( ( c_member @ SV117 @ SV242 @ SV40 )
= $true )
| ( ( SV242 = SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1572,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) ) @ SV41 )
| ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) )
= $false )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1516]) ).
thf(1573,plain,
! [SV188: $i,SV42: $i,SV244: $i,SV119: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ ( sK33_SY981 @ SV42 @ SV188 @ SV244 @ SV119 ) @ SV188 ) @ SV42 ) )
= $false )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1517]) ).
thf(1574,plain,
! [SV42: $i,SV188: $i,SV315: $i,SV244: $i,SV119: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SV315 @ SV188 ) @ SV42 ) )
= $true )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1575,plain,
! [SV120: $i,SV245: $i,SV43: $i,SV189: $i,SV277: $i,SV293: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 ) )
= $true )
| ( ( SV120 = SV43 )
= $true )
| ( ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1576,plain,
! [SV44: $i,SV121: $i,SV311: $i,SV190: $i] :
( ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( ! [SY1053: $i] :
( ~ ( c_member @ SV190 @ SY1053 @ SV121 )
| ~ ( ( SV311 != SY1053 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SY1053 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SY1053 @ SV311 ) @ SV44 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1577,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( c_member @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ SV121 )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1578,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ SV121 )
| ~ ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1522]) ).
thf(1579,plain,
! [SV46: $i,SV304: $i,SV123: $i] :
( ( ( ! [SY1045: $i] :
~ ( c_member @ SV123 @ SY1045 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1580,plain,
! [SV46: $i,SV123: $i] :
( ( ( ! [SY1048: $i] :
~ ( c_member @ SV123 @ SY1048 @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1581,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1582,plain,
! [SV192: $i,SV246: $i,SV47: $i,SV124: $i,SV278: $i] :
( ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV124 @ SV47 ) @ SV246 )
= $false )
| ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV47 ) @ SV246 )
= $true )
| ( ( c_member @ ( tc_prod @ SV278 @ SV278 ) @ ( c_Product__Type_OPair @ SV278 @ SV278 @ SV192 @ SV124 ) @ SV246 )
= $false )
| ( ( c_Relation_Otrans @ SV278 @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1583,plain,
! [SV194: $i,SV248: $i,SV49: $i,SV126: $i] :
( ( ( c_member @ SV126 @ SV49 @ SV248 )
= $false )
| ( ( c_member @ SV126 @ SV49 @ SV194 )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1584,plain,
! [SV248: $i,SV194: $i,SV49: $i,SV126: $i] :
( ( ( c_member @ SV126 @ SV49 @ SV194 )
= $false )
| ( ( c_member @ SV126 @ SV49 @ SV248 )
= $true )
| ( ( SV248 = SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1585,plain,
! [SV57: $i,SV202: $i,SV283: $i,SV294: $i,SV134: $i,SV254: $i] :
( ( ( SV254 = SV134 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1586,plain,
! [SV134: $i,SV254: $i,SV283: $i,SV294: $i,SV57: $i,SV202: $i] :
( ( ( SV202 = SV57 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV294 @ SV283 @ SV254 @ SV202 )
= ( c_Product__Type_OPair @ SV294 @ SV283 @ SV134 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1587,plain,
! [SV58: $i,SV135: $i,SV203: $i] :
( ( ( c_member @ ( tc_prod @ SV203 @ SV135 ) @ ( c_Product__Type_OPair @ SV203 @ SV135 @ ( sK5_SY921 @ SV58 @ SV135 @ SV203 ) @ ( sK25_SY1036 @ SV58 @ SV135 @ SV203 ) ) @ SV58 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV203 @ SV135 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1588,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
| ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) @ SV136 ) @ SV59 ) )
= $false )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1533]) ).
thf(1589,plain,
! [SV258: $i,SV295: $i,SV305: $i,SV63: $i,SV140: $i,SV285: $i,SV207: $i,SV298: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV305 @ SV207 ) @ ( c_Product__Type_OPair @ SV305 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SV305 @ SV298 @ SV207 @ SV258 @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV305 @ SV298 ) @ ( c_Product__Type_OPair @ SV305 @ SV298 @ SV295 @ SV285 ) @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1590,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1591,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 )
| ( c_member @ SV141 @ SV64 @ SV208 ) )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1592,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
| ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) )
= $false )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1593,plain,
! [SV72: $i,SV313: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 ) )
= $true )
| ( ( ! [SY1059: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SY1059 ) @ SV72 )
| ( SV313 = SY1059 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1594,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK27_SY1057 @ SV72 @ SV149 @ SV214 ) ) @ SV72 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1595,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ! [SY1060: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ SY1060 ) @ SV72 )
| ( ( sK27_SY1057 @ SV72 @ SV149 @ SV214 )
= SY1060 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1596,plain,
! [SV314: $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 @ SV314 @ SV314 ) @ v_L )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1597,plain,
! [SV307: $i,SV299: $i] :
( ( ( SV299 = SV307 )
= $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 @ SV307 @ SV299 ) @ 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 @ SV299 @ SV307 ) @ v_L ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1598,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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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)],[1543]) ).
thf(1599,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ ( sK36_SY999 @ SV73 @ SV215 @ SV150 @ SV263 ) ) @ SV73 ) )
= $false )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1544]) ).
thf(1600,plain,
! [SV73: $i,SV317: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SV317 ) @ SV73 ) )
= $true )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1601,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( SV158 = SV85 )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1602,plain,
! [SV85: $i,SV8: $i,SV158: $i,SV220: $i] :
( ( ( c_member @ SV220 @ SV158 @ SV8 )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1603,plain,
! [SV8: $i,SV220: $i,SV85: $i,SV158: $i] :
( ( ( SV158 = SV85 )
= $false )
| ( ( ~ ( c_member @ SV220 @ SV158 @ SV8 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1604,plain,
! [SV15: $i,SV92: $i,SV165: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( ~ ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1605,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1606,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( ( SV226 != SV94 )
| ( SV166 != SV17 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1607,plain,
! [SV19: $i,SV301: $i,SV308: $i,SV96: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV308 @ SV301 ) @ SV19 ) )
= $true )
| ( ( SV301 = SV308 )
= $true )
| ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SV308 ) @ SV19 )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1608,plain,
! [SV19: $i,SV96: $i] :
( ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ ( sK20_SY1040 @ SV19 @ SV96 ) @ ( sK13_SY666 @ SV19 @ SV96 ) ) @ SV19 )
= $true )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1609,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1610,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ( ~ ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1611,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1612,plain,
! [SV170: $i,SV22: $i,SV99: $i,SV229: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) @ SV99 ) @ SV22 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1613,plain,
! [SV303: $i,SV27: $i,SV318: $i,SV310: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SV318 ) @ SV27 )
| ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV318 ) @ SV27 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1614,plain,
! [SV27: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK23_SY1043 @ SV27 @ SV104 ) @ ( sK30_SY1052 @ SV27 @ SV104 ) ) @ SV27 ) )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1615,plain,
! [SV27: $i,SV104: $i] :
( ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK14_SY695 @ SV27 @ SV104 ) @ ( sK30_SY1052 @ SV27 @ SV104 ) ) @ SV27 )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1616,plain,
! [SV29: $i,SV275: $i,SV235: $i,SV106: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV176 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV235 ) @ SV106 ) ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1567]) ).
thf(1617,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV319: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV176 @ SV319 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 ) ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1618,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) ) @ SV34 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1619,plain,
! [SV181: $i,SV34: $i,SV111: $i,SV239: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1620,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) ) @ SV41 ) )
= $false )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1621,plain,
! [SV187: $i,SV41: $i,SV118: $i,SV243: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) ) )
= $false )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1622,plain,
! [SV188: $i,SV42: $i,SV244: $i,SV119: $i] :
( ( ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ ( sK33_SY981 @ SV42 @ SV188 @ SV244 @ SV119 ) @ SV188 ) @ SV42 )
= $true )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1623,plain,
! [SV42: $i,SV188: $i,SV315: $i,SV244: $i,SV119: $i] :
( ( ( c_member @ ( tc_prod @ SV119 @ SV244 ) @ ( c_Product__Type_OPair @ SV119 @ SV244 @ SV315 @ SV188 ) @ SV42 )
= $false )
| ( ( c_member @ SV244 @ SV188 @ ( c_Relation_ORange @ SV119 @ SV244 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1624,plain,
! [SV120: $i,SV245: $i,SV43: $i,SV189: $i,SV277: $i,SV293: $i] :
( ( ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV43 ) @ SV245 )
= $false )
| ( ( SV120 = SV43 )
= $true )
| ( ( c_member @ ( tc_prod @ SV293 @ SV277 ) @ ( c_Product__Type_OPair @ SV293 @ SV277 @ SV189 @ SV120 ) @ SV245 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV293 @ SV277 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1625,plain,
! [SV44: $i,SV311: $i,SV121: $i,SV320: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ SV320 @ SV121 )
| ~ ( ( SV311 != SV320 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1626,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ SV121 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1627,plain,
! [SV190: $i,SV121: $i,SV44: $i] :
( ( ( ~ ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1628,plain,
! [SV46: $i,SV304: $i,SV321: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ SV321 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1629,plain,
! [SV46: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ ( sK38_SY1048 @ SV46 @ SV123 ) @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1580]) ).
thf(1630,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( ~ ( ~ ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1631,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) ) )
= $false )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1632,plain,
! [SV204: $i,SV59: $i,SV136: $i,SV255: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) @ SV136 ) @ SV59 ) )
= $false )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1633,plain,
! [SV258: $i,SV295: $i,SV305: $i,SV63: $i,SV140: $i,SV285: $i,SV207: $i,SV298: $i] :
( ( ( c_member @ ( tc_prod @ SV298 @ SV207 ) @ ( c_Product__Type_OPair @ SV298 @ SV207 @ SV285 @ SV140 ) @ SV63 )
= $false )
| ( ( c_member @ ( tc_prod @ SV305 @ SV207 ) @ ( c_Product__Type_OPair @ SV305 @ SV207 @ SV295 @ SV140 ) @ ( c_Relation_Orel__comp @ SV305 @ SV298 @ SV207 @ SV258 @ SV63 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV305 @ SV298 ) @ ( c_Product__Type_OPair @ SV305 @ SV298 @ SV295 @ SV285 ) @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1634,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 ) )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1590]) ).
thf(1635,plain,
! [SV259: $i,SV208: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV208 )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1590]) ).
thf(1636,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ~ ( c_member @ SV141 @ SV64 @ SV259 ) )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1637,plain,
! [SV259: $i,SV208: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV208 )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1638,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ~ ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) ) )
= $false )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1592]) ).
thf(1639,plain,
! [SV210: $i,SV260: $i,SV67: $i,SV144: $i] :
( ( ( ~ ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) ) )
= $false )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1592]) ).
thf(1640,plain,
! [SV72: $i,SV313: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 )
= $false )
| ( ( ! [SY1059: $i] :
( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SY1059 ) @ SV72 )
| ( SV313 = SY1059 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1641,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK27_SY1057 @ SV72 @ SV149 @ SV214 ) ) @ SV72 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1642,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK39_SY1060 @ SV72 @ SV149 @ SV214 ) ) @ SV72 )
| ( ( sK27_SY1057 @ SV72 @ SV149 @ SV214 )
= ( sK39_SY1060 @ SV72 @ SV149 @ SV214 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1595]) ).
thf(1643,plain,
! [SV299: $i,SV307: $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 @ SV307 @ SV299 ) @ 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 @ SV299 @ SV307 ) @ v_L )
= $true )
| ( ( SV299 = SV307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1644,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 )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1645,plain,
! [SV73: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ ( sK36_SY999 @ SV73 @ SV215 @ SV150 @ SV263 ) ) @ SV73 )
= $true )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1646,plain,
! [SV73: $i,SV317: $i,SV215: $i,SV150: $i,SV263: $i] :
( ( ( c_member @ ( tc_prod @ SV263 @ SV150 ) @ ( c_Product__Type_OPair @ SV263 @ SV150 @ SV215 @ SV317 ) @ SV73 )
= $false )
| ( ( c_member @ SV263 @ SV215 @ ( c_Relation_ODomain @ SV263 @ SV150 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1647,plain,
! [SV85: $i,SV8: $i,SV158: $i,SV220: $i] :
( ( ( c_member @ SV220 @ SV158 @ SV8 )
= $false )
| ( ( SV158 = SV85 )
= $false )
| ( ( c_member @ ( tc_prod @ SV220 @ SV220 ) @ ( c_Product__Type_OPair @ SV220 @ SV220 @ SV158 @ SV85 ) @ ( c_Relation_OId__on @ SV220 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1648,plain,
! [SV92: $i,SV165: $i,SV15: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ! [SY1033: $i,SY1034: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SY1033 @ SY1034 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1649,plain,
! [SV17: $i,SV166: $i,SV270: $i,SV290: $i,SV94: $i,SV226: $i] :
( ( ( SV226 != SV94 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1650,plain,
! [SV94: $i,SV226: $i,SV270: $i,SV290: $i,SV17: $i,SV166: $i] :
( ( ( SV166 != SV17 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1651,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( SV226 != SV94 )
= $true )
| ( ( SV166 != SV17 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1652,plain,
! [SV19: $i,SV301: $i,SV308: $i,SV96: $i] :
( ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV308 @ SV301 ) @ SV19 )
= $false )
| ( ( SV301 = SV308 )
= $true )
| ( ( c_member @ ( tc_prod @ SV96 @ SV96 ) @ ( c_Product__Type_OPair @ SV96 @ SV96 @ SV301 @ SV308 ) @ SV19 )
= $false )
| ( ( c_Relation_Oantisym @ SV96 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1653,plain,
! [SV20: $i,SV97: $i,SV168: $i,SV228: $i,SV271: $i,SV291: $i,SV297: $i,SV302: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1654,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
| ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1655,plain,
! [SV22: $i,SV99: $i,SV170: $i,SV229: $i] :
( ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1656,plain,
! [SV170: $i,SV22: $i,SV99: $i,SV229: $i] :
( ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ ( sK29_SY968 @ SV99 @ SV22 @ SV170 @ SV229 ) @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ SV22 )
= $true )
| ( ( c_member @ ( tc_prod @ SV229 @ SV229 ) @ ( c_Product__Type_OPair @ SV229 @ SV229 @ SV170 @ SV99 ) @ ( c_Transitive__Closure_Otrancl @ SV229 @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1657,plain,
! [SV303: $i,SV27: $i,SV318: $i,SV310: $i,SV104: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SV318 ) @ SV27 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV318 ) @ SV27 )
= $true )
| ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1658,plain,
! [SV27: $i,SV104: $i] :
( ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ ( sK23_SY1043 @ SV27 @ SV104 ) @ ( sK30_SY1052 @ SV27 @ SV104 ) ) @ SV27 )
= $true )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1659,plain,
! [SV29: $i,SV275: $i,SV235: $i,SV106: $i,SV176: $i] :
( ( ( ~ ( ~ ( c_member @ SV176 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV235 ) @ SV106 ) ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1660,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV319: $i,SV176: $i] :
( ( ( ~ ( ~ ( c_member @ SV176 @ SV319 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 ) ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1661,plain,
! [SV34: $i,SV111: $i,SV181: $i,SV239: $i] :
( ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1662,plain,
! [SV181: $i,SV34: $i,SV111: $i,SV239: $i] :
( ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ ( sK31_SY979 @ SV111 @ SV34 @ SV181 @ SV239 ) @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ SV34 )
= $true )
| ( ( c_member @ ( tc_prod @ SV239 @ SV239 ) @ ( c_Product__Type_OPair @ SV239 @ SV239 @ SV181 @ SV111 ) @ ( c_Transitive__Closure_Otrancl @ SV239 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1663,plain,
! [SV41: $i,SV118: $i,SV187: $i,SV243: $i] :
( ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) ) @ SV41 )
= $true )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1664,plain,
! [SV187: $i,SV41: $i,SV118: $i,SV243: $i] :
( ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ ( sK32_SY980 @ SV118 @ SV41 @ SV187 @ SV243 ) @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $true )
| ( ( SV187 = SV118 )
= $true )
| ( ( c_member @ ( tc_prod @ SV243 @ SV243 ) @ ( c_Product__Type_OPair @ SV243 @ SV243 @ SV187 @ SV118 ) @ ( c_Transitive__Closure_Ortrancl @ SV243 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1665,plain,
! [SV44: $i,SV311: $i,SV121: $i,SV320: $i,SV190: $i] :
( ( ( ~ ( c_member @ SV190 @ SV320 @ SV121 ) )
= $true )
| ( ( ~ ( ( SV311 != SV320 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1666,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( c_member @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ SV121 )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1667,plain,
! [SV190: $i,SV121: $i,SV44: $i] :
( ( ( ~ ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1668,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1669,plain,
! [SV46: $i,SV304: $i,SV321: $i,SV123: $i] :
( ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1670,plain,
! [SV46: $i,SV123: $i] :
( ( ( c_member @ SV123 @ ( sK38_SY1048 @ SV46 @ SV123 ) @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1671,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
| ~ ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1672,plain,
! [SV59: $i,SV136: $i,SV204: $i,SV255: $i] :
( ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $true )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1673,plain,
! [SV204: $i,SV59: $i,SV136: $i,SV255: $i] :
( ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ ( sK35_SY992 @ SV136 @ SV59 @ SV204 @ SV255 ) @ SV136 ) @ SV59 )
= $true )
| ( ( SV204 = SV136 )
= $true )
| ( ( c_member @ ( tc_prod @ SV255 @ SV255 ) @ ( c_Product__Type_OPair @ SV255 @ SV255 @ SV204 @ SV136 ) @ ( c_Transitive__Closure_Ortrancl @ SV255 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1674,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( c_member @ SV141 @ SV64 @ SV259 ) )
= $true )
| ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1675,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( ~ ( c_member @ SV141 @ SV64 @ SV259 ) )
= $true )
| ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1676,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
| ( SV144 = SV67 ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1677,plain,
! [SV210: $i,SV260: $i,SV67: $i,SV144: $i] :
( ( ( ( SV144 != SV67 )
| ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1678,plain,
! [SV313: $i,SV72: $i,SV322: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV322 ) @ SV72 )
| ( SV313 = SV322 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1679,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK39_SY1060 @ SV72 @ SV149 @ SV214 ) ) @ SV72 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1680,plain,
! [SV214: $i,SV149: $i,SV72: $i] :
( ( ( ( sK27_SY1057 @ SV72 @ SV149 @ SV214 )
= ( sK39_SY1060 @ SV72 @ SV149 @ SV214 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1681,plain,
( ( ( ! [SY1062: $i] :
( ~ ( ( sK40_SX0 != SY1062 ) )
| ( 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 @ sK40_SX0 @ SY1062 ) @ 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 @ SY1062 @ sK40_SX0 ) @ v_L ) ) )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1644]) ).
thf(1682,plain,
! [SV15: $i,SV165: $i,SV92: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ! [SY1063: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ SY1063 ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ SY1063 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1648]) ).
thf(1683,plain,
! [SV17: $i,SV166: $i,SV270: $i,SV290: $i,SV94: $i,SV226: $i] :
( ( ( SV226 = SV94 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1684,plain,
! [SV94: $i,SV226: $i,SV270: $i,SV290: $i,SV17: $i,SV166: $i] :
( ( ( SV166 = SV17 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1685,plain,
! [SV270: $i,SV290: $i,SV17: $i,SV166: $i,SV94: $i,SV226: $i] :
( ( ( SV226 = SV94 )
= $false )
| ( ( SV166 != SV17 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1686,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1687,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV228: $i,SV291: $i,SV302: $i] :
( ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1688,plain,
! [SV97: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV228: $i,SV291: $i] :
( ( ( ~ ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1689,plain,
! [SV303: $i,SV27: $i,SV318: $i,SV310: $i,SV104: $i] :
( ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV310 @ SV318 ) @ SV27 )
= $false )
| ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV318 ) @ SV27 )
= $true )
| ( ( c_member @ ( tc_prod @ SV104 @ SV104 ) @ ( c_Product__Type_OPair @ SV104 @ SV104 @ SV303 @ SV310 ) @ SV27 )
= $false )
| ( ( c_Relation_Otrans @ SV104 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1690,plain,
! [SV29: $i,SV275: $i,SV235: $i,SV106: $i,SV176: $i] :
( ( ( ~ ( c_member @ SV176 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV235 ) @ SV106 ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1691,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV319: $i,SV176: $i] :
( ( ( ~ ( c_member @ SV176 @ SV319 @ SV29 )
| ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1692,plain,
! [SV44: $i,SV311: $i,SV121: $i,SV320: $i,SV190: $i] :
( ( ( c_member @ SV190 @ SV320 @ SV121 )
= $false )
| ( ( ~ ( ( SV311 != SV320 ) )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1693,plain,
! [SV190: $i,SV121: $i,SV44: $i] :
( ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
!= ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1694,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) ) @ SV44 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1695,plain,
! [SV121: $i,SV44: $i,SV190: $i] :
( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) @ ( sK24_SY901 @ SV44 @ SV121 @ SV190 ) ) @ SV44 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1696,plain,
! [SV321: $i,SV46: $i,SV304: $i,SV123: $i] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( c_member @ SV123 @ SY1046 @ SV304 )
| ~ ! [SY1047: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1047 @ SY1046 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1047 @ SV304 ) ) ) )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1697,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1698,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV259 )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV259 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1699,plain,
! [SV208: $i,SV259: $i,SV64: $i,SV141: $i] :
( ( ( c_member @ SV141 @ SV64 @ SV259 )
= $false )
| ( ( c_member @ SV141 @ SV64 @ SV208 )
= $true )
| ( ( SV259 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1700,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
!= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
= $true )
| ( ( SV144 = SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1701,plain,
! [SV210: $i,SV260: $i,SV67: $i,SV144: $i] :
( ( ( SV144 != SV67 )
= $true )
| ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1702,plain,
! [SV313: $i,SV72: $i,SV322: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV322 ) @ SV72 ) )
= $true )
| ( ( SV313 = SV322 )
= $true )
| ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1703,plain,
! [SV72: $i,SV149: $i,SV214: $i] :
( ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ ( sK26_SY942 @ SV72 @ SV149 @ SV214 ) @ ( sK39_SY1060 @ SV72 @ SV149 @ SV214 ) ) @ SV72 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1704,plain,
( ( ( ~ ( ( sK40_SX0 != sK42_SY1062 ) )
| ( 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 @ sK40_SX0 @ sK42_SY1062 ) @ 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 @ sK42_SY1062 @ sK40_SX0 ) @ v_L ) )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1681]) ).
thf(1705,plain,
! [SV15: $i,SV165: $i,SV92: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) ) @ SV15 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1682]) ).
thf(1706,plain,
! [SV270: $i,SV290: $i,SV94: $i,SV226: $i,SV17: $i,SV166: $i] :
( ( ( SV166 = SV17 )
= $false )
| ( ( SV226 = SV94 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV290 @ SV270 @ SV226 @ SV166 )
= ( c_Product__Type_OPair @ SV290 @ SV270 @ SV94 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1707,plain,
! [SV97: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV228: $i,SV291: $i] :
( ( ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1708,plain,
! [SV97: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV228: $i,SV291: $i] :
( ( ( ( SV291 != SV228 )
| ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1709,plain,
! [SV29: $i,SV275: $i,SV235: $i,SV106: $i,SV176: $i] :
( ( ( ~ ( c_member @ SV176 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV29 ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1710,plain,
! [SV29: $i,SV235: $i,SV106: $i,SV275: $i,SV176: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV235 ) @ SV106 ) )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1711,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV319: $i,SV176: $i] :
( ( ( ~ ( c_member @ SV176 @ SV319 @ SV29 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1712,plain,
! [SV121: $i,SV44: $i,SV190: $i,SV320: $i,SV311: $i] :
( ( ( ~ ( ( SV311 != SV320 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV320 @ SV121 )
= $false )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1713,plain,
! [SV190: $i,SV121: $i,SV44: $i] :
( ( ( ( sK24_SY901 @ SV44 @ SV121 @ SV190 )
= ( sK34_SY1054 @ SV44 @ SV121 @ SV190 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1714,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV123 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) @ SV304 )
| ~ ! [SY1064: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1064 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1064 @ SV304 ) ) ) )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1696]) ).
thf(1715,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( ~ ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1716,plain,
! [SV67: $i,SV144: $i,SV210: $i,SV260: $i] :
( ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
= $false )
| ( ( SV144 = SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1717,plain,
! [SV210: $i,SV260: $i,SV67: $i,SV144: $i] :
( ( ( SV144 = SV67 )
= $false )
| ( ( ( c_Set_Oinsert @ SV260 @ SV210 @ SV144 )
= ( c_Set_Oinsert @ SV260 @ SV210 @ SV67 ) )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV67 )
= $true )
| ( ( c_member @ SV260 @ SV210 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1718,plain,
! [SV313: $i,SV72: $i,SV322: $i,SV312: $i,SV149: $i,SV214: $i] :
( ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV322 ) @ SV72 )
= $false )
| ( ( SV313 = SV322 )
= $true )
| ( ( c_member @ ( tc_prod @ SV214 @ SV149 ) @ ( c_Product__Type_OPair @ SV214 @ SV149 @ SV312 @ SV313 ) @ SV72 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV214 @ SV149 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1719,plain,
( ( ( ~ ( ( sK40_SX0 != sK42_SY1062 ) ) )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1720,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 @ sK40_SX0 @ sK42_SY1062 ) @ 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 @ sK42_SY1062 @ sK40_SX0 ) @ v_L ) )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1721,plain,
! [SV15: $i,SV165: $i,SV92: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) ) @ SV15 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1722,plain,
! [SV269: $i,SV225: $i,SV15: $i,SV165: $i,SV92: $i,SV289: $i,SV296: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1723,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV302: $i,SV228: $i,SV291: $i] :
( ( ( SV291 != SV228 )
= $false )
| ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1724,plain,
! [SV97: $i,SV228: $i,SV291: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1725,plain,
! [SV97: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV228: $i,SV291: $i] :
( ( ( SV291 != SV228 )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1726,plain,
! [SV29: $i,SV275: $i,SV235: $i,SV106: $i,SV176: $i] :
( ( ( c_member @ SV176 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV29 )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1727,plain,
! [SV29: $i,SV235: $i,SV106: $i,SV275: $i,SV176: $i] :
( ( ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ ( sK37_SY1013 @ SV106 @ SV235 @ SV275 @ SV29 @ SV176 ) @ SV235 ) @ SV106 )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1728,plain,
! [SV106: $i,SV235: $i,SV275: $i,SV29: $i,SV319: $i,SV176: $i] :
( ( ( c_member @ SV176 @ SV319 @ SV29 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 ) )
= $true )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1729,plain,
! [SV121: $i,SV44: $i,SV190: $i,SV320: $i,SV311: $i] :
( ( ( SV311 != SV320 )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV320 @ SV121 )
= $false )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1730,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ~ ( ~ ( c_member @ SV123 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) @ SV304 )
| ~ ! [SY1064: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1064 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1064 @ SV304 ) ) ) )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1731,plain,
! [SV46: $i,SV316: $i,SV123: $i] :
( ( ( ! [SY1061: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1061 @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1061 @ ( sK17_SY749 @ SV46 @ SV123 ) ) ) )
= $false )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1732,plain,
( ( ( sK40_SX0 != sK42_SY1062 )
= $true )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1733,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 @ sK40_SX0 @ sK42_SY1062 ) @ v_L )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1734,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 @ sK42_SY1062 @ sK40_SX0 ) @ v_L )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1735,plain,
! [SV15: $i,SV165: $i,SV92: $i,SV225: $i,SV269: $i,SV289: $i,SV296: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) ) @ SV15 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1736,plain,
! [SV269: $i,SV225: $i,SV15: $i,SV165: $i,SV92: $i,SV289: $i,SV296: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ ( sK41_SY1033 @ SV92 @ SV165 @ SV15 @ SV225 @ SV269 @ SV289 @ SV296 ) @ ( sK43_SY1063 @ SV15 @ SV165 @ SV92 @ SV225 @ SV269 @ SV289 @ SV296 ) ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 )
= ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV296 @ SV289 ) @ ( tc_prod @ SV296 @ SV289 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV269 @ SV225 ) @ ( c_Product__Type_OPair @ SV296 @ SV289 @ SV165 @ SV92 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV296 @ SV289 ) @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1737,plain,
! [SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV97: $i,SV302: $i,SV228: $i,SV291: $i] :
( ( ( SV291 = SV228 )
= $true )
| ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1738,plain,
! [SV97: $i,SV228: $i,SV291: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i] :
( ( ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 )
= $true )
| ( ( c_member @ ( tc_prod @ SV302 @ SV302 ) @ ( c_Product__Type_OPair @ SV302 @ SV302 @ SV291 @ SV228 ) @ SV97 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1724]) ).
thf(1739,plain,
! [SV97: $i,SV302: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i,SV228: $i,SV291: $i] :
( ( ( SV291 = SV228 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1740,plain,
! [SV29: $i,SV106: $i,SV235: $i,SV319: $i,SV275: $i,SV176: $i] :
( ( ( c_member @ ( tc_prod @ SV176 @ SV275 ) @ ( c_Product__Type_OPair @ SV176 @ SV275 @ SV319 @ SV235 ) @ SV106 )
= $false )
| ( ( c_member @ SV176 @ SV319 @ SV29 )
= $false )
| ( ( c_member @ SV275 @ SV235 @ ( c_Relation_OImage @ SV176 @ SV275 @ SV106 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1741,plain,
! [SV121: $i,SV44: $i,SV190: $i,SV320: $i,SV311: $i] :
( ( ( SV311 = SV320 )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
| ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 ) )
= $true )
| ( ( c_member @ SV190 @ SV320 @ SV121 )
= $false )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1742,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) @ SV304 )
| ~ ! [SY1064: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1064 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1064 @ SV304 ) ) )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1743,plain,
! [SV316: $i,SV46: $i,SV123: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ SV316 ) @ SV46 )
| ~ ( c_member @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $false )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1731]) ).
thf(1744,plain,
( ( ( sK40_SX0 = sK42_SY1062 )
= $false )
| ( ( 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 @ sK28_SX0 @ sK28_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1745,plain,
! [SV97: $i,SV302: $i,SV228: $i,SV291: $i,SV20: $i,SV168: $i,SV271: $i,SV297: $i] :
( ( ( c_member @ ( tc_prod @ SV297 @ SV297 ) @ ( c_Product__Type_OPair @ SV297 @ SV297 @ SV271 @ SV168 ) @ SV20 )
= $false )
| ( ( SV291 = SV228 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV302 @ SV297 ) @ ( tc_prod @ SV302 @ SV297 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV291 @ SV271 ) @ ( c_Product__Type_OPair @ SV302 @ SV297 @ SV228 @ SV168 ) ) @ ( c_Wellfounded_Olex__prod @ SV302 @ SV297 @ SV97 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1746,plain,
! [SV121: $i,SV44: $i,SV320: $i,SV311: $i,SV190: $i] :
( ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV311 @ SV320 ) @ SV44 )
= $true )
| ( ( c_member @ ( tc_prod @ SV190 @ SV190 ) @ ( c_Product__Type_OPair @ SV190 @ SV190 @ SV320 @ SV311 ) @ SV44 )
= $true )
| ( ( SV311 = SV320 )
= $true )
| ( ( c_member @ SV190 @ SV320 @ SV121 )
= $false )
| ( ( c_member @ SV190 @ SV311 @ SV121 )
= $false )
| ( ( c_Relation_Ototal__on @ SV190 @ SV121 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1747,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) @ SV304 ) )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1748,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ~ ! [SY1064: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1064 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1064 @ SV304 ) ) )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1749,plain,
! [SV316: $i,SV46: $i,SV123: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ SV316 ) @ SV46 ) )
= $false )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1750,plain,
! [SV316: $i,SV46: $i,SV123: $i] :
( ( ( ~ ( c_member @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ ( sK17_SY749 @ SV46 @ SV123 ) ) )
= $false )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1751,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( c_member @ SV123 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) @ SV304 )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1752,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV123: $i] :
( ( ( ! [SY1064: $i] :
( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SY1064 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SY1064 @ SV304 ) ) )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1753,plain,
! [SV316: $i,SV46: $i,SV123: $i] :
( ( ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ SV316 ) @ SV46 )
= $true )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1754,plain,
! [SV316: $i,SV46: $i,SV123: $i] :
( ( ( c_member @ SV123 @ ( sK45_SY1061 @ SV46 @ SV316 @ SV123 ) @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $true )
| ( ( c_member @ SV123 @ SV316 @ ( sK17_SY749 @ SV46 @ SV123 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1755,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV323: $i,SV123: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SV323 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
| ~ ( c_member @ SV123 @ SV323 @ SV304 ) )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1756,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV323: $i,SV123: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SV323 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 ) )
= $true )
| ( ( ~ ( c_member @ SV123 @ SV323 @ SV304 ) )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1757,plain,
! [SV304: $i,SV46: $i,SV321: $i,SV323: $i,SV123: $i] :
( ( ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SV323 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
= $false )
| ( ( ~ ( c_member @ SV123 @ SV323 @ SV304 ) )
= $true )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1758,plain,
! [SV46: $i,SV321: $i,SV304: $i,SV323: $i,SV123: $i] :
( ( ( c_member @ SV123 @ SV323 @ SV304 )
= $false )
| ( ( c_member @ ( tc_prod @ SV123 @ SV123 ) @ ( c_Product__Type_OPair @ SV123 @ SV123 @ SV323 @ ( sK44_SY1046 @ SV321 @ SV46 @ SV304 @ SV123 ) ) @ SV46 )
= $false )
| ( ( c_member @ SV123 @ SV321 @ SV304 )
= $false )
| ( ( c_Wellfounded_Owf @ SV123 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1759,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[764,1758,1754,1753,1751,1746,1745,1744,1740,1738,1737,1736,1735,1734,1733,1727,1726,1718,1717,1716,1713,1706,1703,1699,1698,1695,1694,1689,1687,1684,1683,1680,1673,1672,1670,1666,1664,1663,1662,1661,1658,1656,1655,1652,1647,1646,1645,1643,1641,1637,1635,1633,1624,1623,1622,1615,1608,1602,1601,1596,1587,1586,1585,1584,1583,1582,1577,1571,1570,1565,1563,1562,1560,1559,1556,1554,1549,1537,1532,1513,1512,1503,1501,1489,1488,1487,1484,1478,1475,1474,1473,1471,1466,1465,1464,1461,1459,1458,1457,1456,1455,1452,1439,1435,1434,1433,1430,1426,1418,1411,1407,1393,1389,1387,1380,1376,1374,1367,1366,1343,1333,1332,1327,1326,1324,1321,1320,1319,1293,1270,1222,1187,1186,1181,1139,1135,1073,1069,918,917,842,841,840,838]) ).
thf(1760,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(copy,[status(thm)],[603]) ).
thf(1761,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)],[602]) ).
thf(1762,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(copy,[status(thm)],[601]) ).
thf(1763,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(copy,[status(thm)],[600]) ).
thf(1764,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(copy,[status(thm)],[599]) ).
thf(1765,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(copy,[status(thm)],[598]) ).
thf(1766,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)],[597]) ).
thf(1767,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(copy,[status(thm)],[596]) ).
thf(1768,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(copy,[status(thm)],[595]) ).
thf(1769,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(copy,[status(thm)],[594]) ).
thf(1770,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(copy,[status(thm)],[593]) ).
thf(1771,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)],[592]) ).
thf(1772,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(copy,[status(thm)],[591]) ).
thf(1773,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)],[590]) ).
thf(1774,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)],[589]) ).
thf(1775,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(copy,[status(thm)],[588]) ).
thf(1776,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(copy,[status(thm)],[587]) ).
thf(1777,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)],[586]) ).
thf(1778,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)],[585]) ).
thf(1779,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(copy,[status(thm)],[584]) ).
thf(1780,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(copy,[status(thm)],[583]) ).
thf(1781,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(copy,[status(thm)],[582]) ).
thf(1782,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(copy,[status(thm)],[581]) ).
thf(1783,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(copy,[status(thm)],[580]) ).
thf(1784,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(copy,[status(thm)],[579]) ).
thf(1785,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)],[578]) ).
thf(1786,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)],[577]) ).
thf(1787,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)],[576]) ).
thf(1788,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)],[575]) ).
thf(1789,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(copy,[status(thm)],[574]) ).
thf(1790,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(copy,[status(thm)],[573]) ).
thf(1791,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)],[572]) ).
thf(1792,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(copy,[status(thm)],[571]) ).
thf(1793,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)],[570]) ).
thf(1794,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)],[569]) ).
thf(1795,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)],[568]) ).
thf(1796,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)],[567]) ).
thf(1797,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)],[566]) ).
thf(1798,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)],[565]) ).
thf(1799,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(copy,[status(thm)],[564]) ).
thf(1800,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(copy,[status(thm)],[563]) ).
thf(1801,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(copy,[status(thm)],[562]) ).
thf(1802,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(copy,[status(thm)],[561]) ).
thf(1803,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)],[560]) ).
thf(1804,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)],[559]) ).
thf(1805,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)],[558]) ).
thf(1806,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)],[557]) ).
thf(1807,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)],[556]) ).
thf(1808,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)],[555]) ).
thf(1809,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)],[554]) ).
thf(1810,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)],[553]) ).
thf(1811,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(copy,[status(thm)],[552]) ).
thf(1812,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(copy,[status(thm)],[551]) ).
thf(1813,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(copy,[status(thm)],[550]) ).
thf(1814,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)],[549]) ).
thf(1815,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ T_a @ ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1816,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(copy,[status(thm)],[547]) ).
thf(1817,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(copy,[status(thm)],[546]) ).
thf(1818,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)],[545]) ).
thf(1819,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)],[544]) ).
thf(1820,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(copy,[status(thm)],[543]) ).
thf(1821,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)],[542]) ).
thf(1822,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)],[541]) ).
thf(1823,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(copy,[status(thm)],[540]) ).
thf(1824,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)],[539]) ).
thf(1825,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)],[538]) ).
thf(1826,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(copy,[status(thm)],[537]) ).
thf(1827,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)],[536]) ).
thf(1828,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)],[535]) ).
thf(1829,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)],[534]) ).
thf(1830,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)],[533]) ).
thf(1831,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(copy,[status(thm)],[532]) ).
thf(1832,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(copy,[status(thm)],[531]) ).
thf(1833,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(copy,[status(thm)],[530]) ).
thf(1834,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(copy,[status(thm)],[529]) ).
thf(1835,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)],[528]) ).
thf(1836,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(copy,[status(thm)],[527]) ).
thf(1837,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)],[526]) ).
thf(1838,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(copy,[status(thm)],[607]) ).
thf(1839,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ SX2 @ SX1 @ SX0 )
| ( ( c_Set_Oinsert @ SX2 @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1825]) ).
thf(1840,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [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 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1775]) ).
thf(1841,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1819]) ).
thf(1842,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 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1796]) ).
thf(1843,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1779]) ).
thf(1844,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 ) )
| ( c_member @ ( tc_prod @ SX7 @ SX7 ) @ ( c_Product__Type_OPair @ SX7 @ SX7 @ SX5 @ SX3 ) @ SX1 )
| ~ ( ( SX5 != SX3 )
| ~ ( 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 )
| ~ ( ( SX5 != SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX6 ) @ ( c_Product__Type_OPair @ SX6 @ SX6 @ SX4 @ SX2 ) @ SX0 ) ) )
| ( 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)],[1770]) ).
thf(1845,plain,
( ( ! [SX0: $i,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)],[1789]) ).
thf(1846,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ODomain @ SX3 @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Product__Type_OPair @ SX3 @ SX1 @ SX2 @ SX4 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1783]) ).
thf(1847,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Transitive__Closure_Ortrancl @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1794]) ).
thf(1848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX2 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1811]) ).
thf(1849,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Oantisym @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1818]) ).
thf(1850,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1792]) ).
thf(1851,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( c_member @ SX2 @ SX1 @ ( c_fequal @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1831]) ).
thf(1852,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ( ( c_Transitive__Closure_Otrancl @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1806]) ).
thf(1853,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1828]) ).
thf(1854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Wellfounded_Owf @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX1 @ SX0 ) @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1829]) ).
thf(1855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [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 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1790]) ).
thf(1856,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Transitive__Closure_Otrancl @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1804]) ).
thf(1857,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 = SX1 )
| ( c_member @ SX3 @ SX2 @ SX0 ) )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1822]) ).
thf(1858,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Wellfounded_Owf @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX4 @ SX3 ) @ SX0 )
| ~ ( c_member @ SX1 @ SX4 @ SX2 ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( c_member @ SX1 @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX4 @ SX3 ) @ SX0 )
| ~ ( c_member @ SX1 @ SX4 @ SX2 ) ) ) )
| ( c_Wellfounded_Owf @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1832]) ).
thf(1859,plain,
( ( ! [SX0: $i,SX1: $i,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 )
| ~ ( c_member @ SX3 @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ( 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1772]) ).
thf(1860,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [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 ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1833]) ).
thf(1861,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ! [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 ) ) )
| ( c_Relation_Osingle__valued @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1799]) ).
thf(1862,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Orefl__on @ SX4 @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX2 )
| ( c_member @ SX4 @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1787]) ).
thf(1863,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1766]) ).
thf(1864,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ( ~ ( c_member @ SX1 @ SX0 @ SX2 )
| ( c_member @ SX1 @ SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1768]) ).
thf(1865,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 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1801]) ).
thf(1866,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( c_member @ SX2 @ SX5 @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1834]) ).
thf(1867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Wellfounded_Oacc @ SX3 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX2 ) @ SX1 )
| ( c_member @ SX3 @ SX0 @ ( c_Wellfounded_Oacc @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1785]) ).
thf(1868,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( c_member @ ( tc_prod @ SX7 @ SX6 ) @ ( c_Product__Type_OPair @ SX7 @ SX6 @ SX5 @ SX4 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX6 @ SX2 ) @ ( c_Product__Type_OPair @ SX6 @ SX2 @ SX4 @ SX1 ) @ SX0 )
| ( c_member @ ( tc_prod @ SX7 @ SX2 ) @ ( c_Product__Type_OPair @ SX7 @ SX2 @ SX5 @ SX1 ) @ ( c_Relation_Orel__comp @ SX7 @ SX6 @ SX2 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1837]) ).
thf(1869,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_Owf @ SX2 @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1827]) ).
thf(1870,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ( c_member @ SX4 @ SX2 @ ( c_Relation_ODomain @ SX4 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1774]) ).
thf(1871,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Otrans @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1760]) ).
thf(1872,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Otrans @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX1 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX3 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1761]) ).
thf(1873,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 ) )
| ~ ( ~ ! [SX2: $i] : ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 )
| ( c_Nitpick_Orefl_H @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1763]) ).
thf(1874,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_Otrancl @ SX4 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1810]) ).
thf(1875,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 ) )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ ( c_Transitive__Closure_Ortrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1802]) ).
thf(1876,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ SX0 @ ( c_Relation_OId @ SX1 ) )
| ~ ! [SX2: $i] :
( SX0
!= ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1817]) ).
thf(1877,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_Relation_Ototal__on @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1776]) ).
thf(1878,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX3 @ SX2 ) @ ( c_Relation_OId__on @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1773]) ).
thf(1879,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 ) ) )
| ~ ( ~ ! [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 ) )
| ( c_Relation_Oantisym @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1826]) ).
thf(1880,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Orefl__on @ SX3 @ SX2 @ SX1 )
| ~ ( c_member @ SX3 @ SX0 @ SX2 )
| ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1786]) ).
thf(1881,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 )
| ( SX2 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1765]) ).
thf(1882,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1780]) ).
thf(1883,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_member @ SX5 @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX2 ) @ ( c_Product__Type_OPair @ SX5 @ SX2 @ SX4 @ SX1 ) @ SX0 )
| ( c_member @ SX2 @ SX1 @ ( c_Relation_OImage @ SX5 @ SX2 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1835]) ).
thf(1884,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX4 @ SX3 ) @ ( c_Product__Type_OPair @ SX4 @ SX3 @ SX2 @ SX1 ) @ SX0 )
| ( c_member @ SX3 @ SX1 @ ( c_Relation_ORange @ SX4 @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1771]) ).
thf(1885,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1820]) ).
thf(1886,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 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1797]) ).
thf(1887,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX1 @ SX0 ) @ ( c_Relation_OId @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1816]) ).
thf(1888,plain,
( ( ! [SX0: $i,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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ( c_member @ SX2 @ SX1 @ ( c_Wellfounded_Oacc @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1784]) ).
thf(1889,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Ortrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1795]) ).
thf(1890,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( 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 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1803]) ).
thf(1891,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Relation_Osingle__valued @ SX5 @ SX4 @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX5 @ SX4 @ SX2 @ SX1 ) @ SX3 )
| ~ ( c_member @ ( tc_prod @ SX5 @ SX4 ) @ ( c_Product__Type_OPair @ SX5 @ SX4 @ SX2 @ SX0 ) @ SX3 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1791]) ).
thf(1892,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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 ) ) )
| ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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(unfold_def,[status(thm)],[1838]) ).
thf(1893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ SX1 )
| ( c_member @ SX3 @ SX2 @ ( c_Set_Oinsert @ SX3 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1824]) ).
thf(1894,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 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Set_Oinsert @ SX3 @ SX2 @ SX1 )
= ( c_Set_Oinsert @ SX3 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1823]) ).
thf(1895,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_Otrancl @ SX4 @ SX1 ) )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1809]) ).
thf(1896,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ SX1 )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1807]) ).
thf(1897,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ~ ( c_member @ SX1 @ SX0 @ SX2 ) )
| ~ ( ~ ~ ( c_member @ SX1 @ SX0 @ SX3 )
| ( c_member @ SX1 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1762]) ).
thf(1898,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_Owf @ SX2 @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ ( c_Product__Type_OPair @ SX2 @ SX2 @ SX0 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1830]) ).
thf(1899,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 )
| ( SX2 != SX0 ) ) )
| ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ( ( c_Product__Type_OPair @ SX5 @ SX4 @ SX3 @ SX2 )
= ( c_Product__Type_OPair @ SX5 @ SX4 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1764]) ).
thf(1900,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( c_member @ SX1 @ SX3 @ SX0 )
| ( c_member @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( c_member @ SX1 @ SX2 @ SX0 )
| ( c_member @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1767]) ).
thf(1901,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 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1813]) ).
thf(1902,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 )
| ~ ! [SX4: $i] :
( ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX2 @ SX4 ) @ SX0 )
| ~ ( c_member @ ( tc_prod @ SX3 @ SX3 ) @ ( c_Product__Type_OPair @ SX3 @ SX3 @ SX4 @ SX1 ) @ ( c_Transitive__Closure_Otrancl @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1812]) ).
thf(1903,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX2 ) @ SX1 @ ( c_Relation_OId__on @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( c_member @ SX2 @ SX3 @ SX0 )
| ( SX1
!= ( c_Product__Type_OPair @ SX2 @ SX2 @ SX3 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1781]) ).
thf(1904,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Relation_Otrans @ SX3 @ SX2 )
| ~ ( c_Relation_Otrans @ SX1 @ SX0 )
| ( c_Relation_Otrans @ ( tc_prod @ SX3 @ SX1 ) @ ( c_Wellfounded_Olex__prod @ SX3 @ SX1 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1777]) ).
thf(1905,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 ) @ SX1 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX2 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) )
| ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX3 @ SX0 ) @ ( c_Transitive__Closure_Otrancl @ SX4 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1808]) ).
thf(1906,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_member @ SX4 @ SX3 @ ( c_Relation_OImage @ SX2 @ SX4 @ SX1 @ SX0 ) )
| ~ ! [SX5: $i] :
( ~ ( c_member @ ( tc_prod @ SX2 @ SX4 ) @ ( c_Product__Type_OPair @ SX2 @ SX4 @ SX5 @ SX3 ) @ SX1 )
| ~ ( c_member @ SX2 @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1836]) ).
thf(1907,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 ) )
| ~ ( ~ ! [SX2: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX1 ) @ ( c_Product__Type_OPair @ SX1 @ SX1 @ SX2 @ SX2 ) @ SX0 )
| ( c_Relation_Oirrefl @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1769]) ).
thf(1908,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_member @ SX3 @ SX2 @ ( c_Relation_ORange @ SX1 @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SX1 @ SX3 ) @ ( c_Product__Type_OPair @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1782]) ).
thf(1909,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 ) ) )
| ~ ! [SX7: $i,SX8: $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 @ SX7 @ SX8 ) ) @ 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 @ SX7 @ SX8 ) @ ( c_Product__Type_OPair @ SX6 @ SX5 @ SX2 @ SX1 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SX6 @ SX5 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1800]) ).
thf(1910,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Relation_Orefl__on @ SX4 @ SX3 @ SX2 )
| ~ ( c_member @ ( tc_prod @ SX4 @ SX4 ) @ ( c_Product__Type_OPair @ SX4 @ SX4 @ SX1 @ SX0 ) @ SX2 )
| ( c_member @ SX4 @ SX0 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1788]) ).
thf(1911,plain,
! [SV324: $i] :
( ( ! [SY1065: $i] : ( c_Relation_Otrans @ SY1065 @ ( c_Relation_OId__on @ SY1065 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1912,plain,
! [SV325: $i] :
( ( ! [SY1066: $i,SY1067: $i] : ( c_member @ ( tc_prod @ SY1067 @ SY1067 ) @ ( c_Product__Type_OPair @ SY1067 @ SY1067 @ SY1066 @ SY1066 ) @ ( c_Transitive__Closure_Ortrancl @ SY1067 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1913,plain,
! [SV326: $i] :
( ( ! [SY1068: $i] : ( c_Relation_Otrans @ SY1068 @ ( c_Transitive__Closure_Ortrancl @ SY1068 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1914,plain,
! [SV327: $i] :
( ( ! [SY1069: $i] : ( c_Relation_Otrans @ SY1069 @ ( c_Transitive__Closure_Otrancl @ SY1069 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1915,plain,
! [SV328: $i] :
( ( ! [SY1070: $i] : ( c_member @ ( tc_prod @ SY1070 @ SY1070 ) @ ( c_Product__Type_OPair @ SY1070 @ SY1070 @ SV328 @ SV328 ) @ ( c_Relation_OId @ SY1070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1916,plain,
! [SV329: $i] :
( ( c_Relation_Otrans @ SV329 @ ( c_Relation_OId @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(1917,plain,
! [SV330: $i] :
( ( ! [SY1071: $i,SY1072: $i] : ( c_member @ SY1072 @ SY1071 @ ( c_Set_Oinsert @ SY1072 @ SY1071 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(1918,plain,
! [SV331: $i] :
( ( ! [SY1073: $i,SY1074: $i] :
( ~ ( c_member @ SY1074 @ SY1073 @ SV331 )
| ( ( c_Set_Oinsert @ SY1074 @ SY1073 @ SV331 )
= SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1919,plain,
! [SV332: $i] :
( ( ! [SY1075: $i] :
( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( c_member @ ( tc_prod @ SY1075 @ SY1075 ) @ ( c_Product__Type_OPair @ SY1075 @ SY1075 @ SY1076 @ SY1077 ) @ SV332 )
| ! [SY1078: $i] :
( ~ ( c_member @ ( tc_prod @ SY1075 @ SY1075 ) @ ( c_Product__Type_OPair @ SY1075 @ SY1075 @ SY1077 @ SY1078 ) @ SV332 )
| ( c_member @ ( tc_prod @ SY1075 @ SY1075 ) @ ( c_Product__Type_OPair @ SY1075 @ SY1075 @ SY1076 @ SY1078 ) @ SV332 ) ) )
| ( c_Relation_Otrans @ SY1075 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(1920,plain,
! [SV333: $i] :
( ( ! [SY1079: $i,SY1080: $i,SY1081: $i] :
( ~ ( c_member @ SY1081 @ SY1080 @ ( c_Set_Oinsert @ SY1081 @ SY1079 @ SV333 ) )
| ~ ( ( SY1080 != SY1079 ) )
| ( c_member @ SY1081 @ SY1080 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(1921,plain,
! [SV334: $i] :
( ( ! [SY1082: $i,SY1083: $i,SY1084: $i,SY1085: $i] :
( ~ ( c_member @ ( tc_prod @ SY1085 @ SY1085 ) @ ( c_Product__Type_OPair @ SY1085 @ SY1085 @ SY1084 @ SY1083 ) @ ( c_Transitive__Closure_Ortrancl @ SY1085 @ SY1082 ) )
| ~ ( c_member @ ( tc_prod @ SY1085 @ SY1085 ) @ ( c_Product__Type_OPair @ SY1085 @ SY1085 @ SY1083 @ SV334 ) @ SY1082 )
| ( c_member @ ( tc_prod @ SY1085 @ SY1085 ) @ ( c_Product__Type_OPair @ SY1085 @ SY1085 @ SY1084 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SY1085 @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(1922,plain,
! [SV335: $i] :
( ( ! [SY1086: $i,SY1087: $i,SY1088: $i] :
~ ( ~ ( ~ ( c_member @ SY1088 @ SY1087 @ ( c_Relation_ODomain @ SY1088 @ SY1086 @ SV335 ) )
| ~ ! [SY1089: $i] :
~ ( c_member @ ( tc_prod @ SY1088 @ SY1086 ) @ ( c_Product__Type_OPair @ SY1088 @ SY1086 @ SY1087 @ SY1089 ) @ SV335 ) )
| ~ ( ~ ~ ! [SY1090: $i] :
~ ( c_member @ ( tc_prod @ SY1088 @ SY1086 ) @ ( c_Product__Type_OPair @ SY1088 @ SY1086 @ SY1087 @ SY1090 ) @ SV335 )
| ( c_member @ SY1088 @ SY1087 @ ( c_Relation_ODomain @ SY1088 @ SY1086 @ SV335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(1923,plain,
! [SV336: $i] :
( ( ! [SY1091: $i,SY1092: $i,SY1093: $i,SY1094: $i,SY1095: $i,SY1096: $i,SY1097: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1097 @ SY1096 ) @ ( tc_prod @ SY1097 @ SY1096 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1097 @ SY1096 ) @ ( tc_prod @ SY1097 @ SY1096 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1096 @ SY1095 @ SY1094 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1096 @ SY1093 @ SY1092 ) ) @ ( c_Wellfounded_Olex__prod @ SY1097 @ SY1096 @ SY1091 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1097 @ SY1097 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1097 @ SY1095 @ SY1093 ) @ SY1091 )
| ~ ( ( SY1095 != SY1093 )
| ~ ( c_member @ ( tc_prod @ SY1096 @ SY1096 ) @ ( c_Product__Type_OPair @ SY1096 @ SY1096 @ SY1094 @ SY1092 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1097 @ SY1097 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1097 @ SY1095 @ SY1093 ) @ SY1091 )
| ~ ( ( SY1095 != SY1093 )
| ~ ( c_member @ ( tc_prod @ SY1096 @ SY1096 ) @ ( c_Product__Type_OPair @ SY1096 @ SY1096 @ SY1094 @ SY1092 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1097 @ SY1096 ) @ ( tc_prod @ SY1097 @ SY1096 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1097 @ SY1096 ) @ ( tc_prod @ SY1097 @ SY1096 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1096 @ SY1095 @ SY1094 ) @ ( c_Product__Type_OPair @ SY1097 @ SY1096 @ SY1093 @ SY1092 ) ) @ ( c_Wellfounded_Olex__prod @ SY1097 @ SY1096 @ SY1091 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(1924,plain,
! [SV337: $i] :
( ( ! [SY1098: $i,SY1099: $i] :
( ~ ~ ( c_member @ SY1099 @ SY1098 @ ( c_Wellfounded_Oacc @ SY1099 @ SV337 ) )
| ~ ! [SY1100: $i] :
( ~ ( c_member @ ( tc_prod @ SY1099 @ SY1099 ) @ ( c_Product__Type_OPair @ SY1099 @ SY1099 @ SY1100 @ SY1098 ) @ SV337 )
| ( c_member @ SY1099 @ SY1100 @ ( c_Wellfounded_Oacc @ SY1099 @ SV337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(1925,plain,
! [SV338: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i] :
( ~ ( c_member @ SY1103 @ SY1102 @ ( c_Relation_ODomain @ SY1103 @ SY1101 @ SV338 ) )
| ~ ! [SY1104: $i] :
~ ( c_member @ ( tc_prod @ SY1103 @ SY1101 ) @ ( c_Product__Type_OPair @ SY1103 @ SY1101 @ SY1102 @ SY1104 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(1926,plain,
! [SV339: $i] :
( ( ! [SY1105: $i,SY1106: $i] :
( ~ ( c_member @ ( tc_prod @ SY1106 @ SY1106 ) @ SY1105 @ SV339 )
| ( c_member @ ( tc_prod @ SY1106 @ SY1106 ) @ SY1105 @ ( c_Transitive__Closure_Ortrancl @ SY1106 @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(1927,plain,
! [SV340: $i] :
( ( ! [SY1107: $i,SY1108: $i,SY1109: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SY1109 @ SY1109 ) @ ( c_Product__Type_OPair @ SY1109 @ SY1109 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SY1109 @ SY1108 ) )
| ~ ( c_member @ ( tc_prod @ SY1109 @ SY1109 ) @ ( c_Product__Type_OPair @ SY1109 @ SY1109 @ SY1107 @ SV340 ) @ SY1108 )
| ( SY1107 != SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(1928,plain,
! [SV341: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i] :
( ~ ( c_Relation_Oantisym @ SY1113 @ SY1112 )
| ~ ( c_member @ ( tc_prod @ SY1113 @ SY1113 ) @ ( c_Product__Type_OPair @ SY1113 @ SY1113 @ SY1111 @ SV341 ) @ SY1112 )
| ~ ( c_member @ ( tc_prod @ SY1113 @ SY1113 ) @ ( c_Product__Type_OPair @ SY1113 @ SY1113 @ SV341 @ SY1111 ) @ SY1112 )
| ( SY1111 = SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1929,plain,
! [SV342: $i] :
( ( ! [SY1114: $i,SY1115: $i] :
~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SY1115 @ SY1114 @ SV342 )
| ! [SY1116: $i,SY1117: $i] :
( ~ ( c_member @ ( tc_prod @ SY1115 @ SY1114 ) @ ( c_Product__Type_OPair @ SY1115 @ SY1114 @ SY1116 @ SY1117 ) @ SV342 )
| ! [SY1118: $i] :
( ~ ( c_member @ ( tc_prod @ SY1115 @ SY1114 ) @ ( c_Product__Type_OPair @ SY1115 @ SY1114 @ SY1116 @ SY1118 ) @ SV342 )
| ( SY1117 = SY1118 ) ) ) )
| ~ ( ~ ! [SY1119: $i,SY1120: $i] :
( ~ ( c_member @ ( tc_prod @ SY1115 @ SY1114 ) @ ( c_Product__Type_OPair @ SY1115 @ SY1114 @ SY1119 @ SY1120 ) @ SV342 )
| ! [SY1121: $i] :
( ~ ( c_member @ ( tc_prod @ SY1115 @ SY1114 ) @ ( c_Product__Type_OPair @ SY1115 @ SY1114 @ SY1119 @ SY1121 ) @ SV342 )
| ( SY1120 = SY1121 ) ) )
| ( c_Relation_Osingle__valued @ SY1115 @ SY1114 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1930,plain,
! [SV343: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
~ ( ~ ( ~ ( c_member @ SY1123 @ SY1122 @ ( c_fequal @ SV343 ) )
| ( SY1122 = SV343 ) )
| ~ ( ( SY1122 != SV343 )
| ( c_member @ SY1123 @ SY1122 @ ( c_fequal @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(1931,plain,
! [SV344: $i] :
( ( ! [SY1124: $i] :
( ~ ( c_Relation_Otrans @ SY1124 @ SV344 )
| ( ( c_Transitive__Closure_Otrancl @ SY1124 @ SV344 )
= SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(1932,plain,
! [SV345: $i] :
( ( ! [SY1125: $i,SY1126: $i,SY1127: $i] :
( ~ ( c_Wellfounded_Owf @ SY1127 @ SY1126 )
| ~ ( c_member @ ( tc_prod @ SY1127 @ SY1127 ) @ ( c_Product__Type_OPair @ SY1127 @ SY1127 @ SY1125 @ SV345 ) @ SY1126 )
| ~ ( c_member @ ( tc_prod @ SY1127 @ SY1127 ) @ ( c_Product__Type_OPair @ SY1127 @ SY1127 @ SV345 @ SY1125 ) @ SY1126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(1933,plain,
! [SV346: $i] :
( ( ! [SY1128: $i,SY1129: $i,SY1130: $i] :
( ~ ( c_Wellfounded_Owf @ SY1130 @ SY1129 )
| ~ ( c_member @ ( tc_prod @ SY1130 @ SY1130 ) @ ( c_Product__Type_OPair @ SY1130 @ SY1130 @ SY1128 @ SV346 ) @ SY1129 )
| ~ ( c_member @ ( tc_prod @ SY1130 @ SY1130 ) @ ( c_Product__Type_OPair @ SY1130 @ SY1130 @ SV346 @ SY1128 ) @ SY1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(1934,plain,
! [SV347: $i] :
( ( ! [SY1131: $i,SY1132: $i] :
( ~ ! [SY1133: $i] :
( ~ ( c_member @ ( tc_prod @ SY1132 @ SY1132 ) @ ( c_Product__Type_OPair @ SY1132 @ SY1132 @ SY1133 @ SY1131 ) @ SV347 )
| ( c_member @ SY1132 @ SY1133 @ ( c_Wellfounded_Oacc @ SY1132 @ SV347 ) ) )
| ( c_member @ SY1132 @ SY1131 @ ( c_Wellfounded_Oacc @ SY1132 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(1935,plain,
! [SV348: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ~ ( c_member @ ( tc_prod @ SY1135 @ SY1135 ) @ SY1134 @ SV348 )
| ( c_member @ ( tc_prod @ SY1135 @ SY1135 ) @ SY1134 @ ( c_Transitive__Closure_Otrancl @ SY1135 @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(1936,plain,
! [SV349: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i] :
~ ( ~ ( ~ ( c_member @ SY1138 @ SY1137 @ ( c_Set_Oinsert @ SY1138 @ SY1136 @ SV349 ) )
| ( SY1137 = SY1136 )
| ( c_member @ SY1138 @ SY1137 @ SV349 ) )
| ~ ( ~ ( ( SY1137 = SY1136 )
| ( c_member @ SY1138 @ SY1137 @ SV349 ) )
| ( c_member @ SY1138 @ SY1137 @ ( c_Set_Oinsert @ SY1138 @ SY1136 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(1937,plain,
! [SV350: $i] :
( ( ! [SY1139: $i] :
~ ( ~ ( ~ ( c_Wellfounded_Owf @ SY1139 @ SV350 )
| ! [SY1140: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SY1139 @ SX3 @ SY1140 )
| ~ ! [SY1142: $i] :
~ ~ ( ~ ( c_member @ SY1139 @ SY1142 @ SY1140 )
| ~ ! [SY1143: $i] :
( ~ ( c_member @ ( tc_prod @ SY1139 @ SY1139 ) @ ( c_Product__Type_OPair @ SY1139 @ SY1139 @ SY1143 @ SY1142 ) @ SV350 )
| ~ ( c_member @ SY1139 @ SY1143 @ SY1140 ) ) ) ) )
| ~ ( ~ ! [SY1144: $i] :
( ~ ~ ! [SX3: $i] :
~ ( c_member @ SY1139 @ SX3 @ SY1144 )
| ~ ! [SY1146: $i] :
~ ~ ( ~ ( c_member @ SY1139 @ SY1146 @ SY1144 )
| ~ ! [SY1147: $i] :
( ~ ( c_member @ ( tc_prod @ SY1139 @ SY1139 ) @ ( c_Product__Type_OPair @ SY1139 @ SY1139 @ SY1147 @ SY1146 ) @ SV350 )
| ~ ( c_member @ SY1139 @ SY1147 @ SY1144 ) ) ) )
| ( c_Wellfounded_Owf @ SY1139 @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(1938,plain,
! [SV351: $i] :
( ( ! [SY1148: $i,SY1149: $i,SY1150: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY1150 @ SY1150 ) @ ( c_Product__Type_OPair @ SY1150 @ SY1150 @ SY1149 @ SY1148 ) @ ( c_Relation_OId__on @ SY1150 @ SV351 ) )
| ~ ( ( SY1149 != SY1148 )
| ~ ( c_member @ SY1150 @ SY1149 @ SV351 ) ) )
| ~ ( ~ ~ ( ( SY1149 != SY1148 )
| ~ ( c_member @ SY1150 @ SY1149 @ SV351 ) )
| ( c_member @ ( tc_prod @ SY1150 @ SY1150 ) @ ( c_Product__Type_OPair @ SY1150 @ SY1150 @ SY1149 @ SY1148 ) @ ( c_Relation_OId__on @ SY1150 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1939,plain,
! [SV352: $i] :
( ( ! [SY1151: $i] :
( ~ ! [SY1152: $i,SY1153: $i] :
( ~ ( c_member @ ( tc_prod @ SY1151 @ SY1151 ) @ ( c_Product__Type_OPair @ SY1151 @ SY1151 @ SY1152 @ SY1153 ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SY1151 @ SY1151 ) @ ( c_Product__Type_OPair @ SY1151 @ SY1151 @ SY1153 @ SY1152 ) @ SV352 )
| ( SY1152 = SY1153 ) )
| ( c_Relation_Oantisym @ SY1151 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(1940,plain,
! [SV353: $i] :
( ( ! [SY1154: $i,SY1155: $i] :
( ~ ! [SY1156: $i,SY1157: $i] :
( ~ ( c_member @ ( tc_prod @ SY1155 @ SY1154 ) @ ( c_Product__Type_OPair @ SY1155 @ SY1154 @ SY1156 @ SY1157 ) @ SV353 )
| ! [SY1158: $i] :
( ~ ( c_member @ ( tc_prod @ SY1155 @ SY1154 ) @ ( c_Product__Type_OPair @ SY1155 @ SY1154 @ SY1156 @ SY1158 ) @ SV353 )
| ( SY1157 = SY1158 ) ) )
| ( c_Relation_Osingle__valued @ SY1155 @ SY1154 @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1941,plain,
! [SV354: $i] :
( ( ! [SY1159: $i,SY1160: $i,SY1161: $i,SY1162: $i] :
( ~ ( c_Relation_Orefl__on @ SY1162 @ SY1161 @ SY1160 )
| ~ ( c_member @ ( tc_prod @ SY1162 @ SY1162 ) @ ( c_Product__Type_OPair @ SY1162 @ SY1162 @ SY1159 @ SV354 ) @ SY1160 )
| ( c_member @ SY1162 @ SY1159 @ SY1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1942,plain,
! [SV355: $i] :
( ( ! [SY1163: $i,SY1164: $i,SY1165: $i] :
( ( SY1165 != SY1164 )
| ~ ( c_member @ SY1163 @ SY1164 @ SV355 )
| ( c_member @ SY1163 @ SY1165 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1943,plain,
! [SV356: $i] :
( ( ! [SY1166: $i,SY1167: $i,SY1168: $i] :
( ( SY1168 != SY1167 )
| ~ ( ~ ( ~ ( c_member @ SY1166 @ SV356 @ SY1168 )
| ( c_member @ SY1166 @ SV356 @ SY1167 ) )
| ~ ( ~ ( c_member @ SY1166 @ SV356 @ SY1167 )
| ( c_member @ SY1166 @ SV356 @ SY1168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(1944,plain,
! [SV357: $i] :
( ( ! [SY1169: $i,SY1170: $i,SY1171: $i] :
( ~ ( c_member @ ( tc_prod @ SY1171 @ SY1171 ) @ ( c_Product__Type_OPair @ SY1171 @ SY1171 @ SY1170 @ SY1169 ) @ ( c_Transitive__Closure_Ortrancl @ SY1171 @ SV357 ) )
| ~ ( ( SY1170 != SY1169 ) )
| ~ ! [SY1172: $i] :
( ~ ( c_member @ ( tc_prod @ SY1171 @ SY1171 ) @ ( c_Product__Type_OPair @ SY1171 @ SY1171 @ SY1170 @ SY1172 ) @ ( c_Transitive__Closure_Ortrancl @ SY1171 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SY1171 @ SY1171 ) @ ( c_Product__Type_OPair @ SY1171 @ SY1171 @ SY1172 @ SY1169 ) @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(1945,plain,
! [SV358: $i] :
( ( ! [SY1173: $i,SY1174: $i,SY1175: $i,SY1176: $i] :
~ ( ~ ( ~ ( c_member @ SY1176 @ SY1175 @ ( c_Relation_OImage @ SY1174 @ SY1176 @ SY1173 @ SV358 ) )
| ~ ! [SY1177: $i] :
~ ~ ( ~ ( c_member @ SY1174 @ SY1177 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SY1174 @ SY1176 ) @ ( c_Product__Type_OPair @ SY1174 @ SY1176 @ SY1177 @ SY1175 ) @ SY1173 ) ) )
| ~ ( ~ ~ ! [SY1178: $i] :
~ ~ ( ~ ( c_member @ SY1174 @ SY1178 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SY1174 @ SY1176 ) @ ( c_Product__Type_OPair @ SY1174 @ SY1176 @ SY1178 @ SY1175 ) @ SY1173 ) )
| ( c_member @ SY1176 @ SY1175 @ ( c_Relation_OImage @ SY1174 @ SY1176 @ SY1173 @ SV358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(1946,plain,
! [SV359: $i] :
( ( ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ~ ( c_member @ SY1181 @ SY1180 @ ( c_Wellfounded_Oacc @ SY1181 @ SY1179 ) )
| ~ ( c_member @ ( tc_prod @ SY1181 @ SY1181 ) @ ( c_Product__Type_OPair @ SY1181 @ SY1181 @ SV359 @ SY1180 ) @ SY1179 )
| ( c_member @ SY1181 @ SV359 @ ( c_Wellfounded_Oacc @ SY1181 @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(1947,plain,
! [SV360: $i] :
( ( ! [SY1182: $i,SY1183: $i,SY1184: $i,SY1185: $i,SY1186: $i,SY1187: $i,SY1188: $i] :
( ~ ( c_member @ ( tc_prod @ SY1188 @ SY1187 ) @ ( c_Product__Type_OPair @ SY1188 @ SY1187 @ SY1186 @ SY1185 ) @ SY1184 )
| ~ ( c_member @ ( tc_prod @ SY1187 @ SY1183 ) @ ( c_Product__Type_OPair @ SY1187 @ SY1183 @ SY1185 @ SY1182 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1188 @ SY1183 ) @ ( c_Product__Type_OPair @ SY1188 @ SY1183 @ SY1186 @ SY1182 ) @ ( c_Relation_Orel__comp @ SY1188 @ SY1187 @ SY1183 @ SY1184 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(1948,plain,
! [SV361: $i] :
( ( ! [SY1189: $i,SY1190: $i] :
( ~ ( c_Wellfounded_Owf @ SY1190 @ SY1189 )
| ~ ( c_member @ ( tc_prod @ SY1190 @ SY1190 ) @ ( c_Product__Type_OPair @ SY1190 @ SY1190 @ SV361 @ SV361 ) @ SY1189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(1949,plain,
! [SV362: $i] :
( ( ! [SY1191: $i,SY1192: $i,SY1193: $i,SY1194: $i] :
( ~ ( c_member @ ( tc_prod @ SY1194 @ SY1193 ) @ ( c_Product__Type_OPair @ SY1194 @ SY1193 @ SY1192 @ SY1191 ) @ SV362 )
| ( c_member @ SY1194 @ SY1192 @ ( c_Relation_ODomain @ SY1194 @ SY1193 @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(1950,plain,
! [SV363: $i] :
( ( ! [SY1195: $i] :
~ ( ~ ( ~ ( c_Relation_Otrans @ SY1195 @ SV363 )
| ! [SY1196: $i,SY1197: $i] :
( ~ ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1196 @ SY1197 ) @ SV363 )
| ! [SY1198: $i] :
( ~ ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1197 @ SY1198 ) @ SV363 )
| ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1196 @ SY1198 ) @ SV363 ) ) ) )
| ~ ( ~ ! [SY1199: $i,SY1200: $i] :
( ~ ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1199 @ SY1200 ) @ SV363 )
| ! [SY1201: $i] :
( ~ ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1200 @ SY1201 ) @ SV363 )
| ( c_member @ ( tc_prod @ SY1195 @ SY1195 ) @ ( c_Product__Type_OPair @ SY1195 @ SY1195 @ SY1199 @ SY1201 ) @ SV363 ) ) )
| ( c_Relation_Otrans @ SY1195 @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(1951,plain,
! [SV364: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i,SY1205: $i] :
( ~ ( c_Relation_Otrans @ SY1205 @ SY1204 )
| ~ ( c_member @ ( tc_prod @ SY1205 @ SY1205 ) @ ( c_Product__Type_OPair @ SY1205 @ SY1205 @ SY1203 @ SY1202 ) @ SY1204 )
| ~ ( c_member @ ( tc_prod @ SY1205 @ SY1205 ) @ ( c_Product__Type_OPair @ SY1205 @ SY1205 @ SY1202 @ SV364 ) @ SY1204 )
| ( c_member @ ( tc_prod @ SY1205 @ SY1205 ) @ ( c_Product__Type_OPair @ SY1205 @ SY1205 @ SY1203 @ SV364 ) @ SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(1952,plain,
! [SV365: $i] :
( ( ! [SY1206: $i] :
~ ( ~ ( ~ ( c_Nitpick_Orefl_H @ SY1206 @ SV365 )
| ! [SY1207: $i] : ( c_member @ ( tc_prod @ SY1206 @ SY1206 ) @ ( c_Product__Type_OPair @ SY1206 @ SY1206 @ SY1207 @ SY1207 ) @ SV365 ) )
| ~ ( ~ ! [SY1208: $i] : ( c_member @ ( tc_prod @ SY1206 @ SY1206 ) @ ( c_Product__Type_OPair @ SY1206 @ SY1206 @ SY1208 @ SY1208 ) @ SV365 )
| ( c_Nitpick_Orefl_H @ SY1206 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(1953,plain,
! [SV366: $i] :
( ( ! [SY1209: $i,SY1210: $i,SY1211: $i,SY1212: $i] :
( ~ ( c_member @ ( tc_prod @ SY1212 @ SY1212 ) @ ( c_Product__Type_OPair @ SY1212 @ SY1212 @ SY1211 @ SY1210 ) @ ( c_Transitive__Closure_Otrancl @ SY1212 @ SY1209 ) )
| ~ ( c_member @ ( tc_prod @ SY1212 @ SY1212 ) @ ( c_Product__Type_OPair @ SY1212 @ SY1212 @ SY1210 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1212 @ SY1209 ) )
| ( c_member @ ( tc_prod @ SY1212 @ SY1212 ) @ ( c_Product__Type_OPair @ SY1212 @ SY1212 @ SY1211 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1212 @ SY1209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(1954,plain,
! [SV367: $i] :
( ( ! [SY1213: $i,SY1214: $i,SY1215: $i] :
( ~ ( c_member @ ( tc_prod @ SY1215 @ SY1215 ) @ ( c_Product__Type_OPair @ SY1215 @ SY1215 @ SY1214 @ SY1213 ) @ ( c_Transitive__Closure_Ortrancl @ SY1215 @ SV367 ) )
| ~ ( ( SY1214 != SY1213 ) )
| ~ ! [SY1216: $i] :
( ~ ( c_member @ ( tc_prod @ SY1215 @ SY1215 ) @ ( c_Product__Type_OPair @ SY1215 @ SY1215 @ SY1214 @ SY1216 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SY1215 @ SY1215 ) @ ( c_Product__Type_OPair @ SY1215 @ SY1215 @ SY1216 @ SY1213 ) @ ( c_Transitive__Closure_Ortrancl @ SY1215 @ SV367 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(1955,plain,
! [SV368: $i] :
( ( ! [SY1217: $i] :
( ~ ( c_member @ ( tc_prod @ SY1217 @ SY1217 ) @ SV368 @ ( c_Relation_OId @ SY1217 ) )
| ~ ! [SY1218: $i] :
( SV368
!= ( c_Product__Type_OPair @ SY1217 @ SY1217 @ SY1218 @ SY1218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(1956,plain,
! [SV369: $i] :
( ( ! [SY1219: $i,SY1220: $i] :
~ ( ~ ( ~ ( c_Relation_Ototal__on @ SY1220 @ SY1219 @ SV369 )
| ! [SY1221: $i] :
( ~ ( c_member @ SY1220 @ SY1221 @ SY1219 )
| ! [SY1222: $i] :
( ~ ( c_member @ SY1220 @ SY1222 @ SY1219 )
| ~ ( ( SY1221 != SY1222 ) )
| ( c_member @ ( tc_prod @ SY1220 @ SY1220 ) @ ( c_Product__Type_OPair @ SY1220 @ SY1220 @ SY1221 @ SY1222 ) @ SV369 )
| ( c_member @ ( tc_prod @ SY1220 @ SY1220 ) @ ( c_Product__Type_OPair @ SY1220 @ SY1220 @ SY1222 @ SY1221 ) @ SV369 ) ) ) )
| ~ ( ~ ! [SY1223: $i] :
( ~ ( c_member @ SY1220 @ SY1223 @ SY1219 )
| ! [SY1224: $i] :
( ~ ( c_member @ SY1220 @ SY1224 @ SY1219 )
| ~ ( ( SY1223 != SY1224 ) )
| ( c_member @ ( tc_prod @ SY1220 @ SY1220 ) @ ( c_Product__Type_OPair @ SY1220 @ SY1220 @ SY1223 @ SY1224 ) @ SV369 )
| ( c_member @ ( tc_prod @ SY1220 @ SY1220 ) @ ( c_Product__Type_OPair @ SY1220 @ SY1220 @ SY1224 @ SY1223 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SY1220 @ SY1219 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(1957,plain,
! [SV370: $i] :
( ( ! [SY1225: $i,SY1226: $i,SY1227: $i] :
( ( SY1227 != SY1226 )
| ~ ( c_member @ SY1225 @ SY1227 @ SV370 )
| ( c_member @ ( tc_prod @ SY1225 @ SY1225 ) @ ( c_Product__Type_OPair @ SY1225 @ SY1225 @ SY1227 @ SY1226 ) @ ( c_Relation_OId__on @ SY1225 @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(1958,plain,
! [SV371: $i] :
( ( ! [SY1228: $i] :
~ ( ~ ( ~ ( c_Relation_Oantisym @ SY1228 @ SV371 )
| ! [SY1229: $i,SY1230: $i] :
( ~ ( c_member @ ( tc_prod @ SY1228 @ SY1228 ) @ ( c_Product__Type_OPair @ SY1228 @ SY1228 @ SY1229 @ SY1230 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SY1228 @ SY1228 ) @ ( c_Product__Type_OPair @ SY1228 @ SY1228 @ SY1230 @ SY1229 ) @ SV371 )
| ( SY1229 = SY1230 ) ) )
| ~ ( ~ ! [SY1231: $i,SY1232: $i] :
( ~ ( c_member @ ( tc_prod @ SY1228 @ SY1228 ) @ ( c_Product__Type_OPair @ SY1228 @ SY1228 @ SY1231 @ SY1232 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SY1228 @ SY1228 ) @ ( c_Product__Type_OPair @ SY1228 @ SY1228 @ SY1232 @ SY1231 ) @ SV371 )
| ( SY1231 = SY1232 ) )
| ( c_Relation_Oantisym @ SY1228 @ SV371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(1959,plain,
! [SV372: $i] :
( ( ! [SY1233: $i,SY1234: $i,SY1235: $i] :
( ~ ( c_Relation_Orefl__on @ SY1235 @ SY1234 @ SY1233 )
| ~ ( c_member @ SY1235 @ SV372 @ SY1234 )
| ( c_member @ ( tc_prod @ SY1235 @ SY1235 ) @ ( c_Product__Type_OPair @ SY1235 @ SY1235 @ SV372 @ SV372 ) @ SY1233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1960,plain,
! [SV373: $i] :
( ( ! [SY1236: $i,SY1237: $i,SY1238: $i,SY1239: $i,SY1240: $i] :
( ( ( c_Product__Type_OPair @ SY1240 @ SY1239 @ SY1238 @ SY1237 )
!= ( c_Product__Type_OPair @ SY1240 @ SY1239 @ SY1236 @ SV373 ) )
| ~ ( ( SY1238 != SY1236 )
| ( SY1237 != SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(1961,plain,
! [SV374: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
~ ( ~ ( ~ ( c_member @ SY1243 @ SY1242 @ ( c_Relation_ORange @ SY1241 @ SY1243 @ SV374 ) )
| ~ ! [SY1244: $i] :
~ ( c_member @ ( tc_prod @ SY1241 @ SY1243 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1243 @ SY1244 @ SY1242 ) @ SV374 ) )
| ~ ( ~ ~ ! [SY1245: $i] :
~ ( c_member @ ( tc_prod @ SY1241 @ SY1243 ) @ ( c_Product__Type_OPair @ SY1241 @ SY1243 @ SY1245 @ SY1242 ) @ SV374 )
| ( c_member @ SY1243 @ SY1242 @ ( c_Relation_ORange @ SY1241 @ SY1243 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1962,plain,
! [SV375: $i] :
( ( ! [SY1246: $i,SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i] :
( ~ ( c_member @ SY1250 @ SY1249 @ SY1248 )
| ~ ( c_member @ ( tc_prod @ SY1250 @ SY1247 ) @ ( c_Product__Type_OPair @ SY1250 @ SY1247 @ SY1249 @ SY1246 ) @ SV375 )
| ( c_member @ SY1247 @ SY1246 @ ( c_Relation_OImage @ SY1250 @ SY1247 @ SV375 @ SY1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(1963,plain,
! [SV376: $i] :
( ( ! [SY1251: $i,SY1252: $i,SY1253: $i,SY1254: $i] :
( ~ ( c_member @ ( tc_prod @ SY1254 @ SY1253 ) @ ( c_Product__Type_OPair @ SY1254 @ SY1253 @ SY1252 @ SY1251 ) @ SV376 )
| ( c_member @ SY1253 @ SY1251 @ ( c_Relation_ORange @ SY1254 @ SY1253 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(1964,plain,
! [SV377: $i] :
( ( ! [SY1255: $i,SY1256: $i,SY1257: $i] :
( ~ ( ~ ~ ( c_member @ SY1257 @ SY1256 @ SY1255 )
| ( SY1256 = SV377 ) )
| ( c_member @ SY1257 @ SY1256 @ ( c_Set_Oinsert @ SY1257 @ SV377 @ SY1255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(1965,plain,
! [SV378: $i] :
( ( ! [SY1258: $i,SY1259: $i,SY1260: $i,SY1261: $i] :
( ~ ( c_member @ ( tc_prod @ SY1261 @ SY1261 ) @ ( c_Product__Type_OPair @ SY1261 @ SY1261 @ SY1260 @ SY1259 ) @ ( c_Transitive__Closure_Ortrancl @ SY1261 @ SY1258 ) )
| ~ ( c_member @ ( tc_prod @ SY1261 @ SY1261 ) @ ( c_Product__Type_OPair @ SY1261 @ SY1261 @ SY1259 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1261 @ SY1258 ) )
| ( c_member @ ( tc_prod @ SY1261 @ SY1261 ) @ ( c_Product__Type_OPair @ SY1261 @ SY1261 @ SY1260 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1261 @ SY1258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(1966,plain,
! [SV379: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY1263 @ SY1263 ) @ ( c_Product__Type_OPair @ SY1263 @ SY1263 @ SY1262 @ SV379 ) @ ( c_Relation_OId @ SY1263 ) )
| ( SY1262 = SV379 ) )
| ~ ( ( SY1262 != SV379 )
| ( c_member @ ( tc_prod @ SY1263 @ SY1263 ) @ ( c_Product__Type_OPair @ SY1263 @ SY1263 @ SY1262 @ SV379 ) @ ( c_Relation_OId @ SY1263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1967,plain,
! [SV380: $i] :
( ( ! [SY1264: $i,SY1265: $i] :
~ ( ~ ( ~ ( c_member @ SY1265 @ SY1264 @ ( c_Wellfounded_Oacc @ SY1265 @ SV380 ) )
| ! [SY1266: $i] :
( ~ ( c_member @ ( tc_prod @ SY1265 @ SY1265 ) @ ( c_Product__Type_OPair @ SY1265 @ SY1265 @ SY1266 @ SY1264 ) @ SV380 )
| ( c_member @ SY1265 @ SY1266 @ ( c_Wellfounded_Oacc @ SY1265 @ SV380 ) ) ) )
| ~ ( ~ ! [SY1267: $i] :
( ~ ( c_member @ ( tc_prod @ SY1265 @ SY1265 ) @ ( c_Product__Type_OPair @ SY1265 @ SY1265 @ SY1267 @ SY1264 ) @ SV380 )
| ( c_member @ SY1265 @ SY1267 @ ( c_Wellfounded_Oacc @ SY1265 @ SV380 ) ) )
| ( c_member @ SY1265 @ SY1264 @ ( c_Wellfounded_Oacc @ SY1265 @ SV380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1968,plain,
! [SV381: $i] :
( ( ! [SY1268: $i,SY1269: $i,SY1270: $i,SY1271: $i] :
( ~ ( c_member @ ( tc_prod @ SY1271 @ SY1271 ) @ ( c_Product__Type_OPair @ SY1271 @ SY1271 @ SY1270 @ SY1269 ) @ SY1268 )
| ~ ( c_member @ ( tc_prod @ SY1271 @ SY1271 ) @ ( c_Product__Type_OPair @ SY1271 @ SY1271 @ SY1269 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1271 @ SY1268 ) )
| ( c_member @ ( tc_prod @ SY1271 @ SY1271 ) @ ( c_Product__Type_OPair @ SY1271 @ SY1271 @ SY1270 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1271 @ SY1268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(1969,plain,
! [SV382: $i] :
( ( ! [SY1272: $i,SY1273: $i,SY1274: $i] :
( ~ ( c_member @ ( tc_prod @ SY1274 @ SY1274 ) @ ( c_Product__Type_OPair @ SY1274 @ SY1274 @ SY1273 @ SY1272 ) @ SV382 )
| ( c_member @ ( tc_prod @ SY1274 @ SY1274 ) @ ( c_Product__Type_OPair @ SY1274 @ SY1274 @ SY1273 @ SY1272 ) @ ( c_Transitive__Closure_Otrancl @ SY1274 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(1970,plain,
! [SV383: $i] :
( ( ! [SY1275: $i,SY1276: $i,SY1277: $i,SY1278: $i,SY1279: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1279 @ SY1278 @ SY1277 )
| ~ ( c_member @ ( tc_prod @ SY1279 @ SY1278 ) @ ( c_Product__Type_OPair @ SY1279 @ SY1278 @ SY1276 @ SY1275 ) @ SY1277 )
| ~ ( c_member @ ( tc_prod @ SY1279 @ SY1278 ) @ ( c_Product__Type_OPair @ SY1279 @ SY1278 @ SY1276 @ SV383 ) @ SY1277 )
| ( SY1275 = SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(1971,plain,
( ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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 ) ) )
| ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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_not_pos,[status(thm)],[1892]) ).
thf(1972,plain,
! [SV384: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i] :
( ~ ( c_member @ SY1282 @ SY1281 @ SY1280 )
| ( c_member @ SY1282 @ SY1281 @ ( c_Set_Oinsert @ SY1282 @ SV384 @ SY1280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(1973,plain,
! [SV385: $i] :
( ( ! [SY1283: $i,SY1284: $i,SY1285: $i] :
( ~ ~ ( c_member @ SY1285 @ SY1284 @ SY1283 )
| ~ ~ ( c_member @ SY1285 @ SY1284 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY1285 @ SY1284 @ SY1283 )
!= ( c_Set_Oinsert @ SY1285 @ SY1284 @ SV385 ) )
| ( SY1283 = SV385 ) )
| ~ ( ( SY1283 != SV385 )
| ( ( c_Set_Oinsert @ SY1285 @ SY1284 @ SY1283 )
= ( c_Set_Oinsert @ SY1285 @ SY1284 @ SV385 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(1974,plain,
! [SV386: $i] :
( ( ! [SY1286: $i,SY1287: $i,SY1288: $i,SY1289: $i] :
( ~ ( c_member @ ( tc_prod @ SY1289 @ SY1289 ) @ ( c_Product__Type_OPair @ SY1289 @ SY1289 @ SY1288 @ SY1287 ) @ ( c_Transitive__Closure_Otrancl @ SY1289 @ SY1286 ) )
| ~ ( c_member @ ( tc_prod @ SY1289 @ SY1289 ) @ ( c_Product__Type_OPair @ SY1289 @ SY1289 @ SY1287 @ SV386 ) @ SY1286 )
| ( c_member @ ( tc_prod @ SY1289 @ SY1289 ) @ ( c_Product__Type_OPair @ SY1289 @ SY1289 @ SY1288 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SY1289 @ SY1286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(1975,plain,
! [SV387: $i] :
( ( ! [SY1290: $i,SY1291: $i,SY1292: $i,SY1293: $i] :
( ~ ( c_member @ ( tc_prod @ SY1293 @ SY1293 ) @ ( c_Product__Type_OPair @ SY1293 @ SY1293 @ SY1292 @ SY1291 ) @ SY1290 )
| ~ ( c_member @ ( tc_prod @ SY1293 @ SY1293 ) @ ( c_Product__Type_OPair @ SY1293 @ SY1293 @ SY1291 @ SV387 ) @ SY1290 )
| ( c_member @ ( tc_prod @ SY1293 @ SY1293 ) @ ( c_Product__Type_OPair @ SY1293 @ SY1293 @ SY1292 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SY1293 @ SY1290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(1976,plain,
! [SV388: $i] :
( ( ! [SY1294: $i,SY1295: $i,SY1296: $i] :
( ( SY1296 != SY1295 )
| ~ ( ~ ( c_member @ SY1294 @ SV388 @ SY1296 )
| ~ ( c_member @ SY1294 @ SV388 @ SY1295 ) )
| ~ ( ~ ~ ( c_member @ SY1294 @ SV388 @ SY1296 )
| ( c_member @ SY1294 @ SV388 @ SY1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(1977,plain,
! [SV389: $i] :
( ( ! [SY1297: $i,SY1298: $i] :
( ~ ( c_Wellfounded_Owf @ SY1298 @ SY1297 )
| ~ ( c_member @ ( tc_prod @ SY1298 @ SY1298 ) @ ( c_Product__Type_OPair @ SY1298 @ SY1298 @ SV389 @ SV389 ) @ SY1297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(1978,plain,
! [SV390: $i] :
( ( ! [SY1299: $i,SY1300: $i,SY1301: $i,SY1302: $i,SY1303: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1303 @ SY1302 @ SY1301 @ SY1300 )
!= ( c_Product__Type_OPair @ SY1303 @ SY1302 @ SY1299 @ SV390 ) )
| ~ ( ( SY1301 != SY1299 )
| ( SY1300 != SV390 ) ) )
| ~ ( ~ ~ ( ( SY1301 != SY1299 )
| ( SY1300 != SV390 ) )
| ( ( c_Product__Type_OPair @ SY1303 @ SY1302 @ SY1301 @ SY1300 )
= ( c_Product__Type_OPair @ SY1303 @ SY1302 @ SY1299 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(1979,plain,
! [SV391: $i] :
( ( ! [SY1304: $i,SY1305: $i,SY1306: $i] :
( ( SY1306 != SY1305 )
| ~ ( ~ ( ~ ( c_member @ SY1304 @ SY1306 @ SV391 )
| ( c_member @ SY1304 @ SY1305 @ SV391 ) )
| ~ ( ~ ( c_member @ SY1304 @ SY1305 @ SV391 )
| ( c_member @ SY1304 @ SY1306 @ SV391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(1980,plain,
! [SV392: $i] :
( ( ! [SY1307: $i,SY1308: $i,SY1309: $i] :
( ~ ( c_member @ ( tc_prod @ SY1309 @ SY1309 ) @ ( c_Product__Type_OPair @ SY1309 @ SY1309 @ SY1308 @ SY1307 ) @ ( c_Transitive__Closure_Otrancl @ SY1309 @ SV392 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1309 @ SY1309 ) @ ( c_Product__Type_OPair @ SY1309 @ SY1309 @ SY1308 @ SY1307 ) @ SV392 )
| ~ ! [SY1310: $i] :
( ~ ( c_member @ ( tc_prod @ SY1309 @ SY1309 ) @ ( c_Product__Type_OPair @ SY1309 @ SY1309 @ SY1308 @ SY1310 ) @ ( c_Transitive__Closure_Otrancl @ SY1309 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SY1309 @ SY1309 ) @ ( c_Product__Type_OPair @ SY1309 @ SY1309 @ SY1310 @ SY1307 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(1981,plain,
! [SV393: $i] :
( ( ! [SY1311: $i,SY1312: $i,SY1313: $i] :
( ~ ( c_member @ ( tc_prod @ SY1313 @ SY1313 ) @ ( c_Product__Type_OPair @ SY1313 @ SY1313 @ SY1312 @ SY1311 ) @ ( c_Transitive__Closure_Otrancl @ SY1313 @ SV393 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1313 @ SY1313 ) @ ( c_Product__Type_OPair @ SY1313 @ SY1313 @ SY1312 @ SY1311 ) @ SV393 )
| ~ ! [SY1314: $i] :
( ~ ( c_member @ ( tc_prod @ SY1313 @ SY1313 ) @ ( c_Product__Type_OPair @ SY1313 @ SY1313 @ SY1312 @ SY1314 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SY1313 @ SY1313 ) @ ( c_Product__Type_OPair @ SY1313 @ SY1313 @ SY1314 @ SY1311 ) @ ( c_Transitive__Closure_Otrancl @ SY1313 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(1982,plain,
! [SV394: $i] :
( ( ! [SY1315: $i,SY1316: $i] :
( ~ ( c_member @ ( tc_prod @ SY1316 @ SY1316 ) @ SY1315 @ ( c_Relation_OId__on @ SY1316 @ SV394 ) )
| ~ ! [SY1317: $i] :
( ~ ( c_member @ SY1316 @ SY1317 @ SV394 )
| ( SY1315
!= ( c_Product__Type_OPair @ SY1316 @ SY1316 @ SY1317 @ SY1317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(1983,plain,
! [SV395: $i] :
( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ~ ( c_Relation_Otrans @ SY1320 @ SY1319 )
| ~ ( c_Relation_Otrans @ SY1318 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SY1320 @ SY1318 ) @ ( c_Wellfounded_Olex__prod @ SY1320 @ SY1318 @ SY1319 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(1984,plain,
! [SV396: $i] :
( ( ! [SY1321: $i,SY1322: $i,SY1323: $i,SY1324: $i] :
( ~ ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SY1323 @ SY1322 ) @ SY1321 )
| ~ ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SY1322 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1324 @ SY1321 ) )
| ( c_member @ ( tc_prod @ SY1324 @ SY1324 ) @ ( c_Product__Type_OPair @ SY1324 @ SY1324 @ SY1323 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1324 @ SY1321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(1985,plain,
! [SV397: $i] :
( ( ! [SY1325: $i,SY1326: $i,SY1327: $i,SY1328: $i] :
( ~ ( c_member @ SY1328 @ SY1327 @ ( c_Relation_OImage @ SY1326 @ SY1328 @ SY1325 @ SV397 ) )
| ~ ! [SY1329: $i] :
( ~ ( c_member @ ( tc_prod @ SY1326 @ SY1328 ) @ ( c_Product__Type_OPair @ SY1326 @ SY1328 @ SY1329 @ SY1327 ) @ SY1325 )
| ~ ( c_member @ SY1326 @ SY1329 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(1986,plain,
! [SV398: $i] :
( ( ! [SY1330: $i] :
~ ( ~ ( ~ ( c_Relation_Oirrefl @ SY1330 @ SV398 )
| ! [SY1331: $i] :
~ ( c_member @ ( tc_prod @ SY1330 @ SY1330 ) @ ( c_Product__Type_OPair @ SY1330 @ SY1330 @ SY1331 @ SY1331 ) @ SV398 ) )
| ~ ( ~ ! [SY1332: $i] :
~ ( c_member @ ( tc_prod @ SY1330 @ SY1330 ) @ ( c_Product__Type_OPair @ SY1330 @ SY1330 @ SY1332 @ SY1332 ) @ SV398 )
| ( c_Relation_Oirrefl @ SY1330 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(1987,plain,
! [SV399: $i] :
( ( ! [SY1333: $i,SY1334: $i,SY1335: $i] :
( ~ ( c_member @ SY1335 @ SY1334 @ ( c_Relation_ORange @ SY1333 @ SY1335 @ SV399 ) )
| ~ ! [SY1336: $i] :
~ ( c_member @ ( tc_prod @ SY1333 @ SY1335 ) @ ( c_Product__Type_OPair @ SY1333 @ SY1335 @ SY1336 @ SY1334 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(1988,plain,
! [SV400: $i] :
( ( ! [SY1337: $i,SY1338: $i,SY1339: $i,SY1340: $i,SY1341: $i,SY1342: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1340 @ SY1339 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1338 @ SY1337 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1342 @ SY1341 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1340 @ SY1339 )
!= ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1338 @ SY1337 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1340 @ SY1339 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1343 @ SY1344 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1342 @ SY1341 ) @ ( tc_prod @ SY1342 @ SY1341 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1343 @ SY1344 ) @ ( c_Product__Type_OPair @ SY1342 @ SY1341 @ SY1338 @ SY1337 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1342 @ SY1341 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(1989,plain,
! [SV401: $i] :
( ( ! [SY1345: $i,SY1346: $i,SY1347: $i,SY1348: $i] :
( ~ ( c_Relation_Orefl__on @ SY1348 @ SY1347 @ SY1346 )
| ~ ( c_member @ ( tc_prod @ SY1348 @ SY1348 ) @ ( c_Product__Type_OPair @ SY1348 @ SY1348 @ SY1345 @ SV401 ) @ SY1346 )
| ( c_member @ SY1348 @ SV401 @ SY1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(1990,plain,
! [SV324: $i,SV402: $i] :
( ( c_Relation_Otrans @ SV402 @ ( c_Relation_OId__on @ SV402 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(1991,plain,
! [SV325: $i,SV403: $i] :
( ( ! [SY1349: $i] : ( c_member @ ( tc_prod @ SY1349 @ SY1349 ) @ ( c_Product__Type_OPair @ SY1349 @ SY1349 @ SV403 @ SV403 ) @ ( c_Transitive__Closure_Ortrancl @ SY1349 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(1992,plain,
! [SV326: $i,SV404: $i] :
( ( c_Relation_Otrans @ SV404 @ ( c_Transitive__Closure_Ortrancl @ SV404 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(1993,plain,
! [SV327: $i,SV405: $i] :
( ( c_Relation_Otrans @ SV405 @ ( c_Transitive__Closure_Otrancl @ SV405 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(1994,plain,
! [SV328: $i,SV406: $i] :
( ( c_member @ ( tc_prod @ SV406 @ SV406 ) @ ( c_Product__Type_OPair @ SV406 @ SV406 @ SV328 @ SV328 ) @ ( c_Relation_OId @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(1995,plain,
! [SV330: $i,SV407: $i] :
( ( ! [SY1350: $i] : ( c_member @ SY1350 @ SV407 @ ( c_Set_Oinsert @ SY1350 @ SV407 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1996,plain,
! [SV331: $i,SV408: $i] :
( ( ! [SY1351: $i] :
( ~ ( c_member @ SY1351 @ SV408 @ SV331 )
| ( ( c_Set_Oinsert @ SY1351 @ SV408 @ SV331 )
= SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(1997,plain,
! [SV332: $i,SV409: $i] :
( ( ~ ! [SY1352: $i,SY1353: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1353 ) @ SV332 )
| ! [SY1354: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1353 @ SY1354 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1354 ) @ SV332 ) ) )
| ( c_Relation_Otrans @ SV409 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(1998,plain,
! [SV333: $i,SV410: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ~ ( c_member @ SY1356 @ SY1355 @ ( c_Set_Oinsert @ SY1356 @ SV410 @ SV333 ) )
| ~ ( ( SY1355 != SV410 ) )
| ( c_member @ SY1356 @ SY1355 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(1999,plain,
! [SV334: $i,SV411: $i] :
( ( ! [SY1357: $i,SY1358: $i,SY1359: $i] :
( ~ ( c_member @ ( tc_prod @ SY1359 @ SY1359 ) @ ( c_Product__Type_OPair @ SY1359 @ SY1359 @ SY1358 @ SY1357 ) @ ( c_Transitive__Closure_Ortrancl @ SY1359 @ SV411 ) )
| ~ ( c_member @ ( tc_prod @ SY1359 @ SY1359 ) @ ( c_Product__Type_OPair @ SY1359 @ SY1359 @ SY1357 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SY1359 @ SY1359 ) @ ( c_Product__Type_OPair @ SY1359 @ SY1359 @ SY1358 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SY1359 @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2000,plain,
! [SV335: $i,SV412: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
~ ( ~ ( ~ ( c_member @ SY1361 @ SY1360 @ ( c_Relation_ODomain @ SY1361 @ SV412 @ SV335 ) )
| ~ ! [SY1362: $i] :
~ ( c_member @ ( tc_prod @ SY1361 @ SV412 ) @ ( c_Product__Type_OPair @ SY1361 @ SV412 @ SY1360 @ SY1362 ) @ SV335 ) )
| ~ ( ~ ~ ! [SY1363: $i] :
~ ( c_member @ ( tc_prod @ SY1361 @ SV412 ) @ ( c_Product__Type_OPair @ SY1361 @ SV412 @ SY1360 @ SY1363 ) @ SV335 )
| ( c_member @ SY1361 @ SY1360 @ ( c_Relation_ODomain @ SY1361 @ SV412 @ SV335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2001,plain,
! [SV336: $i,SV413: $i] :
( ( ! [SY1364: $i,SY1365: $i,SY1366: $i,SY1367: $i,SY1368: $i,SY1369: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1369 @ SY1368 ) @ ( tc_prod @ SY1369 @ SY1368 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1369 @ SY1368 ) @ ( tc_prod @ SY1369 @ SY1368 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1368 @ SY1367 @ SY1366 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1368 @ SY1365 @ SY1364 ) ) @ ( c_Wellfounded_Olex__prod @ SY1369 @ SY1368 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1369 @ SY1369 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1369 @ SY1367 @ SY1365 ) @ SV413 )
| ~ ( ( SY1367 != SY1365 )
| ~ ( c_member @ ( tc_prod @ SY1368 @ SY1368 ) @ ( c_Product__Type_OPair @ SY1368 @ SY1368 @ SY1366 @ SY1364 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1369 @ SY1369 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1369 @ SY1367 @ SY1365 ) @ SV413 )
| ~ ( ( SY1367 != SY1365 )
| ~ ( c_member @ ( tc_prod @ SY1368 @ SY1368 ) @ ( c_Product__Type_OPair @ SY1368 @ SY1368 @ SY1366 @ SY1364 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1369 @ SY1368 ) @ ( tc_prod @ SY1369 @ SY1368 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1369 @ SY1368 ) @ ( tc_prod @ SY1369 @ SY1368 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1368 @ SY1367 @ SY1366 ) @ ( c_Product__Type_OPair @ SY1369 @ SY1368 @ SY1365 @ SY1364 ) ) @ ( c_Wellfounded_Olex__prod @ SY1369 @ SY1368 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2002,plain,
! [SV337: $i,SV414: $i] :
( ( ! [SY1370: $i] :
( ~ ~ ( c_member @ SY1370 @ SV414 @ ( c_Wellfounded_Oacc @ SY1370 @ SV337 ) )
| ~ ! [SY1371: $i] :
( ~ ( c_member @ ( tc_prod @ SY1370 @ SY1370 ) @ ( c_Product__Type_OPair @ SY1370 @ SY1370 @ SY1371 @ SV414 ) @ SV337 )
| ( c_member @ SY1370 @ SY1371 @ ( c_Wellfounded_Oacc @ SY1370 @ SV337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2003,plain,
! [SV338: $i,SV415: $i] :
( ( ! [SY1372: $i,SY1373: $i] :
( ~ ( c_member @ SY1373 @ SY1372 @ ( c_Relation_ODomain @ SY1373 @ SV415 @ SV338 ) )
| ~ ! [SY1374: $i] :
~ ( c_member @ ( tc_prod @ SY1373 @ SV415 ) @ ( c_Product__Type_OPair @ SY1373 @ SV415 @ SY1372 @ SY1374 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2004,plain,
! [SV339: $i,SV416: $i] :
( ( ! [SY1375: $i] :
( ~ ( c_member @ ( tc_prod @ SY1375 @ SY1375 ) @ SV416 @ SV339 )
| ( c_member @ ( tc_prod @ SY1375 @ SY1375 ) @ SV416 @ ( c_Transitive__Closure_Ortrancl @ SY1375 @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2005,plain,
! [SV340: $i,SV417: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ~ ! [SX4: $i] :
~ ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SX4 @ SX4 ) @ ( c_Transitive__Closure_Otrancl @ SY1377 @ SY1376 ) )
| ~ ( c_member @ ( tc_prod @ SY1377 @ SY1377 ) @ ( c_Product__Type_OPair @ SY1377 @ SY1377 @ SV417 @ SV340 ) @ SY1376 )
| ( SV417 != SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2006,plain,
! [SV341: $i,SV418: $i] :
( ( ! [SY1379: $i,SY1380: $i] :
( ~ ( c_Relation_Oantisym @ SY1380 @ SY1379 )
| ~ ( c_member @ ( tc_prod @ SY1380 @ SY1380 ) @ ( c_Product__Type_OPair @ SY1380 @ SY1380 @ SV418 @ SV341 ) @ SY1379 )
| ~ ( c_member @ ( tc_prod @ SY1380 @ SY1380 ) @ ( c_Product__Type_OPair @ SY1380 @ SY1380 @ SV341 @ SV418 ) @ SY1379 )
| ( SV418 = SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2007,plain,
! [SV342: $i,SV419: $i] :
( ( ! [SY1381: $i] :
~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SY1381 @ SV419 @ SV342 )
| ! [SY1382: $i,SY1383: $i] :
( ~ ( c_member @ ( tc_prod @ SY1381 @ SV419 ) @ ( c_Product__Type_OPair @ SY1381 @ SV419 @ SY1382 @ SY1383 ) @ SV342 )
| ! [SY1384: $i] :
( ~ ( c_member @ ( tc_prod @ SY1381 @ SV419 ) @ ( c_Product__Type_OPair @ SY1381 @ SV419 @ SY1382 @ SY1384 ) @ SV342 )
| ( SY1383 = SY1384 ) ) ) )
| ~ ( ~ ! [SY1385: $i,SY1386: $i] :
( ~ ( c_member @ ( tc_prod @ SY1381 @ SV419 ) @ ( c_Product__Type_OPair @ SY1381 @ SV419 @ SY1385 @ SY1386 ) @ SV342 )
| ! [SY1387: $i] :
( ~ ( c_member @ ( tc_prod @ SY1381 @ SV419 ) @ ( c_Product__Type_OPair @ SY1381 @ SV419 @ SY1385 @ SY1387 ) @ SV342 )
| ( SY1386 = SY1387 ) ) )
| ( c_Relation_Osingle__valued @ SY1381 @ SV419 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2008,plain,
! [SV343: $i,SV420: $i] :
( ( ! [SY1388: $i] :
~ ( ~ ( ~ ( c_member @ SY1388 @ SV420 @ ( c_fequal @ SV343 ) )
| ( SV420 = SV343 ) )
| ~ ( ( SV420 != SV343 )
| ( c_member @ SY1388 @ SV420 @ ( c_fequal @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2009,plain,
! [SV344: $i,SV421: $i] :
( ( ~ ( c_Relation_Otrans @ SV421 @ SV344 )
| ( ( c_Transitive__Closure_Otrancl @ SV421 @ SV344 )
= SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2010,plain,
! [SV345: $i,SV422: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
( ~ ( c_Wellfounded_Owf @ SY1390 @ SY1389 )
| ~ ( c_member @ ( tc_prod @ SY1390 @ SY1390 ) @ ( c_Product__Type_OPair @ SY1390 @ SY1390 @ SV422 @ SV345 ) @ SY1389 )
| ~ ( c_member @ ( tc_prod @ SY1390 @ SY1390 ) @ ( c_Product__Type_OPair @ SY1390 @ SY1390 @ SV345 @ SV422 ) @ SY1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2011,plain,
! [SV346: $i,SV423: $i] :
( ( ! [SY1391: $i,SY1392: $i] :
( ~ ( c_Wellfounded_Owf @ SY1392 @ SY1391 )
| ~ ( c_member @ ( tc_prod @ SY1392 @ SY1392 ) @ ( c_Product__Type_OPair @ SY1392 @ SY1392 @ SV423 @ SV346 ) @ SY1391 )
| ~ ( c_member @ ( tc_prod @ SY1392 @ SY1392 ) @ ( c_Product__Type_OPair @ SY1392 @ SY1392 @ SV346 @ SV423 ) @ SY1391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2012,plain,
! [SV347: $i,SV424: $i] :
( ( ! [SY1393: $i] :
( ~ ! [SY1394: $i] :
( ~ ( c_member @ ( tc_prod @ SY1393 @ SY1393 ) @ ( c_Product__Type_OPair @ SY1393 @ SY1393 @ SY1394 @ SV424 ) @ SV347 )
| ( c_member @ SY1393 @ SY1394 @ ( c_Wellfounded_Oacc @ SY1393 @ SV347 ) ) )
| ( c_member @ SY1393 @ SV424 @ ( c_Wellfounded_Oacc @ SY1393 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2013,plain,
! [SV348: $i,SV425: $i] :
( ( ! [SY1395: $i] :
( ~ ( c_member @ ( tc_prod @ SY1395 @ SY1395 ) @ SV425 @ SV348 )
| ( c_member @ ( tc_prod @ SY1395 @ SY1395 ) @ SV425 @ ( c_Transitive__Closure_Otrancl @ SY1395 @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2014,plain,
! [SV349: $i,SV426: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
~ ( ~ ( ~ ( c_member @ SY1397 @ SY1396 @ ( c_Set_Oinsert @ SY1397 @ SV426 @ SV349 ) )
| ( SY1396 = SV426 )
| ( c_member @ SY1397 @ SY1396 @ SV349 ) )
| ~ ( ~ ( ( SY1396 = SV426 )
| ( c_member @ SY1397 @ SY1396 @ SV349 ) )
| ( c_member @ SY1397 @ SY1396 @ ( c_Set_Oinsert @ SY1397 @ SV426 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2015,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ( ~ ( ~ ( c_Wellfounded_Owf @ SV427 @ SV350 )
| ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) )
| ~ ( ~ ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) )
| ( c_Wellfounded_Owf @ SV427 @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2016,plain,
! [SV351: $i,SV428: $i] :
( ( ! [SY1406: $i,SY1407: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY1407 @ SY1407 ) @ ( c_Product__Type_OPair @ SY1407 @ SY1407 @ SY1406 @ SV428 ) @ ( c_Relation_OId__on @ SY1407 @ SV351 ) )
| ~ ( ( SY1406 != SV428 )
| ~ ( c_member @ SY1407 @ SY1406 @ SV351 ) ) )
| ~ ( ~ ~ ( ( SY1406 != SV428 )
| ~ ( c_member @ SY1407 @ SY1406 @ SV351 ) )
| ( c_member @ ( tc_prod @ SY1407 @ SY1407 ) @ ( c_Product__Type_OPair @ SY1407 @ SY1407 @ SY1406 @ SV428 ) @ ( c_Relation_OId__on @ SY1407 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2017,plain,
! [SV352: $i,SV429: $i] :
( ( ~ ! [SY1408: $i,SY1409: $i] :
( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1408 @ SY1409 ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1409 @ SY1408 ) @ SV352 )
| ( SY1408 = SY1409 ) )
| ( c_Relation_Oantisym @ SV429 @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2018,plain,
! [SV353: $i,SV430: $i] :
( ( ! [SY1410: $i] :
( ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( c_member @ ( tc_prod @ SY1410 @ SV430 ) @ ( c_Product__Type_OPair @ SY1410 @ SV430 @ SY1411 @ SY1412 ) @ SV353 )
| ! [SY1413: $i] :
( ~ ( c_member @ ( tc_prod @ SY1410 @ SV430 ) @ ( c_Product__Type_OPair @ SY1410 @ SV430 @ SY1411 @ SY1413 ) @ SV353 )
| ( SY1412 = SY1413 ) ) )
| ( c_Relation_Osingle__valued @ SY1410 @ SV430 @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2019,plain,
! [SV354: $i,SV431: $i] :
( ( ! [SY1414: $i,SY1415: $i,SY1416: $i] :
( ~ ( c_Relation_Orefl__on @ SY1416 @ SY1415 @ SY1414 )
| ~ ( c_member @ ( tc_prod @ SY1416 @ SY1416 ) @ ( c_Product__Type_OPair @ SY1416 @ SY1416 @ SV431 @ SV354 ) @ SY1414 )
| ( c_member @ SY1416 @ SV431 @ SY1415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2020,plain,
! [SV355: $i,SV432: $i] :
( ( ! [SY1417: $i,SY1418: $i] :
( ( SY1418 != SY1417 )
| ~ ( c_member @ SV432 @ SY1417 @ SV355 )
| ( c_member @ SV432 @ SY1418 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2021,plain,
! [SV356: $i,SV433: $i] :
( ( ! [SY1419: $i,SY1420: $i] :
( ( SY1420 != SY1419 )
| ~ ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SY1420 )
| ( c_member @ SV433 @ SV356 @ SY1419 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SY1419 )
| ( c_member @ SV433 @ SV356 @ SY1420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2022,plain,
! [SV357: $i,SV434: $i] :
( ( ! [SY1421: $i,SY1422: $i] :
( ~ ( c_member @ ( tc_prod @ SY1422 @ SY1422 ) @ ( c_Product__Type_OPair @ SY1422 @ SY1422 @ SY1421 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SY1422 @ SV357 ) )
| ~ ( ( SY1421 != SV434 ) )
| ~ ! [SY1423: $i] :
( ~ ( c_member @ ( tc_prod @ SY1422 @ SY1422 ) @ ( c_Product__Type_OPair @ SY1422 @ SY1422 @ SY1421 @ SY1423 ) @ ( c_Transitive__Closure_Ortrancl @ SY1422 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SY1422 @ SY1422 ) @ ( c_Product__Type_OPair @ SY1422 @ SY1422 @ SY1423 @ SV434 ) @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2023,plain,
! [SV358: $i,SV435: $i] :
( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( c_member @ SY1426 @ SY1425 @ ( c_Relation_OImage @ SY1424 @ SY1426 @ SV435 @ SV358 ) )
| ~ ! [SY1427: $i] :
~ ~ ( ~ ( c_member @ SY1424 @ SY1427 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SY1424 @ SY1426 ) @ ( c_Product__Type_OPair @ SY1424 @ SY1426 @ SY1427 @ SY1425 ) @ SV435 ) ) )
| ~ ( ~ ~ ! [SY1428: $i] :
~ ~ ( ~ ( c_member @ SY1424 @ SY1428 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SY1424 @ SY1426 ) @ ( c_Product__Type_OPair @ SY1424 @ SY1426 @ SY1428 @ SY1425 ) @ SV435 ) )
| ( c_member @ SY1426 @ SY1425 @ ( c_Relation_OImage @ SY1424 @ SY1426 @ SV435 @ SV358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2024,plain,
! [SV359: $i,SV436: $i] :
( ( ! [SY1429: $i,SY1430: $i] :
( ~ ( c_member @ SY1430 @ SY1429 @ ( c_Wellfounded_Oacc @ SY1430 @ SV436 ) )
| ~ ( c_member @ ( tc_prod @ SY1430 @ SY1430 ) @ ( c_Product__Type_OPair @ SY1430 @ SY1430 @ SV359 @ SY1429 ) @ SV436 )
| ( c_member @ SY1430 @ SV359 @ ( c_Wellfounded_Oacc @ SY1430 @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2025,plain,
! [SV360: $i,SV437: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i,SY1435: $i,SY1436: $i] :
( ~ ( c_member @ ( tc_prod @ SY1436 @ SY1435 ) @ ( c_Product__Type_OPair @ SY1436 @ SY1435 @ SY1434 @ SY1433 ) @ SY1432 )
| ~ ( c_member @ ( tc_prod @ SY1435 @ SY1431 ) @ ( c_Product__Type_OPair @ SY1435 @ SY1431 @ SY1433 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1436 @ SY1431 ) @ ( c_Product__Type_OPair @ SY1436 @ SY1431 @ SY1434 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1436 @ SY1435 @ SY1431 @ SY1432 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2026,plain,
! [SV361: $i,SV438: $i] :
( ( ! [SY1437: $i] :
( ~ ( c_Wellfounded_Owf @ SY1437 @ SV438 )
| ~ ( c_member @ ( tc_prod @ SY1437 @ SY1437 ) @ ( c_Product__Type_OPair @ SY1437 @ SY1437 @ SV361 @ SV361 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2027,plain,
! [SV362: $i,SV439: $i] :
( ( ! [SY1438: $i,SY1439: $i,SY1440: $i] :
( ~ ( c_member @ ( tc_prod @ SY1440 @ SY1439 ) @ ( c_Product__Type_OPair @ SY1440 @ SY1439 @ SY1438 @ SV439 ) @ SV362 )
| ( c_member @ SY1440 @ SY1438 @ ( c_Relation_ODomain @ SY1440 @ SY1439 @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2028,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Otrans @ SV440 @ SV363 )
| ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) )
| ~ ( ~ ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) )
| ( c_Relation_Otrans @ SV440 @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2029,plain,
! [SV364: $i,SV441: $i] :
( ( ! [SY1447: $i,SY1448: $i,SY1449: $i] :
( ~ ( c_Relation_Otrans @ SY1449 @ SY1448 )
| ~ ( c_member @ ( tc_prod @ SY1449 @ SY1449 ) @ ( c_Product__Type_OPair @ SY1449 @ SY1449 @ SY1447 @ SV441 ) @ SY1448 )
| ~ ( c_member @ ( tc_prod @ SY1449 @ SY1449 ) @ ( c_Product__Type_OPair @ SY1449 @ SY1449 @ SV441 @ SV364 ) @ SY1448 )
| ( c_member @ ( tc_prod @ SY1449 @ SY1449 ) @ ( c_Product__Type_OPair @ SY1449 @ SY1449 @ SY1447 @ SV364 ) @ SY1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2030,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
| ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) )
| ~ ( ~ ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 )
| ( c_Nitpick_Orefl_H @ SV442 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2031,plain,
! [SV366: $i,SV443: $i] :
( ( ! [SY1452: $i,SY1453: $i,SY1454: $i] :
( ~ ( c_member @ ( tc_prod @ SY1454 @ SY1454 ) @ ( c_Product__Type_OPair @ SY1454 @ SY1454 @ SY1453 @ SY1452 ) @ ( c_Transitive__Closure_Otrancl @ SY1454 @ SV443 ) )
| ~ ( c_member @ ( tc_prod @ SY1454 @ SY1454 ) @ ( c_Product__Type_OPair @ SY1454 @ SY1454 @ SY1452 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1454 @ SV443 ) )
| ( c_member @ ( tc_prod @ SY1454 @ SY1454 ) @ ( c_Product__Type_OPair @ SY1454 @ SY1454 @ SY1453 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1454 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2032,plain,
! [SV367: $i,SV444: $i] :
( ( ! [SY1455: $i,SY1456: $i] :
( ~ ( c_member @ ( tc_prod @ SY1456 @ SY1456 ) @ ( c_Product__Type_OPair @ SY1456 @ SY1456 @ SY1455 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SY1456 @ SV367 ) )
| ~ ( ( SY1455 != SV444 ) )
| ~ ! [SY1457: $i] :
( ~ ( c_member @ ( tc_prod @ SY1456 @ SY1456 ) @ ( c_Product__Type_OPair @ SY1456 @ SY1456 @ SY1455 @ SY1457 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SY1456 @ SY1456 ) @ ( c_Product__Type_OPair @ SY1456 @ SY1456 @ SY1457 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SY1456 @ SV367 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2033,plain,
! [SV368: $i,SV445: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) )
| ~ ! [SY1458: $i] :
( SV368
!= ( c_Product__Type_OPair @ SV445 @ SV445 @ SY1458 @ SY1458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2034,plain,
! [SV369: $i,SV446: $i] :
( ( ! [SY1459: $i] :
~ ( ~ ( ~ ( c_Relation_Ototal__on @ SY1459 @ SV446 @ SV369 )
| ! [SY1460: $i] :
( ~ ( c_member @ SY1459 @ SY1460 @ SV446 )
| ! [SY1461: $i] :
( ~ ( c_member @ SY1459 @ SY1461 @ SV446 )
| ~ ( ( SY1460 != SY1461 ) )
| ( c_member @ ( tc_prod @ SY1459 @ SY1459 ) @ ( c_Product__Type_OPair @ SY1459 @ SY1459 @ SY1460 @ SY1461 ) @ SV369 )
| ( c_member @ ( tc_prod @ SY1459 @ SY1459 ) @ ( c_Product__Type_OPair @ SY1459 @ SY1459 @ SY1461 @ SY1460 ) @ SV369 ) ) ) )
| ~ ( ~ ! [SY1462: $i] :
( ~ ( c_member @ SY1459 @ SY1462 @ SV446 )
| ! [SY1463: $i] :
( ~ ( c_member @ SY1459 @ SY1463 @ SV446 )
| ~ ( ( SY1462 != SY1463 ) )
| ( c_member @ ( tc_prod @ SY1459 @ SY1459 ) @ ( c_Product__Type_OPair @ SY1459 @ SY1459 @ SY1462 @ SY1463 ) @ SV369 )
| ( c_member @ ( tc_prod @ SY1459 @ SY1459 ) @ ( c_Product__Type_OPair @ SY1459 @ SY1459 @ SY1463 @ SY1462 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SY1459 @ SV446 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2035,plain,
! [SV370: $i,SV447: $i] :
( ( ! [SY1464: $i,SY1465: $i] :
( ( SY1465 != SY1464 )
| ~ ( c_member @ SV447 @ SY1465 @ SV370 )
| ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SY1465 @ SY1464 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2036,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Oantisym @ SV448 @ SV371 )
| ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) )
| ~ ( ~ ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) )
| ( c_Relation_Oantisym @ SV448 @ SV371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2037,plain,
! [SV372: $i,SV449: $i] :
( ( ! [SY1470: $i,SY1471: $i] :
( ~ ( c_Relation_Orefl__on @ SY1471 @ SY1470 @ SV449 )
| ~ ( c_member @ SY1471 @ SV372 @ SY1470 )
| ( c_member @ ( tc_prod @ SY1471 @ SY1471 ) @ ( c_Product__Type_OPair @ SY1471 @ SY1471 @ SV372 @ SV372 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2038,plain,
! [SV373: $i,SV450: $i] :
( ( ! [SY1472: $i,SY1473: $i,SY1474: $i,SY1475: $i] :
( ( ( c_Product__Type_OPair @ SY1475 @ SY1474 @ SY1473 @ SY1472 )
!= ( c_Product__Type_OPair @ SY1475 @ SY1474 @ SV450 @ SV373 ) )
| ~ ( ( SY1473 != SV450 )
| ( SY1472 != SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2039,plain,
! [SV374: $i,SV451: $i] :
( ( ! [SY1476: $i,SY1477: $i] :
~ ( ~ ( ~ ( c_member @ SY1477 @ SY1476 @ ( c_Relation_ORange @ SV451 @ SY1477 @ SV374 ) )
| ~ ! [SY1478: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SY1477 ) @ ( c_Product__Type_OPair @ SV451 @ SY1477 @ SY1478 @ SY1476 ) @ SV374 ) )
| ~ ( ~ ~ ! [SY1479: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SY1477 ) @ ( c_Product__Type_OPair @ SV451 @ SY1477 @ SY1479 @ SY1476 ) @ SV374 )
| ( c_member @ SY1477 @ SY1476 @ ( c_Relation_ORange @ SV451 @ SY1477 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2040,plain,
! [SV375: $i,SV452: $i] :
( ( ! [SY1480: $i,SY1481: $i,SY1482: $i,SY1483: $i] :
( ~ ( c_member @ SY1483 @ SY1482 @ SY1481 )
| ~ ( c_member @ ( tc_prod @ SY1483 @ SY1480 ) @ ( c_Product__Type_OPair @ SY1483 @ SY1480 @ SY1482 @ SV452 ) @ SV375 )
| ( c_member @ SY1480 @ SV452 @ ( c_Relation_OImage @ SY1483 @ SY1480 @ SV375 @ SY1481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2041,plain,
! [SV376: $i,SV453: $i] :
( ( ! [SY1484: $i,SY1485: $i,SY1486: $i] :
( ~ ( c_member @ ( tc_prod @ SY1486 @ SY1485 ) @ ( c_Product__Type_OPair @ SY1486 @ SY1485 @ SY1484 @ SV453 ) @ SV376 )
| ( c_member @ SY1485 @ SV453 @ ( c_Relation_ORange @ SY1486 @ SY1485 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2042,plain,
! [SV377: $i,SV454: $i] :
( ( ! [SY1487: $i,SY1488: $i] :
( ~ ( ~ ~ ( c_member @ SY1488 @ SY1487 @ SV454 )
| ( SY1487 = SV377 ) )
| ( c_member @ SY1488 @ SY1487 @ ( c_Set_Oinsert @ SY1488 @ SV377 @ SV454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2043,plain,
! [SV378: $i,SV455: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i] :
( ~ ( c_member @ ( tc_prod @ SY1491 @ SY1491 ) @ ( c_Product__Type_OPair @ SY1491 @ SY1491 @ SY1490 @ SY1489 ) @ ( c_Transitive__Closure_Ortrancl @ SY1491 @ SV455 ) )
| ~ ( c_member @ ( tc_prod @ SY1491 @ SY1491 ) @ ( c_Product__Type_OPair @ SY1491 @ SY1491 @ SY1489 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1491 @ SV455 ) )
| ( c_member @ ( tc_prod @ SY1491 @ SY1491 ) @ ( c_Product__Type_OPair @ SY1491 @ SY1491 @ SY1490 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1491 @ SV455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2044,plain,
! [SV379: $i,SV456: $i] :
( ( ! [SY1492: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY1492 @ SY1492 ) @ ( c_Product__Type_OPair @ SY1492 @ SY1492 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SY1492 ) )
| ( SV456 = SV379 ) )
| ~ ( ( SV456 != SV379 )
| ( c_member @ ( tc_prod @ SY1492 @ SY1492 ) @ ( c_Product__Type_OPair @ SY1492 @ SY1492 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SY1492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2045,plain,
! [SV380: $i,SV457: $i] :
( ( ! [SY1493: $i] :
~ ( ~ ( ~ ( c_member @ SY1493 @ SV457 @ ( c_Wellfounded_Oacc @ SY1493 @ SV380 ) )
| ! [SY1494: $i] :
( ~ ( c_member @ ( tc_prod @ SY1493 @ SY1493 ) @ ( c_Product__Type_OPair @ SY1493 @ SY1493 @ SY1494 @ SV457 ) @ SV380 )
| ( c_member @ SY1493 @ SY1494 @ ( c_Wellfounded_Oacc @ SY1493 @ SV380 ) ) ) )
| ~ ( ~ ! [SY1495: $i] :
( ~ ( c_member @ ( tc_prod @ SY1493 @ SY1493 ) @ ( c_Product__Type_OPair @ SY1493 @ SY1493 @ SY1495 @ SV457 ) @ SV380 )
| ( c_member @ SY1493 @ SY1495 @ ( c_Wellfounded_Oacc @ SY1493 @ SV380 ) ) )
| ( c_member @ SY1493 @ SV457 @ ( c_Wellfounded_Oacc @ SY1493 @ SV380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2046,plain,
! [SV381: $i,SV458: $i] :
( ( ! [SY1496: $i,SY1497: $i,SY1498: $i] :
( ~ ( c_member @ ( tc_prod @ SY1498 @ SY1498 ) @ ( c_Product__Type_OPair @ SY1498 @ SY1498 @ SY1497 @ SY1496 ) @ SV458 )
| ~ ( c_member @ ( tc_prod @ SY1498 @ SY1498 ) @ ( c_Product__Type_OPair @ SY1498 @ SY1498 @ SY1496 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1498 @ SV458 ) )
| ( c_member @ ( tc_prod @ SY1498 @ SY1498 ) @ ( c_Product__Type_OPair @ SY1498 @ SY1498 @ SY1497 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1498 @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2047,plain,
! [SV382: $i,SV459: $i] :
( ( ! [SY1499: $i,SY1500: $i] :
( ~ ( c_member @ ( tc_prod @ SY1500 @ SY1500 ) @ ( c_Product__Type_OPair @ SY1500 @ SY1500 @ SY1499 @ SV459 ) @ SV382 )
| ( c_member @ ( tc_prod @ SY1500 @ SY1500 ) @ ( c_Product__Type_OPair @ SY1500 @ SY1500 @ SY1499 @ SV459 ) @ ( c_Transitive__Closure_Otrancl @ SY1500 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2048,plain,
! [SV383: $i,SV460: $i] :
( ( ! [SY1501: $i,SY1502: $i,SY1503: $i,SY1504: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1504 @ SY1503 @ SY1502 )
| ~ ( c_member @ ( tc_prod @ SY1504 @ SY1503 ) @ ( c_Product__Type_OPair @ SY1504 @ SY1503 @ SY1501 @ SV460 ) @ SY1502 )
| ~ ( c_member @ ( tc_prod @ SY1504 @ SY1503 ) @ ( c_Product__Type_OPair @ SY1504 @ SY1503 @ SY1501 @ SV383 ) @ SY1502 )
| ( SV460 = SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2049,plain,
( ( ~ ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[1971]) ).
thf(2050,plain,
( ( ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[1971]) ).
thf(2051,plain,
! [SV384: $i,SV461: $i] :
( ( ! [SY1505: $i,SY1506: $i] :
( ~ ( c_member @ SY1506 @ SY1505 @ SV461 )
| ( c_member @ SY1506 @ SY1505 @ ( c_Set_Oinsert @ SY1506 @ SV384 @ SV461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2052,plain,
! [SV385: $i,SV462: $i] :
( ( ! [SY1507: $i,SY1508: $i] :
( ~ ~ ( c_member @ SY1508 @ SY1507 @ SV462 )
| ~ ~ ( c_member @ SY1508 @ SY1507 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY1508 @ SY1507 @ SV462 )
!= ( c_Set_Oinsert @ SY1508 @ SY1507 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SY1508 @ SY1507 @ SV462 )
= ( c_Set_Oinsert @ SY1508 @ SY1507 @ SV385 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2053,plain,
! [SV386: $i,SV463: $i] :
( ( ! [SY1509: $i,SY1510: $i,SY1511: $i] :
( ~ ( c_member @ ( tc_prod @ SY1511 @ SY1511 ) @ ( c_Product__Type_OPair @ SY1511 @ SY1511 @ SY1510 @ SY1509 ) @ ( c_Transitive__Closure_Otrancl @ SY1511 @ SV463 ) )
| ~ ( c_member @ ( tc_prod @ SY1511 @ SY1511 ) @ ( c_Product__Type_OPair @ SY1511 @ SY1511 @ SY1509 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SY1511 @ SY1511 ) @ ( c_Product__Type_OPair @ SY1511 @ SY1511 @ SY1510 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SY1511 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2054,plain,
! [SV387: $i,SV464: $i] :
( ( ! [SY1512: $i,SY1513: $i,SY1514: $i] :
( ~ ( c_member @ ( tc_prod @ SY1514 @ SY1514 ) @ ( c_Product__Type_OPair @ SY1514 @ SY1514 @ SY1513 @ SY1512 ) @ SV464 )
| ~ ( c_member @ ( tc_prod @ SY1514 @ SY1514 ) @ ( c_Product__Type_OPair @ SY1514 @ SY1514 @ SY1512 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SY1514 @ SY1514 ) @ ( c_Product__Type_OPair @ SY1514 @ SY1514 @ SY1513 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SY1514 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2055,plain,
! [SV388: $i,SV465: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ( SY1516 != SY1515 )
| ~ ( ~ ( c_member @ SV465 @ SV388 @ SY1516 )
| ~ ( c_member @ SV465 @ SV388 @ SY1515 ) )
| ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SY1516 )
| ( c_member @ SV465 @ SV388 @ SY1515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2056,plain,
! [SV389: $i,SV466: $i] :
( ( ! [SY1517: $i] :
( ~ ( c_Wellfounded_Owf @ SY1517 @ SV466 )
| ~ ( c_member @ ( tc_prod @ SY1517 @ SY1517 ) @ ( c_Product__Type_OPair @ SY1517 @ SY1517 @ SV389 @ SV389 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2057,plain,
! [SV390: $i,SV467: $i] :
( ( ! [SY1518: $i,SY1519: $i,SY1520: $i,SY1521: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1521 @ SY1520 @ SY1519 @ SY1518 )
!= ( c_Product__Type_OPair @ SY1521 @ SY1520 @ SV467 @ SV390 ) )
| ~ ( ( SY1519 != SV467 )
| ( SY1518 != SV390 ) ) )
| ~ ( ~ ~ ( ( SY1519 != SV467 )
| ( SY1518 != SV390 ) )
| ( ( c_Product__Type_OPair @ SY1521 @ SY1520 @ SY1519 @ SY1518 )
= ( c_Product__Type_OPair @ SY1521 @ SY1520 @ SV467 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2058,plain,
! [SV391: $i,SV468: $i] :
( ( ! [SY1522: $i,SY1523: $i] :
( ( SY1523 != SY1522 )
| ~ ( ~ ( ~ ( c_member @ SV468 @ SY1523 @ SV391 )
| ( c_member @ SV468 @ SY1522 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SY1522 @ SV391 )
| ( c_member @ SV468 @ SY1523 @ SV391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2059,plain,
! [SV392: $i,SV469: $i] :
( ( ! [SY1524: $i,SY1525: $i] :
( ~ ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SY1525 @ SV392 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SV469 ) @ SV392 )
| ~ ! [SY1526: $i] :
( ~ ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1524 @ SY1526 ) @ ( c_Transitive__Closure_Otrancl @ SY1525 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SY1525 @ SY1525 ) @ ( c_Product__Type_OPair @ SY1525 @ SY1525 @ SY1526 @ SV469 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2060,plain,
! [SV393: $i,SV470: $i] :
( ( ! [SY1527: $i,SY1528: $i] :
( ~ ( c_member @ ( tc_prod @ SY1528 @ SY1528 ) @ ( c_Product__Type_OPair @ SY1528 @ SY1528 @ SY1527 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SY1528 @ SV393 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1528 @ SY1528 ) @ ( c_Product__Type_OPair @ SY1528 @ SY1528 @ SY1527 @ SV470 ) @ SV393 )
| ~ ! [SY1529: $i] :
( ~ ( c_member @ ( tc_prod @ SY1528 @ SY1528 ) @ ( c_Product__Type_OPair @ SY1528 @ SY1528 @ SY1527 @ SY1529 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SY1528 @ SY1528 ) @ ( c_Product__Type_OPair @ SY1528 @ SY1528 @ SY1529 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SY1528 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2061,plain,
! [SV394: $i,SV471: $i] :
( ( ! [SY1530: $i] :
( ~ ( c_member @ ( tc_prod @ SY1530 @ SY1530 ) @ SV471 @ ( c_Relation_OId__on @ SY1530 @ SV394 ) )
| ~ ! [SY1531: $i] :
( ~ ( c_member @ SY1530 @ SY1531 @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SY1530 @ SY1530 @ SY1531 @ SY1531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2062,plain,
! [SV395: $i,SV472: $i] :
( ( ! [SY1532: $i,SY1533: $i] :
( ~ ( c_Relation_Otrans @ SY1533 @ SY1532 )
| ~ ( c_Relation_Otrans @ SV472 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SY1533 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SY1533 @ SV472 @ SY1532 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2063,plain,
! [SV396: $i,SV473: $i] :
( ( ! [SY1534: $i,SY1535: $i,SY1536: $i] :
( ~ ( c_member @ ( tc_prod @ SY1536 @ SY1536 ) @ ( c_Product__Type_OPair @ SY1536 @ SY1536 @ SY1535 @ SY1534 ) @ SV473 )
| ~ ( c_member @ ( tc_prod @ SY1536 @ SY1536 ) @ ( c_Product__Type_OPair @ SY1536 @ SY1536 @ SY1534 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1536 @ SV473 ) )
| ( c_member @ ( tc_prod @ SY1536 @ SY1536 ) @ ( c_Product__Type_OPair @ SY1536 @ SY1536 @ SY1535 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1536 @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2064,plain,
! [SV397: $i,SV474: $i] :
( ( ! [SY1537: $i,SY1538: $i,SY1539: $i] :
( ~ ( c_member @ SY1539 @ SY1538 @ ( c_Relation_OImage @ SY1537 @ SY1539 @ SV474 @ SV397 ) )
| ~ ! [SY1540: $i] :
( ~ ( c_member @ ( tc_prod @ SY1537 @ SY1539 ) @ ( c_Product__Type_OPair @ SY1537 @ SY1539 @ SY1540 @ SY1538 ) @ SV474 )
| ~ ( c_member @ SY1537 @ SY1540 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2065,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Oirrefl @ SV475 @ SV398 )
| ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) )
| ~ ( ~ ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 )
| ( c_Relation_Oirrefl @ SV475 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2066,plain,
! [SV399: $i,SV476: $i] :
( ( ! [SY1543: $i,SY1544: $i] :
( ~ ( c_member @ SY1544 @ SY1543 @ ( c_Relation_ORange @ SV476 @ SY1544 @ SV399 ) )
| ~ ! [SY1545: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SY1544 ) @ ( c_Product__Type_OPair @ SV476 @ SY1544 @ SY1545 @ SY1543 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2067,plain,
! [SV400: $i,SV477: $i] :
( ( ! [SY1546: $i,SY1547: $i,SY1548: $i,SY1549: $i,SY1550: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1548 @ SY1547 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1546 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1550 @ SY1549 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1548 @ SY1547 )
!= ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1546 @ SV477 ) ) )
| ~ ! [SY1551: $i,SY1552: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1548 @ SY1547 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1551 @ SY1552 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1550 @ SY1549 ) @ ( tc_prod @ SY1550 @ SY1549 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1551 @ SY1552 ) @ ( c_Product__Type_OPair @ SY1550 @ SY1549 @ SY1546 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1550 @ SY1549 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2068,plain,
! [SV401: $i,SV478: $i] :
( ( ! [SY1553: $i,SY1554: $i,SY1555: $i] :
( ~ ( c_Relation_Orefl__on @ SY1555 @ SY1554 @ SY1553 )
| ~ ( c_member @ ( tc_prod @ SY1555 @ SY1555 ) @ ( c_Product__Type_OPair @ SY1555 @ SY1555 @ SV478 @ SV401 ) @ SY1553 )
| ( c_member @ SY1555 @ SV401 @ SY1554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2069,plain,
! [SV325: $i,SV403: $i,SV479: $i] :
( ( c_member @ ( tc_prod @ SV479 @ SV479 ) @ ( c_Product__Type_OPair @ SV479 @ SV479 @ SV403 @ SV403 ) @ ( c_Transitive__Closure_Ortrancl @ SV479 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2070,plain,
! [SV330: $i,SV407: $i,SV480: $i] :
( ( c_member @ SV480 @ SV407 @ ( c_Set_Oinsert @ SV480 @ SV407 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2071,plain,
! [SV331: $i,SV408: $i,SV481: $i] :
( ( ~ ( c_member @ SV481 @ SV408 @ SV331 )
| ( ( c_Set_Oinsert @ SV481 @ SV408 @ SV331 )
= SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2072,plain,
! [SV332: $i,SV409: $i] :
( ( ( ~ ! [SY1352: $i,SY1353: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1353 ) @ SV332 )
| ! [SY1354: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1353 @ SY1354 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1354 ) @ SV332 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2073,plain,
! [SV333: $i,SV410: $i,SV482: $i] :
( ( ! [SY1556: $i] :
( ~ ( c_member @ SY1556 @ SV482 @ ( c_Set_Oinsert @ SY1556 @ SV410 @ SV333 ) )
| ~ ( ( SV482 != SV410 ) )
| ( c_member @ SY1556 @ SV482 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2074,plain,
! [SV334: $i,SV411: $i,SV483: $i] :
( ( ! [SY1557: $i,SY1558: $i] :
( ~ ( c_member @ ( tc_prod @ SY1558 @ SY1558 ) @ ( c_Product__Type_OPair @ SY1558 @ SY1558 @ SY1557 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SY1558 @ SV411 ) )
| ~ ( c_member @ ( tc_prod @ SY1558 @ SY1558 ) @ ( c_Product__Type_OPair @ SY1558 @ SY1558 @ SV483 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SY1558 @ SY1558 ) @ ( c_Product__Type_OPair @ SY1558 @ SY1558 @ SY1557 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SY1558 @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2075,plain,
! [SV335: $i,SV412: $i,SV484: $i] :
( ( ! [SY1559: $i] :
~ ( ~ ( ~ ( c_member @ SY1559 @ SV484 @ ( c_Relation_ODomain @ SY1559 @ SV412 @ SV335 ) )
| ~ ! [SY1560: $i] :
~ ( c_member @ ( tc_prod @ SY1559 @ SV412 ) @ ( c_Product__Type_OPair @ SY1559 @ SV412 @ SV484 @ SY1560 ) @ SV335 ) )
| ~ ( ~ ~ ! [SY1561: $i] :
~ ( c_member @ ( tc_prod @ SY1559 @ SV412 ) @ ( c_Product__Type_OPair @ SY1559 @ SV412 @ SV484 @ SY1561 ) @ SV335 )
| ( c_member @ SY1559 @ SV484 @ ( c_Relation_ODomain @ SY1559 @ SV412 @ SV335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2076,plain,
! [SV336: $i,SV413: $i,SV485: $i] :
( ( ! [SY1562: $i,SY1563: $i,SY1564: $i,SY1565: $i,SY1566: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1566 @ SY1565 ) @ ( tc_prod @ SY1566 @ SY1565 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1566 @ SY1565 ) @ ( tc_prod @ SY1566 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1565 @ SY1564 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1565 @ SY1562 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1566 @ SY1565 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1566 @ SY1566 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1566 @ SY1564 @ SY1562 ) @ SV413 )
| ~ ( ( SY1564 != SY1562 )
| ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1563 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1566 @ SY1566 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1566 @ SY1564 @ SY1562 ) @ SV413 )
| ~ ( ( SY1564 != SY1562 )
| ~ ( c_member @ ( tc_prod @ SY1565 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1565 @ SY1565 @ SY1563 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1566 @ SY1565 ) @ ( tc_prod @ SY1566 @ SY1565 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1566 @ SY1565 ) @ ( tc_prod @ SY1566 @ SY1565 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1565 @ SY1564 @ SY1563 ) @ ( c_Product__Type_OPair @ SY1566 @ SY1565 @ SY1562 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1566 @ SY1565 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2077,plain,
! [SV337: $i,SV414: $i,SV486: $i] :
( ( ~ ~ ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
| ~ ! [SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SY1567 @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ SY1567 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2078,plain,
! [SV338: $i,SV415: $i,SV487: $i] :
( ( ! [SY1568: $i] :
( ~ ( c_member @ SY1568 @ SV487 @ ( c_Relation_ODomain @ SY1568 @ SV415 @ SV338 ) )
| ~ ! [SY1569: $i] :
~ ( c_member @ ( tc_prod @ SY1568 @ SV415 ) @ ( c_Product__Type_OPair @ SY1568 @ SV415 @ SV487 @ SY1569 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2079,plain,
! [SV339: $i,SV416: $i,SV488: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ SV339 )
| ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2080,plain,
! [SV340: $i,SV417: $i,SV489: $i] :
( ( ! [SY1570: $i] :
( ~ ! [SY1571: $i] :
~ ( c_member @ ( tc_prod @ SY1570 @ SY1570 ) @ ( c_Product__Type_OPair @ SY1570 @ SY1570 @ SY1571 @ SY1571 ) @ ( c_Transitive__Closure_Otrancl @ SY1570 @ SV489 ) )
| ~ ( c_member @ ( tc_prod @ SY1570 @ SY1570 ) @ ( c_Product__Type_OPair @ SY1570 @ SY1570 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2081,plain,
! [SV341: $i,SV418: $i,SV490: $i] :
( ( ! [SY1572: $i] :
( ~ ( c_Relation_Oantisym @ SY1572 @ SV490 )
| ~ ( c_member @ ( tc_prod @ SY1572 @ SY1572 ) @ ( c_Product__Type_OPair @ SY1572 @ SY1572 @ SV418 @ SV341 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SY1572 @ SY1572 ) @ ( c_Product__Type_OPair @ SY1572 @ SY1572 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2082,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
| ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) )
| ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) )
| ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2083,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
| ( SV420 = SV343 ) )
| ~ ( ( SV420 != SV343 )
| ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2084,plain,
! [SV344: $i,SV421: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV421 @ SV344 ) )
= $true )
| ( ( ( c_Transitive__Closure_Otrancl @ SV421 @ SV344 )
= SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2085,plain,
! [SV345: $i,SV422: $i,SV493: $i] :
( ( ! [SY1579: $i] :
( ~ ( c_Wellfounded_Owf @ SY1579 @ SV493 )
| ~ ( c_member @ ( tc_prod @ SY1579 @ SY1579 ) @ ( c_Product__Type_OPair @ SY1579 @ SY1579 @ SV422 @ SV345 ) @ SV493 )
| ~ ( c_member @ ( tc_prod @ SY1579 @ SY1579 ) @ ( c_Product__Type_OPair @ SY1579 @ SY1579 @ SV345 @ SV422 ) @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2086,plain,
! [SV346: $i,SV423: $i,SV494: $i] :
( ( ! [SY1580: $i] :
( ~ ( c_Wellfounded_Owf @ SY1580 @ SV494 )
| ~ ( c_member @ ( tc_prod @ SY1580 @ SY1580 ) @ ( c_Product__Type_OPair @ SY1580 @ SY1580 @ SV423 @ SV346 ) @ SV494 )
| ~ ( c_member @ ( tc_prod @ SY1580 @ SY1580 ) @ ( c_Product__Type_OPair @ SY1580 @ SY1580 @ SV346 @ SV423 ) @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2087,plain,
! [SV347: $i,SV424: $i,SV495: $i] :
( ( ~ ! [SY1581: $i] :
( ~ ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ SY1581 @ SV424 ) @ SV347 )
| ( c_member @ SV495 @ SY1581 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) ) )
| ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2088,plain,
! [SV348: $i,SV425: $i,SV496: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ SV348 )
| ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ ( c_Transitive__Closure_Otrancl @ SV496 @ SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2089,plain,
! [SV349: $i,SV426: $i,SV497: $i] :
( ( ! [SY1582: $i] :
~ ( ~ ( ~ ( c_member @ SY1582 @ SV497 @ ( c_Set_Oinsert @ SY1582 @ SV426 @ SV349 ) )
| ( SV497 = SV426 )
| ( c_member @ SY1582 @ SV497 @ SV349 ) )
| ~ ( ~ ( ( SV497 = SV426 )
| ( c_member @ SY1582 @ SV497 @ SV349 ) )
| ( c_member @ SY1582 @ SV497 @ ( c_Set_Oinsert @ SY1582 @ SV426 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2090,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ( ~ ( c_Wellfounded_Owf @ SV427 @ SV350 )
| ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) )
| ~ ( ~ ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) )
| ( c_Wellfounded_Owf @ SV427 @ SV350 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2091,plain,
! [SV351: $i,SV428: $i,SV498: $i] :
( ( ! [SY1583: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ SY1583 @ SY1583 ) @ ( c_Product__Type_OPair @ SY1583 @ SY1583 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SY1583 @ SV351 ) )
| ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SY1583 @ SV498 @ SV351 ) ) )
| ~ ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SY1583 @ SV498 @ SV351 ) )
| ( c_member @ ( tc_prod @ SY1583 @ SY1583 ) @ ( c_Product__Type_OPair @ SY1583 @ SY1583 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SY1583 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2092,plain,
! [SV352: $i,SV429: $i] :
( ( ( ~ ! [SY1408: $i,SY1409: $i] :
( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1408 @ SY1409 ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1409 @ SY1408 ) @ SV352 )
| ( SY1408 = SY1409 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2093,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ~ ! [SY1584: $i,SY1585: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1585 ) @ SV353 )
| ! [SY1586: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1586 ) @ SV353 )
| ( SY1585 = SY1586 ) ) )
| ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2094,plain,
! [SV354: $i,SV431: $i,SV500: $i] :
( ( ! [SY1587: $i,SY1588: $i] :
( ~ ( c_Relation_Orefl__on @ SY1588 @ SY1587 @ SV500 )
| ~ ( c_member @ ( tc_prod @ SY1588 @ SY1588 ) @ ( c_Product__Type_OPair @ SY1588 @ SY1588 @ SV431 @ SV354 ) @ SV500 )
| ( c_member @ SY1588 @ SV431 @ SY1587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2095,plain,
! [SV355: $i,SV432: $i,SV501: $i] :
( ( ! [SY1589: $i] :
( ( SY1589 != SV501 )
| ~ ( c_member @ SV432 @ SV501 @ SV355 )
| ( c_member @ SV432 @ SY1589 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2096,plain,
! [SV356: $i,SV433: $i,SV502: $i] :
( ( ! [SY1590: $i] :
( ( SY1590 != SV502 )
| ~ ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SY1590 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SY1590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2097,plain,
! [SV357: $i,SV434: $i,SV503: $i] :
( ( ! [SY1591: $i] :
( ~ ( c_member @ ( tc_prod @ SY1591 @ SY1591 ) @ ( c_Product__Type_OPair @ SY1591 @ SY1591 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SY1591 @ SV357 ) )
| ~ ( ( SV503 != SV434 ) )
| ~ ! [SY1592: $i] :
( ~ ( c_member @ ( tc_prod @ SY1591 @ SY1591 ) @ ( c_Product__Type_OPair @ SY1591 @ SY1591 @ SV503 @ SY1592 ) @ ( c_Transitive__Closure_Ortrancl @ SY1591 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SY1591 @ SY1591 ) @ ( c_Product__Type_OPair @ SY1591 @ SY1591 @ SY1592 @ SV434 ) @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2098,plain,
! [SV358: $i,SV435: $i,SV504: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
~ ( ~ ( ~ ( c_member @ SY1594 @ SY1593 @ ( c_Relation_OImage @ SV504 @ SY1594 @ SV435 @ SV358 ) )
| ~ ! [SY1595: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1595 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SY1594 ) @ ( c_Product__Type_OPair @ SV504 @ SY1594 @ SY1595 @ SY1593 ) @ SV435 ) ) )
| ~ ( ~ ~ ! [SY1596: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1596 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SY1594 ) @ ( c_Product__Type_OPair @ SV504 @ SY1594 @ SY1596 @ SY1593 ) @ SV435 ) )
| ( c_member @ SY1594 @ SY1593 @ ( c_Relation_OImage @ SV504 @ SY1594 @ SV435 @ SV358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2099,plain,
! [SV359: $i,SV436: $i,SV505: $i] :
( ( ! [SY1597: $i] :
( ~ ( c_member @ SY1597 @ SV505 @ ( c_Wellfounded_Oacc @ SY1597 @ SV436 ) )
| ~ ( c_member @ ( tc_prod @ SY1597 @ SY1597 ) @ ( c_Product__Type_OPair @ SY1597 @ SY1597 @ SV359 @ SV505 ) @ SV436 )
| ( c_member @ SY1597 @ SV359 @ ( c_Wellfounded_Oacc @ SY1597 @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2100,plain,
! [SV360: $i,SV437: $i,SV506: $i] :
( ( ! [SY1598: $i,SY1599: $i,SY1600: $i,SY1601: $i,SY1602: $i] :
( ~ ( c_member @ ( tc_prod @ SY1602 @ SY1601 ) @ ( c_Product__Type_OPair @ SY1602 @ SY1601 @ SY1600 @ SY1599 ) @ SY1598 )
| ~ ( c_member @ ( tc_prod @ SY1601 @ SV506 ) @ ( c_Product__Type_OPair @ SY1601 @ SV506 @ SY1599 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1602 @ SV506 ) @ ( c_Product__Type_OPair @ SY1602 @ SV506 @ SY1600 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1602 @ SY1601 @ SV506 @ SY1598 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2101,plain,
! [SV361: $i,SV438: $i,SV507: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV507 @ SV438 )
| ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV361 @ SV361 ) @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2102,plain,
! [SV362: $i,SV439: $i,SV508: $i] :
( ( ! [SY1603: $i,SY1604: $i] :
( ~ ( c_member @ ( tc_prod @ SY1604 @ SY1603 ) @ ( c_Product__Type_OPair @ SY1604 @ SY1603 @ SV508 @ SV439 ) @ SV362 )
| ( c_member @ SY1604 @ SV508 @ ( c_Relation_ODomain @ SY1604 @ SY1603 @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2103,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ( ~ ( c_Relation_Otrans @ SV440 @ SV363 )
| ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) )
| ~ ( ~ ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) )
| ( c_Relation_Otrans @ SV440 @ SV363 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2104,plain,
! [SV364: $i,SV441: $i,SV509: $i] :
( ( ! [SY1605: $i,SY1606: $i] :
( ~ ( c_Relation_Otrans @ SY1606 @ SY1605 )
| ~ ( c_member @ ( tc_prod @ SY1606 @ SY1606 ) @ ( c_Product__Type_OPair @ SY1606 @ SY1606 @ SV509 @ SV441 ) @ SY1605 )
| ~ ( c_member @ ( tc_prod @ SY1606 @ SY1606 ) @ ( c_Product__Type_OPair @ SY1606 @ SY1606 @ SV441 @ SV364 ) @ SY1605 )
| ( c_member @ ( tc_prod @ SY1606 @ SY1606 ) @ ( c_Product__Type_OPair @ SY1606 @ SY1606 @ SV509 @ SV364 ) @ SY1605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2105,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
| ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) )
| ~ ( ~ ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 )
| ( c_Nitpick_Orefl_H @ SV442 @ SV365 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2106,plain,
! [SV366: $i,SV443: $i,SV510: $i] :
( ( ! [SY1607: $i,SY1608: $i] :
( ~ ( c_member @ ( tc_prod @ SY1608 @ SY1608 ) @ ( c_Product__Type_OPair @ SY1608 @ SY1608 @ SY1607 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SY1608 @ SV443 ) )
| ~ ( c_member @ ( tc_prod @ SY1608 @ SY1608 ) @ ( c_Product__Type_OPair @ SY1608 @ SY1608 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1608 @ SV443 ) )
| ( c_member @ ( tc_prod @ SY1608 @ SY1608 ) @ ( c_Product__Type_OPair @ SY1608 @ SY1608 @ SY1607 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1608 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2107,plain,
! [SV367: $i,SV444: $i,SV511: $i] :
( ( ! [SY1609: $i] :
( ~ ( c_member @ ( tc_prod @ SY1609 @ SY1609 ) @ ( c_Product__Type_OPair @ SY1609 @ SY1609 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SY1609 @ SV367 ) )
| ~ ( ( SV511 != SV444 ) )
| ~ ! [SY1610: $i] :
( ~ ( c_member @ ( tc_prod @ SY1609 @ SY1609 ) @ ( c_Product__Type_OPair @ SY1609 @ SY1609 @ SV511 @ SY1610 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SY1609 @ SY1609 ) @ ( c_Product__Type_OPair @ SY1609 @ SY1609 @ SY1610 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SY1609 @ SV367 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2108,plain,
! [SV368: $i,SV445: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) ) )
= $true )
| ( ( ~ ! [SY1458: $i] :
( SV368
!= ( c_Product__Type_OPair @ SV445 @ SV445 @ SY1458 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2109,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ( ~ ( ~ ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
| ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) )
| ~ ( ~ ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2110,plain,
! [SV370: $i,SV447: $i,SV513: $i] :
( ( ! [SY1615: $i] :
( ( SY1615 != SV513 )
| ~ ( c_member @ SV447 @ SY1615 @ SV370 )
| ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SY1615 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2111,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ( ~ ( c_Relation_Oantisym @ SV448 @ SV371 )
| ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) )
| ~ ( ~ ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) )
| ( c_Relation_Oantisym @ SV448 @ SV371 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2112,plain,
! [SV372: $i,SV449: $i,SV514: $i] :
( ( ! [SY1616: $i] :
( ~ ( c_Relation_Orefl__on @ SY1616 @ SV514 @ SV449 )
| ~ ( c_member @ SY1616 @ SV372 @ SV514 )
| ( c_member @ ( tc_prod @ SY1616 @ SY1616 ) @ ( c_Product__Type_OPair @ SY1616 @ SY1616 @ SV372 @ SV372 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2113,plain,
! [SV373: $i,SV450: $i,SV515: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i] :
( ( ( c_Product__Type_OPair @ SY1619 @ SY1618 @ SY1617 @ SV515 )
!= ( c_Product__Type_OPair @ SY1619 @ SY1618 @ SV450 @ SV373 ) )
| ~ ( ( SY1617 != SV450 )
| ( SV515 != SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2114,plain,
! [SV374: $i,SV451: $i,SV516: $i] :
( ( ! [SY1620: $i] :
~ ( ~ ( ~ ( c_member @ SY1620 @ SV516 @ ( c_Relation_ORange @ SV451 @ SY1620 @ SV374 ) )
| ~ ! [SY1621: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SY1620 ) @ ( c_Product__Type_OPair @ SV451 @ SY1620 @ SY1621 @ SV516 ) @ SV374 ) )
| ~ ( ~ ~ ! [SY1622: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SY1620 ) @ ( c_Product__Type_OPair @ SV451 @ SY1620 @ SY1622 @ SV516 ) @ SV374 )
| ( c_member @ SY1620 @ SV516 @ ( c_Relation_ORange @ SV451 @ SY1620 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2115,plain,
! [SV375: $i,SV452: $i,SV517: $i] :
( ( ! [SY1623: $i,SY1624: $i,SY1625: $i] :
( ~ ( c_member @ SY1625 @ SY1624 @ SY1623 )
| ~ ( c_member @ ( tc_prod @ SY1625 @ SV517 ) @ ( c_Product__Type_OPair @ SY1625 @ SV517 @ SY1624 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SY1625 @ SV517 @ SV375 @ SY1623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2116,plain,
! [SV376: $i,SV453: $i,SV518: $i] :
( ( ! [SY1626: $i,SY1627: $i] :
( ~ ( c_member @ ( tc_prod @ SY1627 @ SY1626 ) @ ( c_Product__Type_OPair @ SY1627 @ SY1626 @ SV518 @ SV453 ) @ SV376 )
| ( c_member @ SY1626 @ SV453 @ ( c_Relation_ORange @ SY1627 @ SY1626 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2117,plain,
! [SV377: $i,SV454: $i,SV519: $i] :
( ( ! [SY1628: $i] :
( ~ ( ~ ~ ( c_member @ SY1628 @ SV519 @ SV454 )
| ( SV519 = SV377 ) )
| ( c_member @ SY1628 @ SV519 @ ( c_Set_Oinsert @ SY1628 @ SV377 @ SV454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2118,plain,
! [SV378: $i,SV455: $i,SV520: $i] :
( ( ! [SY1629: $i,SY1630: $i] :
( ~ ( c_member @ ( tc_prod @ SY1630 @ SY1630 ) @ ( c_Product__Type_OPair @ SY1630 @ SY1630 @ SY1629 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SY1630 @ SV455 ) )
| ~ ( c_member @ ( tc_prod @ SY1630 @ SY1630 ) @ ( c_Product__Type_OPair @ SY1630 @ SY1630 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1630 @ SV455 ) )
| ( c_member @ ( tc_prod @ SY1630 @ SY1630 ) @ ( c_Product__Type_OPair @ SY1630 @ SY1630 @ SY1629 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1630 @ SV455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2119,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
| ( SV456 = SV379 ) )
| ~ ( ( SV456 != SV379 )
| ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2120,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
| ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
| ~ ( ~ ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
| ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2121,plain,
! [SV381: $i,SV458: $i,SV523: $i] :
( ( ! [SY1633: $i,SY1634: $i] :
( ~ ( c_member @ ( tc_prod @ SY1634 @ SY1634 ) @ ( c_Product__Type_OPair @ SY1634 @ SY1634 @ SY1633 @ SV523 ) @ SV458 )
| ~ ( c_member @ ( tc_prod @ SY1634 @ SY1634 ) @ ( c_Product__Type_OPair @ SY1634 @ SY1634 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1634 @ SV458 ) )
| ( c_member @ ( tc_prod @ SY1634 @ SY1634 ) @ ( c_Product__Type_OPair @ SY1634 @ SY1634 @ SY1633 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1634 @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2122,plain,
! [SV382: $i,SV459: $i,SV524: $i] :
( ( ! [SY1635: $i] :
( ~ ( c_member @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SV524 @ SV459 ) @ SV382 )
| ( c_member @ ( tc_prod @ SY1635 @ SY1635 ) @ ( c_Product__Type_OPair @ SY1635 @ SY1635 @ SV524 @ SV459 ) @ ( c_Transitive__Closure_Otrancl @ SY1635 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2123,plain,
! [SV383: $i,SV460: $i,SV525: $i] :
( ( ! [SY1636: $i,SY1637: $i,SY1638: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1638 @ SY1637 @ SY1636 )
| ~ ( c_member @ ( tc_prod @ SY1638 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1638 @ SY1637 @ SV525 @ SV460 ) @ SY1636 )
| ~ ( c_member @ ( tc_prod @ SY1638 @ SY1637 ) @ ( c_Product__Type_OPair @ SY1638 @ SY1637 @ SV525 @ SV383 ) @ SY1636 )
| ( SV460 = SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2124,plain,
( ( ~ ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[2049]) ).
thf(2125,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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)],[2050]) ).
thf(2126,plain,
! [SV384: $i,SV461: $i,SV526: $i] :
( ( ! [SY1639: $i] :
( ~ ( c_member @ SY1639 @ SV526 @ SV461 )
| ( c_member @ SY1639 @ SV526 @ ( c_Set_Oinsert @ SY1639 @ SV384 @ SV461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2127,plain,
! [SV385: $i,SV462: $i,SV527: $i] :
( ( ! [SY1640: $i] :
( ~ ~ ( c_member @ SY1640 @ SV527 @ SV462 )
| ~ ~ ( c_member @ SY1640 @ SV527 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SY1640 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SY1640 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SY1640 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SY1640 @ SV527 @ SV385 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2128,plain,
! [SV386: $i,SV463: $i,SV528: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ~ ( c_member @ ( tc_prod @ SY1642 @ SY1642 ) @ ( c_Product__Type_OPair @ SY1642 @ SY1642 @ SY1641 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SY1642 @ SV463 ) )
| ~ ( c_member @ ( tc_prod @ SY1642 @ SY1642 ) @ ( c_Product__Type_OPair @ SY1642 @ SY1642 @ SV528 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SY1642 @ SY1642 ) @ ( c_Product__Type_OPair @ SY1642 @ SY1642 @ SY1641 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SY1642 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2129,plain,
! [SV387: $i,SV464: $i,SV529: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ~ ( c_member @ ( tc_prod @ SY1644 @ SY1644 ) @ ( c_Product__Type_OPair @ SY1644 @ SY1644 @ SY1643 @ SV529 ) @ SV464 )
| ~ ( c_member @ ( tc_prod @ SY1644 @ SY1644 ) @ ( c_Product__Type_OPair @ SY1644 @ SY1644 @ SV529 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SY1644 @ SY1644 ) @ ( c_Product__Type_OPair @ SY1644 @ SY1644 @ SY1643 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SY1644 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2130,plain,
! [SV388: $i,SV465: $i,SV530: $i] :
( ( ! [SY1645: $i] :
( ( SY1645 != SV530 )
| ~ ( ~ ( c_member @ SV465 @ SV388 @ SY1645 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
| ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SY1645 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2131,plain,
! [SV389: $i,SV466: $i,SV531: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV531 @ SV466 )
| ~ ( c_member @ ( tc_prod @ SV531 @ SV531 ) @ ( c_Product__Type_OPair @ SV531 @ SV531 @ SV389 @ SV389 ) @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2132,plain,
! [SV390: $i,SV467: $i,SV532: $i] :
( ( ! [SY1646: $i,SY1647: $i,SY1648: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1648 @ SY1647 @ SY1646 @ SV532 )
!= ( c_Product__Type_OPair @ SY1648 @ SY1647 @ SV467 @ SV390 ) )
| ~ ( ( SY1646 != SV467 )
| ( SV532 != SV390 ) ) )
| ~ ( ~ ~ ( ( SY1646 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SY1648 @ SY1647 @ SY1646 @ SV532 )
= ( c_Product__Type_OPair @ SY1648 @ SY1647 @ SV467 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2133,plain,
! [SV391: $i,SV468: $i,SV533: $i] :
( ( ! [SY1649: $i] :
( ( SY1649 != SV533 )
| ~ ( ~ ( ~ ( c_member @ SV468 @ SY1649 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SY1649 @ SV391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2134,plain,
! [SV392: $i,SV469: $i,SV534: $i] :
( ( ! [SY1650: $i] :
( ~ ( c_member @ ( tc_prod @ SY1650 @ SY1650 ) @ ( c_Product__Type_OPair @ SY1650 @ SY1650 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SY1650 @ SV392 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1650 @ SY1650 ) @ ( c_Product__Type_OPair @ SY1650 @ SY1650 @ SV534 @ SV469 ) @ SV392 )
| ~ ! [SY1651: $i] :
( ~ ( c_member @ ( tc_prod @ SY1650 @ SY1650 ) @ ( c_Product__Type_OPair @ SY1650 @ SY1650 @ SV534 @ SY1651 ) @ ( c_Transitive__Closure_Otrancl @ SY1650 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SY1650 @ SY1650 ) @ ( c_Product__Type_OPair @ SY1650 @ SY1650 @ SY1651 @ SV469 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2135,plain,
! [SV393: $i,SV470: $i,SV535: $i] :
( ( ! [SY1652: $i] :
( ~ ( c_member @ ( tc_prod @ SY1652 @ SY1652 ) @ ( c_Product__Type_OPair @ SY1652 @ SY1652 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SY1652 @ SV393 ) )
| ~ ~ ( c_member @ ( tc_prod @ SY1652 @ SY1652 ) @ ( c_Product__Type_OPair @ SY1652 @ SY1652 @ SV535 @ SV470 ) @ SV393 )
| ~ ! [SY1653: $i] :
( ~ ( c_member @ ( tc_prod @ SY1652 @ SY1652 ) @ ( c_Product__Type_OPair @ SY1652 @ SY1652 @ SV535 @ SY1653 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SY1652 @ SY1652 ) @ ( c_Product__Type_OPair @ SY1652 @ SY1652 @ SY1653 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SY1652 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2136,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
| ~ ! [SY1654: $i] :
( ~ ( c_member @ SV536 @ SY1654 @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ SY1654 @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2137,plain,
! [SV395: $i,SV472: $i,SV537: $i] :
( ( ! [SY1655: $i] :
( ~ ( c_Relation_Otrans @ SY1655 @ SV537 )
| ~ ( c_Relation_Otrans @ SV472 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SY1655 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SY1655 @ SV472 @ SV537 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2138,plain,
! [SV396: $i,SV473: $i,SV538: $i] :
( ( ! [SY1656: $i,SY1657: $i] :
( ~ ( c_member @ ( tc_prod @ SY1657 @ SY1657 ) @ ( c_Product__Type_OPair @ SY1657 @ SY1657 @ SY1656 @ SV538 ) @ SV473 )
| ~ ( c_member @ ( tc_prod @ SY1657 @ SY1657 ) @ ( c_Product__Type_OPair @ SY1657 @ SY1657 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1657 @ SV473 ) )
| ( c_member @ ( tc_prod @ SY1657 @ SY1657 ) @ ( c_Product__Type_OPair @ SY1657 @ SY1657 @ SY1656 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1657 @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2139,plain,
! [SV397: $i,SV474: $i,SV539: $i] :
( ( ! [SY1658: $i,SY1659: $i] :
( ~ ( c_member @ SY1659 @ SY1658 @ ( c_Relation_OImage @ SV539 @ SY1659 @ SV474 @ SV397 ) )
| ~ ! [SY1660: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SY1659 ) @ ( c_Product__Type_OPair @ SV539 @ SY1659 @ SY1660 @ SY1658 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1660 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2140,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ( ~ ( c_Relation_Oirrefl @ SV475 @ SV398 )
| ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) )
| ~ ( ~ ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 )
| ( c_Relation_Oirrefl @ SV475 @ SV398 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2141,plain,
! [SV399: $i,SV476: $i,SV540: $i] :
( ( ! [SY1661: $i] :
( ~ ( c_member @ SY1661 @ SV540 @ ( c_Relation_ORange @ SV476 @ SY1661 @ SV399 ) )
| ~ ! [SY1662: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SY1661 ) @ ( c_Product__Type_OPair @ SV476 @ SY1661 @ SY1662 @ SV540 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2142,plain,
! [SV400: $i,SV477: $i,SV541: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i,SY1666: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SY1664 @ SY1663 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1666 @ SY1665 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SY1664 @ SY1663 )
!= ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SV541 @ SV477 ) ) )
| ~ ! [SY1667: $i,SY1668: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SY1664 @ SY1663 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SY1667 @ SY1668 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1666 @ SY1665 ) @ ( tc_prod @ SY1666 @ SY1665 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SY1667 @ SY1668 ) @ ( c_Product__Type_OPair @ SY1666 @ SY1665 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1666 @ SY1665 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2143,plain,
! [SV401: $i,SV478: $i,SV542: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ~ ( c_Relation_Orefl__on @ SY1670 @ SY1669 @ SV542 )
| ~ ( c_member @ ( tc_prod @ SY1670 @ SY1670 ) @ ( c_Product__Type_OPair @ SY1670 @ SY1670 @ SV478 @ SV401 ) @ SV542 )
| ( c_member @ SY1670 @ SV401 @ SY1669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2144,plain,
! [SV331: $i,SV408: $i,SV481: $i] :
( ( ( ~ ( c_member @ SV481 @ SV408 @ SV331 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV481 @ SV408 @ SV331 )
= SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2145,plain,
! [SV332: $i,SV409: $i] :
( ( ( ! [SY1352: $i,SY1353: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1353 ) @ SV332 )
| ! [SY1354: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1353 @ SY1354 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1352 @ SY1354 ) @ SV332 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2146,plain,
! [SV333: $i,SV410: $i,SV482: $i,SV543: $i] :
( ( ~ ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) )
| ~ ( ( SV482 != SV410 ) )
| ( c_member @ SV543 @ SV482 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2147,plain,
! [SV334: $i,SV411: $i,SV483: $i,SV544: $i] :
( ( ! [SY1671: $i] :
( ~ ( c_member @ ( tc_prod @ SY1671 @ SY1671 ) @ ( c_Product__Type_OPair @ SY1671 @ SY1671 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SY1671 @ SV411 ) )
| ~ ( c_member @ ( tc_prod @ SY1671 @ SY1671 ) @ ( c_Product__Type_OPair @ SY1671 @ SY1671 @ SV483 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SY1671 @ SY1671 ) @ ( c_Product__Type_OPair @ SY1671 @ SY1671 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SY1671 @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2148,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
| ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
| ~ ( ~ ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 )
| ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2149,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i] :
( ( ! [SY1674: $i,SY1675: $i,SY1676: $i,SY1677: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1677 @ SY1676 ) @ ( tc_prod @ SY1677 @ SY1676 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1677 @ SY1676 ) @ ( tc_prod @ SY1677 @ SY1676 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1676 @ SY1675 @ SY1674 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1676 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1677 @ SY1676 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1677 @ SY1677 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1677 @ SY1675 @ SV546 ) @ SV413 )
| ~ ( ( SY1675 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1676 @ SY1676 ) @ ( c_Product__Type_OPair @ SY1676 @ SY1676 @ SY1674 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1677 @ SY1677 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1677 @ SY1675 @ SV546 ) @ SV413 )
| ~ ( ( SY1675 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1676 @ SY1676 ) @ ( c_Product__Type_OPair @ SY1676 @ SY1676 @ SY1674 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1677 @ SY1676 ) @ ( tc_prod @ SY1677 @ SY1676 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1677 @ SY1676 ) @ ( tc_prod @ SY1677 @ SY1676 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1676 @ SY1675 @ SY1674 ) @ ( c_Product__Type_OPair @ SY1677 @ SY1676 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1677 @ SY1676 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2150,plain,
! [SV337: $i,SV414: $i,SV486: $i] :
( ( ( ~ ~ ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) )
= $true )
| ( ( ~ ! [SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SY1567 @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ SY1567 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2151,plain,
! [SV338: $i,SV415: $i,SV487: $i,SV547: $i] :
( ( ~ ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) )
| ~ ! [SY1678: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ SY1678 ) @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2152,plain,
! [SV339: $i,SV416: $i,SV488: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ SV339 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2153,plain,
! [SV340: $i,SV417: $i,SV489: $i,SV548: $i] :
( ( ~ ! [SY1679: $i] :
~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SY1679 @ SY1679 ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) )
| ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2154,plain,
! [SV341: $i,SV418: $i,SV490: $i,SV549: $i] :
( ( ~ ( c_Relation_Oantisym @ SV549 @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2155,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ( ~ ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
| ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) )
| ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) )
| ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2156,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ~ ( ~ ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
| ( SV420 = SV343 ) )
| ~ ( ( SV420 != SV343 )
| ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2157,plain,
! [SV344: $i,SV421: $i] :
( ( ( c_Relation_Otrans @ SV421 @ SV344 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV421 @ SV344 )
= SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2158,plain,
! [SV345: $i,SV422: $i,SV493: $i,SV550: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV550 @ SV493 )
| ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 )
| ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2159,plain,
! [SV346: $i,SV423: $i,SV494: $i,SV551: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV551 @ SV494 )
| ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 )
| ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2160,plain,
! [SV347: $i,SV424: $i,SV495: $i] :
( ( ( ~ ! [SY1581: $i] :
( ~ ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ SY1581 @ SV424 ) @ SV347 )
| ( c_member @ SV495 @ SY1581 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) ) ) )
= $true )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2161,plain,
! [SV348: $i,SV425: $i,SV496: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ SV348 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ ( c_Transitive__Closure_Otrancl @ SV496 @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2162,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
| ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ~ ( ~ ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2163,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ( ~ ( c_Wellfounded_Owf @ SV427 @ SV350 )
| ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2164,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ( ~ ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) )
| ( c_Wellfounded_Owf @ SV427 @ SV350 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2165,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
| ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
| ~ ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
| ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2166,plain,
! [SV352: $i,SV429: $i] :
( ( ( ! [SY1408: $i,SY1409: $i] :
( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1408 @ SY1409 ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1409 @ SY1408 ) @ SV352 )
| ( SY1408 = SY1409 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2167,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ~ ! [SY1584: $i,SY1585: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1585 ) @ SV353 )
| ! [SY1586: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1586 ) @ SV353 )
| ( SY1585 = SY1586 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2168,plain,
! [SV354: $i,SV431: $i,SV500: $i,SV554: $i] :
( ( ! [SY1680: $i] :
( ~ ( c_Relation_Orefl__on @ SY1680 @ SV554 @ SV500 )
| ~ ( c_member @ ( tc_prod @ SY1680 @ SY1680 ) @ ( c_Product__Type_OPair @ SY1680 @ SY1680 @ SV431 @ SV354 ) @ SV500 )
| ( c_member @ SY1680 @ SV431 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2169,plain,
! [SV355: $i,SV432: $i,SV501: $i,SV555: $i] :
( ( ( SV555 != SV501 )
| ~ ( c_member @ SV432 @ SV501 @ SV355 )
| ( c_member @ SV432 @ SV555 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2170,plain,
! [SV356: $i,SV433: $i,SV502: $i,SV556: $i] :
( ( ( SV556 != SV502 )
| ~ ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2171,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( ( SV503 != SV434 ) )
| ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2172,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i] :
( ( ! [SY1682: $i] :
~ ( ~ ( ~ ( c_member @ SY1682 @ SV558 @ ( c_Relation_OImage @ SV504 @ SY1682 @ SV435 @ SV358 ) )
| ~ ! [SY1683: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1683 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SY1682 ) @ ( c_Product__Type_OPair @ SV504 @ SY1682 @ SY1683 @ SV558 ) @ SV435 ) ) )
| ~ ( ~ ~ ! [SY1684: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1684 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SY1682 ) @ ( c_Product__Type_OPair @ SV504 @ SY1682 @ SY1684 @ SV558 ) @ SV435 ) )
| ( c_member @ SY1682 @ SV558 @ ( c_Relation_OImage @ SV504 @ SY1682 @ SV435 @ SV358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2173,plain,
! [SV359: $i,SV436: $i,SV505: $i,SV559: $i] :
( ( ~ ( c_member @ SV559 @ SV505 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
| ~ ( c_member @ ( tc_prod @ SV559 @ SV559 ) @ ( c_Product__Type_OPair @ SV559 @ SV559 @ SV359 @ SV505 ) @ SV436 )
| ( c_member @ SV559 @ SV359 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2174,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i] :
( ( ! [SY1685: $i,SY1686: $i,SY1687: $i,SY1688: $i] :
( ~ ( c_member @ ( tc_prod @ SY1688 @ SY1687 ) @ ( c_Product__Type_OPair @ SY1688 @ SY1687 @ SY1686 @ SY1685 ) @ SV560 )
| ~ ( c_member @ ( tc_prod @ SY1687 @ SV506 ) @ ( c_Product__Type_OPair @ SY1687 @ SV506 @ SY1685 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1688 @ SV506 ) @ ( c_Product__Type_OPair @ SY1688 @ SV506 @ SY1686 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1688 @ SY1687 @ SV506 @ SV560 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2175,plain,
! [SV361: $i,SV438: $i,SV507: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV507 @ SV438 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV361 @ SV361 ) @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2176,plain,
! [SV362: $i,SV439: $i,SV508: $i,SV561: $i] :
( ( ! [SY1689: $i] :
( ~ ( c_member @ ( tc_prod @ SY1689 @ SV561 ) @ ( c_Product__Type_OPair @ SY1689 @ SV561 @ SV508 @ SV439 ) @ SV362 )
| ( c_member @ SY1689 @ SV508 @ ( c_Relation_ODomain @ SY1689 @ SV561 @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2177,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ( ~ ( c_Relation_Otrans @ SV440 @ SV363 )
| ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2178,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ( ~ ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) )
| ( c_Relation_Otrans @ SV440 @ SV363 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2179,plain,
! [SV364: $i,SV441: $i,SV509: $i,SV562: $i] :
( ( ! [SY1690: $i] :
( ~ ( c_Relation_Otrans @ SY1690 @ SV562 )
| ~ ( c_member @ ( tc_prod @ SY1690 @ SY1690 ) @ ( c_Product__Type_OPair @ SY1690 @ SY1690 @ SV509 @ SV441 ) @ SV562 )
| ~ ( c_member @ ( tc_prod @ SY1690 @ SY1690 ) @ ( c_Product__Type_OPair @ SY1690 @ SY1690 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SY1690 @ SY1690 ) @ ( c_Product__Type_OPair @ SY1690 @ SY1690 @ SV509 @ SV364 ) @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2180,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ( ~ ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
| ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2181,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ( ~ ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 )
| ( c_Nitpick_Orefl_H @ SV442 @ SV365 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2182,plain,
! [SV366: $i,SV443: $i,SV510: $i,SV563: $i] :
( ( ! [SY1691: $i] :
( ~ ( c_member @ ( tc_prod @ SY1691 @ SY1691 ) @ ( c_Product__Type_OPair @ SY1691 @ SY1691 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SY1691 @ SV443 ) )
| ~ ( c_member @ ( tc_prod @ SY1691 @ SY1691 ) @ ( c_Product__Type_OPair @ SY1691 @ SY1691 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1691 @ SV443 ) )
| ( c_member @ ( tc_prod @ SY1691 @ SY1691 ) @ ( c_Product__Type_OPair @ SY1691 @ SY1691 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SY1691 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2183,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
| ~ ( ( SV511 != SV444 ) )
| ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2184,plain,
! [SV368: $i,SV445: $i] :
( ( ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) )
= $false )
| ( ( ~ ! [SY1458: $i] :
( SV368
!= ( c_Product__Type_OPair @ SV445 @ SV445 @ SY1458 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2185,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ( ~ ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
| ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) )
| ~ ( ~ ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2186,plain,
! [SV370: $i,SV447: $i,SV513: $i,SV565: $i] :
( ( ( SV565 != SV513 )
| ~ ( c_member @ SV447 @ SV565 @ SV370 )
| ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SV565 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2187,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ( ~ ( c_Relation_Oantisym @ SV448 @ SV371 )
| ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2188,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ( ~ ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) )
| ( c_Relation_Oantisym @ SV448 @ SV371 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2189,plain,
! [SV372: $i,SV449: $i,SV514: $i,SV566: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV566 @ SV514 @ SV449 )
| ~ ( c_member @ SV566 @ SV372 @ SV514 )
| ( c_member @ ( tc_prod @ SV566 @ SV566 ) @ ( c_Product__Type_OPair @ SV566 @ SV566 @ SV372 @ SV372 ) @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2190,plain,
! [SV373: $i,SV450: $i,SV515: $i,SV567: $i] :
( ( ! [SY1693: $i,SY1694: $i] :
( ( ( c_Product__Type_OPair @ SY1694 @ SY1693 @ SV567 @ SV515 )
!= ( c_Product__Type_OPair @ SY1694 @ SY1693 @ SV450 @ SV373 ) )
| ~ ( ( SV567 != SV450 )
| ( SV515 != SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2191,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
| ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
| ~ ( ~ ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 )
| ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2192,plain,
! [SV375: $i,SV452: $i,SV517: $i,SV569: $i] :
( ( ! [SY1697: $i,SY1698: $i] :
( ~ ( c_member @ SY1698 @ SY1697 @ SV569 )
| ~ ( c_member @ ( tc_prod @ SY1698 @ SV517 ) @ ( c_Product__Type_OPair @ SY1698 @ SV517 @ SY1697 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SY1698 @ SV517 @ SV375 @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2193,plain,
! [SV376: $i,SV453: $i,SV518: $i,SV570: $i] :
( ( ! [SY1699: $i] :
( ~ ( c_member @ ( tc_prod @ SY1699 @ SV570 ) @ ( c_Product__Type_OPair @ SY1699 @ SV570 @ SV518 @ SV453 ) @ SV376 )
| ( c_member @ SV570 @ SV453 @ ( c_Relation_ORange @ SY1699 @ SV570 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2194,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ~ ( ~ ~ ( c_member @ SV571 @ SV519 @ SV454 )
| ( SV519 = SV377 ) )
| ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2195,plain,
! [SV378: $i,SV455: $i,SV520: $i,SV572: $i] :
( ( ! [SY1700: $i] :
( ~ ( c_member @ ( tc_prod @ SY1700 @ SY1700 ) @ ( c_Product__Type_OPair @ SY1700 @ SY1700 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SY1700 @ SV455 ) )
| ~ ( c_member @ ( tc_prod @ SY1700 @ SY1700 ) @ ( c_Product__Type_OPair @ SY1700 @ SY1700 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1700 @ SV455 ) )
| ( c_member @ ( tc_prod @ SY1700 @ SY1700 ) @ ( c_Product__Type_OPair @ SY1700 @ SY1700 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SY1700 @ SV455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2196,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
| ( SV456 = SV379 ) )
| ~ ( ( SV456 != SV379 )
| ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2197,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ( ~ ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
| ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
| ~ ( ~ ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
| ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2198,plain,
! [SV381: $i,SV458: $i,SV523: $i,SV573: $i] :
( ( ! [SY1701: $i] :
( ~ ( c_member @ ( tc_prod @ SY1701 @ SY1701 ) @ ( c_Product__Type_OPair @ SY1701 @ SY1701 @ SV573 @ SV523 ) @ SV458 )
| ~ ( c_member @ ( tc_prod @ SY1701 @ SY1701 ) @ ( c_Product__Type_OPair @ SY1701 @ SY1701 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1701 @ SV458 ) )
| ( c_member @ ( tc_prod @ SY1701 @ SY1701 ) @ ( c_Product__Type_OPair @ SY1701 @ SY1701 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SY1701 @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2199,plain,
! [SV382: $i,SV459: $i,SV524: $i,SV574: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ SV382 )
| ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ ( c_Transitive__Closure_Otrancl @ SV574 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2200,plain,
! [SV383: $i,SV460: $i,SV525: $i,SV575: $i] :
( ( ! [SY1702: $i,SY1703: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1703 @ SY1702 @ SV575 )
| ~ ( c_member @ ( tc_prod @ SY1703 @ SY1702 ) @ ( c_Product__Type_OPair @ SY1703 @ SY1702 @ SV525 @ SV460 ) @ SV575 )
| ~ ( c_member @ ( tc_prod @ SY1703 @ SY1702 ) @ ( c_Product__Type_OPair @ SY1703 @ SY1702 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2201,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
| ~ ! [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_not_pos,[status(thm)],[2124]) ).
thf(2202,plain,
( ( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $true )
| ( ( ~ ! [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_or_pos,[status(thm)],[2125]) ).
thf(2203,plain,
! [SV384: $i,SV461: $i,SV526: $i,SV576: $i] :
( ( ~ ( c_member @ SV576 @ SV526 @ SV461 )
| ( c_member @ SV576 @ SV526 @ ( c_Set_Oinsert @ SV576 @ SV384 @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2204,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV462 )
| ~ ~ ( c_member @ SV577 @ SV527 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2205,plain,
! [SV386: $i,SV463: $i,SV528: $i,SV578: $i] :
( ( ! [SY1704: $i] :
( ~ ( c_member @ ( tc_prod @ SY1704 @ SY1704 ) @ ( c_Product__Type_OPair @ SY1704 @ SY1704 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SY1704 @ SV463 ) )
| ~ ( c_member @ ( tc_prod @ SY1704 @ SY1704 ) @ ( c_Product__Type_OPair @ SY1704 @ SY1704 @ SV528 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SY1704 @ SY1704 ) @ ( c_Product__Type_OPair @ SY1704 @ SY1704 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SY1704 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2206,plain,
! [SV387: $i,SV464: $i,SV529: $i,SV579: $i] :
( ( ! [SY1705: $i] :
( ~ ( c_member @ ( tc_prod @ SY1705 @ SY1705 ) @ ( c_Product__Type_OPair @ SY1705 @ SY1705 @ SV579 @ SV529 ) @ SV464 )
| ~ ( c_member @ ( tc_prod @ SY1705 @ SY1705 ) @ ( c_Product__Type_OPair @ SY1705 @ SY1705 @ SV529 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SY1705 @ SY1705 ) @ ( c_Product__Type_OPair @ SY1705 @ SY1705 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SY1705 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2207,plain,
! [SV388: $i,SV465: $i,SV530: $i,SV580: $i] :
( ( ( SV580 != SV530 )
| ~ ( ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
| ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2208,plain,
! [SV389: $i,SV466: $i,SV531: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV531 @ SV466 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV531 @ SV531 ) @ ( c_Product__Type_OPair @ SV531 @ SV531 @ SV389 @ SV389 ) @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2209,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1707 @ SY1706 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SY1707 @ SY1706 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
| ~ ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SY1707 @ SY1706 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SY1707 @ SY1706 @ SV467 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2210,plain,
! [SV391: $i,SV468: $i,SV533: $i,SV582: $i] :
( ( ( SV582 != SV533 )
| ~ ( ~ ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2211,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
| ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2212,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
| ~ ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
| ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2213,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) ) )
= $true )
| ( ( ~ ! [SY1654: $i] :
( ~ ( c_member @ SV536 @ SY1654 @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ SY1654 @ SY1654 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2214,plain,
! [SV395: $i,SV472: $i,SV537: $i,SV585: $i] :
( ( ~ ( c_Relation_Otrans @ SV585 @ SV537 )
| ~ ( c_Relation_Otrans @ SV472 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SV585 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SV585 @ SV472 @ SV537 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2215,plain,
! [SV396: $i,SV473: $i,SV538: $i,SV586: $i] :
( ( ! [SY1710: $i] :
( ~ ( c_member @ ( tc_prod @ SY1710 @ SY1710 ) @ ( c_Product__Type_OPair @ SY1710 @ SY1710 @ SV586 @ SV538 ) @ SV473 )
| ~ ( c_member @ ( tc_prod @ SY1710 @ SY1710 ) @ ( c_Product__Type_OPair @ SY1710 @ SY1710 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1710 @ SV473 ) )
| ( c_member @ ( tc_prod @ SY1710 @ SY1710 ) @ ( c_Product__Type_OPair @ SY1710 @ SY1710 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SY1710 @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2216,plain,
! [SV397: $i,SV474: $i,SV539: $i,SV587: $i] :
( ( ! [SY1711: $i] :
( ~ ( c_member @ SY1711 @ SV587 @ ( c_Relation_OImage @ SV539 @ SY1711 @ SV474 @ SV397 ) )
| ~ ! [SY1712: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SY1711 ) @ ( c_Product__Type_OPair @ SV539 @ SY1711 @ SY1712 @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1712 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2217,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ( ~ ( c_Relation_Oirrefl @ SV475 @ SV398 )
| ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2218,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ( ~ ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 )
| ( c_Relation_Oirrefl @ SV475 @ SV398 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2219,plain,
! [SV399: $i,SV476: $i,SV540: $i,SV588: $i] :
( ( ~ ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) )
| ~ ! [SY1713: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ SY1713 @ SV540 ) @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2220,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SY1714 @ SV589 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1716 @ SY1715 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SY1714 @ SV589 )
!= ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SV541 @ SV477 ) ) )
| ~ ! [SY1717: $i,SY1718: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SY1714 @ SV589 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SY1717 @ SY1718 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1716 @ SY1715 ) @ ( tc_prod @ SY1716 @ SY1715 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SY1717 @ SY1718 ) @ ( c_Product__Type_OPair @ SY1716 @ SY1715 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1716 @ SY1715 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2221,plain,
! [SV401: $i,SV478: $i,SV542: $i,SV590: $i] :
( ( ! [SY1719: $i] :
( ~ ( c_Relation_Orefl__on @ SY1719 @ SV590 @ SV542 )
| ~ ( c_member @ ( tc_prod @ SY1719 @ SY1719 ) @ ( c_Product__Type_OPair @ SY1719 @ SY1719 @ SV478 @ SV401 ) @ SV542 )
| ( c_member @ SY1719 @ SV401 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2222,plain,
! [SV331: $i,SV408: $i,SV481: $i] :
( ( ( c_member @ SV481 @ SV408 @ SV331 )
= $false )
| ( ( ( c_Set_Oinsert @ SV481 @ SV408 @ SV331 )
= SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2223,plain,
! [SV332: $i,SV409: $i] :
( ( ( ! [SY1720: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ SY1720 ) @ SV332 )
| ! [SY1721: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ SY1720 @ SY1721 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ SY1721 ) @ SV332 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2145]) ).
thf(2224,plain,
! [SV333: $i,SV410: $i,SV482: $i,SV543: $i] :
( ( ( ~ ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) ) )
= $true )
| ( ( ~ ( ( SV482 != SV410 ) )
| ( c_member @ SV543 @ SV482 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2225,plain,
! [SV334: $i,SV411: $i,SV483: $i,SV544: $i,SV591: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
| ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV483 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2226,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ~ ( ~ ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
| ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
| ~ ( ~ ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 )
| ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2227,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1724 @ SY1723 ) @ ( tc_prod @ SY1724 @ SY1723 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1724 @ SY1723 ) @ ( tc_prod @ SY1724 @ SY1723 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1723 @ SY1722 @ SV592 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1723 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1724 @ SY1723 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1724 @ SY1724 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1724 @ SY1722 @ SV546 ) @ SV413 )
| ~ ( ( SY1722 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1723 @ SY1723 ) @ ( c_Product__Type_OPair @ SY1723 @ SY1723 @ SV592 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1724 @ SY1724 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1724 @ SY1722 @ SV546 ) @ SV413 )
| ~ ( ( SY1722 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1723 @ SY1723 ) @ ( c_Product__Type_OPair @ SY1723 @ SY1723 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1724 @ SY1723 ) @ ( tc_prod @ SY1724 @ SY1723 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1724 @ SY1723 ) @ ( tc_prod @ SY1724 @ SY1723 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1723 @ SY1722 @ SV592 ) @ ( c_Product__Type_OPair @ SY1724 @ SY1723 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1724 @ SY1723 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2228,plain,
! [SV337: $i,SV414: $i,SV486: $i] :
( ( ( ~ ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) )
= $false )
| ( ( ~ ! [SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SY1567 @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ SY1567 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2229,plain,
! [SV338: $i,SV415: $i,SV487: $i,SV547: $i] :
( ( ( ~ ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) ) )
= $true )
| ( ( ~ ! [SY1678: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ SY1678 ) @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2230,plain,
! [SV339: $i,SV416: $i,SV488: $i] :
( ( ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ SV339 )
= $false )
| ( ( c_member @ ( tc_prod @ SV488 @ SV488 ) @ SV416 @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2231,plain,
! [SV340: $i,SV417: $i,SV489: $i,SV548: $i] :
( ( ( ~ ! [SY1679: $i] :
~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SY1679 @ SY1679 ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2232,plain,
! [SV341: $i,SV418: $i,SV490: $i,SV549: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV549 @ SV490 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2233,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ( ~ ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
| ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2234,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) )
| ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2235,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ~ ( ~ ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
| ( SV420 = SV343 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2156]) ).
thf(2236,plain,
! [SV492: $i,SV343: $i,SV420: $i] :
( ( ~ ( ( SV420 != SV343 )
| ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2156]) ).
thf(2237,plain,
! [SV345: $i,SV422: $i,SV493: $i,SV550: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV550 @ SV493 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 )
| ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2238,plain,
! [SV346: $i,SV423: $i,SV494: $i,SV551: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV551 @ SV494 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 )
| ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2239,plain,
! [SV347: $i,SV424: $i,SV495: $i] :
( ( ( ! [SY1581: $i] :
( ~ ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ SY1581 @ SV424 ) @ SV347 )
| ( c_member @ SV495 @ SY1581 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) ) ) )
= $false )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2240,plain,
! [SV348: $i,SV425: $i,SV496: $i] :
( ( ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ SV348 )
= $false )
| ( ( c_member @ ( tc_prod @ SV496 @ SV496 ) @ SV425 @ ( c_Transitive__Closure_Otrancl @ SV496 @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2241,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ~ ( ~ ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
| ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ~ ( ~ ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2242,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ( c_Wellfounded_Owf @ SV427 @ SV350 )
| ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2243,plain,
! [SV350: $i,SV427: $i] :
( ( ~ ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) )
| ( c_Wellfounded_Owf @ SV427 @ SV350 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2244,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
| ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
| ~ ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
| ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2245,plain,
! [SV352: $i,SV429: $i] :
( ( ( ! [SY1725: $i] :
( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK47_SY1408 @ SV352 @ SV429 ) @ SY1725 ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ SY1725 @ ( sK47_SY1408 @ SV352 @ SV429 ) ) @ SV352 )
| ( ( sK47_SY1408 @ SV352 @ SV429 )
= SY1725 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2166]) ).
thf(2246,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ! [SY1584: $i,SY1585: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1585 ) @ SV353 )
| ! [SY1586: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ SY1584 @ SY1586 ) @ SV353 )
| ( SY1585 = SY1586 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2247,plain,
! [SV354: $i,SV431: $i,SV500: $i,SV554: $i,SV593: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV593 @ SV554 @ SV500 )
| ~ ( c_member @ ( tc_prod @ SV593 @ SV593 ) @ ( c_Product__Type_OPair @ SV593 @ SV593 @ SV431 @ SV354 ) @ SV500 )
| ( c_member @ SV593 @ SV431 @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2248,plain,
! [SV355: $i,SV432: $i,SV501: $i,SV555: $i] :
( ( ( SV555 != SV501 )
= $true )
| ( ( ~ ( c_member @ SV432 @ SV501 @ SV355 )
| ( c_member @ SV432 @ SV555 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2249,plain,
! [SV356: $i,SV433: $i,SV502: $i,SV556: $i] :
( ( ( SV556 != SV502 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2250,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) ) )
= $true )
| ( ( ~ ( ( SV503 != SV434 ) )
| ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2251,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ~ ( ~ ( ~ ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
| ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
| ~ ( ~ ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) )
| ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2252,plain,
! [SV359: $i,SV436: $i,SV505: $i,SV559: $i] :
( ( ( ~ ( c_member @ SV559 @ SV505 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV559 @ SV559 ) @ ( c_Product__Type_OPair @ SV559 @ SV559 @ SV359 @ SV505 ) @ SV436 )
| ( c_member @ SV559 @ SV359 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2253,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i] :
( ( ! [SY1728: $i,SY1729: $i,SY1730: $i] :
( ~ ( c_member @ ( tc_prod @ SY1730 @ SY1729 ) @ ( c_Product__Type_OPair @ SY1730 @ SY1729 @ SY1728 @ SV595 ) @ SV560 )
| ~ ( c_member @ ( tc_prod @ SY1729 @ SV506 ) @ ( c_Product__Type_OPair @ SY1729 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1730 @ SV506 ) @ ( c_Product__Type_OPair @ SY1730 @ SV506 @ SY1728 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1730 @ SY1729 @ SV506 @ SV560 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2254,plain,
! [SV361: $i,SV438: $i,SV507: $i] :
( ( ( c_Wellfounded_Owf @ SV507 @ SV438 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV361 @ SV361 ) @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2255,plain,
! [SV362: $i,SV439: $i,SV508: $i,SV561: $i,SV596: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV596 @ SV561 ) @ ( c_Product__Type_OPair @ SV596 @ SV561 @ SV508 @ SV439 ) @ SV362 )
| ( c_member @ SV596 @ SV508 @ ( c_Relation_ODomain @ SV596 @ SV561 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2256,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ( c_Relation_Otrans @ SV440 @ SV363 )
| ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2257,plain,
! [SV363: $i,SV440: $i] :
( ( ~ ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) )
| ( c_Relation_Otrans @ SV440 @ SV363 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2178]) ).
thf(2258,plain,
! [SV364: $i,SV441: $i,SV509: $i,SV562: $i,SV597: $i] :
( ( ~ ( c_Relation_Otrans @ SV597 @ SV562 )
| ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
| ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2259,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
| ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2260,plain,
! [SV365: $i,SV442: $i] :
( ( ~ ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 )
| ( c_Nitpick_Orefl_H @ SV442 @ SV365 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2181]) ).
thf(2261,plain,
! [SV366: $i,SV443: $i,SV510: $i,SV563: $i,SV598: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
| ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
| ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2262,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) )
= $true )
| ( ( ~ ( ( SV511 != SV444 ) )
| ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2263,plain,
! [SV445: $i,SV368: $i] :
( ( ( ! [SY1458: $i] :
( SV368
!= ( c_Product__Type_OPair @ SV445 @ SV445 @ SY1458 @ SY1458 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2264,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ( ~ ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
| ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2265,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ( ~ ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2266,plain,
! [SV370: $i,SV447: $i,SV513: $i,SV565: $i] :
( ( ( SV565 != SV513 )
= $true )
| ( ( ~ ( c_member @ SV447 @ SV565 @ SV370 )
| ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SV565 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2267,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ( c_Relation_Oantisym @ SV448 @ SV371 )
| ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2268,plain,
! [SV371: $i,SV448: $i] :
( ( ~ ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) )
| ( c_Relation_Oantisym @ SV448 @ SV371 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2269,plain,
! [SV372: $i,SV449: $i,SV514: $i,SV566: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV566 @ SV514 @ SV449 ) )
= $true )
| ( ( ~ ( c_member @ SV566 @ SV372 @ SV514 )
| ( c_member @ ( tc_prod @ SV566 @ SV566 ) @ ( c_Product__Type_OPair @ SV566 @ SV566 @ SV372 @ SV372 ) @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2270,plain,
! [SV373: $i,SV450: $i,SV515: $i,SV567: $i,SV599: $i] :
( ( ! [SY1731: $i] :
( ( ( c_Product__Type_OPair @ SY1731 @ SV599 @ SV567 @ SV515 )
!= ( c_Product__Type_OPair @ SY1731 @ SV599 @ SV450 @ SV373 ) )
| ~ ( ( SV567 != SV450 )
| ( SV515 != SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2271,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ~ ( ~ ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
| ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
| ~ ( ~ ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 )
| ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2272,plain,
! [SV375: $i,SV452: $i,SV517: $i,SV569: $i,SV600: $i] :
( ( ! [SY1732: $i] :
( ~ ( c_member @ SY1732 @ SV600 @ SV569 )
| ~ ( c_member @ ( tc_prod @ SY1732 @ SV517 ) @ ( c_Product__Type_OPair @ SY1732 @ SV517 @ SV600 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SY1732 @ SV517 @ SV375 @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2273,plain,
! [SV376: $i,SV453: $i,SV518: $i,SV570: $i,SV601: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV601 @ SV570 ) @ ( c_Product__Type_OPair @ SV601 @ SV570 @ SV518 @ SV453 ) @ SV376 )
| ( c_member @ SV570 @ SV453 @ ( c_Relation_ORange @ SV601 @ SV570 @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2274,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ( ~ ( ~ ~ ( c_member @ SV571 @ SV519 @ SV454 )
| ( SV519 = SV377 ) ) )
= $true )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2275,plain,
! [SV378: $i,SV455: $i,SV520: $i,SV572: $i,SV602: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
| ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
| ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2276,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
| ( SV456 = SV379 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2277,plain,
! [SV521: $i,SV379: $i,SV456: $i] :
( ( ~ ( ( SV456 != SV379 )
| ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2278,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ( ~ ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
| ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2197]) ).
thf(2279,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ( ~ ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
| ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2197]) ).
thf(2280,plain,
! [SV381: $i,SV458: $i,SV523: $i,SV573: $i,SV603: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV523 ) @ SV458 )
| ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
| ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2281,plain,
! [SV382: $i,SV459: $i,SV524: $i,SV574: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ SV382 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ ( c_Transitive__Closure_Otrancl @ SV574 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2282,plain,
! [SV383: $i,SV460: $i,SV525: $i,SV575: $i,SV604: $i] :
( ( ! [SY1733: $i] :
( ~ ( c_Relation_Osingle__valued @ SY1733 @ SV604 @ SV575 )
| ~ ( c_member @ ( tc_prod @ SY1733 @ SV604 ) @ ( c_Product__Type_OPair @ SY1733 @ SV604 @ SV525 @ SV460 ) @ SV575 )
| ~ ( c_member @ ( tc_prod @ SY1733 @ SV604 ) @ ( c_Product__Type_OPair @ SY1733 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2283,plain,
( ( ~ ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2284,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)],[2201]) ).
thf(2285,plain,
( ( ( ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $false )
| ( ( ~ ! [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_pos,[status(thm)],[2202]) ).
thf(2286,plain,
! [SV384: $i,SV461: $i,SV526: $i,SV576: $i] :
( ( ( ~ ( c_member @ SV576 @ SV526 @ SV461 ) )
= $true )
| ( ( c_member @ SV576 @ SV526 @ ( c_Set_Oinsert @ SV576 @ SV384 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2287,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV462 ) )
= $true )
| ( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2288,plain,
! [SV386: $i,SV463: $i,SV528: $i,SV578: $i,SV605: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
| ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV528 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2289,plain,
! [SV387: $i,SV464: $i,SV529: $i,SV579: $i,SV606: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV529 ) @ SV464 )
| ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV529 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SV606 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2290,plain,
! [SV388: $i,SV465: $i,SV530: $i,SV580: $i] :
( ( ( SV580 != SV530 )
= $true )
| ( ( ~ ( ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
| ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2291,plain,
! [SV389: $i,SV466: $i,SV531: $i] :
( ( ( c_Wellfounded_Owf @ SV531 @ SV466 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV531 @ SV531 ) @ ( c_Product__Type_OPair @ SV531 @ SV531 @ SV389 @ SV389 ) @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2292,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i] :
( ( ! [SY1734: $i] :
~ ( ~ ( ( ( c_Product__Type_OPair @ SY1734 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SY1734 @ SV607 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
| ~ ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SY1734 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SY1734 @ SV607 @ SV467 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2293,plain,
! [SV391: $i,SV468: $i,SV533: $i,SV582: $i] :
( ( ( SV582 != SV533 )
= $true )
| ( ( ~ ( ~ ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2294,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) ) )
= $true )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
| ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2295,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) )
= $true )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
| ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2296,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false )
| ( ( ~ ! [SY1654: $i] :
( ~ ( c_member @ SV536 @ SY1654 @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ SY1654 @ SY1654 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2297,plain,
! [SV395: $i,SV472: $i,SV537: $i,SV585: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV585 @ SV537 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV472 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SV585 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SV585 @ SV472 @ SV537 @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2298,plain,
! [SV396: $i,SV473: $i,SV538: $i,SV586: $i,SV608: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV538 ) @ SV473 )
| ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
| ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2299,plain,
! [SV397: $i,SV474: $i,SV539: $i,SV587: $i,SV609: $i] :
( ( ~ ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
| ~ ! [SY1735: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ SY1735 @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1735 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2300,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ( c_Relation_Oirrefl @ SV475 @ SV398 )
| ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2301,plain,
! [SV398: $i,SV475: $i] :
( ( ~ ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 )
| ( c_Relation_Oirrefl @ SV475 @ SV398 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2302,plain,
! [SV399: $i,SV476: $i,SV540: $i,SV588: $i] :
( ( ( ~ ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) ) )
= $true )
| ( ( ~ ! [SY1713: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ SY1713 @ SV540 ) @ SV399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2303,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1737 @ SY1736 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV541 @ SV477 ) ) )
| ~ ! [SY1738: $i,SY1739: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SY1738 @ SY1739 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1737 @ SY1736 ) @ ( tc_prod @ SY1737 @ SY1736 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SY1738 @ SY1739 ) @ ( c_Product__Type_OPair @ SY1737 @ SY1736 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1737 @ SY1736 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2304,plain,
! [SV401: $i,SV478: $i,SV542: $i,SV590: $i,SV611: $i] :
( ( ~ ( c_Relation_Orefl__on @ SV611 @ SV590 @ SV542 )
| ~ ( c_member @ ( tc_prod @ SV611 @ SV611 ) @ ( c_Product__Type_OPair @ SV611 @ SV611 @ SV478 @ SV401 ) @ SV542 )
| ( c_member @ SV611 @ SV401 @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2305,plain,
! [SV332: $i,SV409: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ ( sK48_SY1720 @ SV332 @ SV409 ) ) @ SV332 )
| ! [SY1740: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK48_SY1720 @ SV332 @ SV409 ) @ SY1740 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ SY1740 ) @ SV332 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2223]) ).
thf(2306,plain,
! [SV333: $i,SV410: $i,SV482: $i,SV543: $i] :
( ( ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) )
= $false )
| ( ( ~ ( ( SV482 != SV410 ) )
| ( c_member @ SV543 @ SV482 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2307,plain,
! [SV334: $i,SV411: $i,SV483: $i,SV544: $i,SV591: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV483 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2308,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ~ ( ~ ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
| ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2309,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ~ ( ~ ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 )
| ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2310,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1742 @ SY1741 ) @ ( tc_prod @ SY1742 @ SY1741 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1742 @ SY1741 ) @ ( tc_prod @ SY1742 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1741 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1741 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1742 @ SY1741 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1742 @ SY1742 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1742 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1741 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1741 @ SY1741 @ SV592 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1742 @ SY1742 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1742 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SY1741 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1741 @ SY1741 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1742 @ SY1741 ) @ ( tc_prod @ SY1742 @ SY1741 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1742 @ SY1741 ) @ ( tc_prod @ SY1742 @ SY1741 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1741 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SY1742 @ SY1741 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1742 @ SY1741 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2311,plain,
! [SV337: $i,SV414: $i,SV486: $i] :
( ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true )
| ( ( ~ ! [SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SY1567 @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ SY1567 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2312,plain,
! [SV338: $i,SV415: $i,SV487: $i,SV547: $i] :
( ( ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) )
= $false )
| ( ( ~ ! [SY1678: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ SY1678 ) @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2313,plain,
! [SV340: $i,SV417: $i,SV489: $i,SV548: $i] :
( ( ( ! [SY1679: $i] :
~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SY1679 @ SY1679 ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2314,plain,
! [SV341: $i,SV418: $i,SV490: $i,SV549: $i] :
( ( ( c_Relation_Oantisym @ SV549 @ SV490 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
| ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2315,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
| ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2316,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) )
| ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2317,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ~ ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
| ( SV420 = SV343 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2318,plain,
! [SV492: $i,SV343: $i,SV420: $i] :
( ( ( SV420 != SV343 )
| ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2319,plain,
! [SV345: $i,SV422: $i,SV493: $i,SV550: $i] :
( ( ( c_Wellfounded_Owf @ SV550 @ SV493 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 )
| ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2320,plain,
! [SV346: $i,SV423: $i,SV494: $i,SV551: $i] :
( ( ( c_Wellfounded_Owf @ SV551 @ SV494 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 )
| ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2321,plain,
! [SV424: $i,SV347: $i,SV495: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ ( sK49_SY1581 @ SV347 @ SV424 @ SV495 ) @ SV424 ) @ SV347 )
| ( c_member @ SV495 @ ( sK49_SY1581 @ SV347 @ SV424 @ SV495 ) @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) ) )
= $false )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2239]) ).
thf(2322,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ~ ( ~ ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
| ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2323,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ~ ( ~ ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2324,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV427 @ SV350 ) )
= $true )
| ( ( ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2325,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2326,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
| ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2327,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ~ ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
| ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2328,plain,
! [SV352: $i,SV429: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK47_SY1408 @ SV352 @ SV429 ) @ ( sK50_SY1725 @ SV352 @ SV429 ) ) @ SV352 )
| ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK50_SY1725 @ SV352 @ SV429 ) @ ( sK47_SY1408 @ SV352 @ SV429 ) ) @ SV352 )
| ( ( sK47_SY1408 @ SV352 @ SV429 )
= ( sK50_SY1725 @ SV352 @ SV429 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2245]) ).
thf(2329,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ! [SY1743: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ SY1743 ) @ SV353 )
| ! [SY1744: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ SY1744 ) @ SV353 )
| ( SY1743 = SY1744 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2246]) ).
thf(2330,plain,
! [SV354: $i,SV431: $i,SV500: $i,SV554: $i,SV593: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV593 @ SV554 @ SV500 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV593 @ SV593 ) @ ( c_Product__Type_OPair @ SV593 @ SV593 @ SV431 @ SV354 ) @ SV500 )
| ( c_member @ SV593 @ SV431 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2331,plain,
! [SV355: $i,SV432: $i,SV501: $i,SV555: $i] :
( ( ( SV555 = SV501 )
= $false )
| ( ( ~ ( c_member @ SV432 @ SV501 @ SV355 )
| ( c_member @ SV432 @ SV555 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2332,plain,
! [SV356: $i,SV433: $i,SV502: $i,SV556: $i] :
( ( ( SV556 = SV502 )
= $false )
| ( ( ~ ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2333,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false )
| ( ( ~ ( ( SV503 != SV434 ) )
| ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2334,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ~ ( ~ ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
| ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
| ~ ( ~ ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) )
| ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2335,plain,
! [SV359: $i,SV436: $i,SV505: $i,SV559: $i] :
( ( ( c_member @ SV559 @ SV505 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV559 @ SV559 ) @ ( c_Product__Type_OPair @ SV559 @ SV559 @ SV359 @ SV505 ) @ SV436 )
| ( c_member @ SV559 @ SV359 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2336,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i,SV613: $i] :
( ( ! [SY1745: $i,SY1746: $i] :
( ~ ( c_member @ ( tc_prod @ SY1746 @ SY1745 ) @ ( c_Product__Type_OPair @ SY1746 @ SY1745 @ SV613 @ SV595 ) @ SV560 )
| ~ ( c_member @ ( tc_prod @ SY1745 @ SV506 ) @ ( c_Product__Type_OPair @ SY1745 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1746 @ SV506 ) @ ( c_Product__Type_OPair @ SY1746 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1746 @ SY1745 @ SV506 @ SV560 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2337,plain,
! [SV438: $i,SV361: $i,SV507: $i] :
( ( ( c_member @ ( tc_prod @ SV507 @ SV507 ) @ ( c_Product__Type_OPair @ SV507 @ SV507 @ SV361 @ SV361 ) @ SV438 )
= $false )
| ( ( c_Wellfounded_Owf @ SV507 @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2338,plain,
! [SV362: $i,SV439: $i,SV508: $i,SV561: $i,SV596: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV596 @ SV561 ) @ ( c_Product__Type_OPair @ SV596 @ SV561 @ SV508 @ SV439 ) @ SV362 ) )
= $true )
| ( ( c_member @ SV596 @ SV508 @ ( c_Relation_ODomain @ SV596 @ SV561 @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2339,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV440 @ SV363 ) )
= $true )
| ( ( ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2340,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2341,plain,
! [SV364: $i,SV441: $i,SV509: $i,SV562: $i,SV597: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV597 @ SV562 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
| ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2342,plain,
! [SV365: $i,SV442: $i] :
( ( ( ~ ( c_Nitpick_Orefl_H @ SV442 @ SV365 ) )
= $true )
| ( ( ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2343,plain,
! [SV365: $i,SV442: $i] :
( ( ( ~ ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 ) )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2344,plain,
! [SV366: $i,SV443: $i,SV510: $i,SV563: $i,SV598: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
| ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2345,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false )
| ( ( ~ ( ( SV511 != SV444 ) )
| ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2346,plain,
! [SV445: $i,SV368: $i] :
( ( ( SV368
!= ( c_Product__Type_OPair @ SV445 @ SV445 @ ( sK52_SY1458 @ SV445 @ SV368 ) @ ( sK52_SY1458 @ SV445 @ SV368 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2263]) ).
thf(2347,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
| ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2348,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ~ ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) )
| ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2349,plain,
! [SV370: $i,SV447: $i,SV513: $i,SV565: $i] :
( ( ( SV565 = SV513 )
= $false )
| ( ( ~ ( c_member @ SV447 @ SV565 @ SV370 )
| ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SV565 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2350,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV448 @ SV371 ) )
= $true )
| ( ( ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2351,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2352,plain,
! [SV372: $i,SV449: $i,SV514: $i,SV566: $i] :
( ( ( c_Relation_Orefl__on @ SV566 @ SV514 @ SV449 )
= $false )
| ( ( ~ ( c_member @ SV566 @ SV372 @ SV514 )
| ( c_member @ ( tc_prod @ SV566 @ SV566 ) @ ( c_Product__Type_OPair @ SV566 @ SV566 @ SV372 @ SV372 ) @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2353,plain,
! [SV373: $i,SV450: $i,SV515: $i,SV567: $i,SV599: $i,SV614: $i] :
( ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
!= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
| ~ ( ( SV567 != SV450 )
| ( SV515 != SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2354,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ~ ( ~ ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
| ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2355,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ~ ( ~ ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 )
| ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2356,plain,
! [SV375: $i,SV452: $i,SV517: $i,SV569: $i,SV600: $i,SV615: $i] :
( ( ~ ( c_member @ SV615 @ SV600 @ SV569 )
| ~ ( c_member @ ( tc_prod @ SV615 @ SV517 ) @ ( c_Product__Type_OPair @ SV615 @ SV517 @ SV600 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SV615 @ SV517 @ SV375 @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2357,plain,
! [SV376: $i,SV453: $i,SV518: $i,SV570: $i,SV601: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV601 @ SV570 ) @ ( c_Product__Type_OPair @ SV601 @ SV570 @ SV518 @ SV453 ) @ SV376 ) )
= $true )
| ( ( c_member @ SV570 @ SV453 @ ( c_Relation_ORange @ SV601 @ SV570 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2358,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ( ~ ~ ( c_member @ SV571 @ SV519 @ SV454 )
| ( SV519 = SV377 ) )
= $false )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2359,plain,
! [SV378: $i,SV455: $i,SV520: $i,SV572: $i,SV602: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
| ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2360,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
| ( SV456 = SV379 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2361,plain,
! [SV521: $i,SV379: $i,SV456: $i] :
( ( ( SV456 != SV379 )
| ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2362,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
| ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2363,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ~ ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
| ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2364,plain,
! [SV381: $i,SV458: $i,SV523: $i,SV573: $i,SV603: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV523 ) @ SV458 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
| ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2365,plain,
! [SV382: $i,SV459: $i,SV524: $i,SV574: $i] :
( ( ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ SV382 )
= $false )
| ( ( c_member @ ( tc_prod @ SV574 @ SV574 ) @ ( c_Product__Type_OPair @ SV574 @ SV574 @ SV524 @ SV459 ) @ ( c_Transitive__Closure_Otrancl @ SV574 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2366,plain,
! [SV383: $i,SV460: $i,SV525: $i,SV575: $i,SV604: $i,SV616: $i] :
( ( ~ ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
| ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
| ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2367,plain,
( ( ~ ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2368,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)],[2284]) ).
thf(2369,plain,
( ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
= $true )
| ( ( ~ ! [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)],[2285]) ).
thf(2370,plain,
! [SV384: $i,SV461: $i,SV526: $i,SV576: $i] :
( ( ( c_member @ SV576 @ SV526 @ SV461 )
= $false )
| ( ( c_member @ SV576 @ SV526 @ ( c_Set_Oinsert @ SV576 @ SV384 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2371,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ SV577 @ SV527 @ SV462 ) )
= $false )
| ( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2372,plain,
! [SV386: $i,SV463: $i,SV528: $i,SV578: $i,SV605: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV528 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2373,plain,
! [SV387: $i,SV464: $i,SV529: $i,SV579: $i,SV606: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV529 ) @ SV464 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV529 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SV606 @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2374,plain,
! [SV388: $i,SV465: $i,SV530: $i,SV580: $i] :
( ( ( SV580 = SV530 )
= $false )
| ( ( ~ ( ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
| ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2375,plain,
! [SV466: $i,SV389: $i,SV531: $i] :
( ( ( c_member @ ( tc_prod @ SV531 @ SV531 ) @ ( c_Product__Type_OPair @ SV531 @ SV531 @ SV389 @ SV389 ) @ SV466 )
= $false )
| ( ( c_Wellfounded_Owf @ SV531 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2376,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ~ ( ~ ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
| ~ ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2377,plain,
! [SV391: $i,SV468: $i,SV533: $i,SV582: $i] :
( ( ( SV582 = SV533 )
= $false )
| ( ( ~ ( ~ ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2378,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
| ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2379,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false )
| ( ( ~ ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
| ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2380,plain,
! [SV471: $i,SV394: $i,SV536: $i] :
( ( ( ! [SY1654: $i] :
( ~ ( c_member @ SV536 @ SY1654 @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ SY1654 @ SY1654 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2381,plain,
! [SV395: $i,SV472: $i,SV537: $i,SV585: $i] :
( ( ( c_Relation_Otrans @ SV585 @ SV537 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV472 @ SV395 )
| ( c_Relation_Otrans @ ( tc_prod @ SV585 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SV585 @ SV472 @ SV537 @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2382,plain,
! [SV396: $i,SV473: $i,SV538: $i,SV586: $i,SV608: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV538 ) @ SV473 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
| ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2383,plain,
! [SV397: $i,SV474: $i,SV539: $i,SV587: $i,SV609: $i] :
( ( ( ~ ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) ) )
= $true )
| ( ( ~ ! [SY1735: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ SY1735 @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1735 @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2384,plain,
! [SV398: $i,SV475: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV475 @ SV398 ) )
= $true )
| ( ( ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2385,plain,
! [SV398: $i,SV475: $i] :
( ( ( ~ ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2386,plain,
! [SV399: $i,SV476: $i,SV540: $i,SV588: $i] :
( ( ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ SY1713 @ SV540 ) @ SV399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2387,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i] :
( ( ! [SY1747: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1747 @ SV618 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV541 @ SV477 ) ) )
| ~ ! [SY1748: $i,SY1749: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SY1748 @ SY1749 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1747 @ SV618 ) @ ( tc_prod @ SY1747 @ SV618 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SY1748 @ SY1749 ) @ ( c_Product__Type_OPair @ SY1747 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SY1747 @ SV618 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2388,plain,
! [SV401: $i,SV478: $i,SV542: $i,SV590: $i,SV611: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV611 @ SV590 @ SV542 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV611 @ SV611 ) @ ( c_Product__Type_OPair @ SV611 @ SV611 @ SV478 @ SV401 ) @ SV542 )
| ( c_member @ SV611 @ SV401 @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2389,plain,
! [SV332: $i,SV409: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ ( sK48_SY1720 @ SV332 @ SV409 ) ) @ SV332 ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2390,plain,
! [SV332: $i,SV409: $i] :
( ( ( ! [SY1740: $i] :
( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK48_SY1720 @ SV332 @ SV409 ) @ SY1740 ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ SY1740 ) @ SV332 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2391,plain,
! [SV333: $i,SV543: $i,SV410: $i,SV482: $i] :
( ( ( ~ ( ( SV482 != SV410 ) ) )
= $true )
| ( ( c_member @ SV543 @ SV482 @ SV333 )
= $true )
| ( ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2392,plain,
! [SV334: $i,SV411: $i,SV483: $i,SV544: $i,SV591: $i] :
( ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV483 @ SV334 ) @ SV411 )
| ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2393,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ~ ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
| ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2394,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ~ ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 )
| ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2395,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i] :
( ( ! [SY1750: $i] :
~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SY1750 @ SV619 ) @ ( tc_prod @ SY1750 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1750 @ SV619 ) @ ( tc_prod @ SY1750 @ SV619 ) @ ( c_Product__Type_OPair @ SY1750 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SY1750 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1750 @ SV619 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SY1750 @ SY1750 ) @ ( c_Product__Type_OPair @ SY1750 @ SY1750 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SY1750 @ SY1750 ) @ ( c_Product__Type_OPair @ SY1750 @ SY1750 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SY1750 @ SV619 ) @ ( tc_prod @ SY1750 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SY1750 @ SV619 ) @ ( tc_prod @ SY1750 @ SV619 ) @ ( c_Product__Type_OPair @ SY1750 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SY1750 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SY1750 @ SV619 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2396,plain,
! [SV337: $i,SV414: $i,SV486: $i] :
( ( ( ! [SY1567: $i] :
( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ SY1567 @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ SY1567 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) ) )
= $false )
| ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2397,plain,
! [SV338: $i,SV487: $i,SV415: $i,SV547: $i] :
( ( ( ! [SY1678: $i] :
~ ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ SY1678 ) @ SV338 ) )
= $false )
| ( ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2398,plain,
! [SV489: $i,SV417: $i,SV340: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2313]) ).
thf(2399,plain,
! [SV490: $i,SV341: $i,SV418: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV549 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2400,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 ) )
= $true )
| ( ( ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2401,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2402,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ( ~ ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) ) )
= $true )
| ( ( SV420 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2403,plain,
! [SV492: $i,SV343: $i,SV420: $i] :
( ( ( SV420 != SV343 )
= $true )
| ( ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2404,plain,
! [SV493: $i,SV345: $i,SV422: $i,SV550: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV550 @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2405,plain,
! [SV494: $i,SV346: $i,SV423: $i,SV551: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV551 @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2406,plain,
! [SV424: $i,SV347: $i,SV495: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ ( sK49_SY1581 @ SV347 @ SV424 @ SV495 ) @ SV424 ) @ SV347 ) )
= $false )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2407,plain,
! [SV424: $i,SV347: $i,SV495: $i] :
( ( ( c_member @ SV495 @ ( sK49_SY1581 @ SV347 @ SV424 @ SV495 ) @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $false )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2408,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ~ ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
| ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2409,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ~ ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
| ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2410,plain,
! [SV350: $i,SV427: $i] :
( ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false )
| ( ( ! [SY1398: $i] :
( ~ ~ ! [SY1399: $i] :
~ ( c_member @ SV427 @ SY1399 @ SY1398 )
| ~ ! [SY1400: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1400 @ SY1398 )
| ~ ! [SY1401: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1401 @ SY1400 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1401 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2411,plain,
! [SV350: $i,SV427: $i] :
( ( ( ! [SY1402: $i] :
( ~ ~ ! [SY1403: $i] :
~ ( c_member @ SV427 @ SY1403 @ SY1402 )
| ~ ! [SY1404: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1404 @ SY1402 )
| ~ ! [SY1405: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1405 @ SY1404 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1405 @ SY1402 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2412,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
| ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2413,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
| ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2414,plain,
! [SV352: $i,SV429: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK47_SY1408 @ SV352 @ SV429 ) @ ( sK50_SY1725 @ SV352 @ SV429 ) ) @ SV352 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2415,plain,
! [SV352: $i,SV429: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK50_SY1725 @ SV352 @ SV429 ) @ ( sK47_SY1408 @ SV352 @ SV429 ) ) @ SV352 )
| ( ( sK47_SY1408 @ SV352 @ SV429 )
= ( sK50_SY1725 @ SV352 @ SV429 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2328]) ).
thf(2416,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK54_SY1743 @ SV353 @ SV430 @ SV499 ) ) @ SV353 )
| ! [SY1751: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ SY1751 ) @ SV353 )
| ( ( sK54_SY1743 @ SV353 @ SV430 @ SV499 )
= SY1751 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2329]) ).
thf(2417,plain,
! [SV354: $i,SV431: $i,SV500: $i,SV554: $i,SV593: $i] :
( ( ( c_Relation_Orefl__on @ SV593 @ SV554 @ SV500 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV593 @ SV593 ) @ ( c_Product__Type_OPair @ SV593 @ SV593 @ SV431 @ SV354 ) @ SV500 )
| ( c_member @ SV593 @ SV431 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2418,plain,
! [SV555: $i,SV355: $i,SV501: $i,SV432: $i] :
( ( ( ~ ( c_member @ SV432 @ SV501 @ SV355 ) )
= $true )
| ( ( c_member @ SV432 @ SV555 @ SV355 )
= $true )
| ( ( SV555 = SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2419,plain,
! [SV502: $i,SV556: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
| ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) ) )
= $false )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2420,plain,
! [SV357: $i,SV557: $i,SV434: $i,SV503: $i] :
( ( ( ~ ( ( SV503 != SV434 ) ) )
= $true )
| ( ( ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2421,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ~ ( ~ ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
| ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2334]) ).
thf(2422,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ~ ( ~ ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) )
| ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2334]) ).
thf(2423,plain,
! [SV436: $i,SV505: $i,SV359: $i,SV559: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV559 @ SV559 ) @ ( c_Product__Type_OPair @ SV559 @ SV559 @ SV359 @ SV505 ) @ SV436 ) )
= $true )
| ( ( c_member @ SV559 @ SV359 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
= $true )
| ( ( c_member @ SV559 @ SV505 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2424,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i,SV613: $i,SV620: $i] :
( ( ! [SY1752: $i] :
( ~ ( c_member @ ( tc_prod @ SY1752 @ SV620 ) @ ( c_Product__Type_OPair @ SY1752 @ SV620 @ SV613 @ SV595 ) @ SV560 )
| ~ ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SY1752 @ SV506 ) @ ( c_Product__Type_OPair @ SY1752 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SY1752 @ SV620 @ SV506 @ SV560 @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2425,plain,
! [SV362: $i,SV439: $i,SV508: $i,SV561: $i,SV596: $i] :
( ( ( c_member @ ( tc_prod @ SV596 @ SV561 ) @ ( c_Product__Type_OPair @ SV596 @ SV561 @ SV508 @ SV439 ) @ SV362 )
= $false )
| ( ( c_member @ SV596 @ SV508 @ ( c_Relation_ODomain @ SV596 @ SV561 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2426,plain,
! [SV363: $i,SV440: $i] :
( ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false )
| ( ( ! [SY1441: $i,SY1442: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1442 ) @ SV363 )
| ! [SY1443: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1442 @ SY1443 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1441 @ SY1443 ) @ SV363 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2427,plain,
! [SV363: $i,SV440: $i] :
( ( ( ! [SY1444: $i,SY1445: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1445 ) @ SV363 )
| ! [SY1446: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1445 @ SY1446 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1444 @ SY1446 ) @ SV363 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2428,plain,
! [SV364: $i,SV441: $i,SV509: $i,SV562: $i,SV597: $i] :
( ( ( c_Relation_Otrans @ SV597 @ SV562 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
| ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2429,plain,
! [SV365: $i,SV442: $i] :
( ( ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
= $false )
| ( ( ! [SY1450: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1450 @ SY1450 ) @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2430,plain,
! [SV365: $i,SV442: $i] :
( ( ( ! [SY1451: $i] : ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SY1451 @ SY1451 ) @ SV365 ) )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2431,plain,
! [SV366: $i,SV443: $i,SV510: $i,SV563: $i,SV598: $i] :
( ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
| ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2432,plain,
! [SV367: $i,SV564: $i,SV444: $i,SV511: $i] :
( ( ( ~ ( ( SV511 != SV444 ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2433,plain,
! [SV445: $i,SV368: $i] :
( ( ( SV368
= ( c_Product__Type_OPair @ SV445 @ SV445 @ ( sK52_SY1458 @ SV445 @ SV368 ) @ ( sK52_SY1458 @ SV445 @ SV368 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV445 @ SV445 ) @ SV368 @ ( c_Relation_OId @ SV445 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2434,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ( ~ ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 ) )
= $true )
| ( ( ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2435,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ( ~ ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2436,plain,
! [SV513: $i,SV370: $i,SV565: $i,SV447: $i] :
( ( ( ~ ( c_member @ SV447 @ SV565 @ SV370 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SV565 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) )
= $true )
| ( ( SV565 = SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2437,plain,
! [SV371: $i,SV448: $i] :
( ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false )
| ( ( ! [SY1466: $i,SY1467: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1466 @ SY1467 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1467 @ SY1466 ) @ SV371 )
| ( SY1466 = SY1467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2438,plain,
! [SV371: $i,SV448: $i] :
( ( ( ! [SY1468: $i,SY1469: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1468 @ SY1469 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1469 @ SY1468 ) @ SV371 )
| ( SY1468 = SY1469 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2439,plain,
! [SV449: $i,SV514: $i,SV372: $i,SV566: $i] :
( ( ( ~ ( c_member @ SV566 @ SV372 @ SV514 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV566 @ SV566 ) @ ( c_Product__Type_OPair @ SV566 @ SV566 @ SV372 @ SV372 ) @ SV449 )
= $true )
| ( ( c_Relation_Orefl__on @ SV566 @ SV514 @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2440,plain,
! [SV373: $i,SV450: $i,SV515: $i,SV567: $i,SV599: $i,SV614: $i] :
( ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
!= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $true )
| ( ( ~ ( ( SV567 != SV450 )
| ( SV515 != SV373 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2441,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ~ ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
| ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2442,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ~ ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 )
| ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2443,plain,
! [SV375: $i,SV452: $i,SV517: $i,SV569: $i,SV600: $i,SV615: $i] :
( ( ( ~ ( c_member @ SV615 @ SV600 @ SV569 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV615 @ SV517 ) @ ( c_Product__Type_OPair @ SV615 @ SV517 @ SV600 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SV615 @ SV517 @ SV375 @ SV569 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2444,plain,
! [SV376: $i,SV453: $i,SV518: $i,SV570: $i,SV601: $i] :
( ( ( c_member @ ( tc_prod @ SV601 @ SV570 ) @ ( c_Product__Type_OPair @ SV601 @ SV570 @ SV518 @ SV453 ) @ SV376 )
= $false )
| ( ( c_member @ SV570 @ SV453 @ ( c_Relation_ORange @ SV601 @ SV570 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2445,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ( ~ ~ ( c_member @ SV571 @ SV519 @ SV454 ) )
= $false )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2446,plain,
! [SV454: $i,SV571: $i,SV377: $i,SV519: $i] :
( ( ( SV519 = SV377 )
= $false )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2447,plain,
! [SV378: $i,SV455: $i,SV520: $i,SV572: $i,SV602: $i] :
( ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
| ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2448,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) ) )
= $true )
| ( ( SV456 = SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2449,plain,
! [SV521: $i,SV379: $i,SV456: $i] :
( ( ( SV456 != SV379 )
= $true )
| ( ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2450,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ( ~ ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
= $true )
| ( ( ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2451,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ( ~ ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $true )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2452,plain,
! [SV381: $i,SV458: $i,SV523: $i,SV573: $i,SV603: $i] :
( ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV523 ) @ SV458 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
| ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2453,plain,
! [SV383: $i,SV460: $i,SV525: $i,SV575: $i,SV604: $i,SV616: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
| ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2454,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ 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 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2455,plain,
! [SV621: $i] :
( ( ! [SY1753: $i] :
( ~ ( ( SV621 != SY1753 ) )
| ( 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 @ SV621 @ SY1753 ) @ 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 @ SY1753 @ SV621 ) @ v_L ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2456,plain,
( ( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $true )
| ( ( ~ ! [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 )
| ( ( ~ ! [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_or_pos,[status(thm)],[2369]) ).
thf(2457,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true )
| ( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV385 )
| ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2458,plain,
! [SV386: $i,SV463: $i,SV528: $i,SV578: $i,SV605: $i] :
( ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV528 @ SV386 ) @ SV463 )
| ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2459,plain,
! [SV387: $i,SV464: $i,SV529: $i,SV579: $i,SV606: $i] :
( ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV529 ) @ SV464 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV529 @ SV387 ) @ SV464 )
| ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SV606 @ SV464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2460,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2461,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ~ ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
| ~ ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2462,plain,
! [SV533: $i,SV391: $i,SV582: $i,SV468: $i] :
( ( ( ~ ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
| ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) ) )
= $false )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2463,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 ) )
= $true )
| ( ( ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2464,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( ~ ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 ) )
= $true )
| ( ( ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2465,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ( ~ ( c_member @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ SV394 )
| ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2380]) ).
thf(2466,plain,
! [SV537: $i,SV585: $i,SV395: $i,SV472: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV472 @ SV395 ) )
= $true )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV585 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SV585 @ SV472 @ SV537 @ SV395 ) )
= $true )
| ( ( c_Relation_Otrans @ SV585 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2467,plain,
! [SV396: $i,SV473: $i,SV538: $i,SV586: $i,SV608: $i] :
( ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV538 ) @ SV473 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
| ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2468,plain,
! [SV397: $i,SV474: $i,SV539: $i,SV587: $i,SV609: $i] :
( ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false )
| ( ( ~ ! [SY1735: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ SY1735 @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1735 @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2469,plain,
! [SV398: $i,SV475: $i] :
( ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $false )
| ( ( ! [SY1541: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1541 @ SY1541 ) @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2470,plain,
! [SV398: $i,SV475: $i] :
( ( ( ! [SY1542: $i] :
~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SY1542 @ SY1542 ) @ SV398 ) )
= $false )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2471,plain,
! [SV399: $i,SV540: $i,SV588: $i,SV476: $i] :
( ( ( ! [SY1713: $i] :
~ ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ SY1713 @ SV540 ) @ SV399 ) )
= $false )
| ( ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2472,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
| ~ ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) )
| ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2473,plain,
! [SV401: $i,SV478: $i,SV542: $i,SV590: $i,SV611: $i] :
( ( ( c_Relation_Orefl__on @ SV611 @ SV590 @ SV542 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV611 @ SV611 ) @ ( c_Product__Type_OPair @ SV611 @ SV611 @ SV478 @ SV401 ) @ SV542 )
| ( c_member @ SV611 @ SV401 @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2474,plain,
! [SV332: $i,SV409: $i] :
( ( ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ ( sK48_SY1720 @ SV332 @ SV409 ) ) @ SV332 )
= $true )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2475,plain,
! [SV332: $i,SV409: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK48_SY1720 @ SV332 @ SV409 ) @ ( sK56_SY1740 @ SV332 @ SV409 ) ) @ SV332 )
| ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ ( sK56_SY1740 @ SV332 @ SV409 ) ) @ SV332 ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2390]) ).
thf(2476,plain,
! [SV333: $i,SV543: $i,SV410: $i,SV482: $i] :
( ( ( SV482 != SV410 )
= $false )
| ( ( c_member @ SV543 @ SV482 @ SV333 )
= $true )
| ( ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2477,plain,
! [SV544: $i,SV411: $i,SV334: $i,SV483: $i,SV591: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV483 @ SV334 ) @ SV411 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2478,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ( ~ ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) ) )
= $true )
| ( ( ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2479,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ~ ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 ) )
= $true )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2480,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ~ ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2481,plain,
! [SV414: $i,SV337: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK57_SY1567 @ SV337 @ SV414 @ SV486 ) @ SV414 ) @ SV337 )
| ( c_member @ SV486 @ ( sK57_SY1567 @ SV337 @ SV414 @ SV486 ) @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) ) )
= $false )
| ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2396]) ).
thf(2482,plain,
! [SV338: $i,SV487: $i,SV415: $i,SV547: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ ( sK58_SY1678 @ SV338 @ SV487 @ SV415 @ SV547 ) ) @ SV338 ) )
= $false )
| ( ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2397]) ).
thf(2483,plain,
! [SV489: $i,SV417: $i,SV340: $i,SV548: $i] :
( ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
| ( SV417 != SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2484,plain,
! [SV490: $i,SV341: $i,SV418: $i,SV549: $i] :
( ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
| ( SV418 = SV341 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV549 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2485,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false )
| ( ( ! [SY1573: $i,SY1574: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1574 ) @ SV342 )
| ! [SY1575: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1573 @ SY1575 ) @ SV342 )
| ( SY1574 = SY1575 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2486,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ! [SY1576: $i,SY1577: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1577 ) @ SV342 )
| ! [SY1578: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SY1576 @ SY1578 ) @ SV342 )
| ( SY1577 = SY1578 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2487,plain,
! [SV343: $i,SV420: $i,SV492: $i] :
( ( ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
= $false )
| ( ( SV420 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2488,plain,
! [SV492: $i,SV343: $i,SV420: $i] :
( ( ( SV420 = SV343 )
= $false )
| ( ( c_member @ SV492 @ SV420 @ ( c_fequal @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2489,plain,
! [SV493: $i,SV345: $i,SV422: $i,SV550: $i] :
( ( ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV550 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2490,plain,
! [SV494: $i,SV346: $i,SV423: $i,SV551: $i] :
( ( ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV551 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2491,plain,
! [SV424: $i,SV347: $i,SV495: $i] :
( ( ( c_member @ ( tc_prod @ SV495 @ SV495 ) @ ( c_Product__Type_OPair @ SV495 @ SV495 @ ( sK49_SY1581 @ SV347 @ SV424 @ SV495 ) @ SV424 ) @ SV347 )
= $true )
| ( ( c_member @ SV495 @ SV424 @ ( c_Wellfounded_Oacc @ SV495 @ SV347 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2492,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ( ~ ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) ) )
= $true )
| ( ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2493,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ( ~ ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) ) )
= $true )
| ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2494,plain,
! [SV350: $i,SV624: $i,SV427: $i] :
( ( ( ~ ~ ! [SY1756: $i] :
~ ( c_member @ SV427 @ SY1756 @ SV624 )
| ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2495,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ~ ! [SY1759: $i] :
~ ( c_member @ SV427 @ SY1759 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1760: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1760 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1761: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1761 @ SY1760 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1761 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2411]) ).
thf(2496,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) ) )
= $true )
| ( ( ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2497,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( ~ ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2498,plain,
! [SV352: $i,SV429: $i] :
( ( ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK47_SY1408 @ SV352 @ SV429 ) @ ( sK50_SY1725 @ SV352 @ SV429 ) ) @ SV352 )
= $true )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2499,plain,
! [SV352: $i,SV429: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK50_SY1725 @ SV352 @ SV429 ) @ ( sK47_SY1408 @ SV352 @ SV429 ) ) @ SV352 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2415]) ).
thf(2500,plain,
! [SV429: $i,SV352: $i] :
( ( ( ( sK47_SY1408 @ SV352 @ SV429 )
= ( sK50_SY1725 @ SV352 @ SV429 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2415]) ).
thf(2501,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK54_SY1743 @ SV353 @ SV430 @ SV499 ) ) @ SV353 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2502,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ! [SY1751: $i] :
( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ SY1751 ) @ SV353 )
| ( ( sK54_SY1743 @ SV353 @ SV430 @ SV499 )
= SY1751 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2503,plain,
! [SV554: $i,SV500: $i,SV354: $i,SV431: $i,SV593: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV593 @ SV593 ) @ ( c_Product__Type_OPair @ SV593 @ SV593 @ SV431 @ SV354 ) @ SV500 ) )
= $true )
| ( ( c_member @ SV593 @ SV431 @ SV554 )
= $true )
| ( ( c_Relation_Orefl__on @ SV593 @ SV554 @ SV500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2504,plain,
! [SV555: $i,SV355: $i,SV501: $i,SV432: $i] :
( ( ( c_member @ SV432 @ SV501 @ SV355 )
= $false )
| ( ( c_member @ SV432 @ SV555 @ SV355 )
= $true )
| ( ( SV555 = SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2505,plain,
! [SV502: $i,SV556: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) ) )
= $false )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2506,plain,
! [SV556: $i,SV502: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) ) )
= $false )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2507,plain,
! [SV357: $i,SV557: $i,SV434: $i,SV503: $i] :
( ( ( SV503 != SV434 )
= $false )
| ( ( ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2508,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ~ ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
| ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2509,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ~ ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) )
| ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2510,plain,
! [SV436: $i,SV505: $i,SV359: $i,SV559: $i] :
( ( ( c_member @ ( tc_prod @ SV559 @ SV559 ) @ ( c_Product__Type_OPair @ SV559 @ SV559 @ SV359 @ SV505 ) @ SV436 )
= $false )
| ( ( c_member @ SV559 @ SV359 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
= $true )
| ( ( c_member @ SV559 @ SV505 @ ( c_Wellfounded_Oacc @ SV559 @ SV436 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2511,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i,SV613: $i,SV620: $i,SV625: $i] :
( ( ~ ( c_member @ ( tc_prod @ SV625 @ SV620 ) @ ( c_Product__Type_OPair @ SV625 @ SV620 @ SV613 @ SV595 ) @ SV560 )
| ~ ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SV625 @ SV506 ) @ ( c_Product__Type_OPair @ SV625 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SV625 @ SV620 @ SV506 @ SV560 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2512,plain,
! [SV363: $i,SV626: $i,SV440: $i] :
( ( ( ! [SY1762: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SY1762 ) @ SV363 )
| ! [SY1763: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1762 @ SY1763 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SY1763 ) @ SV363 ) ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2513,plain,
! [SV363: $i,SV440: $i] :
( ( ( ! [SY1764: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ SY1764 ) @ SV363 )
| ! [SY1765: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SY1764 @ SY1765 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ SY1765 ) @ SV363 ) ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2427]) ).
thf(2514,plain,
! [SV364: $i,SV562: $i,SV441: $i,SV509: $i,SV597: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 ) )
= $true )
| ( ( c_Relation_Otrans @ SV597 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2515,plain,
! [SV365: $i,SV627: $i,SV442: $i] :
( ( ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ SV627 @ SV627 ) @ SV365 )
= $true )
| ( ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2516,plain,
! [SV365: $i,SV442: $i] :
( ( ( c_member @ ( tc_prod @ SV442 @ SV442 ) @ ( c_Product__Type_OPair @ SV442 @ SV442 @ ( sK61_SY1451 @ SV365 @ SV442 ) @ ( sK61_SY1451 @ SV365 @ SV442 ) ) @ SV365 )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV442 @ SV365 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2430]) ).
thf(2517,plain,
! [SV563: $i,SV443: $i,SV366: $i,SV510: $i,SV598: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2518,plain,
! [SV367: $i,SV564: $i,SV444: $i,SV511: $i] :
( ( ( SV511 != SV444 )
= $false )
| ( ( ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2519,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false )
| ( ( ! [SY1611: $i] :
( ~ ( c_member @ SV512 @ SY1611 @ SV446 )
| ! [SY1612: $i] :
( ~ ( c_member @ SV512 @ SY1612 @ SV446 )
| ~ ( ( SY1611 != SY1612 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1611 @ SY1612 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1612 @ SY1611 ) @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2520,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ( ! [SY1613: $i] :
( ~ ( c_member @ SV512 @ SY1613 @ SV446 )
| ! [SY1614: $i] :
( ~ ( c_member @ SV512 @ SY1614 @ SV446 )
| ~ ( ( SY1613 != SY1614 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1613 @ SY1614 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1614 @ SY1613 ) @ SV369 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2521,plain,
! [SV513: $i,SV370: $i,SV565: $i,SV447: $i] :
( ( ( c_member @ SV447 @ SV565 @ SV370 )
= $false )
| ( ( c_member @ ( tc_prod @ SV447 @ SV447 ) @ ( c_Product__Type_OPair @ SV447 @ SV447 @ SV565 @ SV513 ) @ ( c_Relation_OId__on @ SV447 @ SV370 ) )
= $true )
| ( ( SV565 = SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2522,plain,
! [SV371: $i,SV628: $i,SV448: $i] :
( ( ( ! [SY1766: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SY1766 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1766 @ SV628 ) @ SV371 )
| ( SV628 = SY1766 ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2523,plain,
! [SV371: $i,SV448: $i] :
( ( ( ! [SY1767: $i] :
( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK62_SY1468 @ SV371 @ SV448 ) @ SY1767 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SY1767 @ ( sK62_SY1468 @ SV371 @ SV448 ) ) @ SV371 )
| ( ( sK62_SY1468 @ SV371 @ SV448 )
= SY1767 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2438]) ).
thf(2524,plain,
! [SV449: $i,SV514: $i,SV372: $i,SV566: $i] :
( ( ( c_member @ SV566 @ SV372 @ SV514 )
= $false )
| ( ( c_member @ ( tc_prod @ SV566 @ SV566 ) @ ( c_Product__Type_OPair @ SV566 @ SV566 @ SV372 @ SV372 ) @ SV449 )
= $true )
| ( ( c_Relation_Orefl__on @ SV566 @ SV514 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2525,plain,
! [SV373: $i,SV450: $i,SV515: $i,SV567: $i,SV599: $i,SV614: $i] :
( ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false )
| ( ( ~ ( ( SV567 != SV450 )
| ( SV515 != SV373 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2526,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ( ~ ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) ) )
= $true )
| ( ( ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2527,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ( ~ ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 ) )
= $true )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2528,plain,
! [SV375: $i,SV452: $i,SV517: $i,SV569: $i,SV600: $i,SV615: $i] :
( ( ( c_member @ SV615 @ SV600 @ SV569 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV615 @ SV517 ) @ ( c_Product__Type_OPair @ SV615 @ SV517 @ SV600 @ SV452 ) @ SV375 )
| ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SV615 @ SV517 @ SV375 @ SV569 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2529,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ( ~ ( c_member @ SV571 @ SV519 @ SV454 ) )
= $true )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2445]) ).
thf(2530,plain,
! [SV572: $i,SV455: $i,SV378: $i,SV520: $i,SV602: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2531,plain,
! [SV379: $i,SV456: $i,SV521: $i] :
( ( ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
= $false )
| ( ( SV456 = SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2532,plain,
! [SV521: $i,SV379: $i,SV456: $i] :
( ( ( SV456 = SV379 )
= $false )
| ( ( c_member @ ( tc_prod @ SV521 @ SV521 ) @ ( c_Product__Type_OPair @ SV521 @ SV521 @ SV456 @ SV379 ) @ ( c_Relation_OId @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2533,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $false )
| ( ( ! [SY1631: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1631 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1631 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2534,plain,
! [SV380: $i,SV457: $i,SV522: $i] :
( ( ( ! [SY1632: $i] :
( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SY1632 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SY1632 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) ) )
= $false )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2535,plain,
! [SV573: $i,SV458: $i,SV381: $i,SV523: $i,SV603: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV523 ) @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2536,plain,
! [SV383: $i,SV460: $i,SV525: $i,SV575: $i,SV604: $i,SV616: $i] :
( ( ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
| ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2537,plain,
( ( ~ ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2454]) ).
thf(2538,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)],[2454]) ).
thf(2539,plain,
! [SV629: $i,SV621: $i] :
( ( ~ ( ( SV621 != SV629 ) )
| ( 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 @ SV621 @ SV629 ) @ 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 @ SV629 @ SV621 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2540,plain,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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 )
| ( ( ~ ! [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_pos,[status(thm)],[2456]) ).
thf(2541,plain,
! [SV462: $i,SV385: $i,SV527: $i,SV577: $i] :
( ( ( ~ ~ ( c_member @ SV577 @ SV527 @ SV385 ) )
= $true )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2542,plain,
! [SV578: $i,SV463: $i,SV386: $i,SV528: $i,SV605: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV528 @ SV386 ) @ SV463 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2543,plain,
! [SV579: $i,SV464: $i,SV387: $i,SV529: $i,SV606: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV529 @ SV387 ) @ SV464 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SV606 @ SV464 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV529 ) @ SV464 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2544,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2545,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ~ ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2546,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ~ ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2547,plain,
! [SV533: $i,SV391: $i,SV582: $i,SV468: $i] :
( ( ( ~ ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) ) )
= $false )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2548,plain,
! [SV582: $i,SV391: $i,SV533: $i,SV468: $i] :
( ( ( ~ ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) ) )
= $false )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2549,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 ) )
= $false )
| ( ( ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2550,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 ) )
= $false )
| ( ( ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2551,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ( ~ ( c_member @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ SV394 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2552,plain,
! [SV394: $i,SV536: $i,SV471: $i] :
( ( ( SV471
!= ( c_Product__Type_OPair @ SV536 @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2553,plain,
! [SV537: $i,SV585: $i,SV395: $i,SV472: $i] :
( ( ( c_Relation_Otrans @ SV472 @ SV395 )
= $false )
| ( ( c_Relation_Otrans @ ( tc_prod @ SV585 @ SV472 ) @ ( c_Wellfounded_Olex__prod @ SV585 @ SV472 @ SV537 @ SV395 ) )
= $true )
| ( ( c_Relation_Otrans @ SV585 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2554,plain,
! [SV586: $i,SV473: $i,SV396: $i,SV538: $i,SV608: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV538 ) @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2555,plain,
! [SV397: $i,SV474: $i,SV587: $i,SV609: $i,SV539: $i] :
( ( ( ! [SY1735: $i] :
( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ SY1735 @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ SY1735 @ SV397 ) ) )
= $false )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2556,plain,
! [SV398: $i,SV630: $i,SV475: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SV630 @ SV630 ) @ SV398 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2557,plain,
! [SV398: $i,SV475: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ ( sK63_SY1542 @ SV398 @ SV475 ) @ ( sK63_SY1542 @ SV398 @ SV475 ) ) @ SV398 ) )
= $false )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2470]) ).
thf(2558,plain,
! [SV540: $i,SV399: $i,SV588: $i,SV476: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ ( sK64_SY1713 @ SV399 @ SV540 @ SV588 @ SV476 ) @ SV540 ) @ SV399 ) )
= $false )
| ( ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2471]) ).
thf(2559,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) )
= $true )
| ( ( ~ ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) )
| ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2560,plain,
! [SV590: $i,SV542: $i,SV401: $i,SV478: $i,SV611: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV611 @ SV611 ) @ ( c_Product__Type_OPair @ SV611 @ SV611 @ SV478 @ SV401 ) @ SV542 ) )
= $true )
| ( ( c_member @ SV611 @ SV401 @ SV590 )
= $true )
| ( ( c_Relation_Orefl__on @ SV611 @ SV590 @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2561,plain,
! [SV332: $i,SV409: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK48_SY1720 @ SV332 @ SV409 ) @ ( sK56_SY1740 @ SV332 @ SV409 ) ) @ SV332 ) )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2562,plain,
! [SV332: $i,SV409: $i] :
( ( ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK46_SY1352 @ SV332 @ SV409 ) @ ( sK56_SY1740 @ SV332 @ SV409 ) ) @ SV332 )
= $false )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2563,plain,
! [SV333: $i,SV543: $i,SV410: $i,SV482: $i] :
( ( ( SV482 = SV410 )
= $true )
| ( ( c_member @ SV543 @ SV482 @ SV333 )
= $true )
| ( ( c_member @ SV543 @ SV482 @ ( c_Set_Oinsert @ SV543 @ SV410 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2564,plain,
! [SV544: $i,SV411: $i,SV334: $i,SV483: $i,SV591: $i] :
( ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV483 @ SV334 ) @ SV411 )
= $false )
| ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV334 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV591 @ SV591 ) @ ( c_Product__Type_OPair @ SV591 @ SV591 @ SV544 @ SV483 ) @ ( c_Transitive__Closure_Ortrancl @ SV591 @ SV411 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2565,plain,
! [SV335: $i,SV412: $i,SV484: $i,SV545: $i] :
( ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $false )
| ( ( ~ ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2566,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ~ ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 ) )
= $false )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2567,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ~ ( ~ ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2568,plain,
! [SV414: $i,SV337: $i,SV486: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK57_SY1567 @ SV337 @ SV414 @ SV486 ) @ SV414 ) @ SV337 ) )
= $false )
| ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2481]) ).
thf(2569,plain,
! [SV414: $i,SV337: $i,SV486: $i] :
( ( ( c_member @ SV486 @ ( sK57_SY1567 @ SV337 @ SV414 @ SV486 ) @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $false )
| ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2481]) ).
thf(2570,plain,
! [SV338: $i,SV487: $i,SV415: $i,SV547: $i] :
( ( ( c_member @ ( tc_prod @ SV547 @ SV415 ) @ ( c_Product__Type_OPair @ SV547 @ SV415 @ SV487 @ ( sK58_SY1678 @ SV338 @ SV487 @ SV415 @ SV547 ) ) @ SV338 )
= $true )
| ( ( c_member @ SV547 @ SV487 @ ( c_Relation_ODomain @ SV547 @ SV415 @ SV338 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2571,plain,
! [SV489: $i,SV340: $i,SV417: $i,SV548: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 ) )
= $true )
| ( ( SV417 != SV340 )
= $true )
| ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2572,plain,
! [SV490: $i,SV418: $i,SV341: $i,SV549: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 ) )
= $true )
| ( ( SV418 = SV341 )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
= $false )
| ( ( c_Relation_Oantisym @ SV549 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2573,plain,
! [SV342: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( ! [SY1768: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SY1768 ) @ SV342 )
| ! [SY1769: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SY1769 ) @ SV342 )
| ( SY1768 = SY1769 ) ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2574,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ! [SY1770: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ SY1770 ) @ SV342 )
| ! [SY1771: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ SY1771 ) @ SV342 )
| ( SY1770 = SY1771 ) ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2486]) ).
thf(2575,plain,
! [SV493: $i,SV422: $i,SV345: $i,SV550: $i] :
( ( ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV345 @ SV422 ) @ SV493 )
= $false )
| ( ( c_member @ ( tc_prod @ SV550 @ SV550 ) @ ( c_Product__Type_OPair @ SV550 @ SV550 @ SV422 @ SV345 ) @ SV493 )
= $false )
| ( ( c_Wellfounded_Owf @ SV550 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2576,plain,
! [SV494: $i,SV423: $i,SV346: $i,SV551: $i] :
( ( ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV346 @ SV423 ) @ SV494 )
= $false )
| ( ( c_member @ ( tc_prod @ SV551 @ SV551 ) @ ( c_Product__Type_OPair @ SV551 @ SV551 @ SV423 @ SV346 ) @ SV494 )
= $false )
| ( ( c_Wellfounded_Owf @ SV551 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2577,plain,
! [SV349: $i,SV426: $i,SV497: $i,SV552: $i] :
( ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $false )
| ( ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2578,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ( ( SV497 = SV426 )
| ( c_member @ SV552 @ SV497 @ SV349 ) )
= $false )
| ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2579,plain,
! [SV350: $i,SV624: $i,SV427: $i] :
( ( ( ~ ~ ! [SY1756: $i] :
~ ( c_member @ SV427 @ SY1756 @ SV624 ) )
= $true )
| ( ( ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2580,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ~ ! [SY1759: $i] :
~ ( c_member @ SV427 @ SY1759 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2581,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ! [SY1760: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1760 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1761: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1761 @ SY1760 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1761 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2582,plain,
! [SV351: $i,SV428: $i,SV498: $i,SV553: $i] :
( ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false )
| ( ( ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2583,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( ~ ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2584,plain,
! [SV352: $i,SV429: $i] :
( ( ( c_member @ ( tc_prod @ SV429 @ SV429 ) @ ( c_Product__Type_OPair @ SV429 @ SV429 @ ( sK50_SY1725 @ SV352 @ SV429 ) @ ( sK47_SY1408 @ SV352 @ SV429 ) ) @ SV352 )
= $true )
| ( ( c_Relation_Oantisym @ SV429 @ SV352 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2585,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK54_SY1743 @ SV353 @ SV430 @ SV499 ) ) @ SV353 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2501]) ).
thf(2586,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK66_SY1751 @ SV353 @ SV430 @ SV499 ) ) @ SV353 )
| ( ( sK54_SY1743 @ SV353 @ SV430 @ SV499 )
= ( sK66_SY1751 @ SV353 @ SV430 @ SV499 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2502]) ).
thf(2587,plain,
! [SV554: $i,SV500: $i,SV354: $i,SV431: $i,SV593: $i] :
( ( ( c_member @ ( tc_prod @ SV593 @ SV593 ) @ ( c_Product__Type_OPair @ SV593 @ SV593 @ SV431 @ SV354 ) @ SV500 )
= $false )
| ( ( c_member @ SV593 @ SV431 @ SV554 )
= $true )
| ( ( c_Relation_Orefl__on @ SV593 @ SV554 @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2588,plain,
! [SV502: $i,SV556: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( c_member @ SV433 @ SV356 @ SV556 )
| ( c_member @ SV433 @ SV356 @ SV502 ) )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2589,plain,
! [SV556: $i,SV502: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( c_member @ SV433 @ SV356 @ SV502 )
| ( c_member @ SV433 @ SV356 @ SV556 ) )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2590,plain,
! [SV357: $i,SV557: $i,SV434: $i,SV503: $i] :
( ( ( SV503 = SV434 )
= $true )
| ( ( ~ ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2591,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ( ~ ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) ) )
= $true )
| ( ( ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2592,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ( ~ ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2593,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i,SV613: $i,SV620: $i,SV625: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV625 @ SV620 ) @ ( c_Product__Type_OPair @ SV625 @ SV620 @ SV613 @ SV595 ) @ SV560 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SV625 @ SV506 ) @ ( c_Product__Type_OPair @ SV625 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SV625 @ SV620 @ SV506 @ SV560 @ SV360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2594,plain,
! [SV363: $i,SV632: $i,SV626: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 )
| ! [SY1772: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SY1772 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SY1772 ) @ SV363 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2595,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ ( sK67_SY1764 @ SV363 @ SV440 ) ) @ SV363 )
| ! [SY1773: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK67_SY1764 @ SV363 @ SV440 ) @ SY1773 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ SY1773 ) @ SV363 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2513]) ).
thf(2596,plain,
! [SV364: $i,SV562: $i,SV441: $i,SV509: $i,SV597: $i] :
( ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
| ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 ) )
= $true )
| ( ( c_Relation_Otrans @ SV597 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2597,plain,
! [SV563: $i,SV443: $i,SV366: $i,SV510: $i,SV598: $i] :
( ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV510 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV366 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV598 @ SV598 ) @ ( c_Product__Type_OPair @ SV598 @ SV598 @ SV563 @ SV510 ) @ ( c_Transitive__Closure_Otrancl @ SV598 @ SV443 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2598,plain,
! [SV367: $i,SV564: $i,SV444: $i,SV511: $i] :
( ( ( SV511 = SV444 )
= $true )
| ( ( ~ ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2599,plain,
! [SV369: $i,SV446: $i,SV633: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ SV633 @ SV446 )
| ! [SY1774: $i] :
( ~ ( c_member @ SV512 @ SY1774 @ SV446 )
| ~ ( ( SV633 != SY1774 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SY1774 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1774 @ SV633 ) @ SV369 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2600,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ SV446 )
| ! [SY1775: $i] :
( ~ ( c_member @ SV512 @ SY1775 @ SV446 )
| ~ ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= SY1775 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ SY1775 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1775 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2520]) ).
thf(2601,plain,
! [SV371: $i,SV634: $i,SV628: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SV634 ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV634 @ SV628 ) @ SV371 )
| ( SV628 = SV634 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2602,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK62_SY1468 @ SV371 @ SV448 ) @ ( sK69_SY1767 @ SV371 @ SV448 ) ) @ SV371 )
| ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK69_SY1767 @ SV371 @ SV448 ) @ ( sK62_SY1468 @ SV371 @ SV448 ) ) @ SV371 )
| ( ( sK62_SY1468 @ SV371 @ SV448 )
= ( sK69_SY1767 @ SV371 @ SV448 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2523]) ).
thf(2603,plain,
! [SV599: $i,SV614: $i,SV373: $i,SV515: $i,SV450: $i,SV567: $i] :
( ( ( ( SV567 != SV450 )
| ( SV515 != SV373 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2604,plain,
! [SV374: $i,SV451: $i,SV516: $i,SV568: $i] :
( ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $false )
| ( ( ~ ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2605,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ( ~ ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 ) )
= $false )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2606,plain,
! [SV569: $i,SV375: $i,SV452: $i,SV600: $i,SV517: $i,SV615: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV615 @ SV517 ) @ ( c_Product__Type_OPair @ SV615 @ SV517 @ SV600 @ SV452 ) @ SV375 ) )
= $true )
| ( ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SV615 @ SV517 @ SV375 @ SV569 ) )
= $true )
| ( ( c_member @ SV615 @ SV600 @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2607,plain,
! [SV377: $i,SV454: $i,SV519: $i,SV571: $i] :
( ( ( c_member @ SV571 @ SV519 @ SV454 )
= $false )
| ( ( c_member @ SV571 @ SV519 @ ( c_Set_Oinsert @ SV571 @ SV377 @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2608,plain,
! [SV572: $i,SV455: $i,SV378: $i,SV520: $i,SV602: $i] :
( ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV520 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV378 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV602 @ SV602 ) @ ( c_Product__Type_OPair @ SV602 @ SV602 @ SV572 @ SV520 ) @ ( c_Transitive__Closure_Ortrancl @ SV602 @ SV455 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2609,plain,
! [SV380: $i,SV457: $i,SV635: $i,SV522: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SV635 @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ SV635 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
= $true )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2610,plain,
! [SV457: $i,SV380: $i,SV522: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ ( sK70_SY1632 @ SV380 @ SV457 @ SV522 ) @ SV457 ) @ SV380 )
| ( c_member @ SV522 @ ( sK70_SY1632 @ SV380 @ SV457 @ SV522 ) @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) ) )
= $false )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2534]) ).
thf(2611,plain,
! [SV573: $i,SV458: $i,SV381: $i,SV523: $i,SV603: $i] :
( ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV523 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV381 ) @ ( c_Transitive__Closure_Ortrancl @ SV603 @ SV458 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV603 @ SV603 ) @ ( c_Product__Type_OPair @ SV603 @ SV603 @ SV573 @ SV523 ) @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2612,plain,
! [SV383: $i,SV575: $i,SV460: $i,SV525: $i,SV604: $i,SV616: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2613,plain,
( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2537]) ).
thf(2614,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)],[2538]) ).
thf(2615,plain,
! [SV629: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV629 ) ) )
= $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 @ SV621 @ SV629 ) @ 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 @ SV629 @ SV621 ) @ v_L ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2616,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 )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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_pos,[status(thm)],[2540]) ).
thf(2617,plain,
! [SV462: $i,SV385: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( c_member @ SV577 @ SV527 @ SV385 ) )
= $false )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2618,plain,
! [SV578: $i,SV463: $i,SV386: $i,SV528: $i,SV605: $i] :
( ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV528 @ SV386 ) @ SV463 )
= $false )
| ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV386 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV605 @ SV605 ) @ ( c_Product__Type_OPair @ SV605 @ SV605 @ SV578 @ SV528 ) @ ( c_Transitive__Closure_Otrancl @ SV605 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2619,plain,
! [SV579: $i,SV464: $i,SV387: $i,SV529: $i,SV606: $i] :
( ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV529 @ SV387 ) @ SV464 )
= $false )
| ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV387 ) @ ( c_Transitive__Closure_Otrancl @ SV606 @ SV464 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV606 @ SV606 ) @ ( c_Product__Type_OPair @ SV606 @ SV606 @ SV579 @ SV529 ) @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2620,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( c_member @ SV465 @ SV388 @ SV580 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2621,plain,
! [SV580: $i,SV530: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( c_member @ SV465 @ SV388 @ SV530 ) )
= $false )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2622,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
| ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2623,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
| ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2624,plain,
! [SV533: $i,SV391: $i,SV582: $i,SV468: $i] :
( ( ( ~ ( c_member @ SV468 @ SV582 @ SV391 )
| ( c_member @ SV468 @ SV533 @ SV391 ) )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2625,plain,
! [SV582: $i,SV391: $i,SV533: $i,SV468: $i] :
( ( ( ~ ( c_member @ SV468 @ SV533 @ SV391 )
| ( c_member @ SV468 @ SV582 @ SV391 ) )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2626,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( ~ ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2627,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( ~ ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2628,plain,
! [SV394: $i,SV471: $i,SV536: $i] :
( ( ( c_member @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ SV394 )
= $true )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2629,plain,
! [SV394: $i,SV536: $i,SV471: $i] :
( ( ( SV471
= ( c_Product__Type_OPair @ SV536 @ SV536 @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) @ ( sK55_SY1654 @ SV471 @ SV394 @ SV536 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV536 @ SV536 ) @ SV471 @ ( c_Relation_OId__on @ SV536 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2630,plain,
! [SV586: $i,SV473: $i,SV396: $i,SV538: $i,SV608: $i] :
( ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV538 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV396 ) @ ( c_Transitive__Closure_Otrancl @ SV608 @ SV473 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV608 @ SV608 ) @ ( c_Product__Type_OPair @ SV608 @ SV608 @ SV586 @ SV538 ) @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2631,plain,
! [SV587: $i,SV474: $i,SV397: $i,SV609: $i,SV539: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV587 ) @ SV474 )
| ~ ( c_member @ SV539 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV397 ) )
= $false )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2555]) ).
thf(2632,plain,
! [SV398: $i,SV630: $i,SV475: $i] :
( ( ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ SV630 @ SV630 ) @ SV398 )
= $false )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2633,plain,
! [SV398: $i,SV475: $i] :
( ( ( c_member @ ( tc_prod @ SV475 @ SV475 ) @ ( c_Product__Type_OPair @ SV475 @ SV475 @ ( sK63_SY1542 @ SV398 @ SV475 ) @ ( sK63_SY1542 @ SV398 @ SV475 ) ) @ SV398 )
= $true )
| ( ( c_Relation_Oirrefl @ SV475 @ SV398 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2634,plain,
! [SV540: $i,SV399: $i,SV588: $i,SV476: $i] :
( ( ( c_member @ ( tc_prod @ SV476 @ SV588 ) @ ( c_Product__Type_OPair @ SV476 @ SV588 @ ( sK64_SY1713 @ SV399 @ SV540 @ SV588 @ SV476 ) @ SV540 ) @ SV399 )
= $true )
| ( ( c_member @ SV588 @ SV540 @ ( c_Relation_ORange @ SV476 @ SV588 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2635,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false )
| ( ( ~ ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) )
| ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2636,plain,
! [SV590: $i,SV542: $i,SV401: $i,SV478: $i,SV611: $i] :
( ( ( c_member @ ( tc_prod @ SV611 @ SV611 ) @ ( c_Product__Type_OPair @ SV611 @ SV611 @ SV478 @ SV401 ) @ SV542 )
= $false )
| ( ( c_member @ SV611 @ SV401 @ SV590 )
= $true )
| ( ( c_Relation_Orefl__on @ SV611 @ SV590 @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2637,plain,
! [SV332: $i,SV409: $i] :
( ( ( c_member @ ( tc_prod @ SV409 @ SV409 ) @ ( c_Product__Type_OPair @ SV409 @ SV409 @ ( sK48_SY1720 @ SV332 @ SV409 ) @ ( sK56_SY1740 @ SV332 @ SV409 ) ) @ SV332 )
= $true )
| ( ( c_Relation_Otrans @ SV409 @ SV332 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2638,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ! [SY1672: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1672 ) @ SV335 ) )
= $false )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2639,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ! [SY1673: $i] :
~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SY1673 ) @ SV335 ) )
= $true )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2640,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ~ ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2567]) ).
thf(2641,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ~ ( ~ ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2567]) ).
thf(2642,plain,
! [SV414: $i,SV337: $i,SV486: $i] :
( ( ( c_member @ ( tc_prod @ SV486 @ SV486 ) @ ( c_Product__Type_OPair @ SV486 @ SV486 @ ( sK57_SY1567 @ SV337 @ SV414 @ SV486 ) @ SV414 ) @ SV337 )
= $true )
| ( ( c_member @ SV486 @ SV414 @ ( c_Wellfounded_Oacc @ SV486 @ SV337 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2643,plain,
! [SV489: $i,SV340: $i,SV417: $i,SV548: $i] :
( ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
= $false )
| ( ( SV417 != SV340 )
= $true )
| ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2644,plain,
! [SV490: $i,SV418: $i,SV341: $i,SV549: $i] :
( ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV341 @ SV418 ) @ SV490 )
= $false )
| ( ( SV418 = SV341 )
= $true )
| ( ( c_member @ ( tc_prod @ SV549 @ SV549 ) @ ( c_Product__Type_OPair @ SV549 @ SV549 @ SV418 @ SV341 ) @ SV490 )
= $false )
| ( ( c_Relation_Oantisym @ SV549 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2645,plain,
! [SV342: $i,SV636: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 )
| ! [SY1776: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SY1776 ) @ SV342 )
| ( SV636 = SY1776 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2646,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK72_SY1770 @ SV342 @ SV419 @ SV491 ) ) @ SV342 )
| ! [SY1777: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ SY1777 ) @ SV342 )
| ( ( sK72_SY1770 @ SV342 @ SV419 @ SV491 )
= SY1777 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2574]) ).
thf(2647,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ( SV497 = SV426 )
= $true )
| ( ( c_member @ SV552 @ SV497 @ SV349 )
= $true )
| ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2648,plain,
! [SV349: $i,SV552: $i,SV426: $i,SV497: $i] :
( ( ( SV497 = SV426 )
= $false )
| ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2649,plain,
! [SV426: $i,SV349: $i,SV497: $i,SV552: $i] :
( ( ( c_member @ SV552 @ SV497 @ SV349 )
= $false )
| ( ( c_member @ SV552 @ SV497 @ ( c_Set_Oinsert @ SV552 @ SV426 @ SV349 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2650,plain,
! [SV350: $i,SV624: $i,SV427: $i] :
( ( ( ~ ! [SY1756: $i] :
~ ( c_member @ SV427 @ SY1756 @ SV624 ) )
= $false )
| ( ( ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2651,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ! [SY1759: $i] :
~ ( c_member @ SV427 @ SY1759 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2652,plain,
! [SV350: $i,SV427: $i] :
( ( ( ! [SY1760: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1760 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1761: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1761 @ SY1760 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1761 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2653,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2654,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( ( SV498 != SV428 )
| ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2655,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK66_SY1751 @ SV353 @ SV430 @ SV499 ) ) @ SV353 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2656,plain,
! [SV499: $i,SV430: $i,SV353: $i] :
( ( ( ( sK54_SY1743 @ SV353 @ SV430 @ SV499 )
= ( sK66_SY1751 @ SV353 @ SV430 @ SV499 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2657,plain,
! [SV502: $i,SV556: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( c_member @ SV433 @ SV356 @ SV556 ) )
= $true )
| ( ( c_member @ SV433 @ SV356 @ SV502 )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2658,plain,
! [SV556: $i,SV502: $i,SV356: $i,SV433: $i] :
( ( ( ~ ( c_member @ SV433 @ SV356 @ SV502 ) )
= $true )
| ( ( c_member @ SV433 @ SV356 @ SV556 )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2659,plain,
! [SV434: $i,SV357: $i,SV503: $i,SV557: $i] :
( ( ( ! [SY1681: $i] :
( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SY1681 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SY1681 @ SV434 ) @ SV357 ) ) )
= $false )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2660,plain,
! [SV358: $i,SV435: $i,SV504: $i,SV558: $i,SV594: $i] :
( ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false )
| ( ( ~ ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2661,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ( ~ ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2662,plain,
! [SV360: $i,SV437: $i,SV506: $i,SV560: $i,SV595: $i,SV613: $i,SV620: $i,SV625: $i] :
( ( ( c_member @ ( tc_prod @ SV625 @ SV620 ) @ ( c_Product__Type_OPair @ SV625 @ SV620 @ SV613 @ SV595 ) @ SV560 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 )
| ( c_member @ ( tc_prod @ SV625 @ SV506 ) @ ( c_Product__Type_OPair @ SV625 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SV625 @ SV620 @ SV506 @ SV560 @ SV360 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2663,plain,
! [SV363: $i,SV632: $i,SV626: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 ) )
= $true )
| ( ( ! [SY1772: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SY1772 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SY1772 ) @ SV363 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2664,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ ( sK67_SY1764 @ SV363 @ SV440 ) ) @ SV363 ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2595]) ).
thf(2665,plain,
! [SV363: $i,SV440: $i] :
( ( ( ! [SY1773: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK67_SY1764 @ SV363 @ SV440 ) @ SY1773 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ SY1773 ) @ SV363 ) ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2595]) ).
thf(2666,plain,
! [SV509: $i,SV562: $i,SV364: $i,SV441: $i,SV597: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 )
= $true )
| ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
= $false )
| ( ( c_Relation_Otrans @ SV597 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2667,plain,
! [SV444: $i,SV367: $i,SV511: $i,SV564: $i] :
( ( ( ! [SY1692: $i] :
( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SY1692 ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SY1692 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) ) )
= $false )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2668,plain,
! [SV369: $i,SV446: $i,SV633: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ SV633 @ SV446 ) )
= $true )
| ( ( ! [SY1774: $i] :
( ~ ( c_member @ SV512 @ SY1774 @ SV446 )
| ~ ( ( SV633 != SY1774 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SY1774 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1774 @ SV633 ) @ SV369 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2669,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ SV446 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2600]) ).
thf(2670,plain,
! [SV369: $i,SV446: $i,SV512: $i] :
( ( ( ! [SY1775: $i] :
( ~ ( c_member @ SV512 @ SY1775 @ SV446 )
| ~ ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= SY1775 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ SY1775 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1775 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2600]) ).
thf(2671,plain,
! [SV371: $i,SV634: $i,SV628: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SV634 ) @ SV371 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV634 @ SV628 ) @ SV371 )
| ( SV628 = SV634 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2672,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK62_SY1468 @ SV371 @ SV448 ) @ ( sK69_SY1767 @ SV371 @ SV448 ) ) @ SV371 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2673,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK69_SY1767 @ SV371 @ SV448 ) @ ( sK62_SY1468 @ SV371 @ SV448 ) ) @ SV371 )
| ( ( sK62_SY1468 @ SV371 @ SV448 )
= ( sK69_SY1767 @ SV371 @ SV448 ) ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2602]) ).
thf(2674,plain,
! [SV373: $i,SV515: $i,SV599: $i,SV614: $i,SV450: $i,SV567: $i] :
( ( ( SV567 != SV450 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2675,plain,
! [SV450: $i,SV567: $i,SV599: $i,SV614: $i,SV373: $i,SV515: $i] :
( ( ( SV515 != SV373 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2676,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ( ! [SY1695: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1695 @ SV516 ) @ SV374 ) )
= $false )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2677,plain,
! [SV374: $i,SV516: $i,SV568: $i,SV451: $i] :
( ( ( ! [SY1696: $i] :
~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SY1696 @ SV516 ) @ SV374 ) )
= $true )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2678,plain,
! [SV569: $i,SV375: $i,SV452: $i,SV600: $i,SV517: $i,SV615: $i] :
( ( ( c_member @ ( tc_prod @ SV615 @ SV517 ) @ ( c_Product__Type_OPair @ SV615 @ SV517 @ SV600 @ SV452 ) @ SV375 )
= $false )
| ( ( c_member @ SV517 @ SV452 @ ( c_Relation_OImage @ SV615 @ SV517 @ SV375 @ SV569 ) )
= $true )
| ( ( c_member @ SV615 @ SV600 @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2679,plain,
! [SV380: $i,SV457: $i,SV635: $i,SV522: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SV635 @ SV457 ) @ SV380 ) )
= $true )
| ( ( c_member @ SV522 @ SV635 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2680,plain,
! [SV457: $i,SV380: $i,SV522: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ ( sK70_SY1632 @ SV380 @ SV457 @ SV522 ) @ SV457 ) @ SV380 ) )
= $false )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2610]) ).
thf(2681,plain,
! [SV457: $i,SV380: $i,SV522: $i] :
( ( ( c_member @ SV522 @ ( sK70_SY1632 @ SV380 @ SV457 @ SV522 ) @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $false )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2610]) ).
thf(2682,plain,
! [SV383: $i,SV575: $i,SV460: $i,SV525: $i,SV604: $i,SV616: $i] :
( ( ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
| ( SV460 = SV383 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2683,plain,
! [SV637: $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 @ SV637 @ SV637 ) @ v_L ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(2684,plain,
! [SV629: $i,SV621: $i] :
( ( ( SV621 != SV629 )
= $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 @ SV621 @ SV629 ) @ 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 @ SV629 @ SV621 ) @ v_L ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2685,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 @ sK73_SX0 @ sK73_SX0 ) @ v_L ) )
= $false )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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_forall_neg,[status(esa)],[2616]) ).
thf(2686,plain,
! [SV462: $i,SV385: $i,SV527: $i,SV577: $i] :
( ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( ~ ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2687,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2620]) ).
thf(2688,plain,
! [SV580: $i,SV530: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( ~ ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) ) )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2689,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
!= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true )
| ( ( ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2690,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( ~ ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2691,plain,
! [SV533: $i,SV391: $i,SV582: $i,SV468: $i] :
( ( ( ~ ( c_member @ SV468 @ SV582 @ SV391 ) )
= $true )
| ( ( c_member @ SV468 @ SV533 @ SV391 )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2692,plain,
! [SV582: $i,SV391: $i,SV533: $i,SV468: $i] :
( ( ( ~ ( c_member @ SV468 @ SV533 @ SV391 ) )
= $true )
| ( ( c_member @ SV468 @ SV582 @ SV391 )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2693,plain,
! [SV469: $i,SV392: $i,SV534: $i,SV583: $i] :
( ( ( ! [SY1708: $i] :
( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SY1708 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SY1708 @ SV469 ) @ SV392 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2694,plain,
! [SV470: $i,SV393: $i,SV535: $i,SV584: $i] :
( ( ( ! [SY1709: $i] :
( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SY1709 ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SY1709 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2695,plain,
! [SV587: $i,SV474: $i,SV397: $i,SV609: $i,SV539: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV587 ) @ SV474 ) )
= $false )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2696,plain,
! [SV609: $i,SV587: $i,SV474: $i,SV397: $i,SV539: $i] :
( ( ( ~ ( c_member @ SV539 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV397 ) )
= $false )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2697,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ~ ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) ) )
= $true )
| ( ( ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2698,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ ( sK74_SY1672 @ SV335 @ SV484 @ SV412 @ SV545 ) ) @ SV335 ) )
= $false )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2638]) ).
thf(2699,plain,
! [SV335: $i,SV638: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SV638 ) @ SV335 ) )
= $true )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2700,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
| ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2701,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ~ ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
| ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2702,plain,
! [SV489: $i,SV548: $i,SV340: $i,SV417: $i] :
( ( ( SV417 = SV340 )
= $false )
| ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ SV417 @ SV340 ) @ SV489 )
= $false )
| ( ( c_member @ ( tc_prod @ SV548 @ SV548 ) @ ( c_Product__Type_OPair @ SV548 @ SV548 @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) @ ( sK53_SY1679 @ SV340 @ SV417 @ SV489 @ SV548 ) ) @ ( c_Transitive__Closure_Otrancl @ SV548 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2703,plain,
! [SV342: $i,SV636: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 ) )
= $true )
| ( ( ! [SY1776: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SY1776 ) @ SV342 )
| ( SV636 = SY1776 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2704,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK72_SY1770 @ SV342 @ SV419 @ SV491 ) ) @ SV342 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2705,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ! [SY1777: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ SY1777 ) @ SV342 )
| ( ( sK72_SY1770 @ SV342 @ SV419 @ SV491 )
= SY1777 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2706,plain,
! [SV350: $i,SV624: $i,SV427: $i] :
( ( ( ! [SY1756: $i] :
~ ( c_member @ SV427 @ SY1756 @ SV624 ) )
= $true )
| ( ( ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2707,plain,
! [SV350: $i,SV427: $i] :
( ( ( ! [SY1759: $i] :
~ ( c_member @ SV427 @ SY1759 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2708,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2709,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( SV498 != SV428 )
= $false )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2653]) ).
thf(2710,plain,
! [SV428: $i,SV351: $i,SV498: $i,SV553: $i] :
( ( ( ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2653]) ).
thf(2711,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( SV498 != SV428 )
= $true )
| ( ( ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2712,plain,
! [SV353: $i,SV430: $i,SV499: $i] :
( ( ( c_member @ ( tc_prod @ SV499 @ SV430 ) @ ( c_Product__Type_OPair @ SV499 @ SV430 @ ( sK51_SY1584 @ SV353 @ SV430 @ SV499 ) @ ( sK66_SY1751 @ SV353 @ SV430 @ SV499 ) ) @ SV353 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV499 @ SV430 @ SV353 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2713,plain,
! [SV502: $i,SV556: $i,SV356: $i,SV433: $i] :
( ( ( c_member @ SV433 @ SV356 @ SV556 )
= $false )
| ( ( c_member @ SV433 @ SV356 @ SV502 )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2714,plain,
! [SV556: $i,SV502: $i,SV356: $i,SV433: $i] :
( ( ( c_member @ SV433 @ SV356 @ SV502 )
= $false )
| ( ( c_member @ SV433 @ SV356 @ SV556 )
= $true )
| ( ( SV556 = SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2715,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
| ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) @ SV434 ) @ SV357 ) )
= $false )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2659]) ).
thf(2716,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ( ! [SY1726: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1726 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1726 @ SV558 ) @ SV435 ) ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2717,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV504: $i] :
( ( ( ! [SY1727: $i] :
~ ~ ( ~ ( c_member @ SV504 @ SY1727 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SY1727 @ SV558 ) @ SV435 ) ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2661]) ).
thf(2718,plain,
! [SV560: $i,SV613: $i,SV625: $i,SV360: $i,SV437: $i,SV595: $i,SV506: $i,SV620: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV625 @ SV506 ) @ ( c_Product__Type_OPair @ SV625 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SV625 @ SV620 @ SV506 @ SV560 @ SV360 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV625 @ SV620 ) @ ( c_Product__Type_OPair @ SV625 @ SV620 @ SV613 @ SV595 ) @ SV560 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2719,plain,
! [SV363: $i,SV632: $i,SV626: $i,SV440: $i] :
( ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 )
= $false )
| ( ( ! [SY1772: $i] :
( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SY1772 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SY1772 ) @ SV363 ) ) )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2720,plain,
! [SV363: $i,SV440: $i] :
( ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ ( sK67_SY1764 @ SV363 @ SV440 ) ) @ SV363 )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2721,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK67_SY1764 @ SV363 @ SV440 ) @ ( sK76_SY1773 @ SV363 @ SV440 ) ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ ( sK76_SY1773 @ SV363 @ SV440 ) ) @ SV363 ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2665]) ).
thf(2722,plain,
! [SV509: $i,SV562: $i,SV364: $i,SV441: $i,SV597: $i] :
( ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV441 @ SV364 ) @ SV562 )
= $false )
| ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV364 ) @ SV562 )
= $true )
| ( ( c_member @ ( tc_prod @ SV597 @ SV597 ) @ ( c_Product__Type_OPair @ SV597 @ SV597 @ SV509 @ SV441 ) @ SV562 )
= $false )
| ( ( c_Relation_Otrans @ SV597 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2723,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) ) @ SV367 )
| ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) )
= $false )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2667]) ).
thf(2724,plain,
! [SV369: $i,SV446: $i,SV633: $i,SV512: $i] :
( ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( ! [SY1774: $i] :
( ~ ( c_member @ SV512 @ SY1774 @ SV446 )
| ~ ( ( SV633 != SY1774 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SY1774 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SY1774 @ SV633 ) @ SV369 ) ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2725,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( c_member @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ SV446 )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2726,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ SV446 )
| ~ ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2670]) ).
thf(2727,plain,
! [SV371: $i,SV634: $i,SV628: $i,SV448: $i] :
( ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SV634 ) @ SV371 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV634 @ SV628 ) @ SV371 )
| ( SV628 = SV634 ) )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2728,plain,
! [SV371: $i,SV448: $i] :
( ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK62_SY1468 @ SV371 @ SV448 ) @ ( sK69_SY1767 @ SV371 @ SV448 ) ) @ SV371 )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2729,plain,
! [SV371: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK69_SY1767 @ SV371 @ SV448 ) @ ( sK62_SY1468 @ SV371 @ SV448 ) ) @ SV371 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2730,plain,
! [SV448: $i,SV371: $i] :
( ( ( ( sK62_SY1468 @ SV371 @ SV448 )
= ( sK69_SY1767 @ SV371 @ SV448 ) )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2731,plain,
! [SV373: $i,SV515: $i,SV599: $i,SV614: $i,SV450: $i,SV567: $i] :
( ( ( SV567 = SV450 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2674]) ).
thf(2732,plain,
! [SV450: $i,SV567: $i,SV599: $i,SV614: $i,SV373: $i,SV515: $i] :
( ( ( SV515 = SV373 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV614 @ SV599 @ SV567 @ SV515 )
= ( c_Product__Type_OPair @ SV614 @ SV599 @ SV450 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2675]) ).
thf(2733,plain,
! [SV516: $i,SV374: $i,SV568: $i,SV451: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ ( sK79_SY1695 @ SV374 @ SV516 @ SV568 @ SV451 ) @ SV516 ) @ SV374 ) )
= $false )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2676]) ).
thf(2734,plain,
! [SV374: $i,SV516: $i,SV640: $i,SV568: $i,SV451: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SV640 @ SV516 ) @ SV374 ) )
= $true )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(2735,plain,
! [SV380: $i,SV457: $i,SV635: $i,SV522: $i] :
( ( ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ SV635 @ SV457 ) @ SV380 )
= $false )
| ( ( c_member @ SV522 @ SV635 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2736,plain,
! [SV457: $i,SV380: $i,SV522: $i] :
( ( ( c_member @ ( tc_prod @ SV522 @ SV522 ) @ ( c_Product__Type_OPair @ SV522 @ SV522 @ ( sK70_SY1632 @ SV380 @ SV457 @ SV522 ) @ SV457 ) @ SV380 )
= $true )
| ( ( c_member @ SV522 @ SV457 @ ( c_Wellfounded_Oacc @ SV522 @ SV380 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2737,plain,
! [SV460: $i,SV575: $i,SV383: $i,SV525: $i,SV604: $i,SV616: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 ) )
= $true )
| ( ( SV460 = SV383 )
= $true )
| ( ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2738,plain,
! [SV637: $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 @ SV637 @ SV637 ) @ v_L )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2739,plain,
! [SV629: $i,SV621: $i] :
( ( ( SV621 = SV629 )
= $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 @ SV621 @ SV629 ) @ 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 @ SV629 @ SV621 ) @ v_L ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2740,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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true )
| ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
= $false )
| ( ( ~ ! [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)],[2685]) ).
thf(2741,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
| ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) )
= $false )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2742,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2743,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 )
| ( c_member @ SV465 @ SV388 @ SV530 ) )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2744,plain,
! [SV390: $i,SV467: $i,SV532: $i,SV581: $i,SV607: $i,SV617: $i] :
( ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false )
| ( ( ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2745,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( ~ ( ( SV581 != SV467 )
| ( SV532 != SV390 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2746,plain,
! [SV533: $i,SV391: $i,SV582: $i,SV468: $i] :
( ( ( c_member @ SV468 @ SV582 @ SV391 )
= $false )
| ( ( c_member @ SV468 @ SV533 @ SV391 )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2747,plain,
! [SV582: $i,SV391: $i,SV533: $i,SV468: $i] :
( ( ( c_member @ SV468 @ SV533 @ SV391 )
= $false )
| ( ( c_member @ SV468 @ SV582 @ SV391 )
= $true )
| ( ( SV582 = SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2748,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
| ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) @ SV469 ) @ SV392 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2693]) ).
thf(2749,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) ) @ SV393 )
| ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2694]) ).
thf(2750,plain,
! [SV587: $i,SV474: $i,SV397: $i,SV609: $i,SV539: $i] :
( ( ( c_member @ ( tc_prod @ SV539 @ SV609 ) @ ( c_Product__Type_OPair @ SV539 @ SV609 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV587 ) @ SV474 )
= $true )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2751,plain,
! [SV609: $i,SV587: $i,SV474: $i,SV397: $i,SV539: $i] :
( ( ( c_member @ SV539 @ ( sK71_SY1735 @ SV397 @ SV474 @ SV587 @ SV609 @ SV539 ) @ SV397 )
= $true )
| ( ( c_member @ SV609 @ SV587 @ ( c_Relation_OImage @ SV539 @ SV609 @ SV474 @ SV397 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2696]) ).
thf(2752,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
!= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $false )
| ( ( ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2753,plain,
! [SV335: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ ( sK74_SY1672 @ SV335 @ SV484 @ SV412 @ SV545 ) ) @ SV335 )
= $true )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2754,plain,
! [SV335: $i,SV638: $i,SV484: $i,SV412: $i,SV545: $i] :
( ( ( c_member @ ( tc_prod @ SV545 @ SV412 ) @ ( c_Product__Type_OPair @ SV545 @ SV412 @ SV484 @ SV638 ) @ SV335 )
= $false )
| ( ( c_member @ SV545 @ SV484 @ ( c_Relation_ODomain @ SV545 @ SV412 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2755,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(2756,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ( ~ ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2757,plain,
! [SV342: $i,SV636: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 )
= $false )
| ( ( ! [SY1776: $i] :
( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SY1776 ) @ SV342 )
| ( SV636 = SY1776 ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2758,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK72_SY1770 @ SV342 @ SV419 @ SV491 ) ) @ SV342 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2759,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK82_SY1777 @ SV342 @ SV419 @ SV491 ) ) @ SV342 )
| ( ( sK72_SY1770 @ SV342 @ SV419 @ SV491 )
= ( sK82_SY1777 @ SV342 @ SV419 @ SV491 ) ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2705]) ).
thf(2760,plain,
! [SV350: $i,SV624: $i,SV641: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ SV641 @ SV624 ) )
= $true )
| ( ( ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2761,plain,
! [SV350: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ ( sK83_SY1759 @ SV350 @ SV427 ) @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2707]) ).
thf(2762,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( ~ ( ~ ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2763,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( SV498 = SV428 )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2709]) ).
thf(2764,plain,
! [SV428: $i,SV351: $i,SV498: $i,SV553: $i] :
( ( ( c_member @ SV553 @ SV498 @ SV351 )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2710]) ).
thf(2765,plain,
! [SV351: $i,SV553: $i,SV428: $i,SV498: $i] :
( ( ( SV498 = SV428 )
= $false )
| ( ( ~ ( c_member @ SV553 @ SV498 @ SV351 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2766,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) ) )
= $false )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2715]) ).
thf(2767,plain,
! [SV503: $i,SV357: $i,SV434: $i,SV557: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) @ SV434 ) @ SV357 ) )
= $false )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2715]) ).
thf(2768,plain,
! [SV358: $i,SV594: $i,SV558: $i,SV435: $i,SV504: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV504 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV558 ) @ SV435 ) ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2716]) ).
thf(2769,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV642: $i,SV504: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV504 @ SV642 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 ) ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(2770,plain,
! [SV560: $i,SV613: $i,SV625: $i,SV360: $i,SV437: $i,SV595: $i,SV506: $i,SV620: $i] :
( ( ( c_member @ ( tc_prod @ SV620 @ SV506 ) @ ( c_Product__Type_OPair @ SV620 @ SV506 @ SV595 @ SV437 ) @ SV360 )
= $false )
| ( ( c_member @ ( tc_prod @ SV625 @ SV506 ) @ ( c_Product__Type_OPair @ SV625 @ SV506 @ SV613 @ SV437 ) @ ( c_Relation_Orel__comp @ SV625 @ SV620 @ SV506 @ SV560 @ SV360 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV625 @ SV620 ) @ ( c_Product__Type_OPair @ SV625 @ SV620 @ SV613 @ SV595 ) @ SV560 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2771,plain,
! [SV626: $i,SV363: $i,SV643: $i,SV632: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SV643 ) @ SV363 )
| ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV643 ) @ SV363 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(2772,plain,
! [SV363: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK67_SY1764 @ SV363 @ SV440 ) @ ( sK76_SY1773 @ SV363 @ SV440 ) ) @ SV363 ) )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2773,plain,
! [SV363: $i,SV440: $i] :
( ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK60_SY1444 @ SV363 @ SV440 ) @ ( sK76_SY1773 @ SV363 @ SV440 ) ) @ SV363 )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2774,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) ) @ SV367 ) )
= $false )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2723]) ).
thf(2775,plain,
! [SV511: $i,SV367: $i,SV444: $i,SV564: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) ) )
= $false )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2723]) ).
thf(2776,plain,
! [SV369: $i,SV633: $i,SV446: $i,SV644: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ SV644 @ SV446 )
| ~ ( ( SV633 != SV644 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(2777,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ SV446 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2778,plain,
! [SV512: $i,SV446: $i,SV369: $i] :
( ( ( ~ ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2779,plain,
! [SV371: $i,SV628: $i,SV634: $i,SV448: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV634 @ SV628 ) @ SV371 ) )
= $true )
| ( ( SV628 = SV634 )
= $true )
| ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SV634 ) @ SV371 )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(2780,plain,
! [SV371: $i,SV448: $i] :
( ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ ( sK69_SY1767 @ SV371 @ SV448 ) @ ( sK62_SY1468 @ SV371 @ SV448 ) ) @ SV371 )
= $true )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2781,plain,
! [SV516: $i,SV374: $i,SV568: $i,SV451: $i] :
( ( ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ ( sK79_SY1695 @ SV374 @ SV516 @ SV568 @ SV451 ) @ SV516 ) @ SV374 )
= $true )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2733]) ).
thf(2782,plain,
! [SV374: $i,SV516: $i,SV640: $i,SV568: $i,SV451: $i] :
( ( ( c_member @ ( tc_prod @ SV451 @ SV568 ) @ ( c_Product__Type_OPair @ SV451 @ SV568 @ SV640 @ SV516 ) @ SV374 )
= $false )
| ( ( c_member @ SV568 @ SV516 @ ( c_Relation_ORange @ SV451 @ SV568 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2783,plain,
! [SV460: $i,SV575: $i,SV383: $i,SV525: $i,SV604: $i,SV616: $i] :
( ( ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV383 ) @ SV575 )
= $false )
| ( ( SV460 = SV383 )
= $true )
| ( ( c_member @ ( tc_prod @ SV616 @ SV604 ) @ ( c_Product__Type_OPair @ SV616 @ SV604 @ SV525 @ SV460 ) @ SV575 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV616 @ SV604 @ SV575 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2784,plain,
! [SV629: $i,SV621: $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 @ SV621 @ SV629 ) @ 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 @ SV629 @ SV621 ) @ v_L )
= $true )
| ( ( SV621 = SV629 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2785,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 )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2786,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ~ ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) ) )
= $false )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2787,plain,
! [SV527: $i,SV577: $i,SV385: $i,SV462: $i] :
( ( ( ~ ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) ) )
= $false )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2788,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 ) )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2742]) ).
thf(2789,plain,
! [SV580: $i,SV530: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV530 )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2742]) ).
thf(2790,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ~ ( c_member @ SV465 @ SV388 @ SV580 ) )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2791,plain,
! [SV580: $i,SV530: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV530 )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2792,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2793,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( ( SV581 != SV467 )
| ( SV532 != SV390 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(2794,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2795,plain,
! [SV534: $i,SV392: $i,SV469: $i,SV583: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) @ SV469 ) @ SV392 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2796,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) ) @ SV393 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2749]) ).
thf(2797,plain,
! [SV535: $i,SV393: $i,SV470: $i,SV584: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2749]) ).
thf(2798,plain,
! [SV400: $i,SV477: $i,SV541: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( ~ ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2799,plain,
! [SV336: $i,SV413: $i,SV485: $i,SV546: $i,SV592: $i,SV612: $i,SV619: $i,SV623: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2800,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
| ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2801,plain,
! [SV636: $i,SV342: $i,SV645: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV645 ) @ SV342 )
| ( SV636 = SV645 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(2802,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK82_SY1777 @ SV342 @ SV419 @ SV491 ) ) @ SV342 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2759]) ).
thf(2803,plain,
! [SV491: $i,SV419: $i,SV342: $i] :
( ( ( ( sK72_SY1770 @ SV342 @ SV419 @ SV491 )
= ( sK82_SY1777 @ SV342 @ SV419 @ SV491 ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2759]) ).
thf(2804,plain,
! [SV350: $i,SV624: $i,SV641: $i,SV427: $i] :
( ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( ~ ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2805,plain,
! [SV350: $i,SV427: $i] :
( ( ( c_member @ SV427 @ ( sK83_SY1759 @ SV350 @ SV427 ) @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2806,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
| ~ ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2807,plain,
! [SV428: $i,SV351: $i,SV498: $i,SV553: $i] :
( ( ( c_member @ SV553 @ SV498 @ SV351 )
= $false )
| ( ( SV498 = SV428 )
= $false )
| ( ( c_member @ ( tc_prod @ SV553 @ SV553 ) @ ( c_Product__Type_OPair @ SV553 @ SV553 @ SV498 @ SV428 ) @ ( c_Relation_OId__on @ SV553 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2808,plain,
! [SV357: $i,SV434: $i,SV503: $i,SV557: $i] :
( ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $true )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2809,plain,
! [SV503: $i,SV357: $i,SV434: $i,SV557: $i] :
( ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ ( sK75_SY1681 @ SV434 @ SV357 @ SV503 @ SV557 ) @ SV434 ) @ SV357 )
= $true )
| ( ( SV503 = SV434 )
= $true )
| ( ( c_member @ ( tc_prod @ SV557 @ SV557 ) @ ( c_Product__Type_OPair @ SV557 @ SV557 @ SV503 @ SV434 ) @ ( c_Transitive__Closure_Ortrancl @ SV557 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2810,plain,
! [SV358: $i,SV594: $i,SV558: $i,SV435: $i,SV504: $i] :
( ( ( ~ ( ~ ( c_member @ SV504 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV558 ) @ SV435 ) ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2811,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV642: $i,SV504: $i] :
( ( ( ~ ( ~ ( c_member @ SV504 @ SV642 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 ) ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2812,plain,
! [SV626: $i,SV363: $i,SV643: $i,SV632: $i,SV440: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SV643 ) @ SV363 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV643 ) @ SV363 )
= $true )
| ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(2813,plain,
! [SV363: $i,SV440: $i] :
( ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ ( sK67_SY1764 @ SV363 @ SV440 ) @ ( sK76_SY1773 @ SV363 @ SV440 ) ) @ SV363 )
= $true )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2814,plain,
! [SV367: $i,SV444: $i,SV511: $i,SV564: $i] :
( ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) ) @ SV367 )
= $true )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2815,plain,
! [SV511: $i,SV367: $i,SV444: $i,SV564: $i] :
( ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ ( sK77_SY1692 @ SV444 @ SV367 @ SV511 @ SV564 ) @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $true )
| ( ( SV511 = SV444 )
= $true )
| ( ( c_member @ ( tc_prod @ SV564 @ SV564 ) @ ( c_Product__Type_OPair @ SV564 @ SV564 @ SV511 @ SV444 ) @ ( c_Transitive__Closure_Ortrancl @ SV564 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2816,plain,
! [SV369: $i,SV633: $i,SV446: $i,SV644: $i,SV512: $i] :
( ( ( ~ ( c_member @ SV512 @ SV644 @ SV446 ) )
= $true )
| ( ( ~ ( ( SV633 != SV644 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2817,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( c_member @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ SV446 )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2777]) ).
thf(2818,plain,
! [SV512: $i,SV446: $i,SV369: $i] :
( ( ( ~ ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2819,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2820,plain,
! [SV371: $i,SV628: $i,SV634: $i,SV448: $i] :
( ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV634 @ SV628 ) @ SV371 )
= $false )
| ( ( SV628 = SV634 )
= $true )
| ( ( c_member @ ( tc_prod @ SV448 @ SV448 ) @ ( c_Product__Type_OPair @ SV448 @ SV448 @ SV628 @ SV634 ) @ SV371 )
= $false )
| ( ( c_Relation_Oantisym @ SV448 @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2821,plain,
( ( ( ! [SY1779: $i] :
( ~ ( ( sK85_SX0 != SY1779 ) )
| ( 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 @ SY1779 @ sK85_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 @ sK85_SX0 @ SY1779 ) @ v_L ) ) )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2785]) ).
thf(2822,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
| ( SV462 = SV385 ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2786]) ).
thf(2823,plain,
! [SV527: $i,SV577: $i,SV385: $i,SV462: $i] :
( ( ( ( SV462 != SV385 )
| ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2787]) ).
thf(2824,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( c_member @ SV465 @ SV388 @ SV580 ) )
= $true )
| ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2825,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( ~ ( c_member @ SV465 @ SV388 @ SV580 ) )
= $true )
| ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2826,plain,
! [SV390: $i,SV532: $i,SV607: $i,SV617: $i,SV467: $i,SV581: $i] :
( ( ( SV581 != SV467 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2827,plain,
! [SV467: $i,SV581: $i,SV607: $i,SV617: $i,SV390: $i,SV532: $i] :
( ( ( SV532 != SV390 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2828,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( SV581 != SV467 )
= $true )
| ( ( SV532 != SV390 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2829,plain,
! [SV392: $i,SV469: $i,SV534: $i,SV583: $i] :
( ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2830,plain,
! [SV534: $i,SV392: $i,SV469: $i,SV583: $i] :
( ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ ( sK80_SY1708 @ SV469 @ SV392 @ SV534 @ SV583 ) @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ SV392 )
= $true )
| ( ( c_member @ ( tc_prod @ SV583 @ SV583 ) @ ( c_Product__Type_OPair @ SV583 @ SV583 @ SV534 @ SV469 ) @ ( c_Transitive__Closure_Otrancl @ SV583 @ SV392 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2831,plain,
! [SV393: $i,SV470: $i,SV535: $i,SV584: $i] :
( ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2832,plain,
! [SV535: $i,SV393: $i,SV470: $i,SV584: $i] :
( ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ ( sK81_SY1709 @ SV470 @ SV393 @ SV535 @ SV584 ) @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ SV393 )
= $true )
| ( ( c_member @ ( tc_prod @ SV584 @ SV584 ) @ ( c_Product__Type_OPair @ SV584 @ SV584 @ SV535 @ SV470 ) @ ( c_Transitive__Closure_Otrancl @ SV584 @ SV393 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2833,plain,
! [SV477: $i,SV541: $i,SV400: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ! [SY1754: $i,SY1755: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SY1754 @ SY1755 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2834,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2835,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV546: $i,SV612: $i,SV623: $i] :
( ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2836,plain,
! [SV413: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV546: $i,SV612: $i] :
( ( ( ~ ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) ) )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2837,plain,
! [SV636: $i,SV342: $i,SV645: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV645 ) @ SV342 ) )
= $true )
| ( ( SV636 = SV645 )
= $true )
| ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(2838,plain,
! [SV342: $i,SV419: $i,SV491: $i] :
( ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ ( sK65_SY1576 @ SV342 @ SV419 @ SV491 ) @ ( sK82_SY1777 @ SV342 @ SV419 @ SV491 ) ) @ SV342 )
= $true )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(2839,plain,
! [SV641: $i,SV350: $i,SV624: $i,SV427: $i] :
( ( ( ! [SY1757: $i] :
~ ~ ( ~ ( c_member @ SV427 @ SY1757 @ SV624 )
| ~ ! [SY1758: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1758 @ SY1757 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1758 @ SV624 ) ) ) )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2840,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $true )
| ( ( ~ ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2841,plain,
! [SV358: $i,SV594: $i,SV558: $i,SV435: $i,SV504: $i] :
( ( ( ~ ( c_member @ SV504 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV558 ) @ SV435 ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2842,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV642: $i,SV504: $i] :
( ( ( ~ ( c_member @ SV504 @ SV642 @ SV358 )
| ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2843,plain,
! [SV626: $i,SV363: $i,SV643: $i,SV632: $i,SV440: $i] :
( ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV632 @ SV643 ) @ SV363 )
= $false )
| ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV643 ) @ SV363 )
= $true )
| ( ( c_member @ ( tc_prod @ SV440 @ SV440 ) @ ( c_Product__Type_OPair @ SV440 @ SV440 @ SV626 @ SV632 ) @ SV363 )
= $false )
| ( ( c_Relation_Otrans @ SV440 @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2844,plain,
! [SV369: $i,SV633: $i,SV446: $i,SV644: $i,SV512: $i] :
( ( ( c_member @ SV512 @ SV644 @ SV446 )
= $false )
| ( ( ~ ( ( SV633 != SV644 ) )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(2845,plain,
! [SV512: $i,SV446: $i,SV369: $i] :
( ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
!= ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2818]) ).
thf(2846,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) ) @ SV369 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2819]) ).
thf(2847,plain,
! [SV446: $i,SV369: $i,SV512: $i] :
( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) @ ( sK68_SY1613 @ SV369 @ SV446 @ SV512 ) ) @ SV369 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2819]) ).
thf(2848,plain,
( ( ( ~ ( ( sK85_SX0 != sK86_SY1779 ) )
| ( 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 @ sK86_SY1779 @ sK85_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 @ sK85_SX0 @ sK86_SY1779 ) @ v_L ) )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2821]) ).
thf(2849,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
!= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
= $true )
| ( ( SV462 = SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(2850,plain,
! [SV527: $i,SV577: $i,SV385: $i,SV462: $i] :
( ( ( SV462 != SV385 )
= $true )
| ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2851,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV580 )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV580 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2852,plain,
! [SV530: $i,SV580: $i,SV388: $i,SV465: $i] :
( ( ( c_member @ SV465 @ SV388 @ SV580 )
= $false )
| ( ( c_member @ SV465 @ SV388 @ SV530 )
= $true )
| ( ( SV580 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2853,plain,
! [SV390: $i,SV532: $i,SV607: $i,SV617: $i,SV467: $i,SV581: $i] :
( ( ( SV581 = SV467 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2854,plain,
! [SV467: $i,SV581: $i,SV607: $i,SV617: $i,SV390: $i,SV532: $i] :
( ( ( SV532 = SV390 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2827]) ).
thf(2855,plain,
! [SV607: $i,SV617: $i,SV390: $i,SV532: $i,SV467: $i,SV581: $i] :
( ( ( SV581 = SV467 )
= $false )
| ( ( SV532 != SV390 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2856,plain,
! [SV400: $i,SV541: $i,SV477: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ! [SY1780: $i] :
( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ SY1780 ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ SY1780 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2833]) ).
thf(2857,plain,
! [SV413: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV546: $i,SV612: $i] :
( ( ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2858,plain,
! [SV413: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV546: $i,SV612: $i] :
( ( ( ( SV612 != SV546 )
| ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2859,plain,
! [SV636: $i,SV342: $i,SV645: $i,SV631: $i,SV419: $i,SV491: $i] :
( ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV645 ) @ SV342 )
= $false )
| ( ( SV636 = SV645 )
= $true )
| ( ( c_member @ ( tc_prod @ SV491 @ SV419 ) @ ( c_Product__Type_OPair @ SV491 @ SV419 @ SV631 @ SV636 ) @ SV342 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV491 @ SV419 @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2860,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ~ ~ ( ~ ( c_member @ SV427 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) @ SV624 )
| ~ ! [SY1781: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1781 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1781 @ SV624 ) ) ) )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2839]) ).
thf(2861,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( ~ ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2862,plain,
! [SV358: $i,SV594: $i,SV558: $i,SV435: $i,SV504: $i] :
( ( ( ~ ( c_member @ SV504 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV358 ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2863,plain,
! [SV358: $i,SV558: $i,SV435: $i,SV594: $i,SV504: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV558 ) @ SV435 ) )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2864,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV642: $i,SV504: $i] :
( ( ( ~ ( c_member @ SV504 @ SV642 @ SV358 ) )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(2865,plain,
! [SV446: $i,SV369: $i,SV512: $i,SV644: $i,SV633: $i] :
( ( ( ~ ( ( SV633 != SV644 ) ) )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV644 @ SV446 )
= $false )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2866,plain,
! [SV512: $i,SV446: $i,SV369: $i] :
( ( ( ( sK68_SY1613 @ SV369 @ SV446 @ SV512 )
= ( sK78_SY1775 @ SV369 @ SV446 @ SV512 ) )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2867,plain,
( ( ( ~ ( ( sK85_SX0 != sK86_SY1779 ) ) )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2868,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 @ sK86_SY1779 @ sK85_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 @ sK85_SX0 @ sK86_SY1779 ) @ v_L ) )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2869,plain,
! [SV385: $i,SV462: $i,SV527: $i,SV577: $i] :
( ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
= $false )
| ( ( SV462 = SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2870,plain,
! [SV527: $i,SV577: $i,SV385: $i,SV462: $i] :
( ( ( SV462 = SV385 )
= $false )
| ( ( ( c_Set_Oinsert @ SV577 @ SV527 @ SV462 )
= ( c_Set_Oinsert @ SV577 @ SV527 @ SV385 ) )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV385 )
= $true )
| ( ( c_member @ SV577 @ SV527 @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2871,plain,
! [SV607: $i,SV617: $i,SV467: $i,SV581: $i,SV390: $i,SV532: $i] :
( ( ( SV532 = SV390 )
= $false )
| ( ( SV581 = SV467 )
= $false )
| ( ( ( c_Product__Type_OPair @ SV617 @ SV607 @ SV581 @ SV532 )
= ( c_Product__Type_OPair @ SV617 @ SV607 @ SV467 @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2872,plain,
! [SV400: $i,SV541: $i,SV477: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) ) @ SV400 )
| ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2856]) ).
thf(2873,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV623: $i,SV546: $i,SV612: $i] :
( ( ( SV612 != SV546 )
= $false )
| ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2874,plain,
! [SV413: $i,SV546: $i,SV612: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) )
= $false )
| ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2857]) ).
thf(2875,plain,
! [SV413: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV546: $i,SV612: $i] :
( ( ( SV612 != SV546 )
= $true )
| ( ( ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2876,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ~ ( ~ ( c_member @ SV427 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) @ SV624 )
| ~ ! [SY1781: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1781 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1781 @ SV624 ) ) ) )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2877,plain,
! [SV350: $i,SV639: $i,SV427: $i] :
( ( ( ! [SY1778: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1778 @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1778 @ ( sK59_SY1402 @ SV350 @ SV427 ) ) ) )
= $false )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2878,plain,
! [SV358: $i,SV594: $i,SV558: $i,SV435: $i,SV504: $i] :
( ( ( c_member @ SV504 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV358 )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2879,plain,
! [SV358: $i,SV558: $i,SV435: $i,SV594: $i,SV504: $i] :
( ( ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ ( sK84_SY1726 @ SV435 @ SV558 @ SV594 @ SV358 @ SV504 ) @ SV558 ) @ SV435 )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2880,plain,
! [SV435: $i,SV558: $i,SV594: $i,SV358: $i,SV642: $i,SV504: $i] :
( ( ( c_member @ SV504 @ SV642 @ SV358 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 ) )
= $true )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2881,plain,
! [SV446: $i,SV369: $i,SV512: $i,SV644: $i,SV633: $i] :
( ( ( SV633 != SV644 )
= $false )
| ( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV644 @ SV446 )
= $false )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2882,plain,
( ( ( sK85_SX0 != sK86_SY1779 )
= $true )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2883,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 @ sK86_SY1779 @ sK85_SX0 ) @ v_L )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2884,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 @ sK85_SX0 @ sK86_SY1779 ) @ v_L )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2885,plain,
! [SV400: $i,SV541: $i,SV477: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) ) @ SV400 ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2872]) ).
thf(2886,plain,
! [SV610: $i,SV589: $i,SV400: $i,SV541: $i,SV477: $i,SV618: $i,SV622: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) ) )
= $false )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2872]) ).
thf(2887,plain,
! [SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV413: $i,SV623: $i,SV546: $i,SV612: $i] :
( ( ( SV612 = SV546 )
= $true )
| ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2873]) ).
thf(2888,plain,
! [SV413: $i,SV546: $i,SV612: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i] :
( ( ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 )
= $true )
| ( ( c_member @ ( tc_prod @ SV623 @ SV623 ) @ ( c_Product__Type_OPair @ SV623 @ SV623 @ SV612 @ SV546 ) @ SV413 )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(2889,plain,
! [SV413: $i,SV623: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i,SV546: $i,SV612: $i] :
( ( ( SV612 = SV546 )
= $false )
| ( ( ~ ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2890,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) @ SV624 )
| ~ ! [SY1781: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1781 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1781 @ SV624 ) ) )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2891,plain,
! [SV639: $i,SV350: $i,SV427: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ SV639 ) @ SV350 )
| ~ ( c_member @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $false )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2877]) ).
thf(2892,plain,
! [SV358: $i,SV435: $i,SV558: $i,SV642: $i,SV594: $i,SV504: $i] :
( ( ( c_member @ ( tc_prod @ SV504 @ SV594 ) @ ( c_Product__Type_OPair @ SV504 @ SV594 @ SV642 @ SV558 ) @ SV435 )
= $false )
| ( ( c_member @ SV504 @ SV642 @ SV358 )
= $false )
| ( ( c_member @ SV594 @ SV558 @ ( c_Relation_OImage @ SV504 @ SV594 @ SV435 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2893,plain,
! [SV446: $i,SV369: $i,SV512: $i,SV644: $i,SV633: $i] :
( ( ( SV633 = SV644 )
= $true )
| ( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
| ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 ) )
= $true )
| ( ( c_member @ SV512 @ SV644 @ SV446 )
= $false )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(2894,plain,
( ( ( sK85_SX0 = sK86_SY1779 )
= $false )
| ( ( 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 @ sK73_SX0 @ sK73_SX0 ) @ v_L )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2895,plain,
! [SV400: $i,SV541: $i,SV477: $i,SV589: $i,SV610: $i,SV618: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) ) @ SV400 )
= $true )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2896,plain,
! [SV610: $i,SV589: $i,SV400: $i,SV541: $i,SV477: $i,SV618: $i,SV622: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ ( sK87_SY1754 @ SV477 @ SV541 @ SV400 @ SV589 @ SV610 @ SV618 @ SV622 ) @ ( sK89_SY1780 @ SV400 @ SV541 @ SV477 @ SV589 @ SV610 @ SV618 @ SV622 ) ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $true )
| ( ( ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 )
= ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) )
= $true )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV622 @ SV618 ) @ ( tc_prod @ SV622 @ SV618 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV610 @ SV589 ) @ ( c_Product__Type_OPair @ SV622 @ SV618 @ SV541 @ SV477 ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ SV622 @ SV618 ) @ SV400 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(2897,plain,
! [SV413: $i,SV623: $i,SV546: $i,SV612: $i,SV336: $i,SV485: $i,SV592: $i,SV619: $i] :
( ( ( c_member @ ( tc_prod @ SV619 @ SV619 ) @ ( c_Product__Type_OPair @ SV619 @ SV619 @ SV592 @ SV485 ) @ SV336 )
= $false )
| ( ( SV612 = SV546 )
= $false )
| ( ( c_member @ ( tc_prod @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ SV623 @ SV619 ) @ ( tc_prod @ SV623 @ SV619 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV612 @ SV592 ) @ ( c_Product__Type_OPair @ SV623 @ SV619 @ SV546 @ SV485 ) ) @ ( c_Wellfounded_Olex__prod @ SV623 @ SV619 @ SV413 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2898,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) @ SV624 ) )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2899,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ~ ! [SY1781: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1781 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1781 @ SV624 ) ) )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2900,plain,
! [SV639: $i,SV350: $i,SV427: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ SV639 ) @ SV350 ) )
= $false )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(2901,plain,
! [SV639: $i,SV350: $i,SV427: $i] :
( ( ( ~ ( c_member @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ ( sK59_SY1402 @ SV350 @ SV427 ) ) )
= $false )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(2902,plain,
! [SV446: $i,SV369: $i,SV644: $i,SV633: $i,SV512: $i] :
( ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV633 @ SV644 ) @ SV369 )
= $true )
| ( ( c_member @ ( tc_prod @ SV512 @ SV512 ) @ ( c_Product__Type_OPair @ SV512 @ SV512 @ SV644 @ SV633 ) @ SV369 )
= $true )
| ( ( SV633 = SV644 )
= $true )
| ( ( c_member @ SV512 @ SV644 @ SV446 )
= $false )
| ( ( c_member @ SV512 @ SV633 @ SV446 )
= $false )
| ( ( c_Relation_Ototal__on @ SV512 @ SV446 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(2903,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( c_member @ SV427 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) @ SV624 )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(2904,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV427: $i] :
( ( ( ! [SY1781: $i] :
( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SY1781 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SY1781 @ SV624 ) ) )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2899]) ).
thf(2905,plain,
! [SV639: $i,SV350: $i,SV427: $i] :
( ( ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ SV639 ) @ SV350 )
= $true )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(2906,plain,
! [SV639: $i,SV350: $i,SV427: $i] :
( ( ( c_member @ SV427 @ ( sK90_SY1778 @ SV350 @ SV639 @ SV427 ) @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $true )
| ( ( c_member @ SV427 @ SV639 @ ( sK59_SY1402 @ SV350 @ SV427 ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2907,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV646: $i,SV427: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SV646 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
| ~ ( c_member @ SV427 @ SV646 @ SV624 ) )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(2908,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV646: $i,SV427: $i] :
( ( ( ~ ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SV646 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 ) )
= $true )
| ( ( ~ ( c_member @ SV427 @ SV646 @ SV624 ) )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(2909,plain,
! [SV624: $i,SV350: $i,SV641: $i,SV646: $i,SV427: $i] :
( ( ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SV646 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
= $false )
| ( ( ~ ( c_member @ SV427 @ SV646 @ SV624 ) )
= $true )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2910,plain,
! [SV350: $i,SV641: $i,SV624: $i,SV646: $i,SV427: $i] :
( ( ( c_member @ SV427 @ SV646 @ SV624 )
= $false )
| ( ( c_member @ ( tc_prod @ SV427 @ SV427 ) @ ( c_Product__Type_OPair @ SV427 @ SV427 @ SV646 @ ( sK88_SY1757 @ SV641 @ SV350 @ SV624 @ SV427 ) ) @ SV350 )
= $false )
| ( ( c_member @ SV427 @ SV641 @ SV624 )
= $false )
| ( ( c_Wellfounded_Owf @ SV427 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2911,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1916,2910,2906,2905,2903,2902,2897,2896,2895,2894,2892,2888,2887,2884,2883,2879,2878,2871,2870,2869,2866,2859,2854,2853,2852,2851,2847,2846,2843,2838,2835,2832,2831,2830,2829,2820,2817,2815,2814,2813,2809,2808,2807,2805,2803,2791,2789,2784,2783,2782,2781,2780,2773,2770,2764,2763,2758,2754,2753,2751,2750,2747,2746,2738,2736,2735,2732,2731,2730,2728,2725,2722,2720,2714,2713,2712,2702,2681,2678,2656,2649,2648,2647,2644,2642,2637,2636,2634,2633,2632,2630,2629,2628,2619,2618,2613,2611,2608,2607,2597,2587,2585,2584,2576,2575,2570,2569,2564,2563,2562,2553,2532,2531,2524,2521,2516,2515,2510,2504,2500,2498,2491,2488,2487,2474,2446,2444,2433,2425,2407,2375,2370,2365,2337,2240,2230,2222,2157,2070,2069,1994,1993,1992,1990]) ).
thf(2912,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2911,1759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n017.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 14:17:15 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.21/8.58 ...
% 49.21/8.58
% 49.21/8.58 No.of.Axioms: 78
% 49.21/8.58
% 49.21/8.58 Length.of.Defs: 0
% 49.21/8.58
% 49.21/8.58 Contains.Choice.Funs: false
% 49.21/8.58 ......................................................................................................................................................................
% 49.21/8.58
% 49.21/8.58 ********************************
% 49.21/8.58 * All subproblems solved! *
% 49.21/8.58 ********************************
% 49.21/8.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:78,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2911,loop_count:0,foatp_calls:1,translation:fof_full)
% 49.21/8.58
% 49.21/8.58 %**** Beginning of derivation protocol ****
% 49.21/8.58 % SZS output start CNFRefutation
% See solution above
% 8.54/8.62
% 8.54/8.62 %**** End of derivation protocol ****
% 8.54/8.62 %**** no. of clauses in derivation: 2468 ****
% 8.54/8.62 %**** clause counter: 2911 ****
% 8.54/8.62
% 8.54/8.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:78,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2911,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------